How Does the World Look Like Through a Rotating Window?

[Left to Right] Sonja Franke-Arnold, Graham Gibson, Robert W Boyd and Miles J Padgett

Authors:
Sonja Franke-Arnold¹, Graham Gibson¹, Robert W Boyd^2,3 and Miles J Padgett¹

Affiliation:
¹School of Physics and Astronomy, SUPA, University of Glasgow, UK
²Department of Physics, University of Ottawa, Canada
³The Institute of Optics and Department of Physics and Astronomy, University of Rochester, USA.

What do you expect to see if you look through a window spinning at faster and faster speeds? According to the theory by Augustin-Jean Fresnel the image is predicted to be dragged along with the window and should be rotated ever so slightly. Unfortunately under normal conditions the rotation angle is so minute that it cannot be observed by eye. At the Optics Group at Glasgow University we have slowed down light to around the speed of sound during its passage through a ruby window spinning at 30 Hz. This increases the dragging effect a million fold and we can rotate an image by 5 degrees [1].

Dragging light by a spinning medium

The speed of light is constant only in vacuum. Once it enters a material, its velocity decreases, and it can be dragged along with the material – a phenomenon first predicted by Fresnel in 1818 [2]. An experiment 50 years later investigated the longitudinal drag of light in an ingenious experiment shining light through tubes of water flowing along or against the propagation of the light [3]. Similarly, spinning a window as fast as possible should drag the light in the transverse direction and rotate the view ever so slightly [4]. The rotation angle is predicted to increase with the thickness of the material, with the spinning speed and with the refractive index. However, even if the window is spinning as fast as a dentist’s drill, this rotation is too small to be observed – in the order or a millionth of a degree. We overcame this problem by vastly increasing the refractive index, to slow the light down to that of the speed of sound.

In our experiment we used a ruby rod spinning at up to 30 Hz as our “window” and an elliptical light beam as “image.” This increased the refractive group index to around one million, or in other words, slowed down the light to roughly the speed of sound. Under these conditions, the light spent long enough within the rotating ruby so the transmitted image was dragged by up to 5 degrees.

Fig.1 An intense line of laser light at 532nm is transmitted through a 10cm long ruby rod, spinning at ±30 Hz. The false color images show the light for an anticlockwise (red) and clockwise (blue) spinning of the ruby rod, rotated by about ±5 degrees compared to the image seen through a stationary crystal.


Slow light

Ruby is a crystal with an extremely long upper-state lifetime of about 20 ms. (This long life-time of ruby was employed in the first laser, as it allows the build-up of population inversion and laser action.) We used the technique of “coherent population oscillations” pioneered by our co-worker Robert Boyd to produce slow light in ruby [5].

Because of the long lifetime, the absorption of ruby changes rapidly over a frequency range of around 36 Hz. The narrow absorption line is linked via Kramers-Kronig relations to a very rapid variation of the refractive index, and hence to a very large group index of the order of one million. In principle an intense pump laser could excite this transition, thereby generating a very narrow frequency hole, which could then be probed with a weak probe laser. Instead, we generate “pump” and “probe” with a single laser, using an intensity-modulated beam. The modulation components experience then an extremely high group index.

In our case, the elliptical intensity profile shining onto the ruby rod produced the required intensity modulation and is therefore slowed down. At the same time, the elliptical beam allowed us to define the orientation of our image and measure the rotation of its major axis as a function of how fast the ruby window was spinning. In a control experiment under better defined conditions we have studied the rotation of an elliptical light beam (aspect ratio of 2) through a 6mm thick ruby window and found good agreement of the image rotation with a model based on slow light under coherent population oscillations.











Fig.2 Transmitting an elliptical beam through a spinning rod produces locally a modulation in the light intensity which in turn modulates the number of atoms in the ruby crystal driven to the excited state. This generates a delay of the intensity transmitted through the crystal which depends on the rotation speed. The left image shows the calculated delay of the intensity modulation for an input beam power of 1W (blue curve) and 2W (red curve) respectively. The corresponding rotation of the orientation angle is the product of the time delay with the rotation speed, shown on the right.

Conclusions

Our experiments have shown that light can indeed be dragged along by a spinning window resulting in an image rotation – just as Fresnel predicted 200 years ago. This effect may also be useful to store and manipulate quantum images. The rotational drag applies not only for classical images, but also for single photons, keeping both intensity and phase profile intact. We are looking into the option to rotate a more complicated image by arbitrary angles in order to encode, store and manipulate quantum information.

References
[1] S Franke-Arnold, G Gibson, R W Boyd, and M J Padgett, “Rotary Photon Drag Enhanced by a Slow Light Medium”, Science 333, 65-67 (2011). Abstract.
[2] A Fresnel, "Lettre d’Augustin Fresnel à François Arago sur l’influence du mouvement terrestre dans quelques phénomènes d’optique", Annales de chimie et de physique 9: 57 (1818).
[3] H. Fizeau, “On the effect of the motion of a body upon the velocity with which it is traversed by light”, Phil. Mag. 19 245 (1860).
[4] J Leach, A J Wright, J B Götte, J M Girkin, L Allen, S Franke-Arnold, S M Barnett, and M J Padgett, “‘Aether Drag’ and Moving Images”, Phys Rev Lett 100, 153902 (2008). Abstract.
[5] M S Bigelow, N N Lepeshkin and R W Boyd “Observation of Ultraslow Light Propagation in a Ruby Crystal at Room Temperature”, Phys Rev Lett 90, 113903 (2003). Abstract; M S Bigelow, N N Lepeshkin and R W Boyd “Superluminal and slow light propagation in a room-temperature solid”, Science 301, 200 (2003). Abstract.

Towards the Ideal Quantum Measurement

Juergen Volz

Author: Juergen Volz

Affiliation: Laboratoire Kastler Brossel de l'E.N.S., Paris, France

Measurement lies at the heart of quantum physics and gives rise to many of the counter-intuitive aspects of the theory. In a classical world, a measurement can in principle be performed with arbitrary precision without disturbing the system. In contrast, a quantum mechanical measurement inevitably projects the system into one of its basis states, although initially the system may have been in a superposition of these states. For example, it is possible to prepare an atom in a superposition of two internal states. However, a state measurement will always yield the result that the atom is either in one or the other state, which is typically referred to as 'collapse of the wave function'. This collapse during the measurement process constitutes the unavoidable back-action of the measurement on the measured system and gives rise to phenomena as for example Heisenberg's uncertainty relation[1].

While theoretically well described, experimental realizations typically fall short of these predictions, always causing a back-action on the system being measured -- with orders of magnitude larger than required for an ideal measurement. This additional back-action typically results in a energy transfer to the quantum system and heating which is a major drawback for many experiments.

The modern field of quantum optics and quantum information, relies on the accurate readout of quantum information stored in so-called quantum bits, i.e. single quantum objects that for example can be realized using the internal states of single atoms or ions. The most efficient detection method for internal atomic states is the fluorescence detection[2]. Here an atom with two stable ground states is subject to an incident light field resonant to a transition of one of the two ground states to an excited state. If the atom is in the resonant state, it will be repeatedly excited and - after spontaneously emitting a photon - decay back into the original state, while an atom in the off-resonant state is not affected by light field. The presence (or absence) of fluorescence photons then indicates the atomic state. However, this requires the atom to undergo a large amount of spontaneous emissions events, leading to an inevitable energy exchange between atom and light field.






















Fig 1: (a) Simplified level scheme of Rubidium. (b) Principle of the resonator measurement where the transmission properties of the resonator yield information on the atomic state (all light reflected: atom is in the resonant state, all light transmitted: atom is in the off-resonant state). (c) Schematic view of the experimental setup with the fiber-resonator implemented on an atomchip.

Theoretically, an ideal atomic state measurement only projects the atom onto its basis states and requires no spontaneous scattering. Therefore, our research team at the Ecole Normale Supérieure in Paris decided to investigate if we can reach a regime where we can perform a measurement with significantly less than one spontaneous emission event[3]. In our experiments we use as measurement device a so-called Fabry-Perot resonator which consists of two highly reflecting mirrors facing each other. This allows to keep light inside the resonator for approximately 38000 round trips before it is lost. With the help of a novel fiber-optical technology, the mirrors are directly imprinted on the tips of two optical fibers. In this way we can produce miniaturized resonators with a small enough volume so that a single atom placed between its mirrors is enough to shift the resonance frequency by a sizeable amount. As long as the atom is in the off resonant state it does not affect the resonator and a laser tuned to the empty cavity’s resonance is fully transmitted through the cavity. If, however, the atom is in the resonant state the resonance frequency changes and nearly all of the incident light is reflected without ever entering the resonator, thereby avoiding spontaneous scattering.






















Fig 2: Experimental results for the detection process. The blue data points are the residual error of the atomic state measurement, plotted as function of average number of scattered photons. The green curve is the minimum error possible for our resonator and the grey area corresponds to the regime accessible without resonator.

To investigate the exact amount of residual scattering in our experiment, we determine the state of the atom after each measurement from which we can deduce that our measurement allows us to infer the atomic state with a fidelity of more than 90% while scattering only 0.2 photons on average. The main limit of our measurement scheme is the small probability to finally detect the incident photons. In order to measure how our system would perform under ideal circumstances, we also directly analyzed the fundamental measurement back-action on the atom using the quantum Zeno effect[4]. This effect states that permanently measuring a physical system will stop its temporal evolution and freeze it in its current state. In our experiment, we apply a microwave pulse to transfer the atomic state to the other. At the same time we perform our state detection which permanently projects the atom into its initial state an thereby prevents the transfer. This allows us to directly measure the projection rate of the atom into its basis states, from which we conclude that three photons incident on the cavity are enough for a full collapse of the atomic state.

These results demonstrate that during the measurement (nearly) no spontaneous emission occurred and the back-action on the atom approaches the fundamental limit given by the uncertainty principle. Besides giving a compelling illustration of the quantum measurement process, these results have important consequences for quantum information applications with atoms or ions, allowing internal state readout without any heating, hereby allowing much higher cycling rates. In addition, this new detection scheme promises the development of efficient optical detectors for complex quantum systems as e.g. single molecules.

References:
[1] Maximilian Schlosshauer, "Decoherence, the measurement problem, and interpretations of quantum mechanics", Rev. Mod. Phys. 76, 1267 (2005). Abstract.
[2] A. H. Myerson, et al., "High-Fidelity Readout of Trapped-Ion Qubits", Phys. Rev. Lett 100, 200502 (2008). Abstract.
[3] Jürgen Volz, Roger Gehr, Guilhem Dubois, Jérôme Estève and Jakob Reichel, "Measurement of the internal state of a single atom without energy exchange", Nature 475, 210 (2011). Abstract.
[4] Wayne M. Itano, "Perspectives on the quantum Zeno paradox.", arXiv:quant-ph/0612187v1 (2006).

Chilling of Micromechanical Motion to the Quantum Ground State

NIST research affiliate John Teufel, who designed the micro drum, with a chip holder used to contain the drum during experiments in which the drum was cooled to its lowest possible energy level, the quantum ground state [photo credit: Burrus/National Institute of Standards and Technology].

Showcasing new tools for widespread development of quantum circuits made of mechanical parts, scientists from the National Institute of Standards and Technology (NIST) have demonstrated a flexible, broadly usable technique for steadily calming the vibrations of an engineered mechanical object down to the quantum "ground state," the lowest possible energy level.

Described in a Nature paper posted online July 6 [1], the NIST experiments nearly stop the beating motion of a microscopic aluminum drum made of about 1 trillion atoms, placing the drum in a realm governed by quantum mechanics with its energy below a single quantum, or one unit of energy. Like a plucked guitar string that plays the same tone while the sound dissipates, the drum continues to beat 11 million times per second, but its range of motion approaches zero. The cooling technique and drum device together promise new machinery for quantum computing and tests of quantum theory, and could help advance the field of quantum acoustics exploring the quantum nature of mechanical vibrations.

NIST scientists used the pressure of microwave radiation, or light, to calm the motion of the drum, which is embedded in a superconducting circuit [2]. The circuit is designed so that the drum motion can influence the microwaves inside an electromagnetic cavity. The cooling method takes advantage of the microwave light's tendency to change frequency, if necessary, to match the frequency, or tone, at which the cavity naturally resonates.

Multiple versions of NIST’s superconducting circuit containing a “micro drum” were fabricated on this sapphire chip, shown next to a penny for scale. NIST scientists cooled one such drum to its quantum ground state [image credit: Teufel/NIST]

"I put in the light at the wrong frequency, and it comes out at the right frequency, and it does that by stealing energy from the drum motion," says John Teufel, a NIST research affiliate who designed the drum. Teufel led the cooling experiments in NIST physicist and co-author Konrad Lehnert's lab at JILA, a joint institute of NIST and the University of Colorado Boulder.

Compared to the first engineered object to be coaxed into the quantum ground state, reported by California researchers last year, the NIST drum has a higher quality factor, so it can hold a beat longer, and it beats at a much slower rate, or lower frequency. As a result, individual packets of energy, or quanta, can be stored 10,000 times longer (about 100 microseconds)—long enough to serve as a temporary memory for a quantum computer and a platform for exploring complex mechanical and quantum states. In addition, the drum motion is 40 times greater per quantum, offering the possibility, for instance, of generating larger entangled "cat states"—objects that are in two places at once and also entangled, with properties that are linked even at a distance—for tests of theories such as quantum gravity. The NIST apparatus also allows researchers to measure the position of the drum directly, which is useful for force detection, with a precision closer than ever to the ultimate limit allowed by quantum mechanics.

To make engineered bulk objects obey the rules of quantum mechanics, typically observed only in atoms and smaller particles, scientists must lower an object's temperature beyond the reach of conventional refrigeration. The California researchers were able to use a passive cryogenic refrigeration technique to chill their high-frequency device enough to reach the ground state, avoiding the need for specialized techniques.

NIST's drum required the use of "sideband cooling" to reach much colder temperatures, taking advantage of strong interactions between the drum and the microwaves. This is the same idea as laser cooling of individual atoms, first demonstrated at NIST in 1978 [3], concurrently with another research group in Germany [4], opening a new field of research on ultracold atoms. Now a basic tool of atomic physics worldwide, laser cooling enabled many significant advances by allowing researchers to reduce the vibrational motion of trapped atoms to less than a single quantum. Sideband refers to a collection of light particles (photons) just above or below a specific target frequency. In the case of NIST's superconducting circuit, this stray radiation pressure, as it adjusts to the surrounding environment of the cavity, steadily removes energy from the drum motion in the same way that laser cooling slows atoms in a gas.

In the NIST experiments, the drum is first chilled in a cryogenic refrigerator using liquid helium. This lowers the drum energy to about 30 quanta. Sideband cooling then reduces the drum temperature from 20 milliKelvin (thousandths of a degree above absolute zero) to below 400 microKelvin (millionths of a degree above absolute zero), steadily lowering the drum energy to just one-third of 1 quantum.

Scientists begin the sideband cooling process by applying a drive tone to the circuit at a particular frequency below the cavity resonance. The drumbeats generate sideband photons, which naturally convert to the higher frequency of the cavity. These photons leak out of the cavity as it fills up. Each departing photon takes with it one mechanical unit of energy—one phonon—from the drum motion. At a drive intensity that corresponds to 4,000 photons in the cavity, the drum motion slows to less than 1 quantum. By detecting the scattered photons leaving the cavity, scientists can measure the mechanical motion near the lowest possible limits of uncertainty. Collectively, these steps proved that the mechanical drum entered the quantum regime.

The drum apparatus has applications in quantum computers, which could someday solve certain problems that are intractable today, even with the best supercomputers. Quantum information can be stored in the mechanical state for more than 100 microseconds before absorbing one phonon from the environment—much longer than conventional superconducting quantum bits can maintain information. The drum, thus, might serve as a short-term memory device in a superconducting quantum computer circuit, a technology under development by the same NIST research group. In addition, because mechanical oscillators can interact with light of any frequency, they could act as intermediaries for transferring quantum information between microwave and optical components.

References
[1] J.D. Teufel, T. Donner, Dale Li, J.W. Harlow, M.S. Allman, K. Cicak, A.J. Sirois, J.D. Whittaker, K.W. Lehnert and R.W. Simmonds, "Sideband cooling of micromechanical motion to the quantum ground state", Nature. Posted online July 6, 2011. doi:10.1038/nature10261. Abstract.
[2] J.D. Teufel, D. Li, M.S. Allman, K. Cicak, A.J. Sirois, J.D. Whittaker, and R.W. Simmonds, "Circuit cavity electromechanics in the strong coupling regime", Nature, 471, 204–208 (10 March 2011). Abstract.
[3] D. J. Wineland, R. E. Drullinger, and F. L. Walls, "Radiation-Pressure Cooling of Bound Resonant Absorbers", Physical Review Letters, 40, 1639–1642 (1978). Abstract.
[4] W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, "Optical-Sideband Cooling of Visible Atom Cloud Confined in Parabolic Well", Physical Review Letters, 41, 233–236 (1978). Abstract.

Quantum Metrology Meets Noise

[From Left to Right] Ruynet L. de Matos Filho, Luiz Davidovich, Bruno M. Escher


Authors: Bruno M. Escher, Ruynet L. de Matos Filho, and Luiz Davidovich

Affiliation: Instituto de Física, Universidade Federal do Rio de Janeiro, Brazil


Link to the Quantum Optics and Quantum Information Group >>

The estimation of parameters is an essential part of the scientific analysis of experimental data. It may play an important role at a very fundamental level, involving the measurement of fundamental constants of Nature – as for instance the speed of light in vacuum, the Planck constant, and the gravitational constant. Furthermore, it has widespread practical implications, in the characterization of parameter-dependent physical processes – as for instance the estimation of the duration of a phenomenon, of the depth of an oil deposit through the scattering of seismic waves, of the transition frequency of an atom, or yet of the phase shift in an interferometric measurement, due to the presence of gravitational waves.

Detailed techniques for parameter estimation, dating back to the work of R. A. Fisher in 1922 [1, 2] and of H. Cramér [3] and C. R. Rao [4] a decade later, have allowed the characterization of the achievable limits in the precision of estimation. The basic steps in parameter estimation are illustrated in Figure 1: one prepares a probe in a known initial configuration, one sends it through the parameter-dependent process to be investigated, one measures then the final configuration of the probe, and from this measurement one estimates the value of the parameter.

Figure 1: General protocol to estimate an unknown parameter. In the first step (first box on the left), the probe is initialized in a fiducial configuration. It is, then, sent through a parameter-dependent process, which modifies its configuration (second and third boxes). In the next step (fourth box), the probe is submitted to a measurement. Finally, an estimative of the real value of the parameter is made relying on the results of the previous measurement (last box).

Due to the fact that realistic experimental data are noisy, it is not possible to biunivocally associate an experimental result (through an estimative) with the true value of the parameter. The error in an estimative may be quantified by the statistical average of the square of the difference between the estimated and the true value of the parameter, then the so-called Cramér-Rao limit yields a lower-bound to this error, which is inversely proportional to the square root of the number N of repetitions of the measurement process. In single-parameter estimation, this bound is expressed in terms of a quantity known as Fisher Information: the larger this quantity, the more accurate can be the estimative.

Indeed, the amount of information that can be extracted from experiments about the true value of an unknown parameter is given by the Fisher Information. This quantifier of information depends on properties of the probe, the parameter-dependent process, and the measurement on the probe used to investigate the process. An important aim of metrology is to calculate the Fisher Information, to find ways to maximize it, and to find protocols that allow for better estimation.

Quantum Metrology [5, 6] takes into account the quantum character of the systems and processes involved in the estimation of parameters. In this case, the estimation error is still limited by the Cramér-Rao bound, expressed in terms of the Fisher Information, which as before quantifies the maximum amount of information that can be extracted about the parameter, but considering the constraints imposed by quantum physics; in particular, its intrinsic probabilistic nature, the dependence of the result on the measurement scheme, and the more restricted set of possible measurements.

The so-called Quantum Fisher Information [7] involves a maximization over all possible measurement strategies allowed by quantum mechanics. It characterizes the maximum amount of information that can be extracted from quantum experiments about an unknown parameter using the best (and ideal) measurement device. It establishes the best precision that can be attained with a given quantum probe. The ultimate precision limit in quantum parameter estimation is obtained by maximizing the Quantum Fisher Information over all initial states of the probe. In the ideal situation of systems isolated from the environment, useful analytic results allow the calculation of this ultimate bound. It can be shown then that quantum strategies, involving non-classical characteristics of the probes, like entanglement and squeezing, lead to much better bounds, as compared to standard approaches that do not profit from these properties [8]. Thus, for a noiseless optical interferometer (Figure 2), use of entangled states of n photons leads to a precision in the measurement of phase shifts proportional to 1/n, a considerable improvement over the standard limit, which is inversely proportional to the square root of the number of photons.

Figure 2: Optical interferometer. A light field, in a well-known state, is sent through the interferometer. A phase shift θ, due to a refringent material in one of the interferomter arms, can be estimated by measurements on the output field.

In practice, systems cannot be completely isolated from their environment. This leads to the phenomenon of decoherence, which mitigates quantum effects, thus limiting the usefulness of quantum strategies. In this case, it is important to establish the robustness of those strategies. However, the determination of the ultimate precision bound for systems under the influence of the environment involves usually painstaking numerical work [9, 10], since there has been up to now no general approach for this more realistic situation [11,12]. The work by Escher et al. [13], recently published in Nature Physics, provides a general framework for quantum metrology in the presence of noise. It can be used to circumvent this difficulty, leading to useful analytic bounds for important problems.

The main idea behind the proposed approach is to consider the probe together with an environment as a single entity, and to consider the Quantum Fisher Information corresponding to this enlarged system, which implies a maximization over all possible measurement strategies applied to the ensemble probe plus environment. This quantity is, then, an upper bound to the Quantum Fisher Information of the probe alone. It can be shown that there are several (in fact, infinite!) equivalent environments that lead to the same noisy dynamics of the probe. The work by Escher et al. shows however that it is always possible to choose an environment so that the information about the parameter, obtained from measurements on the probe plus environment, is redundant with respect to the information obtained from the probe alone. In this case, the Quantum Fisher Information of the enlarged system coincides with the corresponding quantity for the probe. This allows in principle the determination of the ultimate precision limit by using the methods previously developed for isolated systems.

Even though finding this special class of environment is in general a difficult problem, useful approximations, based on physical insights, can be found, which yield analytical bounds for the precision in noisy systems. The power of this framework was demonstrated in the paper published in Nature Physics, by applying it to lossy optical interferometry and atomic spectroscopy under dephasing, displaying in both cases how noise affects the precision in the estimation of the relevant parameter. Thus, for a noisy optical interferometer, probed by n photons, it was shown that there is a continuous transition of the precision in the estimation of phase shifts, as the number of photons increases, from a 1/n scaling, the ultimate quantum limit in the absence of noise, to the so-called standard limit, inversely proportional to the square root of the number of photons. This result shows that noise leads unavoidably to the standard limit scaling, as the number of photons reaches a critical value, which depends on the noise strength.

Due to its generality, this framework may be applied to a large variety of systems, thus offering a useful tool for the determination of the ultimate limits of precision in the estimation of parameters in realistic scenarios.

References
[1] R. A. Fisher, “On the mathematical foundations of theoretical statistical”, Phil. Trans. R. Soc. A, v. 222, pp. 309–368 (1922) Full text in pdf.
[2] R. A. Fisher, “Theory of statistical estimation”, Proc. Camb. Phil. Soc., v. 22, pp. 700–725, 1925. Abstract.
[3] H. Cramér, "Mathematical methods of statistics". (Princeton University Press,1946).
[4] C. R. Rao, "Linear statistical inference and its applications". 2nd ed. (John Wiley & Sons, 1973).
[5] C. Helstrom, "Quantum detection and estimation theory". (Academic, 1976).
[6] A. Holevo, "Probabilistic and statistical aspects of quantum theory". (North-Holland, 1982).
[7] S. Braunstein, C. Caves, “Statistical distance and the geometry of quantum states”, Physical Review Letters, v. 22, pp. 3439–3443 (1994). Abstract.
[8] V. Giovannetti, S. Lloyd, L. Maccone, “Quantum-enhanced measurements: beating
the standard quantum limit”, Science, v. 306, pp. 1330–1336 (2004). Abstract.
[9] S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, J. I. Cirac, “Improvement of frequency standards with quantum entanglement”, Physical Review Letters, v. 79, pp. 3865–3868 (1997). Abstract.
[10] U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation”, Physical Review Letters, v. 102, pp. 040403 (2009). Abstract.
[11] V. Giovannetti, S. Lloyd, L. Maccone, “Advances in quantum metrology”, Nature Photonics, v. 5, pp. 222–229 (2011). Abstract.
[12] L. Maccone, V. Giovannetti, “Quantum metrology: Beauty and the noisy beast”, Nature Physics, v. 7, pp. 376–377 (2011). Abstract.
[13] B. M. Escher, R. L. de Mattos Filho, L. Davidovich “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology”, Nature Physics, v. 7, pp. 406–411, 2011. Abstract.

Quantum Simulation with Light: Frustrations between Photon Pairs

Philip Walther

Author: Philip Walther

Affiliation: Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Austria.

Quantum information science will revolutionize our society if we are able to harness its power. Therefore, worldwide theoretical and experimental efforts are focused on the realization of the Holy Grail of quantum-enhanced applications: the quantum computer. But the difficulties encountered in realizing hundreds of coherent quantum gate operations that act on almost the same number of qubits for the implementation of useful quantum algorithms [1, 2] may seem very discouraging.

On the other side, more than a quarter of a century ago, Richard Feynman [3, 4] envisioned that a well-controlled quantum-mechanical system can be efficiently used for the simulation of other quantum systems and thus is capable of calculating properties that are unfeasible for classical computers. Quantum simulation promises potential returns in understanding detailed quantum phenomenon of inaccessible quantum systems, from molecular structure to the behavior of high-temperature superconductors [5]. Moreover, quantum simulations are conjectured to be less demanding than quantum computations by being less stringent on explicit gate operations or error corrections [6]. The tradeoff, however, is that the level of coherent control of quantum systems necessary for the physical realization of quantum simulators is very demanding.

Photonic quantum systems are not only the natural choice for quantum communication and metrology applications, but have also been proven to be a suitable system for scalable quantum computing [7]. Moreover, the single-particle addressability and tunable measurement-induced interactions make single photons also very promising for the simulation of other quantum systems. In addition to the superior level of quantum control, such photonic quantum simulators allow to utilize quantum interference at beamsplitters which can lead to interesting photon-entanglement that corresponds to ground states of complex correlations in chemical or solid-state systems.

The ground state properties of frustrated quantum systems raised significant interest due to the conjecture that these quantum phenomena may be important for the understanding of high-temperature superconductivity [8]. A quantum system is frustrated if competing requirements cannot be satisfied simultaneously.

A research team from the University of Vienna and the Institute of Quantum Optics and Quantum Information at the Austrian Academy of Sciences headed by Anton Zeilinger realized for the first time an experimental quantum simulation, where the frustration regarding the pairing of quantum correlations was closely investigated [9]. Such pairing of quantum correlations is an important mechanism in chemical or so-called valence bonds, where two electrons from different atoms share an anti-correlated spin state due to the Pauli principle. Obviously this leads to maximally entangled spins, where the spins are always oriented in opposite directions.

The same quantum correlation of valence-bond states can be simulated by a pair of photons that is maximally entangled in polarization, i.e. that the two photons are always orthogonal polarized. Therefore, we were able to simulate four spin-1/2 particles whose ground states exist in two valence-bond states by using two entangled photon pairs. For simulating the interesting entanglement dynamics of these states, however, an effective nonlinear interaction among the photons was implemented by superimposing photons from each pair (Figure 1) at a beamsplitter with a tunable splitting ratio, followed by a measurement of the photons in the output ports.

Figure 1 : Scheme of the photonic setup for studying frustrated spin-1/2 tetramers. The variable beamsplitters (VBS) of this analog quantum simulator allows for tuning the interaction from localized to delocalized of frustrated valence-bond states.

Depending on the interaction strength single photons from originally localized valence-bonds are facing the conflict over partnerships between each other. Each photon can establish a single bond to only one partner exclusively, but wants to get correlated with several partners – obviously this leads to frustration. As a result, the quantum system uses “tricks” that allow quantum fluctuations in which different pairings can coexist as superposition. In the scientific community such superpositions of valence-bond states are called spin liquid states and are an active area of research.

Figure 2: Photonic quantum simulation of the ground state energy of a frustrated Heisenberg spin system.

The precise quantum control of our single photons enabled us to extract the total energy (Figure 2) and the pair-wise quantum correlations for arbitrary configurations within this spin tetramer (Figure 3). Our simulation also proves that the pairwise quantum correlations and energy distribution are restricted by the role of quantum monogamy: only two photons can share a valence-bond independent of the coupling to other single photons. This can be nicely seen as complementarity relation among the various valence-bond configurations when tuning the coupling by changing the beamsplitter's reflectivity.

Figure 3: Experimental observation of the complementarity relation for the pair-wise quantum correlation (or Heisenberg energy) among the individual partners when changing the interaction.

This recent work underlines that quantum simulation is a very good tool for calculating quantum states of matter, and is thus opening the path for the investigation of more complex systems.

References
[1] P. W. Shor, "Algorithms for quantum computation: discrete logarithms and factoring", Proc. 35th Annual Symposium on "Foundations of Computer Science" (ed. S. Goldwasser) 124-134 (1994). Abstract.
[2] L. K. Grover, "Quantum Mechanics Helps in Searching for a Needle in a Haystack", Phys. Rev. Lett. 79, 325 (1997). Abstract.
[3] R. Feynman, "Simulating physics with computers," International Journal of Theoretical Physics, 21, 467 (1982). Abstract.
[4] R. P. Feynman, "Quantum mechanical computers," Foundations of Physics 16, 507 (1986). Abstract.
[5] I. Buluta, F. Nori, "Quantum Simulators," Science 326, 108 (2009). Abstract.
[6] A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, M. Head-Gordon, "Simulated Quantum Computation of Molecular Energies," Science 309, 1704 (2005). Abstract.
[7] E. Knill, R. Laflamme, G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46 (2001). Abstract.
[8] P. W. Anderson, "The Resonating Valence Bond State in La₂CuO₄ and Superconductivity," Science 235, 1196 (1987).
[9] Xiao-song Ma, Borivoje Dakic, William Naylor, Anton Zeilinger & Philip Walther, "Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems," Nature Physics, 7, 399 (May, 2011). Abstract.

Exploring Macroscopic Quantum Mechanics with Gravitational-wave Detectors

Haixing Miao

[Haixing Miao is the recipient of the 2010 GWIC (Gravitational Wave International Committee) Thesis Prize for his PhD thesis “Exploring Macroscopic Quantum Mechanics in Optomechanical Devices" (PDF). -- 2Physics.com]

Author: Haixing Miao

Affiliation:
Australian International Gravitational Research Centre (AIGRC), University of Western Australia, Perth, Australia;
Theoretical AstroPhysics Including Relativity (TAPIR), California Institute of Technology, Pasadena, USA.

Do macroscopic objects have wavy behaviors predicted by quantum mechanics, the same as microscopic atoms? Is there any boundary or transition between the quantum world and the classical world which we experience daily? Interestingly, advanced laser interferometer gravitational-wave (GW) detectors may give answers to these fundamental questions.

Fig. 1 LIGO detector at Livingston (left). It consists of a Michelson interferometer which uses a highpower laser to measure differential motions of input test masses (ITM) and end test masses (ETM) caused by gravitational waves.

It might seem unlikely, at least from the first sight, that a GW detector (e.g., LIGO detector [1] shown in Fig. 1) can study something quantum, given its apparent classical features: (i) using a high-power laser and kilogram-scale mirrors as test masses, (ii) having these test masses widely separated by kilometers, and (iii) operating at the room temperature. How can we probe delicate quantum mechanics with such a giant? The answer lies in the fact that, to detect weak GWs from the distant universe, the GW detector has to be extremely sensitive to the tiny displacement of the kilogram test mass, even sensitive enough to probe the quantum zero-point motion of macroscopic test masses.

2Physics articles by past winners of the GWIC Thesis Prize:
Holger J. Pletsch (2009): "Deepest All-Sky Surveys for Continuous Gravitational Waves"
Henning Vahlbruch (2008): "Squeezed Light – the first real application starts now"
Keisuke Goda (2007): "Beating the Quantum Limit in Gravitational Wave Detectors"
Yoichi Aso (2006): "Novel Low-Frequency Vibration Isolation Technique for Interferometric Gravitational Wave Detectors"
Rana Adhikari (2003-5)*: "Interferometric Detection of Gravitational Waves : 5 Needed Breakthroughs"
*Note, the gravitational wave thesis prize was started initially by LIGO as a biannual prize, limited to students of the LIGO Scientific Collaboration (LSC). The first award covered the period from 1 July 2003 to 30 June 2005. In 2006, the thesis prize was adopted by GWIC, renamed, converted to an annual prize, and opened to the broader international community.

Fig. 2 Plot showing the sensitivity of LIGO Hanford detector compared with the standard quantum limit (SQL) -- a benchmark for quantumness. This figure is adopted from Ref.[2], which reports cooling of kilogram test masses down to an effective temperature of 1.4μK (Experiment is led by Nergis Mavalvala and Thomas Corbitt from MIT).

Indeed, with state-of-the-art technology, initial LIGO detector is only a factor of 10 away from the Standard Quantum Limit (SQL) that is imposed by the Heisenberg Uncertainty Principle [3] (illustrated in Fig. 2). Currently, in the GW community, significant efforts have been put into improving the detector sensitivity by reducing the classical thermal noises that cause random jittering of test masses. The future AdvLIGO [4] and other advanced GW detectors [5] under construction are anticipated to be operating at or beyond the SQL, with their sensitivities limited by noises that have purely quantum origin. To further increase the detector sensitivity, we need to manipulate the light at the quantum level, e.g. the use of quantum squeezed light [6-7]. Advanced GW detectors can be viewed as quantum devices, regardless of their bulky appearance.

Fig. 3 Figure showing schematically the creation of quantum superposition of macroscopic test masses by coherently amplifying the momentum of a single photon with advanced GW detectors. Please refer to Ref. [10] for more details of the experimental protocol.

With a sequence of studies [8-11], it is shown that, by using appropriate protocols, advanced GW detectors allow us to prepare kilogram test masses in different quantum states, and to study their quantum dynamics. For example, by superimposing a single photon―the light quantum―onto a strong light field in the GW detector, the momentum of the photon can be coherently amplified, and can even place the macroscopic test masses into a quantum superposition, as depicted schematically in Fig. 3. The GW detector, in some sense, acts as a “quantum amplifier”, and brings the quantumness of the microscopic photon into the macroscopic world.

Besides, if we simultaneously measure the common and differential motions of test masses, we can create Einstein-Podolsky-Rosen type quantum entanglement among widely separated test masses [9]. Furthermore, we can study the dynamics of such a macroscopic quantum entanglement, which allows us to explore some interesting decoherence effects that could be unique to macroscopic objects [12].

Future advanced GW detectors can, therefore, not only detect tiny ripples in the spacetime and open up a new window into observing our universe, but also help us to gain deeper understanding of quantum behaviors of macroscopic objects, which might reveal exciting new phenomena.

References:
[1] LIGO website: ligo.caltech.edu and a recent review article by the LIGO Scientific Collaboration (LSC), “LIGO: the Laser Interferometer Gravitational-wave Observatory”, Rep. Prog. Phys. 72, 076901 (2009). Abstract.
[2] LIGO Scientific Collaboration (LSC), “Observation of a kilogram-scale oscillator near its quantum ground state”, New J. Phys. 11 073032 (2009). Abstract.
[3] V. B. Braginsky and F. Y. Khalili, "Quantum Measurement", publisher: Cambridge
University Press (1992).
[4] Advanced LIGO website: advancedligo.mit.edu
[5] Advanced VIRGO website: cascina.virgo.infn.it/advirgo ; Large-scale Cryogenic Gravitational wave Telescope (LCGT) website: gw.icrr.u-tokyo.ac.jp/lcgt/
[6] H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Gossler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10dB quantum noise reduction”, Phys. Rev. Lett. 100, 033602 (2008). Abstract.
[7] K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, Nature Physics 4, 472 (2008). Abstract.
[8] Helge Müller-Ebhardt, Henning Rehbein, Chao Li, Yasushi Mino, Kentaro Somiya, Roman Schnabel, Karsten Danzmann, and Yanbei Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors”, Phys. Rev. A 80, 043802 (2009). Abstract.
[9] Helge Müller-Ebhardt, Henning Rehbein, Roman Schnabel, Karsten Danzmann, and Yanbei Chen, “Entanglement of Macroscopic Test Masses and the Standard Quantum Limit in Laser Interferometry”, Phys. Rev. Lett. 100, 013601 (2008). Abstract.
[10] Farid Ya. Khalili, Stefan Danilishin, Haixing Miao, Helge Müller-Ebhardt, Huan Yang, and Yanbei Chen, “Preparing a Mechanical Oscillator in Non- Gaussian Quantum States”, Phys. Rev. Lett. 105, 070403 (2010). Abstract.
[11] Haixing Miao, Stefan Danilishin, Helge Müller-Ebhardt, Henning Rehbein, Kentaro Somiya, and Yanbei Chen, “Probing macroscopic quantum states with a sub-Heisenberg accuracy”, Phys. Rev. A 81, 012114 (2010). Abstract.
[12] Lajos Diósi, “A universal master equation for the gravitational violation of the quantum mechanics”, Phys. Lett. A 120, 377 (1987). Abstract ; Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, Publisher: Alfred A. Knopf (2005).

Interaction-based Quantum Metrology Showing Scaling Beyond the Heisenberg Limit

Mario Napolitano (left) and Morgan W. Mitchell (right)














Authors: Mario Napolitano and Morgan W. Mitchell

Affiliation: ICFO – Institute of Photonic Sciences, 08860 Castelldefels - Barcelona, Spain

The most precise modern measurement techniques are based on related interferometric techniques: whether the application is defining time-standards, measuring accelerations, magnetic fields, or even detecting the space-time distortion caused by gravitational-waves. All interferometers use the quantum superposition principle and wave-particle duality [1]: the probes, photons or atoms depending on the case, follow simultaneously two different evolutions, and these experience a phase difference due to the quantity being measured. When the paths are recombined, the flux of particles is measured, giving the result of the measurement.

The precision of such interferometers improves by using more probing particles provided that technical sources of noise are suppressed. The square-root law in Poisson statistics of random counts fixes the scale of this improvement saying that the sensitivity, namely the minimum phase difference measurable at a certain level of noise, get better as 1/√N, where N is the total number of probing particles in use. Usually, the scientific community refers to this scaling law for the sensitivity as the Standard Quantum Limit (SQL), or Shot-Noise limit.

The quest for ever-more precise measurements has motivated much of the latest research in atomic physics and quantum optics [2]. For example, most of the achievements regarding entanglement or squeezing find a natural framework in the context of quantum metrology. When applied to interferometry, entanglement means that the inherent fluctuations of each probing particle are correlated with those of another particle: in this way, the intrinsic noise of the probing system as a whole is squeezed, removing uncertainty from critical degrees of freedom and putting it into less-critical ones. In this way, the sensitivity can surpass the 1/√N standard quantum limit. In the ideal case of perfect entanglement, a NooN state, the sensitivity scales as 1/N, a law that in the community is known as the 'Heisenberg limit' [3].

Is this the best that can be done? Are there other ways to use better the probing resources? Does the Heisenberg limit apply always? Only a few years ago, theoretical studies discovered that entanglement is not the only resource that can improve measurement precision in the face of quantum noise [4,5]. According to those works, also the dynamics of the measurement process plays a very important role to establish the best achievable precision. For example, nonlinear dynamics, that is to say interaction between the probing particles, can make a difference and extend, in principle, the limit in the sensitivity.

As presented in a recent letter published in Nature [6], we were able to create the appropriate nonlinear dynamics in a polarization-based interferometer where photons are used to probe the magnetization of an ensemble of cold atoms. We investigated the sensitivity of such measurement as function of the number of photons used to probe, looking for a scaling law beyond the Heisenberg limit. In a particular regime of light intensity and detuning, we detected a polarization rotation of the probing photons due to the atomic magnetization, dependent of the photon number itself. Both this nonlinearity, and the high quality of the light-atom coupling we developed, contributed in amplifying the signal from the atoms, keeping at the same time the noise at the level of the light shot noise.

The sensitivity to the magnetization, in the nonlinear probing, was in fact scaling better than the Heisenberg limit as the photon number was increased, over a range of two orders of magnitude, Fig 1. In fact, the measured scaling was very close to the expected 1/N^3/2 for two-particle interaction [7]. With more than 20 million photons, however, incoherent processes such as optical pumping damaged to the atomic preparation and the measurement no longer improved.

Fig.1 (click on the image to see higher resolution version) : Sensitivity of the nonlinear probe versus number of interacting photons. Blue circles indicate the measured sensitivity, curves show results of numerical modeling, and the black lines indicate SQL, HL, and SH scaling for reference. Scaling surpassing the Heisenberg limit is observed over two orders of magnitude. The measured damage to the magnetization, shown as green diamonds, confirms the non-destructive nature of the measurement. Error bars for standard errors would be smaller than the symbols and are not shown.

With this experiment we opened the possibility of investigating experimentally nonlinear dynamics and interaction between quantum probes as new fundamental resources in the quest for greater sensitivity in quantum-interference-based measurements. We think that similar interaction-based measurement will soon start to be extended and tested with other techniques [8,9] although, as also we noticed in our experiment, the range of applicability will depend on the specific implementation.

Description of the experiment:

In our lab, we work with a sample of about one million of cold 87Rb atoms, held in a single-beam optical dipole trap. Pulses of polarized laser light propagate through the sample along the trap axis experiencing a very high coupling with the atomic ensemble, Fig 2a. Previous experiments demonstrated an on-resonance optical depth of above 50, which gives the figure of merit of such good coupling [10]. When instead the light is tuned off-resonant, it can probe in a dispersive, non-destructive way the angular momentum of the atomic ensemble. In particular, the polarization experiences a paramagnetic Faraday rotation proportional to the spin component along the light propagation axis.

Fig.2a (click on the image to see higher resolution version): Experimental schematic: an ensemble of 87Rb atoms,held in an optical dipole trap, is polarized by optical pumping (OP). Linear (P_1), nonlinear (P_{NL}), and a second linear (P_2) Faraday rotation probe pulses measure the atomic magnetization, detected by a shot-noise-limited polarimeter (PM). The atom number is measured by quantitative absorption imaging (AI). Fig.2b : Spectral positions of the pumping, probing, and imaging light on the D2 transition.

A key point in our experiment was the ability to calibrate the newly developed, nonlinear-probing technique against a well established and tested linear one, Fig 3. Actually, our light-atom interface is very versatile and different regimes of interaction can be addressed: in particular we could easy switch between a linear and a nonlinear interaction case. After the trap loading and an initial atomic state preparation via optical pumping with on-resonance, circular-polarized light, we probed the polarized sample under both in a linear regimes and in a nonlinear one.

Fig.3 (click on the image to see higher resolution version): 3a) Ratio of nonlinear rotation, φ_NL, to linear rotation, φ_L, vs. nonlinear probe photon number, N_NL. The data points and error bars indicate best fit and standard errors from a linear regression for a given N_NL. The red curve is a fit showing the expected nonlinear behavior, with some saturation for large N_NL. 3b)&c) φ_L, φ_NL correlation plots for two values of N_NL. The atom number N_A is varied to produce a range of φ_L and φ_NL. Green squares: no atoms N_A = 0, red circles: 1.5 x 10⁵ < N_A < 3.5 x 10⁵, blue triangles N_A ‚ 7 x 10⁵. The blue triangles are shown as a check on detector saturation, and are not included in the analysis.

In previous experiments, we demonstrated projection noise sensitivity in the linear regime, namely when low intensity and large (GHz) detuning from the resonances are used. Conversely, in this experiment we also operated in a regime of probing designed specifically to show clearly atom-mediated photon-photon interactions. We expected to excite nonlinearities like fast electronic nonlinearities, namely saturation effects in the photon absorption and stimulated emission. We used intense pulses of about 50ns, a time scale short compared with relaxation process, like optical pumping by spontaneous emission, but still long enough to define the frequency of the light within few tens of MHz. At a particular detuning, due to the symmetry of the electronic structure in alkali atoms, all the linear responses from the different atomic transitions compensate, hence only the nonlinear contributions remain, Fig 2b. Moreover, we carefully checked and excluded any possible other source of nonlinearity apart from the atoms, for example, we showed that the photodetectors continue to be linear even for the largest photon numbers.

References:
[1] Giovannetti, V., Lloyd, S. & Maccone, L. "Quantum metrology". Phys. Rev. Lett. 96, 010401 (2006). Abstract.
[2] Lee, H., Kok, P. & Dowling, J. P. "A quantum Rosetta stone for interferometry". J. Mod. Opt. 49, 2325-2338 (2002). Abstract.
[3] Holland, M. J., & Burnett, K. "Interferometric detection of optical phase shifts at the Heisenberg limit". Phys. Rev. Lett. 71, 1355 (1993). Abstract.
[4] Boixo, S., Flammia, S. T., Caves, C. M. & Geremia, J. "Generalized limits for single-parameter quantum estimation". Phys. Rev. Lett. 98, 090401(2007). Abstract.
[5] Sergio Boixo, Animesh Datta, Matthew J. Davis, Steven T. Flammia, Anil Shaji, and Carlton M. Caves, "Quantum metrology: Dynamics versus entanglement". Phys. Rev. Lett. 101, 040403 (2008). Abstract.
[6] M. Napolitano, M. Koschorreck, B. Dubost, N. Behbood, R. J. Sewell & M. W. Mitchell, "Interaction-based quantum metrology showing scaling beyond the Heisenberg limit". Nature 471, 486–489 (2011). Abstract.
[7] Napolitano, M. & Mitchell, M. W. "Nonlinear metrology with a quantum interface". New J. Phys. 12, 093016 (2010). Abstract.
[8] Woolley, M. J., Milburn, G. J. & Caves, C. M. "Nonlinear quantum metrology using coupled nanomechanical resonators". New J. Phys. 10, 125018(2008). Abstract.
[9] Choi, S. & Sundaram, B. "Bose-Einstein condensate as a nonlinear Ramsey interferometer operating beyond the Heisenberg limit". Phys. Rev. A 77, 053613 (2008). Abstract.
[10] Koschorreck, M., Napolitano, M., Dubost, B. & Mitchell, M. W. "Sub-projection-noise sensitivity in broadband atomic magnetometry". Phys. Rev. Lett. 104, 093602 (2010). Abstract.

First Demonstration of Spin-Orbit Coupling in Ultracold Atomic Gases

Ian Spielman (photo courtesy: Joint Quantum Institute, USA)

Physicists at the Joint Quantum Institute (JQI), a collaboration of the National Institute of Standards and Technology (NIST) and the University of Maryland-College Park, have for the first time caused a gas of atoms to exhibit an important quantum phenomenon known as spin-orbit coupling. Their technique opens new possibilities for studying and better understanding fundamental physics and has potential applications to quantum computing, next-generation "spintronics" devices and even "atomtronic" devices built from ultracold atoms.

In the researchers' demonstration of spin-orbit coupling, two lasers allow an atom's motion to flip it between a pair of energy states. The new work, published in Nature*, demonstrates this effect for the first time in bosons, which make up one of the two major classes of particles. The same technique could be applied to fermions, the other major class of particles, according to the researchers. The special properties of fermions would make them ideal for studying new kinds of interactions between two particles—for example those leading to novel "p-wave" superconductivity, which may enable a long-sought form of quantum computing known as topological quantum computation.

In an unexpected development, the team also discovered that the lasers modified how the atoms interacted with each other and caused atoms in one energy state to separate in space from atoms in the other energy state.

Fig 1. [image courtesy: Ian Spielman, JQI] : In an ultracold gas of nearly 200,000 rubidium-87 atoms (shown as the large humps) the atoms can occupy one of two energy levels (represented as red and blue); lasers then link together these levels as a function of the atoms’ motion. At first atoms in the red and blue energy states occupy the same region (Phase Mixed), then at higher laser strengths, they separate into different regions (Phase Separated). Also, see related phase diagrams in Fig.3 .

One of the most important phenomena in quantum physics, spin-orbit coupling describes the interplay that can occur between a particle’s internal properties and its external properties. In atoms, it usually describes interactions that only occur within an atom: how an electron’s orbit around an atom’s core (nucleus) affects the orientation of the electron’s internal bar-magnet-like “spin.” In semiconductor materials such as gallium arsenide, spin-orbit coupling is an interaction between an electron’s spin and its linear motion in a material.

“Spin-orbit coupling is often a bad thing,” said JQI’s Ian Spielman, senior author of the paper. “Researchers make ‘spintronic’ devices out of gallium arsenide, and if you’ve prepared a spin in some desired orientation, the last thing you’d want it to do is to flip to some other spin when it’s moving.”

“But from the point of view of fundamental physics, spin-orbit coupling is really interesting,” he said. “It’s what drives these new kinds of materials called ‘topological insulators.’”

One of the hottest topics in physics right now, topological insulators are special materials in which location is everything: the ability of electrons to flow depends on where they are located within the material. Most regions of such a material are insulating, and electric current does not flow freely. But in a flat, two-dimensional topological insulator, current can flow freely along the edge in one direction for one type of spin, and the opposite direction for the opposite kind of spin. In 3-D topological insulators, electrons would flow freely on the surface but be inhibited inside the material. While researchers have been making higher and higher quality versions of this special class of material in solids, spin-orbit coupling in trapped ultracold gases of atoms could help realize topological insulators in their purest, most pristine form, as gases are free of impurity atoms and the other complexities of solid materials.

Usually, atoms do not exhibit the same kind of spin-orbit coupling as electrons exhibit in gallium-arsenide crystals. While each individual atom has its own spin-orbit coupling going on between its internal components (electrons and nucleus), the atom’s overall motion generally is not affected by its internal energy state.

But the researchers were able to change that. In their experiment, researchers trapped and cooled a gas of about 200,000 rubidium-87 atoms down to 100 nanokelvins, 3 billion times colder than room temperature. The researchers selected a pair of energy states, analogous to the “spin-up” and “spin-down” states in an electron, from the available atomic energy levels. An atom could occupy either of these “pseudospin” states. Then researchers shined a pair of lasers on the atoms so as to change the relationship between the atom’s energy and its momentum (its mass times velocity), and therefore its motion. This created spin-orbit coupling in the atom: the moving atom flipped between its two “spin” states at a rate that depended upon its velocity.

Fig 2. [image courtesy: Ian Spielman, JQI]: Construction of spin-orbit coupling. a, the red and blue lines denote the two laser-coupled atomic levels and the solid black lines denote the laser coupling. b, computed eigen-energies (dispersion relation) for an atom coupled under this laser-coupling. c, measurement of the quasi-momentum where the dispersion has its minima or minimum. d, representative data used to construct c.

“This demonstrates that the idea of using laser light to create spin-orbit coupling in atoms works. This is all we expected to see,” Spielman said. “But something else really neat happened.”

They turned up the intensity of their lasers, and atoms of one spin state began to repel the atoms in the other spin state, causing them to separate.

“We changed fundamentally how these atoms interacted with one another,” Spielman said. “We hadn’t anticipated that and got lucky.”

Fig 3. [image courtesy: Ian Spielman, JQI; click on the image to see a larger version]: Phase diagrams. a, computed phase diagram of the spin-orbit coupled system taking into account only single-particle energies (ignoring interactions). b, phase diagram including interactions, showing the appearance of a phase mixed (hashed) to phase separated (bold line) transition. d, data at fixed total spin (magnetization) showing the transition from phase mixed the phase separated.

The rubidium atoms in the researchers’ experiment were bosons, sociable particles that can all crowd into the same space even if they possess identical values in their properties including spin. But Spielman’s calculations show that they could also create this same effect in ultracold gases of fermions. Fermions, the more antisocial type of atoms, cannot occupy the same space when they are in an identical state. And compared to other methods for creating new interactions between fermions, the spin states would be easier to control and longer lived.

A spin-orbit-coupled Fermi gas could interact with itself because the lasers effectively split each atom into two distinct components, each with its own spin state, and two such atoms with different velocities could then interact and pair up with one other. This kind of pairing opens up possibilities, Spielman said, for studying novel forms of superconductivity, particularly “p-wave” superconductivity, in which two paired atoms have a quantum-mechanical phase that depends on their relative orientation. Such p-wave superconductors may enable a form of quantum computing known as topological quantum computation.

Reference
[1] Y.-J. Lin, K. Jiménez-García and I.B. Spielman, "Spin-orbit-coupled Bose-Einstein condensates", Nature, Nature, 471, 83–86 (03 March 2011). Abstract.

[We thank National Institute of Standard and Technology for materials used in this report]

Single Photon Management for Quantum Computers

Alan Migdall [photo courtesy: Joint Quantum Institute, University of Maryland]

The quantum computers of tomorrow might use photons, or particles of light, to move around the data they need to make calculations, but photons are tricky to work with. Two new papers[1,2] by researchers working at the National Institute of Standards and Technology (NIST) have brought science closer to creating reliable sources of photons for these long-heralded devices.

In principle, quantum computers can perform calculations that are impossible or impractical using conventional computers by taking advantage of the peculiar rules of quantum mechanics. To do this, they need to operate on things that can be manipulated into specific quantum states. Photons are among the leading contenders.

The new NIST papers address one of the many challenges to a practical quantum computer: the need for a device that produces photons in ready quantities, but only one at a time, and only when the computer's processor is ready to receive them. Just as garbled data will confuse a standard computer, an information-bearing photon that enters a quantum processor together with other particles—or when the processor is not expecting it—can ruin a calculation.

The single-photon source has been elusive for nearly two decades, in part because no method of producing these particles individually is ideal. "It's a bit like playing a game of whack-a-mole, where solving one problem creates others," says Alan Migdall of NIST's Optical Technology Division. "The best you can do is keep all the issues under control somewhat. You can never get rid of them."

The team's first paper[1] addresses the need to be certain that a photon is indeed coming when the processor is expecting it, and that none show up unexpected. Many kinds of single-photon sources create a pair of photons and send one of them to a detector, which tips off the processor to the fact that the second, information-bearing photon is on its way. But since detectors are not completely accurate, sometimes they miss the "herald" photon—and its twin zips into the processor, gumming up the works.

The team effort, in collaboration with researchers from the Italian metrology laboratory L'Istituto Nazionale di Ricerca Metrologica (INRIM), handled the issue by building a simple gate into the source. When a herald photon reaches the detector, the gate opens, allowing the second photon past. "You get a photon when you expect one, and you don't get one when you don't," Migdall says. "It was an obvious solution; others proposed it long ago, we were just the first ones to build it. It makes the single photon source better."

Gated photon source starts with the bright green 532nm wavelength laser beam that strikes a crystal (bright green spot, center) and is converted into pairs of photons at 810nm (false colored blue here, it's at the end of the red spectrum) and 1550nm (in the infrared, false colored red here.). The "blue" beam is the herald channel, the "red" beam goes through a spool of optical fiber (right) to delay it long enough for the gate to open or shut.[photo credit: G. Brida, INRIM]

In a second paper[2], the NIST team describes a photon source to address two other requirements. Quantum computers will need many such sources working in parallel, so sources must be able to be built in large numbers and operate reliably; and so that the computer can tell the photons apart, the sources must create multiple individual photons, but all at different wavelengths. The team outlines a way to create just such a source out of silicon, which has been well-understood by the electronics industry for decades as the material from which standard computer chips are built.

"Ordinarily a particular material can produce only pairs in a specific pair of wavelengths, but our design allows production of photons at a number of regular and distinct wavelengths simultaneously, all from one source," Migdall says. "Because the design is compatible with microfabrication techniques, this accomplishment is the first step in the process of creating sources that are part of integrated circuits, not just prototype computers that work in the hothouse of the lab."

References
[1] G. Brida, I. P. Degiovanni1, M. Genovese, A. Migdall, F. Piacentini, S. V. Polyakov and I. Ruo Berchera, "Experimental realization of a low-noise heralded single-photon source", Optics Express, Jan. 14, 2011, pp. 1484 – 1492. Abstract.
[2] J. Chen, Z.H. Levine, J. Fan and A.L. Migdal, "Frequency-bin entangled comb of photon pairs from a Silicon-on-Insulator micro-resonator", Optics Express, Jan. 14, 2011, pp. 1470 – 1483. Abstract.

[We thank National Institute of Standards and Technology (NIST) for materials used in this report]