Atom Interferometry in a 10 Meter Atomic Fountain

[From left to right] Mark Kasevich; the 10 m fountain team in 2013: Alex Sugarbaker, Tim Kovachy, Jason Hogan, Susannah Dickerson, Sheng-wey Chiow; and Dave Johnson

Authors: Alex Sugarbaker, Susannah M. Dickerson, Jason M. Hogan, David M. S. Johnson, and Mark A. Kasevich

Affiliation: Department of Physics, Stanford University, USA

Link to Kasevich Group Website >>

The equivalence principle states that all objects fall with the same acceleration under the influence of gravity. It is the conceptual foundation of Einstein’s general relativity, but is it true exactly? If not, there are profound implications for our understanding of gravity and the nature of the universe. It is therefore important to continue to test the equivalence principle as precisely as we can.

Galileo reportedly tested it by dropping spheres from the Leaning Tower of Pisa. Apollo astronauts tested it by dropping a hammer and a feather on the moon. More recent measurements have shown that the accelerations of two falling objects differ by no more than one part in 10¹³ [1, 2]. We aim to test the equivalence principle to one part in 10¹⁵ by dropping atoms of two different isotopes of rubidium in a 10 meter tower.

We will precisely measure acceleration differences between the two isotopes using atom interferometry. According to quantum mechanics, atoms are waves. Just as in optical interferometry, it is possible to split and recombine them to form an interference pattern [3, 4, 5]. In our interferometer, we send each atom along two different paths through space – each is in two places at once. When the atom waves are brought back together, the interference pattern depends on the phase difference between the two paths taken.

This phase difference in turn depends sensitively on the forces that act differently on the two parts of the atom while they are separated. This sensitivity to forces is what makes atom interferometry so useful. Compact atom interferometers have been made that can precisely measure rotation and acceleration, which can aid in navigation, mineral exploration, and geophysics. Atom interferometers have also measured the gravitational and fine-structure constants [6, 7]. They could also be used to search for gravitational waves [8].

The sensitivity of an atom interferometer increases with longer interferometer durations. Therefore, as recently described in Physical Review Letters [9, 10, 11], we have built an atom interferometer in which ⁸⁷Rb atoms are separated for 2.3 seconds before being recombined and interfered (Fig. 1). Three times longer than previous records [12], this multiple-second duration is well into the range of macroscopic, human-perceivable timescales. Furthermore, the two halves of each atom are separated by 1.4 centimeters before recombination – that's enough for you to swing your hand between them!

Fig. 1 Photograph of the 10 meter atomic fountain in a pit in the basement of the physics building at Stanford University.

How do we make a long-duration atom interferometer? We prepare a cloud of atoms at the bottom of a 10 meter vacuum tower and then launch them to the top. The interferometry is performed while the atoms rise up and fall back down to the bottom of the tower. The atoms are in free-fall, isolated from the noisy environment.

The cloud of atoms used must be very cold – a few billionths of a degree above absolute zero. At room temperature, the atoms in a gas move at speeds of hundreds of meters per second. Room-temperature rubidium atoms would collide with the walls of our vacuum chamber long before they fell back to the bottom. We therefore cool a few million rubidium atoms to a few nanokelvin before launching them into the tower. (The cooling process builds upon the same techniques used to generate Bose-Einstein condensates [13].)

Even at a few nanokelvin, individual atoms follow slightly different trajectories through the interferometer (like the droplets in a fountain of water), experiencing different position- and velocity-dependent forces. This yields a spatially-dependent phase, which in turn yields a spatial variation in the output atom density distribution that we can observe directly with a CCD camera (Fig. 2). This might at first appear undesirable, but it actually reveals rich details about the forces that generate the spatial interference pattern. Similar spatial fringe patterns have been used to great benefit in optical interferometers for centuries, but it is only recently that the effect has been leveraged in atom interferometry.

Fig. 2 Atomic interference patterns observed at the output of the interferometer. The images are sorted by phase, which can be measured for each experimental shot.

The long drift time of our interferometer enables it to have an acceleration sensitivity of 7 X 10^-12 g for each experimental shot, a hundredfold improvement over previous limits [14]. This is roughly the same as the gravitational attraction you would feel towards a person 10 meters away from you. We have used the sensitive interferometer and the spatial fringe patterns mentioned above to make precise measurements of Earth's rotation [9, 10].

The high sensitivity of the interferometer also holds great promise for our design goal – testing the equivalence principle (as mentioned above). By averaging more measurements or implementing advanced interferometry techniques, we can achieve the desired 10^-15 g sensitivity. Adding a simultaneous ⁸⁵Rb interferometer and comparing the results for the two isotopes will then enable us to make a new precision test of the equivalence principle. This will probe the fundamental assumptions of our current theory of gravity.

References:
[1] S. Schlamminger, K.Y. Choi, T.A. Wagner, J.H. Gundlach, and E.G. Adelberger, “Test of the Equivalence Principle Using a Rotating Torsion Balance”, Physical Review Letters, 100, 041101 (2008). Abstract.
[2] James G. Williams, Slava G. Turyshev, Dale H. Boggs, “Progress in Lunar Laser Ranging Tests of Relativistic Gravity”, Physical Review Letters, 93, 261101 (2004). Abstract.
[3] Mark Kasevich and Steven Chu, “Atomic interferometry using stimulated Raman transitions”, Physical Review Letters, 67, 181 (1991). Abstract.
[4] Alexander D. Cronin, Jörg Schmiedmayer, David E. Pritchard, “Optics and interferometry with atoms and molecules”, Reviews of Modern Physics, 81, 1051 (2009). Abstract.
[5] We focus on light-pulse atom interferometry, where pulses of laser light are used to split, recombine, and interfere the atoms.
[6] G. Lamporesi, A. Bertoldi, L. Cacciapuoti, M. Prevedelli, and G.M. Tino, “Determination of the Newtonian Gravitational Constant Using Atom Interferometry”, Physical Review Letters, 100, 050801 (2008). Abstract.
[7] Rym Bouchendira, Pierre Cladé, Saïda Guellati-Khélifa, François Nez, and François Biraben, “New Determination of the Fine Structure Constant and Test of the Quantum Electrodynamics”, Physical Review Letters, 106, 080801 (2011). Abstract.
[8] Jason Hogan, “A new method for detecting gravitational waves”, SPIE Newsroom, 6 May (2013). Article.
[9] Susannah M. Dickerson, Jason M. Hogan, Alex Sugarbaker, David M. S. Johnson, Mark A. Kasevich, “Multiaxis Inertial Sensing with Long-Time Point Source Atom Interferometry”, Physical Review Letters, 111, 083001 (2013).  Abstract.
[10] Alex Sugarbaker, Susannah M. Dickerson, Jason M. Hogan, David M. S. Johnson, Mark A. Kasevich, “Enhanced Atom Interferometer Readout through the Application of Phase Shear”, Physical Review Letters, 111, 113002 (2013). Abstract.
[11] P. Bouyer, “Viewpoint: A New Starting Point for Atom Interferometry”, Physics, 6, 92 (2013). Article.
[12] H. Müntinga, H. Ahlers, M. Krutzik, A. Wenzlawski, S. Arnold, D. Becker, K. Bongs, H. Dittus, H. Duncker, N. Gaaloul, C. Gherasim, E. Giese, C. Grzeschik, T. W. Hänsch, O. Hellmig, W. Herr, S. Herrmann, E. Kajari, S. Kleinert, C. Lämmerzahl, W. Lewoczko-Adamczyk, J. Malcolm, N. Meyer, R. Nolte, A. Peters, M. Popp, J. Reichel, A. Roura, J. Rudolph, M. Schiemangk, M. Schneider, S. T. Seidel, K. Sengstock, V. Tamma, T. Valenzuela, A. Vogel, R. Walser, T. Wendrich, P. Windpassinger, W. Zeller, T. van Zoest, W. Ertmer, W. P. Schleich, E. M. Rasel, “Interferometry with Bose-Einstein Condensates in Microgravity”, Physical Review Letters, 110, 093602 (2013). Abstract.
[13] “Bose-Einstein condensate”. Past 2Physics Article.
[14] Holger Müller, Sheng-wey Chiow, Sven Herrmann, Steven Chu, Keng-Yeow Chung, “Atom-Interferometry Tests of the Isotropy of Post-Newtonian Gravity”, Physical Review Letters, 100, 031101 (2008). Abstract.

Physics Nobel Prize 2012: Quantum Measurement

Serge Haroche (left) and David J. Wineland (right)










The 2012 Nobel Prize in Physics has been awarded to Serge Haroche (Collège de France and Ecole Normale Supérieure, Paris, France) and David J. Wineland (National Institute of Standards and Technology (NIST) and University of Colorado Boulder, CO, USA) "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems".

Serge Haroche and David J. Wineland have independently invented and developed methods for measuring and manipulating individual particles while preserving their quantum-mechanical nature, in ways that were previously thought unattainable.

The Nobel Laureates have opened the door to a new era of experimentation with quantum physics by demonstrating the direct observation of individual quantum particles without destroying them. For single particles of light or matter the laws of classical physics cease to apply and quantum physics takes over. But single particles are not easily isolated from their surrounding environment and they lose their mysterious quantum properties as soon as they interact with the outside world. Thus many seemingly bizarre phenomena predicted by quantum physics could not be directly observed, and researchers could only carry out thought experiments that might in principle manifest these bizarre phenomena.

Past 2Physics articles on works of Serge Haroche and David J. Wineland:

Jul 10, 2011: "Chilling of Micromechanical Motion to the Quantum Ground State"
Sep 26, 2010: "Aluminum Atomic Clocks Reveal Einstein's Relativity at a Personal Scale"
Feb 21, 2010: "World’s Most Precise Clock : NIST Developed Second ‘Quantum Logic Clock’ Based on Aluminum Ion"
Aug 15, 2009: "NIST Physicists Demonstrate Sustained Quantum Processing in Step Toward Building Quantum Computers "
Mar 28, 2008: "‘Quantum Logic Clock’ Rivals Mercury Ion as World’s Most Accurate Clock : A new limit on change in fine-structure constant"
Mar 15, 2007: "Life & Death of a Single Photon Observed"

Through their ingenious laboratory methods Haroche and Wineland together with their research groups have managed to measure and control very fragile quantum states, which were previously thought inaccessible for direct observation. The new methods allow them to examine, control and count the particles.

Their methods have many things in common. David Wineland traps electrically charged atoms, or ions, controlling and measuring them with light, or photons.

Serge Haroche takes the opposite approach: he controls and measures trapped photons, or particles of light, by sending atoms through a trap.

Homepage of Serge Haroche at Collège de France, Paris >>

Both Laureates work in the field of quantum optics studying the fundamental interaction between light and matter, a field which has seen considerable progress since the mid-1980s. Their ground-breaking methods have enabled this field of research to take the very first steps towards building a new type of super fast computer based on quantum physics. Perhaps the quantum computer will change our everyday lives in this century in the same radical way as the classical computer did in the last century. The research has also led to the construction of extremely precise clocks that could become the future basis for a new standard of time, with more than hundred-fold greater precision than present-day caesium clocks.

The World's Most Stable Laser : Impact on Atomic Clocks, Precision Tests in Fundamental Physics, Gravitational Wave Detection

Jun Ye [photo courtesy: JILA/University of Colorado, USA]

No more than only 2 parts in 10,000 trillion -- that's the new world record set for the frequency variation by the most stable laser as reported in an advance on-line publication in Nature Photonics [1]. The laser is developed and tested by an international collaboration of scientists at NIST/JILA in Boulder, Colorado, USA and a group at Physikalisch-Technische Bundesanstalt (PTB), the German counterpart of the National Institute of Standards and Technology (NIST).

Their work represents a new approach for constructing high-quality optical cavities that will bring more than an order of magnitude improvement over prior designs. In particular, it will accelerate progress in development of optical clocks, which operate at frequencies more than 10,000 times higher than the approximately 9.2 GHz microwaves used as the basis of the current worldwide time standard.

In addition, the novel laser design is expected to usher in a new level of precision to research in gravitational wave detection on Earth and in space, and precision tests of relativity as well as fundamental physics research in cavity quantum electrodynamics and quantum optomechanics.

“The previous stability limit of about 2 X 10^-16 was good,” says study co-author Jun Ye of JILA and PML’s Quantum Physics Division. “But it prevented us from exploring the full potential of modern optical atomic clocks where the atomic coherence time can be exceedingly long. The potential of pushing the laser stability better by an order of magnitude will allow us to realize atomic clocks that have unprecedented stability approaching 1 x 10^-17 over 1 second.

“It will also have a dramatic impact on large-scale precision measurement instruments such as space-borne optical interferometers for gravitational-wave detection with baselines of many thousands of kilometers. And it may be of intense interest to the communications industry, since our system was tested at a familiar telecomm wavelength of 1.5 micrometers.” That is the wavelength with the lowest loss in fiber-optic networks.

This shows the size of the new silicon resonator compared to the size of a coin [image courtesy: Physikalisch-Technische Bundesanstalt, Germany]

Research on ultra-stable lasers typically employs some kind of optical-cavity interferometer, comprising a spacer with mirrors at each end. That design severely restricts the range of optical frequency which can resonate in the cavity. By superimposing the cavity output beam on another highly controlled reference beam, the interference effects (periodic reinforcement “beats”) can reveal stability with exquisite sensitivity. Such systems, however, have historically been subject to thermal fluctuations that alter the cavity dimensions, and hence reduce frequency stability.

“We addressed that problem in several ways,” says Ye, who began to collaborate on the project in 2007 while visiting PTB in Germany on a grant from the Alexander von Humboldt Foundation. The German team was headed by Uwe Sterr and Fritz Riehle. Ye also recruited a student, Michael Martin, and a visitor in his lab, Lisheng Chen. “By far the most significant factor was our decision to substitute single-crystal silicon for the ultralow expansion glass (ULE) or fused silica customarily employed in the cavity mirrors and spacers.”

Single-crystal silicon has a coefficient of thermal expansion that approaches zero at 124 K, “so an all-silicon interferometer can be made insensitive to temperature fluctuations” at that point, the authors write in Nature Photonics. In addition, at 124 K the crystal has a much lower mechanical loss compared to conventional optical glass, and a much higher Young’s modulus. Both mechanical properties combine to minimize the fundamental thermal fluctuations. The group used extensive computer modeling to create a design that reduced the effects of environmental vibrations on the 21 cm long resonator, which they mounted in a vertical configuration after testing its response to external forces in all three dimensions.

Finally, the German researchers devised a novel and simple cryostat design using evaporated liquid nitrogen gas as the coolant. The gas flows through superinsulated vacuum tubes to an outer heat shield, and careful control of the flow limits temperature deviations in the system to about 1 mK from the 124 K target.

Diagram of the device interior [image credit: Thomas Kessler, Physikalisch-Technische Bundesanstalt, Germany].

The new all-silicon unit was tested for 24 hours against two of the best-performing conventional ULE-based optical cavity-stabilized lasers – one from JILA and one from PTB, with thermal noise variation in the range of 6 X 10^-16 and 2 X 10^-16 respectively. The results, Ye says, “show that the all-silicon system surpasses the performance of any other optical cavities ever reported.” As a long-term stable frequency reference, a preliminary test has shown that it is equivalent to the stability of a hydrogen maser at time intervals up to 1,000 seconds.

The scientists are already at work to improve those figures. Among other modifications, they will attempt to reduce feedback errors due to spurious amplitude modulation, suppress noise from the cryostat, and experiment with different optical coatings on the silicon mirrors. The very thin optical coatings now remain the only significant contribution to the thermal noise of the cavity and new approaches are already being investigated jointly with Markus Aspelmeyer’s group at the University of Vienna.

Graph comparing average instability over time of the new design (green) to two ultra-stable ULE units: Ref. 1 (blue), a PTB laser, and Ref. 2 (orange), a JILA laser [image courtesy: NIST, USA].

Many of most critical experiments in atomic physics require lasers with extremely narrow linewidth and extremely stable output to interrogate clusters of ultracold atoms or single trapped ions. “Stable lasers such as the one reported are already unlocking some of the mysteries of minute atomic interactions that are otherwise hidden,” Ye says.

Reference
[1] T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, J. Ye, "A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity", Nature Photonics (Published online September 9th, 2012). doi:10.1038/nphoton.2012.217. 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).

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.

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.

Quantum Quirk: Packing Atoms Together to Prevent Collisions in Atomic Clock

Jun Ye [photo courtesy: JILA/University of Colorado]

In a paradox typical of the quantum world, JILA scientists have eliminated collisions between atoms in an atomic clock by packing the atoms closer together. The surprising discovery, described in the Feb. 3 issue of Science Express [1], can boost the performance of experimental atomic clocks made of thousands or tens of thousands of neutral atoms trapped by intersecting laser beams.

[JILA is jointly operated by the National Institute of Standards and Technology (NIST) and the University of Colorado Boulder. Once upon a time, JILA was the Joint Institute for Laboratory Astrophysics. These days, that name doesn't encompass the breadth of science conducted at JILA. So, after extended discussion in 1994, JILA's fellows decided to keep the word JILA but drop the meaning.]

JILA scientists demonstrated the new approach using their experimental clock made of about 4,000 strontium atoms. Instead of loading the atoms into a stack of pancake-shaped optical traps as in their previous work, scientists packed the atoms into thousands of horizontal optical tubes. The result was a more than tenfold improvement in clock performance because the atoms interacted so strongly that, against all odds, they stopped hitting each other. The atoms, which normally like to hang out separately and relaxed, get so perturbed from being forced close together that the ensemble is effectively frozen in place.

The idea was proposed by JILA theorist Ana Maria Rey and demonstrated in the lab by Ye's group.

Ana Maria Rey [photo courtesy: JILA/University of Colorado]

"The atoms used to have the whole dance floor to move around on and now they are confined in alleys, so the interaction energy goes way up," says NIST/JILA Fellow Jun Ye, leader of the experimental team.

How exactly does high interaction energy—the degree to which an atom's behavior is modified by the presence of others—prevent collisions? The results make full sense in the quantum world. Strontium atoms are a class of particles known as fermions. If they are in identical energy states, they cannot occupy the same place at the same time—that is, they cannot collide. Normally the laser beam used to operate the clock interacts with the atoms unevenly, leaving the atoms dissimilar enough to collide [Read past 2Physics report dated May 2, 2009] But the interaction energy of atoms packed in optical tubes is now higher than any energy shifts that might be caused by the laser, preventing the atoms from differentiating enough to collide.

Intersecting laser beams create "optical tubes" to pack atoms close together, enhancing their interaction and the performance of JILA's strontium atomic clock.[Image Credit: Baxley/JILA]

Given the new knowledge, Ye believes his clock and others based on neutral atoms will become competitive in terms of accuracy with world-leading experimental clocks based on single ions (electrically charged atoms). The JILA strontium clock is currently the best performing experimental clock based on neutral atoms and, along with several NIST ion and neutral atom clocks, a possible candidate for a future international time standard. The devices provide highly accurate time by measuring oscillations (which serve as "ticks") between the energy levels in the atoms.

In addition to preventing collisions, the finding also means that the more atoms in the clock, the better. "As atom numbers increase, both measurement precision and accuracy increase accordingly," Ye says.

To trap the atoms in optical tubes, scientists first use blue and red lasers to cool strontium atoms to about 2 microKelvin in a trap that uses light and magnetic fields. A vertical lattice of light waves is created using an infrared laser beam that spans and traps the atom cloud. Then a horizontal infrared laser beam is turned on, creating optical tube traps at the intersection with the vertical laser.

Reference:
[1] Matthew D. Swallows, Michael Bishof, Yige Lin, Sebastian Blatt, Michael J. Martin, Ana Maria Rey, Jun Ye, "Suppression of collisional shifts in a strongly interacting lattice clock", Science Express (Posted online Feb.3, 2011). DOI: 10.1126/science.1196442. Abstract.

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

Aluminum Atomic Clocks Reveal Einstein's Relativity at a Personal Scale

James Chin-wen Chou with the world’s most precise clock, based on the vibrations of a single aluminum ion. The ion is trapped inside the metal cylinder (center right) [Photo credit: J. Burrus/NIST]

Scientists have known for decades that time passes faster at higher elevations—a curious aspect of Einstein's theories of relativity that previously has been measured by comparing clocks on the Earth's surface and a high-flying rocket.

Now, physicists at the National Institute of Standards and Technology (NIST) have measured this effect at a more down-to-earth scale of 33 centimeters, or about 1 foot, demonstrating, for instance, that you age faster when you stand a couple of steps higher on a staircase.

Described in the Sept. 24 issue of Science [1], the difference is much too small for humans to perceive directly—adding up to approximately 90 billionths of a second over a 79-year lifetime—but may provide practical applications in geophysics and other fields.

Similarly, the NIST researchers observed another aspect of relativity—that time passes more slowly when you move faster—at speeds comparable to a car travelling about 20 miles per hour, a more comprehensible scale than previous measurements made using jet aircraft.

NIST scientists performed the new "time dilation" experiments by comparing operations of a pair of the world's best experimental atomic clocks. The nearly identical clocks are each based on the "ticking" of a single aluminum ion (electrically charged atom) as it vibrates between two energy levels over a million billion times per second. One clock keeps time to within 1 second in about 3.7 billion years (Read past 2Physics report: World’s Most Precise Clock : NIST Developed Second ‘Quantum Logic Clock’ Based on Aluminum Ion) and the other is close behind in performance. The two clocks are located in different laboratories at NIST and connected by a 75-meter-long optical fiber.

NIST's aluminum clocks—also called "quantum logic clocks" because they borrow logical decision-making techniques from experimental quantum computing—are precise and stable enough to reveal slight differences that could not be seen until now. The clocks operate by shining laser light on the ions at optical frequencies, which are higher than the microwave frequencies used in today's standard atomic clocks based on the cesium atom. Optical clocks could someday lead to time standards 100 times more accurate than today's standard clocks.

The aluminum clocks can detect small relativity-based effects because of their extreme precision and high "Q factor"—a quantity that reflects how reliably the ion absorbs and retains optical energy in changing from one energy level to another—says NIST postdoctoral researcher James Chin-Wen Chou, first author of the paper.

"We have observed the highest Q factor in atomic physics," Chou says. "You can think about it as how long a tuning fork would vibrate before it loses the energy stored in the resonating structure. We have the ion oscillating in sync with the laser frequency for about 400 thousand billion cycles."

The NIST experiments focused on two scenarios predicted by Einstein's theories of relativity. First, when two clocks are subjected to unequal gravitational forces due to their different elevations above the surface of the Earth, the higher clock—experiencing a smaller gravitational force—runs faster. Second, when an observer is moving, a stationary clock's tick appears to last longer, so the clock appears to run slow. Scientists refer to this as the "twin paradox," in which a twin sibling who travels on a fast-moving rocket ship would return home younger than the other twin. The crucial factor is the acceleration (speeding up and slowing down) of the travelling twin in making the round-trip journey.

NIST scientists observed these effects by making specific changes in one of the two aluminum clocks and measuring the resulting differences in the two ions' relative ticking rates, or frequencies.

Cartoon credit: Loel Barr of NIST

In one set of experiments, scientists raised one of the clocks by jacking up the laser table to a height one-third of a meter (about a foot) above the second clock. Sure enough, the higher clock ran at a slightly faster rate than the lower clock, exactly as predicted.

The second set of experiments examined the effects of altering the physical motion of the ion in one clock. (The ions are almost completely motionless during normal clock operations.) NIST scientists tweaked the one ion so that it gyrated back and forth at speeds equivalent to several meters per second. That clock ticked at a slightly slower rate than the second clock, as predicted by relativity. The moving ion acts like the traveling twin in the twin paradox.

Such comparisons of super-precise clocks eventually may be useful in geodesy, the science of measuring the Earth and its gravitational field, with applications in geophysics and hydrology, and possibly in space-based tests of fundamental physics theories, suggests physicist Till Rosenband, leader of NIST's aluminum ion clock team.

NIST scientists hope to improve the precision of the aluminum clocks even further, as much as 10-fold, through changes in ion trap geometry and better control of ion motion and environmental interference. The aim is to measure differences in timekeeping well enough to measure heights to an accuracy of 1 centimeter, a performance level suitable for making geodetic measurements. The paper suggests that optical clocks could be linked to form a network of "inland tidal gauges" to measure the distance from the earth's surface to the geoid (the surface of the earth's gravity field that matches the global mean sea level). Such a network could be updated far more frequently than current techniques.

References
[1] C.W. Chou, D.B. Hume, T. Rosenband and D.J. Wineland, "Optical Clocks and Relativity", Science, Vol.329, pp.1630-1633 (Sept. 24, 2010). Abstract.

[We thank National Institute of Standards and Technology, Boulder, CO for materials used in this report]

World’s Most Precise Clock : NIST Developed Second ‘Quantum Logic Clock’ Based on Aluminum Ion

NIST postdoctoral researcher James Chin-wen Chou with the world’s most precise clock, based on the vibrations of a single aluminum ion. The ion is trapped inside the metal cylinder (center right) [Photo credit: J. Burrus/NIST]

In a paper published in the Feb 17th issue of Physical Review Letters [1], a team of physicists from National Institute of Standards and Technology (NIST) reported the successful development of the world’s most precise clock -- an enhanced version of an experimental atomic clock based on a single aluminum atom [2]. The new clock is more than twice as precise as the previous pacesetter based on a mercury atom [3].

The new aluminum clock would neither gain nor lose one second in about 3.7 billion years, according to measurements reported in Physical Review Letters. The new clock is the second version of NIST’s “quantum logic clock”, so called because it borrows the logical processing used for atoms storing data in experimental quantum computing, another major focus of the same NIST research group.

Background: The Origin of the Name ‘Quantum Logic Clock’

Logic is reasoning that determines an action or result based on which one of different possible options is received as input. In the NIST clock, the input options are two different quantum states, or internal energy levels, of an aluminum ion. Information about this state is transferred to a beryllium ion, which, depending on the input, produces different signals that are easily detected.

NIST scientists use lasers to cool the two ions which are held 4 thousandths of a millimeter apart in an electromagnetic trap. Aluminum is the larger of the two ions, while the beryllium emits light under the conditions of this experiment. Scientists hit the ions with pulses from a “clock laser” within a narrow frequency range. If the laser frequency is at the center of the frequency range, the precise “resonance frequency” of aluminum, this ion jumps to a higher energy level, or 1 in the binary language of computers. Otherwise, the ion remains in the lower energy state, or 0.

If there is no change in the aluminum ion, then another laser pulse causes both ions to begin rocking side to side in unison because of their physical proximity and the interaction of their electrical charges. An additional laser pulse converts this motion into a change in the internal energy level of the beryllium ion. This pulse reverses the direction of the ion’s magnetic “spin,” and the beryllium goes dark, a signal that the aluminum remained in the 0 state.

On the other hand, if the aluminum ion jumps to the higher energy level, then the additional laser pulses fail to stimulate a shared rocking motion and have no effect on the beryllium ion, which keeps emitting light. Scientists detect this light as a signal that the aluminum ion jumped from 0 to 1.

The goal is to tune the clock laser to the exact frequency that prompts the aluminum to jump from 0 to 1. The actual measurement of the ticking of the clock is provided not by the ions but rather by the clock laser’s precisely tuned center frequency, which is measured with a “frequency comb,” a tool for measuring very high optical frequencies, or colors of light.

“This paper is a milestone for atomic clocks” for a number of reasons, says NIST postdoctoral researcher James Chou, who developed most of the improvements.

In addition to demonstrating that aluminum is now a better timekeeper than mercury, the latest results confirm that optical clocks are widening their lead—in some respects—over the NIST-F1 cesium fountain clock, the U.S. civilian time standard, which currently keeps time to within 1 second in about 100 million years.

Because the international definition of the second (in the International System of Units, or SI) is based on the cesium atom, cesium remains the “ruler” for official timekeeping, and no clock can be more accurate than cesium-based standards such as NIST-F1.

The logic clock is based on a single aluminum ion (electrically charged atom) trapped by electric fields and vibrating at ultraviolet light frequencies, which are 100,000 times higher than microwave frequencies used in NIST-F1 and other similar time standards around the world. Optical clocks thus divide time into smaller units, and could someday lead to time standards more than 100 times as accurate as today’s microwave standards. Higher frequency is one of a variety of factors that enables improved precision and accuracy.

The ion trap where the main action takes place in the NIST aluminum ion clock. The aluminum ion and partner magnesium ion sit in the slit running down the center of the device between the electrodes [Photo credit: J. Koelemeij/NIST]

Aluminum is one contender for a future time standard to be selected by the international community. NIST scientists are working on five different types of experimental optical clocks, each based on different atoms and offering its own advantages. NIST’s construction of a second, independent version of the logic clock proves it can be replicated, making it one of the first optical clocks to achieve that distinction. Any future time standard will need to be reproduced in many laboratories.

NIST scientists evaluated the new logic clock by probing the aluminum ion with a laser to measure the exact "resonant" frequency at which the ion jumps to a higher-energy state, carefully accounting for all possible deviations such as those caused by ion motions. No measurement is perfect, so the clock’s precision is determined based on how closely repeated measurements can approach the atom’s exact resonant frequency. The smaller the deviations from the true value of the resonant frequency, the higher the precision of the clock.

Physicists also evaluate the performance of new optical clocks by comparing them to older optical clocks. In this case, NIST scientists compared their two logic clocks by using the resonant laser frequency from one clock to probe the ion in the other clock. Fifty-six separate comparisons were made, each lasting between 15 minutes and 3 hours.

The two logic clocks exhibit virtually identical “tick” rates—differences don’t show up until measurements are extended to 17 decimal places. The agreement between the two aluminum clocks is more than 10 times closer than any previous two-clock comparison, with the lowest measurement uncertainty ever achieved in such an evaluation, according to the paper.

The enhanced logic clock differs from the original version in several ways. Most importantly, it uses a different type of “partner” ion to enable more efficient operations. Aluminum is an exceptionally stable source of clock ticks but its properties are not easily manipulated or detected with lasers. In the new clock, a magnesium ion is used to cool the aluminum and to signal its ticks. The original version of the clock used beryllium, a smaller and lighter ion that is a less efficient match for aluminum.

Clocks have myriad applications. The extreme precision offered by optical clocks is already providing record measurements of possible changes in the fundamental “constants” of nature, a line of inquiry that has important implications for cosmology and tests of the laws of physics, such as Einstein’s theories of special and general relativity. Next-generation clocks might lead to new types of gravity sensors for exploring underground natural resources and fundamental studies of the Earth. Other possible applications may include ultra-precise autonomous navigation, such as landing planes by GPS.

Reference
[1] C.-W. Chou, D.B. Hume, J.C.J. Koelemeij, D.J. Wineland, and T. Rosenband, "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks", Physical Review Letters, 104, 070802 (2010). Abstract.
[2] T. Rosenband, D.B. Hume, P.O. Schmidt, C.W. Chou, A. Brusch, L. Lorini, W.H. Oskay, R.E. Drullinger, T.M. Fortier, J.E. Stalnaker, S.A. Diddams, W.C. Swann, N.R. Newbury, W.M. Itano, D.J. Wineland, and J.C. Bergquist, "Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place", Science, 319, 1808 (2008). Abstract. 2Physics Report.
[3] W.H. Oskay, S.A. Diddams, E.A. Donley, T.M. Fortier, T.P. Heavner, L. Hollberg, W.M. Itano, S.R. Jefferts, M.J. Jensen, K. Kim, F. Levi, T.E. Parker and J.C. Bergquist, "A single-atom optical clock with high accuracy. Physical Review Letters. July 14 (2006) Abstract. 2Physics Report.

[We thank National Institute of Standards and Technology for materials used in this posting]