Quantum Data Buffering

Alberto Marino

In a paper published in Feb. 12 issue of the journal Nature [1], a team of researchers at the Joint Quantum Institute (JQI) of the University of Maryland and National Institute of Standards and Technology (NIST) demonstrated the development of a "quantum buffer," a technique that could be used to control the data flow inside a quantum computer.

This new work follows up on the researchers' landmark creation in 2008 [2] of pairs of multi-pixel quantum images (past posting in 2Physics). A pair of quantum images is "entangled" which means that their properties are linked in such a way that they exist as a unit rather than individually. In this work, each quantum image is carried by a light beam and consists of up to 100 "pixels." A pixel in one quantum image displays random and unpredictable changes say, in intensity, yet the corresponding pixel in the other image exhibits identical intensity fluctuations at the same time, and these fluctuations are independent from fluctuations in other pixels. This entanglement can persist even if the two images are physically disconnected from one another.

[Image credit: A. Marino, JQI] Closeup of two "quantum images" created with the help of a "pump" laser beam. The two images are "entangled," so that if there is a change in the intensity in one region ("pixel") of the image, there would be an identical change in the intensity in the corresponding pixel in the second image. In this experiment, one of the images is delayed on its arrival to a detector, so that the correlations between the two images can be out of sync by up to 27 nanoseconds, something that is potentially useful for managing data to a future "quantum computer."

"If you want to set up some sort of communications system or a quantum information-processing system, you need to control the arrival time of one data stream relative to other data streams coming in," says JQI's Alberto Marino, lead author of the paper. "We can accomplish the delay in a compact setup, and we can rapidly change the delay if we want, something that would not be possible with usual laboratory apparatus such as beamsplitters and mirrors," he says.

By using a gas cell to slow down one of the light beams to 500 times slower than the speed of light, the group has demonstrated that they could delay the arrival time of one of the entangled images at a detector by up to 27 nanoseconds. The correlations between the two entangled images still occur—but they are out of sync. A flicker in the first image would have a corresponding flicker in the slowed-down image up to 27 nanoseconds later.

While such "delayed entanglement" has been demonstrated before, it has never been accomplished in information-rich quantum images. Up to now, the "spooky action at a distance" has usually been delayed in single-photon systems.

"What gives our system the potential to store lots of data is the combination of having multiple-pixel images and the possibility of each pixel containing 'continuous' values for properties such as the intensity," says co-author Raphael Pooser.

To generate the entanglement, the researchers use a technique known as four-wave mixing, in which incoming light waves are mixed with a "pump" laser beam in a rubidium gas cell to generate a pair of entangled light beams. In their experiment, the researchers then send one of the entangled light beams through a second cell of rubidium gas where a similar four-wave mixing process is used to slow down the beam. The beam is slowed down as a result of the light being absorbed and re-emitted repeatedly in the gas. The amount of delay caused by the gas cell can be controlled by changing the temperature of the cell (by modifying the density of the gas atoms) and also by changing the intensity of the pump beam for the second cell.

[Image credit: A. Marino, JQI] In this simplified representation of the experimental setup for a ‘quantum buffer,’ a cell containing rubidium gas is used to produce a pair of information-rich entangled images. One of the images goes through a second rubidium gas cell and slows down, which is potentially useful for feeding data at properly timed intervals to future quantum computers. The delay can be controlled such that, during the time it takes one image to travel a centimeter, the other image can travel up to 8 meters. The twisted loops illustrate the entanglement between the images.

This demonstration shows that this type of quantum buffer could be particularly useful for quantum computers, both in its information capacity and its potential to deliver data at precisely defined times. Quantum computers could potentially speed up or expand present capabilities in decrypting data, searching large databases, and other tasks.

References
[1] "Tunable Delay of Einstein-Podolsky-Rosen Entanglement"
A.M. Marino, R.C. Pooser, V. Boyer, and P.D. Lett, Nature, 457, 859-862 (2009), Abstract.
[2] "Entangled Images from Four-Wave Mixing"
V. Boyer, A. Marino, R. Pooser, and P. Lett, Science, 321, 544 - 547 (2008), Abstract.

[We thank NIST for materials used in this article, and Institut de Ciències Fotòniques, Barcelona for Alberto Marino's photo]

Adding and Subtracting Photons for Fundamental Tests of Physics and for Optical Quantum Technologies

(from left to right) Alessandro Zavatta, Marco Bellini, and Valentina Parigi

Author: Marco Bellini

Affiliation: Istituto Nazionale di Ottica Applicata – CNR
and
European Laboratory for Non-linear Spectroscopy (LENS), Florence, Italy.
>>Link to the Group Homepage.

[This is an invited article based on recent work of the author and his colleagues -- 2Physics.com]

Imagine a magician’s hat containing some rabbits whose precise number is unknown, but whose number probability distribution is well defined, so that, for a large ensemble of identical hats with the same probability distribution, one may define an average number of rabbits.

Now, if the magician puts one more rabbit in each hat, the mean rabbit number will, quite naturally, increase by one, while it will decrease by one if he takes one away (unless, of course, the hat was initially empty, in which case he would not be able to extract anything). Moreover, whatever the initial distribution, if the magician performs the two actions in a sequence, by first adding one rabbit and then taking one away, he/she will end up with exactly the same distribution for the number of rabbits remaining in the hat.

What would happen if, instead of normal rabbits, the magician used a microscopic hat containing quantum rabbits?

According to quantum physics, an electromagnetic field is composed of photons, which are so small that even a laser pointer with a typical power of 1mW emits a few millions of billions of them each second. Pure single photons are the ideal means to carry and encode information in emerging quantum technologies, but generating and manipulating them is still a very challenging task.

If the rabbits were identical quantum particles, one could assimilate them to photons in a radiation field (the hat), and would naturally use the so-called creation and annihilation operators to perform the addition and the subtraction of quantum rabbits to/from the hat. Indeed, as undergraduate physics students know, the photon creation operator acts on a state with a well-defined number of photons (also called a Fock state) by increasing this number by one. Conversely, when the photon annihilation operator acts on the same state, it subtracts a quantum of excitation, thus reducing the number of photons in the state by exactly one.

However, the situation becomes completely different as soon as one starts dealing with general superpositions or mixtures of Fock states. If the magician were using a distribution of quantum rabbits, the operation of adding one animal to the hat by a “rabbit creation operator” and then, immediately after, subtracting another by a “rabbit annihilation operator”, would lead to a final probability distribution of rabbits in the hat completely different from the initial one. Furthermore, the reverse sequence of operations would lead to a third outcome, different from both, i.e. the two operations do not commute.

This is the manifestation of one of the most profound laws in quantum physics. Indeed, the non-commutativity of particular quantum operations leads to many of the counterintuitive and fascinating aspects of quantum mechanics, including the famous Heisenberg uncertainty principle.

In 2007 our team (A. Zavatta, V. Parigi, and M. Bellini) at the Istituto Nazionale di Ottica Applicata – CNR (Florence, Italy), in collaboration with M. S. Kim from the Queen’s University (Belfast, UK), succeeded in performing the first direct tests of this fundamental principle of quantum physics in a laboratory [1]. We chose to use photons (which are much easier to manipulate than rabbits) and applied sequences of the creation and annihilation operators to an ordinary light pulse by making use of beam-splitters [2] and non-linear crystals [3]. As non-commutativity predicts, we found that the order of the operations makes a big difference to the outcome.

Figure 2: Setups to conditionally subtract (a) and add (b) a single photon from/to a light field. BS is a low-reflectivity beam-splitter; PDC is a nonlinear crystal where parametric down-conversion takes place; the two white boxes denote on/off photodetectors that herald the success of the corresponding quantum operation on the initial field state.

During those experiments we also found that the quantum operations behave so unusually that, under particular conditions, subtracting a photon changed the quantum state of the light pulse to the extent that its mean number of photons increased instead of diminishing. Taking a quantum rabbit away from the hat could actually increase the mean number of the remaining ones!

In one of our recent works [4] we decided to verify this behavior in a systematic way for some paradigmatic states of light. By applying photon annihilation to a Fock state with a well-defined number of photons we confirmed the intuitive decrease of the photon number by exactly one unit. Surprises appeared when we subtracted a single photon from a thermal state, the most common state of light (both the sun and ordinary light bulbs emit chaotic thermal light). We found that the mean number of photons in the pulse after subtraction was the double of the initial one.

Figure 3: Experimental density matrices and Wigner functions for a thermal state (left panel) and for the same state after a single-photon subtraction (right panel). The photon-subtracted state has a broader Wigner and photon number distribution than the original one.

Finally, when we tried to subtract a photon from a coherent state (the most classical, wave-like, state of light) we found that nothing changed in the state. In other words, we performed the first experimental demonstration that coherent states are invariant under photon annihilation. Since their introduction by Nobel laureate Roy Glauber in the 60’s, coherent states have been a cornerstone in the quantum description of light, but their definition as eigenstates of the annihilation operator had never been verified so directly in an experiment.

Figure 4: Experimental density matrices and Wigner functions for a coherent state (left panel) and for the same state after a single-photon subtraction (right panel). Photon annihilation does not modify a coherent state.

Although counterintuitive, the strange behavior of quantum operations is not unphysical and does not put energy conservation at stake: most of its weirdness simply derives from the misleading implicit assumption that a deterministic addition and subtraction of particles can be represented by the creation and annihilation operators which, on the contrary, work in a probabilistic way (i.e., the probability of extracting a particle from the hat scales with the number of particles already there) [5].

Apart from providing some beautiful demonstrations of the inner working of quantum mechanics, the techniques used in these experiments could in principle be used to arbitrarily engineer light at the most accurate levels by the appropriate sequence of photon additions and subtractions. This capability will open the way to “tailor-made” quantum light for future technologies, like the secure exchange of information through quantum cryptography or the development of novel protocols for quantum-enhanced measurements and communications.

For further info, please contact: Dr. Marco Bellini, Email: bellini@inoa.it

References
[1] “Probing Quantum Commutation Rules by Addition and Subtraction of Single Photons to/from a Light Field”, V. Parigi, A. Zavatta, M.S. Kim, and M. Bellini, Science, 317, 1890-1893 (2007). Abstract.
[2] “Non-Gaussian Statistics from Individual Pulses of Squeezed Light”, J. Wenger, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 92, 153601 (2004). Abstract.
[3] “Quantum-to-classical transition with single-photon-added coherent states of light”, A. Zavatta, S. Viciani and M. Bellini, Science, 306, 660-662 (2004). Abstract.
[4] “Subtracting photons from arbitrary light fields: experimental test of coherent state invariance by single-photon annihilation”, A. Zavatta, V. Parigi, M. S. Kim, and M. Bellini, New Journal of Physics, 10, 123006 (2008). Abstract.
[5] “Recent developments in photon-level operations on travelling light fields”, M. S. Kim, J. Phys. B 41, 133001 (2008). Abstract.

Quantum Entangled Images

Paul Lett [photo courtesy: Joint Quantum Institute]

Conventional photographic films or digital camera sensors only record the color and intensity of a light wave striking their surfaces. A hologram additionally records a light wave’s “phase”—the precise locations of the crests and valleys in the wave. However, much more happens in a light wave. Even the most stable laser beam brightens and dims randomly over time because, as quantum mechanics has shown, light has inherent “uncertainties” in its features, manifested as moment-to-moment fluctuations in its properties. Controlling these fluctuations—which represent a sort of “noise”—can improve detection of faint objects, produce better amplified images, and allow workers to more accurately position laser beams.

Quantum mechanics has revealed light’s unavoidable noise, but it also provides subtle ways of reducing it to values lower than physicists once imagined possible. Researchers can’t completely eliminate the noise, but they can rearrange it to improve desired features in images. A quantum-mechanical technique called “squeezing” (read our past postings on squeezed light) lets physicists reduce noise in one property—such as intensity—at the expense of increasing the noise in a complementary property, such as phase. Modern physics not only enables useful noise reduction, but also opens new applications for images—such as transferring heaps of encrypted data protected by the laws of quantum mechanics and performing parallel processing of information for quantum computers.

In a recent communication published in Science Express, a team of researchers led by Paul Lett of the Joint Quantum Institute (JQI) of the Commerce Department’s National Institute of Standards and Technology (NIST) and the University of Maryland reported a convenient and flexible method for creating twin light beams to produce “quantum images,” pairs of information-rich visual patterns whose features are “entangled,” or inextricably linked by the laws of quantum physics. In addition to promising better detection of faint objects and improved amplification and positioning of light beams, the researchers’ technique for producing quantum images—unprecedented in its simplicity, versatility, and efficiency—may someday be useful for storing patterns of data in quantum computers and transmitting large amounts of highly secure encrypted information.

“Images have always been a preferred method of communication because they carry so much information in their details,” says Vincent Boyer, lead author of the new paper. “Up to now, however, cameras and other optical detectors have largely ignored a lot of useful information in images. By taking advantage of the quantum-mechanical aspects of images, we can improve applications ranging from taking pictures of hard-to-see objects to storing data in futuristic quantum computers.”

Perhaps most strikingly, the quantum images produced by these researchers are born in pairs. Transmitted by two light beams originating from the same point, the two images are like twins separated at birth. Look at one quantum image, and it displays random and unpredictable changes over time. Look at the other image, and it exhibits very similar random fluctuations at the same time, even if the two images are far apart and unable to transmit information to one another. They are “entangled”—their properties are linked in such a way that they exist as a unit rather than individually. Together, they are squeezed: Matching up both quantum images and subtracting their fluctuations, their noise is lower—and their information content potentially higher—than it is from any two classical images.

A laser beam (marked as “probe”) first passes through a mask that imprints a visual pattern. Along with a second laser beam (marked “pump”), it enters a cell containing a gas of rubidium atoms. Interactions between the rubidium gas and the beams produce an amplified version of the imprinted image as well as a second version of the image, rotated 180 degrees around the pump. The bottom panel shows, from left to right, an incoming probe beam imprinted with the letters “N” and “T,” an outgoing probe beam with an amplified image, and an upside-down version of the letters. The middle image is “entangled” with the rightmost image; the images’ changes over time are highly related to one another [Credit: Vincent Boyer et al., JQI]

To create quantum images, the researchers use a simple yet powerful method known as “four-wave mixing,” a technique in which incoming light waves enter a gas and interact to produce outgoing light waves. In the setup, a faint “probe” beam passes through a stencil-like “mask” with a visual pattern. Imprinted with an image, the probe beam joins an intense “pump” beam inside a cell of rubidium gas. The atoms of the gas interact with the light, absorbing energy and re-emitting an amplified version of the original image. In addition, a complementary second image is created by the light emitted by the atoms. To satisfy nature’s requirement for the set of outgoing light beams to have the same energy and momentum as the set of incoming light beams, the second image comes out as an inverted, upside-down copy of the first image, rotated by 180 degrees with respect to the pump beam and at a slightly different color.

In this photo montage of actual quantum images, two laser beams coming from the bright glare in the distance transmit images of a cat-like face at two slightly different frequencies (represented by the orange and the purple colors). The twisted lines indicate that the seemingly random changes or fluctuations that occur over time in any part of the orange image are strongly interconnected or “entangled” with the fluctuations of the corresponding part in the purple image. Though false color has been added to the cats’ faces, they are otherwise actual images obtained in the experiment. [Credit: Vincent Boyer/JQI]





Reference
"Entangled Images from Four-Wave Mixing" by V. Boyer, A. Marino, R. Pooser, and P. Lett,
Science Express, 12 June 2008, Abstract Link.

[We thank Media Relations, National Institute of Standards and Technology (NIST) for materials used in this posting. -- 2Physics.com]

Non-commutative Gravity, a Quantum-Classical Duality, and the Cosmological Constant Puzzle

Tejinder Pal Singh

[Every year since 1949, the Gravity Research Foundation honors best submitted essays in the field of Gravity. This year's list of awardees has something unique about it. While the first prize for the award winning essay goes to T. Padmanabhan, the second prize goes to his former Ph.D student, Tejinder Pal Singh. The five award-winning essays will be published in the Journal of General Relativity and Gravitation (GRG) and subsequently, in a special issue of the International Journal of Modern Physics D (IJMPD). Today we present here an invited article from Prof. Singh on his current work.
-- 2Physics.com ]

Author: Tejinder Pal Singh
Affiliation: Tata Institute of Fundamental Research, India

The evolution of a system in quantum mechanics is described by the Schrodinger equation. What happens to this quantum system when a measurement is made on it by a classical measuring apparatus? What we have learnt from standard text-books in quantum mechanics is that the wave-function for the quantum system ‘collapses’ into one of the eigenstates of the observable being measured. For instance, if a double slit interference experiment is performed on a beam of photons, one observes an interference pattern on the photographic screen. The interference pattern arises because the wave-function of a photon is a linear superposition of two wave-functions: one corresponding to its passing through the upper slit, and the other corresponding to its passing through the lower slit. It is as if the photon is simultaneously passing through both the slits [1]. However, if now a detector is placed behind one of the slits (this is a measurement) the interference pattern disappears, and the photon is interpreted as having passed through one or the other of the two slits, depending on whether the detector has clicked or not. The wave-function of the photon is said to have collapsed, from being originally in a linear superposition, to being a wave-function corresponding to the photon passing through only one of the two slits, not both.

What is often not emphasized in text-books is that this so-called collapse of the wave-function cannot be explained by the Schrodinger equation. This is because the Schrodinger equation is linear in the wave-function, and preserves superposition during evolution. The collapse process, on the other hand, breaks superposition, because the system goes from being in a superposition of many states (before measurement), to being in only one of those states (after measurement). What is the physical process which causes this collapse to take place? The honest answer is that as of today we do not know the correct answer, although an enormous effort has been invested, for nearly a century, in finding the answer. It is not some vague issue of ‘interpreting’ quantum mechanics; rather we are looking for a physical answer, based on sound mathematics, to the question: if we treat the original quantum system, along with the classical measuring apparatus, as one larger quantum system, why does this larger (macroscopic) system not obey the linear superposition principle of quantum mechanics? It is a physical question in precisely the same sense in which understanding planetary motion was a physical question : long ago, people did not know what caused planets to wander in the sky; until through observation and theory it became established that planets revolve around the Sun, and their motion is explained by Newton’s law of gravitation. Today we do not understand what causes the wave-function to collapse, but one day, through experiment and theory, we hope to have a clear understanding of the physics involved.

A remarkable aspect of the collapse process is the Born probability rule. During a measurement, when the wave-function collapses to one of the eigenstates, which eigenstate does it collapse to? This is where probabilities enter quantum mechanics, and this is the only place where they do (The Schrodinger evolution, prior to the measurement, is completely deterministic). The probability that the wave-function goes into one particular eigenstate is proportional to the square of the absolute magnitude of the wave-function for that eigenstate. Repeated experimental measurements on the same quantum system will produce different outcomes, always in accordance with this Born probability rule. There is no explanation in standard quantum mechanics for this rule, and the correct explanation of the collapse process must also include a derivation of this probability rule.

The possible explanations of the collapse process broadly fall into two classes. The first is the Everett many-worlds interpretation [2] of quantum mechanics, according to which the collapse never really takes place in fact, and is in essence an illusion. According to this explanation, at the time of a quantum measurement, the Universe (this includes the measuring apparatus and the observer) splits into many branches, and one outcome is realized in one branch, and a different outcome in another branch. For our double slit experiment, this means that when the detector is placed behind the slit (say the upper slit), then in one branch of the Universe (say ours) it will click, and the photon will have gone through the upper slit. In another branch of the Universe, a ‘different copy’ of the observer will find that the detector did not click, and the photon went through the lower slit. Linear superposition is preserved, and Schrodinger evolution continues to be preserved during and after the measurement. The different branches of the Universe do not interfere with each other because of the (experimentally observed) phenomenon of decoherence [3]. This is the process wherein, because of the interaction of a macroscopic system with its environment, interference between different outcomes is strongly destroyed, even though superposition among the outcomes continues to be preserved. This would explain why in the double slit experiment the detector either clicks or it does not, but is never seen in a superposition of the two states `detector clicks’ and ‘detector does not click’ even though the superposition is in reality present.

The many-worlds interpretation is completely consistent with standard quantum mechanics, but it is not clear how it can be experimentally tested, because by construction one is not supposed to be able to observe the other branches of the Universe. Also, it is not yet clear how the Born probability rule will be arrived at within the framework of this explanation of a quantum measurement.

The second class of explanations of the collapse process assumes that there is only one branch of the Universe, not many branches, and that collapse is a real physical process, not an illusion. It is then immediately obvious that the Schrodinger equation, and hence quantum mechanics, must be modified [4] in order to explain the collapse process, because only then will it become possible to break linear superposition during the measurement process. For instance, it could be that the Schrodinger equation that we know of is only a linear approximation to a more general, non-linear, Schrodinger equation. The non-linearity might become significant only during a quantum measurement, and be responsible for breakdown of superposition, driving the quantum system to one of the eigenstates, in accordance with the Born rule.

As it turns out, as of today there is absolutely no experimental evidence that the Schrodinger equation needs to be modified. We thus find ourselves in this unpalatable position that if the Schrodinger equation is not modified, we must accept the many-worlds interpretation, but there seems to be no way to experimentally test this interpretation! So, does the collapse take place or not? Do we have to wait for more and more precise experimental tests of quantum mechanics to know the answer? Or is there some theoretical reason, over and above quantum mechanics as we know it, which favours collapse over no collapse, or vice versa? Fortunately, the answer to this question seems to be yes, and there is a theoretical argument suggesting that collapse does take place [5]. Furthermore, it may be possible to test this argument experimentally.

The theoretical argument is based on another incompleteness in quantum mechanics, more serious but much less appreciated in comparison with the quantum measurement problem. Quantum systems evolve with time; but this time is a classical concept. Time is a part of space-time, whose geometry is determined by classical bodies such as stars and galaxies, through the Einstein equations of the general theory of relativity. If there were no classical bodies in the Universe, there would be no classical time – this is a consequence of something known as the Einstein hole argument [5]. But even in such a situation, one should be able to describe quantum systems – there must exist a reformulation of quantum mechanics which does not refer to an external classical time. In looking for such a reformulation, one is led to the conclusion that standard linear quantum mechanics is a limiting case of a more general non-linear quantum theory. The non-linearity becomes significant when the mass-energy of the quantum system becomes comparable to or larger than Planck mass, but is completely negligible for smaller systems such as atoms. Planck mass is a fundamental unit of mass made out of Planck’s constant, speed of light, and Newton’s gravitational constant, and its numerical value is about a hundred-thousandth of a gram. Since this non-linearity in the Schrodinger equation becomes significant in about the same mass range where quantum measurement takes place, it suggests the possibility that linear superposition might break down during a measurement. Hence the many-worlds interpretation is disfavoured, as a consequence of the theoretical arguments described in this paragraph.

A programme, still tentative, is being developed to arrive at such a reformulation of quantum mechanics, and at the consequent non-linear Schrodinger equation [5]. One starts by noting that in the absence of a classical space-time, the point structure of space-time is lost, and space-time points are themselves subject to quantum fluctuations. An inevitable mathematical way to express such fluctuations is to impose commutation relations amongst these coordinates, and also amongst the components of momenta of a particle in the presence of such spacetime fluctuations. The branch of mathematics which can naturally accommodate these features is known as noncommutative geometry [6]. In such a geometry, which is a natural extension of the Riemannean geometry of general relativity, space-time coordinates do not commute with each other.

The aforesaid reformulation is motivated by the following new proposal : basic laws of physics are invariant under general coordinate transformations of non-commuting coordinates. This seems like a natural step forward from the general theory of relativity, which is based on the principle of invariance under general coordinate transformations of (commuting) coordinates. Standard linear quantum mechanics is reformulated as a non-commutative special relativity. As and when an external classical time becomes available, the reformulation reduces to the standard linear quantum theory. The generalization from non-commutative special relativity to non-commutative general relativity leads to a non-linear quantum mechanics. The latter reduces to the former when the mass-energy of the quantum system is much less than Planck mass. The relation between the non-linear quantum theory and its linear limit is the same as the relation between general relativity and special relativity. The second is recovered from the first in the limit in which Newton’s gravitational constant goes to zero. When the mass-energy of the system is much larger than Planck mass, the non-linear quantum theory goes over to standard classical mechanics.

The non-linear Schrodinger equation which arises here can in principle explain the collapse of the wave-function, under a further assumption whose validity remains to be established. The essential idea is that at the onset of quantum measurement the non-linearity drives the quantum system to one or the other outcomes, depending on certain initial conditions in the quantum system (for instance the phase of the wave-function) at the time when the measurement begins. Superposition is thus broken. One can also give a quantitative estimate of the life-time of a quantum superposition – predictably this life-time goes from astronomically large values to extremely small values as the number of degrees of freedom in the system is increased.

An interesting fall-out of this study is that one might obtain some understanding of the origin of the observed acceleration of the Universe, and of dark energy, for which the most likely explanation is a non-zero value for the cosmological constant. Why is this constant non-zero, and yet so small when expressed in fundamental units? In the present study, it appears that the dynamics of a quantum particle whose mass m₁ is much less than Planck mass can be recovered from the knowledge of the dynamics of a classical particle whose mass m₂ is much greater than Planck mass. We call this a quantum-classical duality [7]. The product of the masses m₁ and m₂ is equal to the square of Planck mass. If one assumes that the classical ‘particle’ is the whole observed Universe, then the cosmological constant can be shown to be equal to the (finite) zero-point energy of the dual quantum field, and this matches with the value currently seen in cosmological observations.

The programme described here should strictly be described as ‘work in progress’, and there is still quite some way to go before these ideas can be put on a firm footing, and before one knows that this is the right track. Nonetheless, the ideas appear aesthetically appealing and natural, and a distinct advantage of the programme is that it is experimentally falsifiable. The non-linear theory agrees with standard quantum mechanics for small masses such as atomic masses, and it agrees with classical mechanics for large macroscopic masses. However its predictions differ from those of linear quantum mechanics in the mesoscopic mass range, which very crudely could be taken to be the mass range 10^-20 grams to 10^-8 grams. It is a significant fact that quantum mechanics has not been experimentally verified in this vast mass range, simply because such experiments are very difficult to perform with the currently available technology. The non-linear Schrodinger equation that we have predicts that the lifetime of a quantum superposition will decrease with increasing mass of the system. If the disturbing effects of the environment could be shielded (avoidance of decoherence) such a dependence of the superposition life-time on mass could be experimentally tested. Avoiding decoherence is however a great experimental challenge. An easier class of experiments is one for which the predictions of the non-linear theory for some measurable constant differ from that of the linear theory. For instance, the non-linear theory predicts a different value of the ratio h/m in the mesoscopic range, as compared to the linear theory, and this should be testable. Another possible prediction of the non-linear theory is that the outcome of a quantum measurement is not probabilistic, but deterministic, and possibly depends on the phase of the wave-function at the onset of measurement. Suitable correlation experiments might be able to test this by making fast successive measurements on a quantum system.

References
[1] "Feynman Lectures in Physics", Vol. III, Chapter I",
R. P. Feynman, R. B. Leighton and M. Sands, (Addison-Wesley, Reading, 1965).
[2] " 'Relative State' Formulation of Quantum Mechanics",
Hugh Everett, III, Reviews of Modern Physics 29, 454 (1957). Abstract Link.
[3] "Decoherence and the appearance of a classical world in quantum theory",
E. Joos, H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch and I.-O. Stamatescu, (Springer, New York) 2nd Edn.
[4] "Collapse Models", P. Pearle, http://in.arxiv.org/abs/quant-ph/9901077 .
[5] "Quantum measurement and quantum gravity : many-worlds or collapse of the wave-function?"
T. P. Singh, http://arxiv.org/abs/0711.3773.
[6] "An introduction to non-commutative differential geometry and its physical applications",
J. Madore (Cambridge University Press, 1999).
[7] "Noncommutative gravity, a `no strings attached' quantum-classical duality, and the cosmological constant puzzle", T.P. Singh, http://arxiv.org/abs/0805.2124.

The Frontier of Quantum Communication is the Space

Paolo Villoresi

Author: Paolo Villoresi

Affiliation: Department of Information Engineering,
University of Padua, Italy

[This is an invited article based on recent work of the author and his collaborators. - 2Physics.com]

As the advancements in the implementation of single light-quanta exchange in the quantum channels is constantly progressing and refining, one may think that the quantum communications (QC) will soon widespread in everyday life. The appeals of this perspective may be synthesised by choosing the quality versus the quantity or to encode information in the quantum state of a single particle instead of sending a large bunch of photons to express just one bit.

But quality has its price. Each photon that is carrying information has to be clearly sorted out from these wandering around as general background, and its quantum state has also to be kept unblemished along its propagation until the receiver. As expected, QC had its cradle in the research labs, where effective countermeasures against decoherence and background photons are relatively easy to adopt. Significant steps were done in quantum communication along optical fibres, for which already viable technologies were proposed for the distribution of cryptographic keys over legs of several tens of kilometres. In the free space counterpart, where a beam with the train of quanta is aimed toward a received with no needs of infrastructures in between, the difficulties are stronger. The intense backlights, the atmospheric turbulence, the diffusion and absorption of light are some of the issues to fight against in order to implement QC. Beside, the Earth curvature set a final limit to the leg length. The actual limit is represented by a quantum channel in which the nature of quantum entanglement has been demonstrated between two parties separated by 144 km. The experiment was done between two islands of Canary archipelagos, with the stations located quite high in the mountains. But the further extension of the free-space QC has a natural direction: going in space and communicate with the Earth.

Indeed, in our experiment we aimed to establish a link between an orbiting source of single photons and a ground telescope. Our team was set up with my coworkers at the LUXOR Labs at DEI, University of Padova in Italy and colleagues in Austria, of the group of Anton Zeilinger at the University of Vienna and Academy of Science of Austria, of the group of Cesare Barbieri at the Astronomy Department of University of Padova, Italy and of Giuseppe Bianco of Italian Space Agency in Matera. The realization of this link is the first step in the communication space-ground or space-space and based on the coding of the bits of information in the quantum state of a photon, or qubit. The experiment also demonstrated that present technology is mature enough for this purpose, and the crucial crossing from the theoretical predictions and the experimental demonstration was possible. On the other hand, the experiment required a combined effort from different expertises, from classical Optics, to satellite laser-ranging for Geodesy, to Quantum Optics, to advanced electronics. Our team synthesized these points of view and succeeded in the single photon link.

More in detail, in this experiment we have essentially simulated a quantum communication source onboard a satellite, and showed how the very dim signals could be detected. Such a quantum source has to fulfill the particular requirement, that only one single photon per pulse is emitted. In this work this is realized by sending a rapid sequence of weak laser pulses (outward pulses in the figure) towards a Japanese satellite equipped with retroflectors (Ajisai) at about 1600 km of slant distance. There is a very small probability that the photons hit the satellite and are reflected back to ground, therefore this is just as if we would have a suitable quantum source on the satellite. The main challenge was to detect the very view reflected photons amongst a huge background signal which is exactly the same situation is would be if we had the real quantum communication system. The detector is an avalance-photon-detector (APD) connected to a timing circuit. the orbital data of the satellite were used to identify the returned photons out of the background.

The next step will be to board a quantum sender on a satellite. This will allow quantum physics experiments over distances impossible on ground. In particular, it will push the limits of fundamental physics tests addressing experimentally questions as if there is a spatial limit to the entanglement, the "spooky" action? Beside, technologies as the quantum key distribution may be implemented on a global scale. And a real economic impact of the quantum communication from satellite may be expected, to be based on the cryptography, on novel paradigms as quantum teleportation, on advanced atmospheric monitoring, based on the modification of the optical signal during the downlink. There could also be impact in the global distribution of temporal information, as in the case of the so called “legal time”, and advanced methods for the clock synchronization using entangled photon pairs.

The study of the quantum satellite is ongoing, under the auspices of Italian Space Agency as well also of the European Space Agency, and we really hope that the quantum satellite will soon be on its way, that is along an orbit some hundred kilometres above us.

References
[1] "Experimental verification of the feasibility of a quantum channel between space and Earth",
P Villoresi, T Jennewein, F Tamburini, M Aspelmeyer, C Bonato, R Ursin, C Pernechele, V Luceri, G Bianco, A Zeilinger and C Barbieri,
New J. Phys., v10, 033038 (March, 2008) [IOP select paper], Abstract Link.
[2] "Ground to satellite secure key exchange using quantum cryptography",
Rarity J G, Tapster P R, Gorman P M and Knight P,
New J. Phys., v4, 82 (2002), Abstract Link.
[3] European Quantum Roadmap: http://qist.ect.it/
[4] "The Physics of Quantum Information",
D Bouwmeester, A Ekert, A Zeilinger, (Springer, 2000).

Silicon Photonics for Optical Quantum Technologies

Jeremy O’Brien

[This is an invited article based on recent works of the authors. -- 2Physics.com]

Authors: Jeremy O’Brien and Alberto Politi

Affiliation: Centre for Quantum Photonics, Department of Physics and Department of Electrical & Electronic Engineering, University of Bristol

Quantum information science has shown that quantum mechanical effects can dramatically improve performance for certain tasks in communication, computation and measurement. Single particles of light – photons – are an excellent choice for quantum technologies because they are relatively noise free; information can be moved around quickly – at the speed of light; and manipulating single photons is easy. For these reasons photons have been widely used in quantum communication, quantum metrology, and quantum lithography settings, as well as quantum bits (or qubits) for quantum information processing [1].

The fact that photons see low noise during the propagation is a great advantage, but, at the same time, makes two photons interact with a negligible probability. Two photons interaction is a fundamental task for quantum information processing, and it is at the heart of the Controlled-NOT (CNOT) gate –one of the building block of a future quantum computer. A 2 photon CNOT gate was demonstrated experimentally back in 2003 [2].

A conspicuous number of different experimental realizations of this CNOT gate have since been developed in recent years by different groups, but all the realizations performed so far are based on bulk optical elements on an optical table and photon propagation in air. This approach is useful for proof of principle quantum logic operation, however, photonic quantum technologies will require scalable, miniaturized gates, with improved performances.

The Team at Bristol University has designed and measured integrated optical devices on a chip, with dimensions measured in millimetres [3]. This impressive miniaturisation was permitted thanks to the silica-on-silicon technology used in commercial devices for modern optical telecommunications, which guides light on a chip in the same way as in optical fibers.

For the first time, the feasibility of integrated quantum information was demonstrated, by achieving the key element of all quantum optics experiments, namely non-classical interference. This effect appears when two indistinguishable photons arrive at the different inputs of a beam-splitter (a half refractive mirror) at the same time. In this case, contrary to the classical analysis, the two photons always exit together from one of the two ports, and they never exit different outputs. The simplest integrated analogous of a free space bream-splitter is a directional coupler, (illustrated in Figure 1). When two waveguides are close one to each other there is a non-zero overlap between the modes of the waveguides. By choosing the waveguide separation and the length of the coupling region, it is possible to choose the amount of power that goes to one waveguide to the other (coupling ratio).


Figure 1 shows a directional coupler on a chip, the integrated analogue of a beam splitter.

Sending pairs of single photons in the two inputs of the directional coupler, it was possible to demonstrate the quantum interference effect, with a very high visibility of the quantum behaviour.

Using the same technology and various directional couplers with different coupling ratios it is possible to realise a CNOT gate, schematically represented in Figure 1. With this scheme it was possible to achieve a fidelity of the CNOT operation of more than 94%.

Figure 2 shows the schematic representation of an integrated CNOT gate. The “1/2” and “1/3” numbers indicate the coupling ratio of the different couplers that compose the CNOT gate.

The experimental characterisation of the quantum chips also proved that one of the strangest phenomena of the quantum world, namely “quantum entanglement”, was achieved on-chip. Quantum entanglement of two particles means that the state of either of the particles is not defined, but only their collective state.

This on-chip entanglement has important applications in quantum metrology. Last year Dr O’Brien and his collaborator Professor Takeuchi and co-workers at Hokkaido University reported such a quantum metrology measurement with four photons [4].

The results achieved using integrated chips show that it is possible to realize sophisticated photonic quantum circuits on a silicon chip, which will be of benefit to future quantum technologies based on photons as well as the next generation of fundamental studies in quantum optics.

References
[1] “Optical Quantum Computing”
Jeremy L. O’Brien,
Science 318, 1567 (2007), Abstract.
[2] “Demonstration of an all-optical quantum controlled-NOT gate”
J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, D. Branning,
Nature 426, 264 (2003), Abstract.
[3] “Silica-on-Silicon Waveguide Quantum Circuits”
A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, J. L. O'Brien,
Science, Vol. 320. no. 5876, pp. 646 - 649 (May 2, 2008)
Published Online March 27, 2008 (10.1126/science.1155441)
Abstract, Link to Full text in the website of Bristol Centre for Quantum Photonics.
[4] "Beating the Standard Quantum Limit with Four-Entangled Photons"
T. Nagata, R. Okamoto, J. L. O'Brien, K. Sasaki, S. Takeuchi,
Science 316, 726 (2007), Abstract.

Ion Interferometers, the Bane of Chubby Photons?

Dallin S. Durfee poses with an elusive "fat photon" during the 2007 meeting of the APS Division of Atomic, Molecular, and Optical Physics (DAMOP).

[This is an invited article based on recent work of the author. -- 2Physics.com]

Author:
Dallin S. Durfee

Affiliation: Department of Physics, Brigham Young University

Our current model of electromagnetism has held up to 2.5 centuries of scrutiny. But like nearly every other theory that science has embraced, it will probably eventually be shown to be incomplete. In a recent article in Physical Review Letters, researchers at Brigham Young University examined the potential of using ion interferometry to search for Coulomb’s-law violating electric fields inside of a conducting cavity. If Coulomb’s law is correct, the absolute voltage of the cavity should not affect the fields inside the cavity. But if it is violated, changing the voltage should alter the fields in the cavity.

The proposed experiment was recently funded by a NIST Precision Measurement Grant and is currently under construction. In this experiment laser beams will be used to split the quantum wave functions of Strontium ions in two. The two waves will then recoil away from each other before being deflected back together and recombined by two additional laser beams. The last laser beam will cause the two waves to interfere, such that the final state of an ion will depend on the relative quantum phase of the two halves of its wave function.

The presence of electric fields inside the conducting shell would cause the two waves to travel through different potentials and acquire different quantum phase shifts. This would change the overall phase of the interference in a predictable way, making it possible to determine the magnitude of the electric field from the final state of the ions. By monitoring the state of ions exiting the apparatus as a changing voltage is applied to the conducting shell, a very sensitive test of Coulomb’s law can be conducted.

The theory of massive photons provides a useful way to compare experimental searches for Coulomb’s-law violations. This theory assumes that photons have a small, but non-zero rest mass, resulting in a limited range for Coulomb interactions. Although it is widely believed that the photon has zero rest mass, in today’s image conscious world it is just possible that photons aren’t telling us their true weight (after all, the neutrino maintained its massless image for decades). Based on calculations in their paper, the researchers predict that the experiment will be able to detect a rest mass of a few times 10^-50 grams, about 100 times smaller than previous laboratory measurements.

Reference
"Testing Nonclassical Theories of Electromagnetism with Ion Interferometry"
by B. Neyenhuis, D. Christensen, and D. S. Durfee
Phys. Rev. Lett. 99, 200401 (2007), Abstract Link

Entangled Memory

Jeff Kimble [Photo courtesy: Caltech]

In a paper published in today's issue of the journal Nature, Caltech's Valentine Professor of Physics H. Jeff Kimble and his colleagues have laid the groundwork for a crucial step in quantum information science. They demonstrate for the first time an important capability required for the control of quantum information and quantum networks, namely the coherent conversion of photonic entanglement into and out of separated quantum memories.

Entanglement lies at the heart of quantum physics, and is a state where parts of a composite system are more strongly correlated than is possible for any classical counterparts regardless of the distance separating them. Entanglement is a critical resource for diverse applications in quantum information science, such as for quantum metrology, computation, and communication. Quantum networks rely on entanglement for the teleportation of quantum states from place to place.

Entanglement lies at the heart of quantum physics, and is a state where parts of a composite system are more strongly correlated than is possible for any classical counterparts regardless of the distance separating them. Entanglement is a critical resource for diverse applications in quantum information science, such as for quantum metrology, computation, and communication. Quantum networks rely on entanglement for the teleportation of quantum states from place to place.

In a quest to turn these abstract ideas into real laboratory systems and to distribute entanglement to remote locations (even on a continental scale), Kimble explains that quantum physicists have studied ways to propagate photonic information into and out of quantum memory using a system called a quantum repeater, invented in 1998 by H. Briegel, J.I. Cirac, and P. Zoller at the University of Innsbruck. Until now, work in Kimble's group on the realization of a quantum repeater with atomic ensembles relied upon the probabilistic creation of entanglement. In this setting entanglement between two clouds of atoms was generated probabilistically but with an unambiguous heralding event.

While such systems hold the potential for scalable quantum networks, it has been difficult for Kimble's Quantum Optics Group to apply such schemes to certain protocols necessary for quantum networks, such as entanglement connection. Now, with the new protocol and future improvements, "We can push a button and generate entanglement," says physics graduate student Kyung Soo Choi, one of four authors of the Caltech experiment.

[Image Courtesy: Nature]

In the Caltech experiment, a single photon is first split, generating an entangled state of light with quantum amplitudes for the photon to propagate two distinct paths, taking both at once. The Caltech team in turn transcribed, or mapped, the entanglement onto distinct atomic ensembles separated by one millimeter. To create the interface between the light and matter, the team employed laser-cooled cesium atoms whose atomic states interact with a control laser to create destructive quantum interference, making the atomic ensembles either invisible or highly opaque to the input light. Called Electromagnetically Induced Transparency and pioneered by S. Harris at Stanford University, the mechanism manipulates the speed of the light for the incoming entangled photon and that kicks off the entire procedure.

In this experiment, the photonic entanglement was mapped into the atomic ensembles in a time ~ 20 nanoseconds and then stored in the atomic ensembles for one microsecond, with storage times extendable up to 10 microseconds. The photonic entanglements of the input and output of the quantum interface were explicitly quantified with a conversion efficiency of 20 percent. However, the researchers emphasize, real-world realization of a quantum network remains far out of reach even with these parameters and the state-of-the-art of quantum controls. Choi comments, "Further improvements in quantum control and storage capabilities in matter-light interfaces will lead to fruitful and exciting discoveries in Quantum Information Science, including for the realization of quantum networks."

In addition to Kimble and Choi, other authors are Hui Deng, a postdoctoral scholar at the Center for the Physics of Information; and Julien Laurat, a former Caltech physics postdoctoral scholar who is now an associate professor at Laboratoire Kastler Brossel (Universite P. et M. Curie, Ecole Normale Superieure and CNRS) in Paris, France.

Reference
"Mapping photonic entanglement into and out of a quantum memory"
K. S. Choi, H. Deng, J. Laurat & H. J. Kimble,
Nature 452, 67-71 (6 March 2008), Abstract Link

[We thank Caltech Media Relations for materials used in this posting]

Observation of the Spin Hall Effect of Light

Onur Hosten (left) and Paul Kwiat (right) [Photo credit: L. Brian Stauffer]

Physicists Onur Hosten and Paul G. Kwiat, at the University of Illinois at Urbana-Champaign showed that light exhibits a Spin Hall effect, analogous to the Spin Hall effect in electronic systems, showing the universality of the effect for particles of different nature. The researchers used a novel technique from quantum weak measurements to enhance the tiny Spin Hall displacements prior to observation.

Whenever the propagation direction of a beam of light changes due to a variation in the refractive index of the medium (in the experiment, refraction at an air-glass interface serves this purpose), the beam center experiences a spin-dependent (or circular polarization-dependent) displacement perpendicular both to the initial propagation direction and the change in the propagation direction, i.e. a lateral shift. Two different spin components (parallel and anti-parallel to the propagation direction) acquire opposite displacements. This is the spin Hall effect as it applies to light. Therefore, when a beam of linearly polarized light (which is an equal combination of spin parallel and anti-parallel to the propagation direction) changes direction, the beam slightly splits into two beams, each containing different spin states.

Figure 1: Spin Hall effect of Light. (Click on figure to watch it) In the animation, a beam of linearly polarized light incident on an air-glass interface slightly splits into its two spin components -- spin parallel or anti-parallel to the propagation direction (or right and left circular polarizations) -- upon refraction at the interface. [Animation credit: Onur Hosten]

The effect takes place due to conservation of angular momentum (spin plus orbital). Due to the rotational symmetry around the axis perpendicular to the interface (z-axis), the total angular momentum of light around this axis has to be conserved. Assume that, initially the spin angular momentum of light is either parallel or anti-parallel to the propagation direction, and has a certain component along the z-axis. When light refracts at the interface, the spin still remains either parallel or anti-parallel to the new propagation direction. But this time the spin makes a different angle with the z-axis, therefore the spin angular momentum component along the z-axis changes. The spin Hall effect compensates for this change in the angular momentum component, and light acquires an orbital angular momentum by shifting itself laterally from the z-axis.

In the experiment a linearly polarized laser beam was incident on a glass prism at an angle. Upon refraction, the two different spin components acquired opposite displacements out of the plane of incidence. Because the separation between these two beams was only on the order of nanometers, and the beam widths themselves on the order of millimeters, the two beams overlap to a great extent. The researchers measured the separation between the two beams using a novel metrological method (quantum weak measurements in pre- and post-selected systems) to measure the miniscule effect.

Essentially, the spin Hall effect performs a weak measurement of the spin state of the photons. If the measurement were to be strong, the beams corresponding to different spin states would completely separate from each other, and one would be able to tell the spin state by looking at the beam position. But, in the University of Illinois experiment, the spin state measurement was a weak measurement, because the beams were still overlapping to a great extent and one could tell only very little about the spin state by looking at the position of the beam.

When the researchers made a particular pre- and post-selection on the polarization state of the photons before and after the weak measurement (i.e., the spin Hall effect), due to an interference effect between the two beams, there resulted an enhancement of the original displacement by a factor of ten thousand. This pre- and post-selection step experimentally amounts to sending the photons through two calcite polarizers, one before and one after the spin Hall effect, oriented at angles almost perpendicular to each other. Therefore, for instance, an angstrom displacement was enhanced to a micron displacement. Then the enhanced displacement was read by a position-sensitive photodiode (a photodiode split into two halves – the difference signal is proportional to the beam displacement). The researchers were thus able to characterize the Spin Hall effect of light with angstrom resolution.

The measurement technique holds further promise for achieving better resolutions. In particular, the researchers believe that by incorporating standard signal modulation and lock-in detection techniques, a resolution of picometers can be achieved. Moreover, the technique is not limited to position measurements; similar tricks in the appropriate experimental conditions will enhance any kind of signal, e.g., position or momentum of any particle, intensity (e.g. photon number) or amplitude (e.g. electric field) of a field.

The researchers think that it would be interesting to demonstrate the case when the index of refraction varies continuously (as opposed to observing the effect at a discrete air-glass interface), which is the analogous case for the spin Hall effect in semiconductors. The researchers are also theoretically looking for systems where they can separate the spin states into two completely separate beams, and use this for both quantum and classical optical information processing applications.

Reference:
"Observation of the Spin Hall Effect of Light via Weak Measurements"
O. Hosten and P. Kwiat,
Science 319, 787 (2008); published online 10 January 2008 (10.1126/Science.1152697).
Link to Abstract
Link to Full text in the website of Kwiat Quantum Information Group

First Observation of ‘Persistent Flow’ in a Gas

In a paper to be published in a forthcoming issue of Physical Review Letters, a team of scientists from the National Institute of Standards and Technology (NIST) and the Joint Quantum Institute (NIST/University of Maryland) have reported the first observation of “persistent” current in an ultracold atomic gas —a frictionless flow of particles.

The researchers first created a Bose-Einstein condensate (BEC), a gas of atoms cooled to such low temperatures that it transforms into matter with unusual properties. One of these properties is superfluidity, the fluid version of superconductivity (whereby electrical currents can flow essentially forever in a loop of wire). Although BECs in principle could support everlasting flows of gas, traditional setups for creating and observing BECs have not provided the most stable environments for the generally unstable superfluid flows, which have tended to break up after short periods of time.

To address this issue, the team used laser light and magnetic fields on a gas of sodium atoms to create a donut-shaped BEC—one with a hole in the center—as opposed to the usual ball- or cigar-shaped BEC. This configuration ends up stabilizing circular superfluid flows because it would take too much energy for the hole—containing no atoms—to disturb matters by moving into the donut—which contains lots of atoms.

(a) In a donut-shaped, or “toroidal” trap, atoms mostly exist in a red ring and do not reside in the center (blue region), which represents an energy hill they cannot climb. (b) Image of a Bose-Einstein condensate (BEC) in the donut trap. (c) When there is no fluid flow around the donut and the trap is turned off, atoms (red) rush to the center. (d) When fluid flows around the donut and the trap is turned off, the current around the donut persists and does not rush to fill the hole [Image courtesy: National Institute of Standard and Technology]

To stir the superfluid, the researchers zap the gas with laser light that has a property known as orbital angular momentum. Acting like a boat paddle sweeping water in a circle, the orbital angular momentum creates a fluid flow around the donut. After the stirring, the researchers have observed the gas flowing around the donut for up to 10 seconds. Even more striking, this persistent flow exists even when only 20% of the gas atoms were in the special BEC state.

This relatively long-lived flow, a hallmark of a special property known as “superfluidity,” might help bring to the surface some deep physics insights by providing ways to study the fundamental connection between BECs and superfluids.

This may also enable super-sensitive rotation sensors that could someday make navigation more precise. A BEC superfluid is very sensitive to rotation; its flow would change in fixed steps in response to small changes in rotation [Note that some research groups around the world already have taken the first step in this direction by demonstrating BECs on a chip].

Reference
"Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap"
C. Ryu, M. F. Andersen, P. Cladé, Vasant Natarajan, K. Helmerson, and W. D. Phillips,
Physical Review Letters, 99, 260401 (2007)
Abstract (link updated on Dec 29, 2007 after the paper is published)

[We thank Media Relations, NIST for materials used in this posting]

Quantum Entanglement between Single Atoms One Meter Apart !

Christopher Monroe in his lab in Department of Physics, University of Michigan (photo credit: Mary Monroe)

A team of physicists has exploited one of the most mysterious phenomena in nature to make a major advance toward the long-sought goal of super-fast quantum computing. Christopher Monroe and colleagues at the University of Michigan and now at the University of Maryland established a spooky, intimate quantum-mechanical condition called “entanglement” between two completely unconnected individual atoms a meter apart in separate enclosures by carefully manipulating photons emitted by the atoms. As a result, even though the atoms have never come in physical contact, their properties are entangled: inextricably linked and giving precisely corresponding values if measured.

“This type of long-distance entanglement generation is a radically new way to propagate quantum information and perform quantum computations over long distances,” Monroe says. “It should be possible to scale it up to networks of many interconnected components that will eventually be necessary for a general-purpose quantum internet.” The team reported its results in the September 6 issue of the journal Nature [1].

Entangled entities are doubly strange. First, they have a property peculiar to the atomic-scale world of quantum mechanics: Each exists in a “superposition” of different states at the same time – like a coin with sides that are neither heads nor tails, but somehow both at once – and remains that way until a measurement forces it to take on a specific state.

This aspect of quantum mechanics makes it very attractive for potential information processing. Conventional computer bits are stored in tiny capacitors, each of which can have only one of two values (on or off, 0 or 1) as determined by a measurable electrical charge. But thanks to superposition, a quantum bit, or “qubit,” can be a 0, a 1, or both at the same time. If arranged into a computer, qubits could exponentially increase the speed at which certain kinds of problems can be solved.

Quantum entanglement allows the “wiring” of qubits together and is the key to such massive parallelism. Even though they are physically unconnected, entangled qubits always have complementary characteristics. If the state of first is known, then the state of the second is known as well – even when the second state is not measured. In the coin analogy, an entangled pair would work like this: If one coin were flipped and came up heads, then the other would always come up tails, even if it were simultaneously flipped 10,000 miles away.

Figure 1: Two trapped atomic ions (glowing "stars" at center of each disc), with entanglement depicted by the ambiguous perspective of the discs: when one is seen a particular way, so is the other. (picture credit: Boris Blinov, Univ. Washington)

The problem with all this is that entangled quantum superpositions are incredibly fragile – if any part of the entangled system interacts with its environment or gets measured, then the quantum nature of the entire system is generally lost in a process called “decoherence.”

Before the experiment reported today, entanglement of distant individual atoms had never been achieved. “Atoms make ideal qubits,” Monroe says, “because they can be trapped and maintained in the same condition for long time periods. But photons are the ideal medium for transferring and controlling information. This work shows how to combine the best of both systems.”

The researchers began by confining two ytterbium ions, one in each of two chambers separated by about 1 meter. Once trapped, the ions stay in their positions for several days. The atomic qubits are realized as stable states of electron and nuclear spin within each ion. The team excited the ions simultaneously with precisely tuned laser pulses so brief that each ion emitted at most a single photon as it fell back to one of the qubit states. The color of each photon became entangled with its parent atomic qubit, and the photons were guided through optical fibers. The emerging photons were combined on a beamsplitter, and quantum interference of the photons [2] ensures that whenever photons are simultaneously detected behind each port of the beamsplitter, the atomic qubits become entangled.

This entanglement was verified by probing the trapped ions with specially tuned laser beams that directly measured the state of each qubit. Not only were correlations in the qubit states clearly visible, but the correlations persisted after each qubit state was scrambled in a particular way before measurement – a proof of entanglement.

Figure 2: Schematic of experiment to entangle two remote trapped ions. Laser pulses simultaneously excite the two atoms, and their emitted photons are guided by fibers onto a beamsplitter. Whenever two photons emerge from the beamsplitter and are detected in coincidence, the trapped ions are entangled.

Because of the numerous sources of light-gathering inefficiencies (imperfect laser pulse excitation of the ions, imperfections in the optical fibers, inefficiencies in the filters and detectors, and so forth), the team observed the telltale signature of an entanglement event only about three times in every billion pulses. That’s about once every few minutes. But “it’s okay that it almost never works,” says David Moehring, the lead graduate student on the project, and now a Research Fellow at the Max Planck Institute for Quantum Optics near Munich, Germany. “Once we receive the clicks from the detectors, we know right then that the two ions are entangled and ready for use.”

The entanglement events were measured with extremely high efficiency, and detected with sufficient fidelity to demonstrate the phenomenon and constitute a proof of concept for controlling future quantum networks. The group has identified a number of ways to increase the yield in subsequent experiments, and improvements have recently been implemented.

[We thank Curt Suplee for writing this piece]

References:
[1] D. L. Moehring, P. Maunz, S. Olmschenk, K. C. Younge, D. N. Matsukevich, L.-M. Duan, and C. Monroe, "Entanglement of single-atom quantum bits at a distance," Nature 449, 68 (2007). Abstract
[2] C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044 (1987). Abstract

Quantum Square Dance

William Phillips [photo courtesy: NIST]

A team of physicists led by 1997 Nobel Laureate William Phillips at the National Institute of Standards and Technology (NIST)could induce thousands of atoms trapped by laser beams to swap their internal spin states with partners simultaneously. Such repeated exchanges, like a quantum version of swinging your partner in a square dance but lasting a total of just 10 milliseconds, might someday carry out logic operations in quantum computers.

In the binary language of computers, the atoms swap values from 1 (“spin up”) to 0 (“spin down”), or vice versa. Unlike classical bits, which would either swap or not, quantum bits can be simultaneously in an unusual state of having swapped and not swapped at the same time. Under these conditions, spin swapping has the effect of “entangling” the pairs, a quantum phenomenon that links the atoms' properties even when they are physically separated. Entanglement is one of the features that make quantum computers potentially so powerful.

[image credit: Trey Porto/NIST]

The NIST experiment was performed with about 60,000 rubidium atoms in a Bose-Einstein condensate (BEC), a special state of matter in which all atoms are in the same quantum state. They were trapped within a three-dimensional grid of light formed by three pairs of infrared laser beams. The lasers were arranged to create two horizontal lattices overlapping like two mesh screens, one twice as fine as the other in one dimension. This created many pairs of energy “wells” for trapping atoms.

The swapping process is a way of creating logical connections among data, crucial in any computer. A logic operation is the equivalent of an “if/then” statement, such as: If two qubits have opposite states, then they should exchange values. The logical connections in quantum computers are created using entanglement, which in effect allows for multiple simultaneous, correlated possibilities.

The scientists attempted to place a single atom in each well, with one atom spin up (or 1) and the other down (or 0). Then, they merged all double wells to force each pair of atoms into the same well, where they could interact with each other. When two such identical atoms are forced into the same physical location, quantum mechanics imposes a specific type of symmetry (only two of four seemingly possible combinations of quantum states are allowed). Due to this restriction, the merged atoms oscillate between the condition in which one atom is 1 and the other is 0, to the opposite condition. This behavior is unique to identical particles.

As they swap spins, the atoms pass in and out of entanglement. At the “half-swap” points the spin of each atom is uncertain and, if measured, might turn out to be either up or down. But whatever the result, a measurement on the other atom, equally uncertain before the measurement, would be sure to be the opposite. This entanglement is the key feature that enables quantum computation.

"This is the first time these spin-entangling interactions have been demonstrated between pairs of atoms in an optical lattice,” says Trey Porto, one of the authors. “Other research groups have entangled atoms in lattices as extended clusters. By isolating pairs, we can focus on the simplest units for quantum logic.” The current set-up is not directly scalable to an arbitrary computer architecture, Porto says, since it performs the same spin-swap in parallel for all pairs of atoms.

Researchers are developing ways to address and manipulate any pair of atoms in the lattice, which should allow for scalable architectures. Furthermore, not all atoms participated in the swap process, primarily because of imperfect initial loading of the atoms in the lattice. (Some double-wells contained only one atom and had no partner to exchange with). The scientists estimate that the swap worked for at least 65% of the double wells. The NIST group is continuing to work on improving the reliability of each step and on completing the logic operation by separating atoms after they interact.

Reference:
"Controlled exchange interaction between pairs of neutral atoms in an optical lattice"
M. Anderlini, P.J. Lee, B.L. Brown, J. Sebby-Strabley, W.D. Phillips, and J.V. Porto.
Nature, 448, p452-456 (2007). Link to Article

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