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]

Hanbury Brown and Twiss Interferometry with Interacting Photons

Left to right: Eran Small, Yoav Lahini, Yaron Bromberg and Yaron Silberberg

[This is an invited article based on a recently published work by the authors
-- 2Physics.com]

Authors: Yoav Lahini, Yaron Bromberg, Eran Small and Yaron Silberberg
Affiliation: Department of Physics of Complex Systems, the Weizmann Institute of Science, Rehovot, Israel.

The next time you go out on a sunny day, take a minute to consider the sunlight you see reflected from the ground near you. If you could have frozen time, you would see that actually, the light pattern on the ground is not homogenous, but rather it is speckled – it is made out of patches of light and darkness, similar to the speckle pattern you see when a laser light hits a rough surface like a wall. For sunlight, the typical speckle size is around 100 microns, but that is not the reason why the sunlight speckles are not observed in everyday life. The real reason is that this speckle pattern changes much faster than the human eye – and in fact, faster than any man made detector – can follow. As a result we see an averaged, smeared homogenous light reflected around us.

To understand this phenomenon, and its relation to the Hanbury-Brown and Twiss effect and the birth of quantum optics, let’s first consider the sun as observed by a spectator on earth. The sun is an incoherent light source – that is, there is no fixed phase relation between the rays of light coming from different parts of the sun’s surface. In fact, it is more accurate to say that there is a phase relation between the rays only that this phase difference continuously fluctuates. The rate of the phase fluctuations is very fast, typically on the scale of femtoseconds. Nevertheless, let’s assume for a moment that we could freeze time while looking at the sunlight on Earth. What would we see? Since everything is “frozen”, the phase between all the rays coming from the sun is fixed, and the rays will interfere. The result of such interference of many rays with a random phase leads to the speckle pattern – patches of light and darkness. Bright regions are formed where the rays interfere constructively, and dark regions where the rays interfere destructively. The typical size of the patches is determined by the distance over which constructive interference changes to destructive. This happens when the path lengths from the emitters on the sun (or any incoherent source) to the Earth change by about half a wavelength. In fact it can be shown that the typical size of such speckle, if one could ever be photographed, goes like the wavelength over the angular size of the source, as seen from the earth [1]. This means that the size of a typical speckle is larger the further the distance between the source and the observer - the speckles diffract, their size increases as they propagate.

As noted earlier, the sun will create a speckle pattern on Earth with a typical speckle size of 100 microns, while a distant star (with a much smaller angular size) will create a speckle size of a few meters and even kilometers. So in theory, if the speckle size can be somehow measured, it will allow to determine the angular size of stars, or any other incoherent light source.

In 1956, two astronomers, Hanbury Brown and Twiss, did just that [2]. They found a way to determine the typical speckle size in starlight with just two detectors instead of a camera. The trick was to use two fast detectors, and look into the noise measured by the two detectors, instead of the averaged signal as we usually do in the lab. So how does it work? The intensities measured by the two detectors are noisy, since the speckle pattern that impinges on the detectors continuously varies. But, as long as the two detectors are separated by a distance smaller than the typical speckle size, they will be illuminated most of the time by the same speckle. The signals measured by the two detectors will therefore be noisy but correlated, i.e. the two signals will fluctuate together. However, if the two detectors are separated by a distance larger than the typical speckle size, the signals' fluctuations will be totally uncorrelated, since each detector sees different speckles. Therefore the distance in which noise in the two detectors becomes uncorrelated is a measure of the typical speckle size, and therefore a measure of the angular size of the observed star.

Hanbury Brown and Twiss (HBT) proved their theory several times [3,4], by giving accurate measures of the angular size of several stars using radio and optical interferometry. These experiments gave rise to a vigorous debate about the nature of light: it is easy to prove the HBT effect if you think of light as classical waves, but what happens if you try to take the particle view of light? How can two photons, coming from two distant atoms on the surface of a star and measures by two distant detectors on the surface of the earth, be correlated? The answer to this question was given only after a few years by the Nobel Prize laureate Roy Glauber [5], an answer that marked the birth of the field of Quantum Optics.

Since those days, the HBT technique was adopted and used in many different fields in physics as a tool to remotely measure properties of different sources. For example, the HBT method was used to measure the properties subatomic particles created in nuclear collisions [6], of Bose-Einstein Condensates (BEC) in lattice potentials [7,8] and other systems [9-13]. In a work recently published in Nature Photonics [14], we note that these modern uses of HBT interferometry rely on an assumption that there are no interactions between the particles on their way from the source to the detectors. Such interactions (or nonlinear effects in the case of classical waves) would affect the correlations while the particles (or waves) propagate from the source to the detectors. The assumption of no interactions is probably valid in the astronomical case (although due to the very long distances involved that might also be questioned), but is not necessarily true for atom-matter waves released from their confining potential, or for charged sub-atomic particles propagating from the point of interest to the detection.

To see how one can cope with such complications we analyzed the effect of interactions on the resulting HBT correlation by considering light propagation in a nonlinear medium – a scenario physically similar to matter waves released from a confining potential (the equations describing the dynamics of matter waves are identical, in certain limits, to the equations used in our paper). Using a spatial light modulator and diffusers we mimicked a spatially incoherent light source in a controlled manner, and measured the HBT correlations after propagation of the speckle field in a nonlinear medium. We investigated both repulsive and attractive interactions, in two and three dimensional space. Using these measurements, we have shown how the interactions modify the measured HBT correlations. While the fact the interactions modify correlations is expected, our work provides an intuitive picture for the source of this modification. The key idea is to follow the propagation of the speckle patterns in the nonlinear medium. As discussed above, when there are no interactions the speckles diffract along the propagation. But in the presence of interactions, or nonlinearity, each speckle can turn into what is known as a soliton – a self trapped entity, with a size that does not change along the propagation. This means that the size of the speckles is no longer a measure for the angular size of the source. It is in fact a measure for the strength of the interactions.

Experimental observation of a speckle pattern propagating in a nonlinear medium. In the interaction free case, the width of a typical speckle is inversely proportional to the width of the source, W. In the presence of interactions, one needs to take into account the strength of the intensity fluctuations as well. Image credit: Adi Natan
But perhaps more importantly, we provide a new framework that can include interactions in HBT interferometry. We found that the information on the source can still be retrieved if the interactions are taken into account correctly. We show that in the presence of interactions the angular size of the source can be recovered, but one needs in addition to the spatial correlation also to measure the strength of the signals' fluctuations. Intuitively, this stems from the fact that speckles which have became “solitons” still propagate at different angles. Since these “speckolitons” keep their size along the propagation, the chance that a speckoliton will hit the detectors goes down as the distance from the source to the detector increases. But the intensity the speckolitons carries is much higher than the intensity of a linear speckle which diffracts along the propagation. Careful analysis of this phenomena leads to the conclusion that in the presence of interactions the intensity fluctuations carry the missing information on the angular size of the source.

One can measure the strength of the fluctuations by simply looking at the variance of the detectors' readouts, which is closely related to the contrast of the bright to dark patches in the speckle pattern. As a possible application, consider HBT interferometry with trapped BEC. A recent paper [7] identified the complication of using HBT interferometry arising due to interactions during the time-of-flight, after the condensate is released from the trap. That paper suggests an intricate manipulation of the condensate during the time-of-flight, to scale out the effects of interactions. Our paper provides a framework to include the interactions in the analysis, without the need for such complicated experiments.

References:
[1] Goodman, J. W. , "Speckle Phenomena in Optics" (Roberts & Co., 2007)
[2] Hanbury Brown, R. &. Twiss, R. Q. "A test of a new type of stellar interferometer on Sirius", Nature 178, 1046–1048 (1956). Abstract.
[3] Hanbury Brown, R. &. Twiss, R. Q. Correlations between photons in two coherent beams of light. Nature 177, 27–29 (1956). Abstract.
[4] Hanbury Brown, R. "The Intensity Interferometer: Its Application to Astronomy" (Taylor & Francis, 1974).
[5] Glauber, R. G. "Photon correlations", Phys. Rev. Lett. 10, 84–86 (1963). Abstract.
[6] Baym, G. "The physics of Hanbury Brown–Twiss intensity interferometry: from stars to nuclear collisions", Acta. Phys. Pol. B 29, 1839–1884 (1998). Article.
[7] Simon Fölling, Fabrice Gerbier, Artur Widera, Olaf Mandel, Tatjana Gericke & Immanuel Bloch, "Spatial quantum noise interferometry in expanding ultracold atom clouds", Nature 434, 481–484 (2005). Abstract.
[8] Altman, E., Demler, E. & Lukin, M. D. "Probing many body correlations of ultra-cold atoms via noise correlations", Phys. Rev. A 70, 013603 (2004). Abstract.
[9] M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, C. I. Westbrook, "Hanbury Brown Twiss effect for ultracold quantum gases", Science 310, 648–651 (2005). Abstract.
[10] Oliver, W. D., Kim, J., Liu J. & Yamamoto, Y. "Hanbury Brown and Twiss-type experiment with electrons", Science 284, 299–301 (1999). Abstract.
[11] Kiesel, H., Renz, A. & Hasselbach, F. "Observation of Hanbury Brown–Twiss anticorrelations for free electrons", Nature 418, 392–394 (2002). Abstract.
[12] T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect & C. I. Westbrook, "Comparison of the Hanbury Brown–Twiss effect for bosons and fermions", Nature 445, 402–405 (2007). Abstract.
[13] I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu & V. Umansky, "Interference between two indistinguishable electrons from independent sources", Nature 448, 333–337 (2007). Abstract.
[14] Bromberg, Y., Lahini, Y., Small, E. & Silberberg, Y. Hanbury Brown and Twiss interferometry with interacting photons. Nature Photonics 4, 721-726 (2010). Abstract.

Transition from Superfluid to Mott Insulator

Karina Jiménez-García [photo courtesy: Joint Quantum Institute, Maryland]

Researchers studying a gas of trapped ultracold atoms have identified a set of conditions, never before observed but in excellent agreement with new theoretical predictions, that determine the onset of a critical “phase transition” in atomic arrays used to model the behavior of condensed-matter systems.

The findings provide a novel insight into the way collections of atoms suddenly cease to be a superfluid, which flows without resistance, and switch to a very different state called a “Mott insulator.” That transition and similar phenomena are of central interest to the science of solid-state materials, including superconductors.

“This work shows that the transition can be precisely controlled and confirms that it can be described by only two independent variables,” says lead researcher Karina Jiménez-García, a member of Ian Spielman’s group at the National Institute of Standards and Technology (NIST) and the Joint Quantum Institute (JQI). The group reports its findings in a forthcoming issue of Physical Review Letters [1].

In order to understand the behavior of materials on the atomic and molecular scale, researchers often cannot experiment directly with samples. In many cases, they need model systems – analogous, at microscopic dimensions, to the physical models built by engineers to test the dynamics of a planned structure – that allow them to change one or two experimental parameters at a time while holding the rest constant. That can be prohibitively difficult, if not impossible, in bulk samples of real material.

But in recent years, quantum science has made it possible to create accurate and highly illuminating models of condensed-matter systems by using ensembles of individual atoms which are confined by electrical and magnetic forces into patterns that mimic the fundamental physics of the repeating structural pattern, or “lattice,” of a solid material.

Improving these quantum-mechanical models is an important research area at JQI, and Spielman’s group has been investigating a model for the superfluid-to-Mott insulator (SF-MI) phase transition – the point at which the atoms cease to share the same quantum properties, as if each atom were spread over the entire lattice, and change into a set of individual atoms trapped at specific locations, that do not communicate with one another.

Figure 1

The group’s experimental setup at NIST’s Gaithersburg, MD facility uses a cloud of about 200,000 atoms of rubidium that have been cooled to near absolute zero and confined in a combination of magnetic and optical potentials. In those conditions, a majority of the atoms forms a Bose-Einstein condensate (BEC), an exotic condition in which all the atoms coalesce into exactly the same quantum state.

Then the team loads the BEC – which is about 10 micrometers in diameter, or about one-tenth the width of a human hair – into an “optical lattice” that forms at the intersection of three laser beams placed at right angles to one another [See Figure 1], two horizontal and one vertical. Interference patterns in the beams’ waves cause regularly spaced areas of higher and lower energy; atoms naturally tend to settle into the lowest-energy locations like eggs in an egg carton.

The depth of the lattice wells (the cavities in the egg carton) is adjusted by varying the intensity of the laser beams. [See Figure 2] In a relatively shallow lattice, atoms can easily “tunnel” from one site to another in the condensate superfluid state, whereas deep lattice wells tend to hold each atom in place, producing the non-condensate insulator state. “We can tune the depth of all the wells in the carton by adjusting the intensity of the laser beams which create it,” Jiménez-García explains. “We can go from a flat carton to a carton with very deep wells.”

Figure 2 (click to view hi resolution image)

That general lab arrangement – ultracold trapped atoms suspended in an optical lattice – is the current standard worldwide for experiments on condensed-matter models. But it has a serious problem: The mathematical theory behind the model is predicated on a completely homogenous system, whereas arrays such as the JQI group uses are only homogenous on small spatial scales. Globally, they are inhomogenous because the magnetic trapping potential is not uniform across the width of the trap. As a result, the equations used to calculate expected outcomes do not accurately predict the SF-MI transition, compromising their utility.

Last year, however, an international collaboration of theorists determined [2] that in such configurations, where there were spatially separated SF and MI phases, the quantum state of the system could be fully specified by the relationship between only two variables: the characteristic density of the system (a composite of trapping potential, total number of trapped atoms, tunneling energy, lattice spacing and dimensionality); and the strength of the interactions between neighboring atoms.

Jiménez-García and colleagues in the JQI group set out to see if they could make an experimental system that performed according to the theorists’ specifications.

They set the depth of the vertical lattice beam such that it partitioned the roughly spherical BEC into about 60 two-dimensional, pancake-shaped segments, and then used a method similar to medical MRI scanning to select and analyze just a couple of individual 2D segments at the same time. The inhomogeneity of the originally 3D atomic sample results in the selection of 2D systems with different total number of atoms, ranging from 0 (at the edges of the system) to 4000 atoms (in the center of the system), allowing the researchers to examine a broad range of total atom numbers and lattice depths.

Because the trapping potential was not homogenous across the BEC, the group’s lattices were not completely orthogonal. “What we get instead,” Jiménez-García says, “is an array of egg cartons which have a parabolic curvature. Imagine each egg carton with the overall shape of a bowl, and the whole system as a stack of egg carton bowls.”

To determine the state of the atoms in the 2D slice, the scientists abruptly turn off the trap and let the atoms begin to fly apart. After a few thousandths of a second, they take a picture of the expanding population. If the atoms were deep into the SF state, the images will show a tightly focused bunch. If they were in the MI state, the bunch will have dispersed farther and appear more diffuse. “We detect a sharp peak in the momentum distribution which we associate with the condensate fraction,” Jiménez-García says. “Wider dispersion – that is, less condensate fraction -- would mean more MI.”

After measuring about 1300 different samples, the group was able to determine that the two-variable theory completely described the state of each slice.

References
[1] K. Jimenez-Garcia, R.L. Compton, Y.-J. Lin, W.D. Phillips, J.V. Porto and I.B. Spielman, "Phases of a 2D Bose Gas in an Optical Lattice", accepted for publication in Physical Review Letters. arXiv:1003.1541.
[2] Marcos Rigol, George G. Batrouni, Valery G. Rousseau, Richard T. Scalettar, "State diagrams for harmonically trapped bosons in optical lattices", Phys. Rev. A 79, 053605 (2009). Abstract.

Interface Between Two Worlds Ultracold atoms coupled to a micromechanical oscillator

Stephan Camerer, David Hunger, and Philipp Treutlein (left to right)



[This is an invited article based on a recently published work by the authors and their collaborators from Germany and France. -- 2Physics.com]





Authors: Philipp Treutlein, David Hunger, Stephan Camerer

Affiliation: Ludwig-Maximilians-Universität München, Max-Planck-Institut für Quantenoptik, Germany

Link to the Munich atom chip experiments >>

Bose-Einstein condensates of ultracold atoms and micromechanical oscillators are usually thought to belong to different areas of science. The condensates are elusive gaseous objects that display the intriguing phenomena of quantum physics in a very clean way. Mechanical oscillators are tangible tools with widespread technological applications. In a recent experiment [1], we have coupled the vibrations of a mechanical oscillator to the motion of a Bose-Einstein condensate in a trap. Such a coupling could lead to quantum-level control and readout of mechanical oscillators [2,3], with applications in quantum information processing or precision force sensing.

Bose-Einstein condensates (BECs) of ultracold neutral atoms are quantum systems par excellence. Due to their electric neutrality, the atoms can be very well isolated from the environment. In recent years, a sophisticated experimental toolbox has been developed for cooling, readout and control of the atoms at the quantum level [4]. This has enabled many beautiful experiments in which interesting quantum states of BECs are prepared and studied.

It is an intriguing question to investigate whether this high level of control can be transferred to other systems such as micromechanical oscillators. At low temperatures, the vibrations of mechanical oscillators show quantum behaviour [5]. A sufficiently strong coupling between ultracold atoms and a mechanical oscillator would allow one to create a hybrid quantum system, in which coherent transfer of quantum information or atom-oscillator entanglement could be studied. In applications of micromechanical oscillators as force sensors, it could lead to higher sensitivity.

In our experiment, which is part of the Nanosystems Initiative Munich and involves researchers from the Ludwig-Maximilians-University in Munich, the Max-Planck-Institute of Quantum Optics in Garching, and the Ecole Normale Superieure in Paris, we have made a first step in this direction and coupled a BEC to the vibrations of a micromechanical oscillator. We use an “atom chip” – a chip with microfabricated current-carrying wires – to create magnetic trapping potentials for the atoms. In addition, the chip carries a micromechanical cantilever oscillator, similar to those used in atomic force microscopes. Using the magnetic traps on the atom chip, we prepare a Bose-Einstein condensate and position it close to the cantilever tip.

At small distances of about one micrometer, atom-surface forces such as the Casimir-Polder force result in an attraction between the atoms and the oscillator. This attractive force couples the vibrations of the oscillator and the motion of the atoms in the trap. The system can be thought of as two oscillating pendula with extremely different masses that are coupled with a spring. Through the coupling, the mechanical oscillator excites collective vibrations of the atoms in the trap – in this way we use the atoms to detect the oscillator vibrations.

Figure 1: a) Schematic setup: Micro-cantilever mounted on an atom chip with gold wires. A ⁸⁷Rb BEC can be trapped and positioned near the cantilever with magnetic fields from wire currents. Cantilever vibrations can be excited with a piezo and independently probed with a readout laser. b) Photograph of the atom chip (scale bar: 1 mm). c) Combined magnetic and surface potential. The surface potential reduces the trap depth to U₀. Cantilever oscillations modulate the potential, thereby coupling to atomic motion.

The BEC has a discrete spectrum of vibrational modes, whose frequencies can be tuned by adjusting the magnetic trapping potential. We use this feature to control the coupling and to resonantly couple the oscillator vibrations to selected mechanical modes of the BEC.

The cantilever oscillator that is used in our current experiment has a length of 200 micrometers and is excited to vibrations with several nanometers amplitude, which are then detected with the atoms. By replacing the cantilever with a nanoscale oscillator, such as a carbon nanotube, it could be possible to detect vibrations close to the quantum mechanical ground state motion of the oscillator. To prepare the oscillator close to its ground state, such an experiment has to be performed at very low temperatures in a cryogenic setup. Under these conditions, the atoms could influence the nanotube strongly, opening a path to quantum manipulations.

References:
[1] David Hunger, Stephan Camerer, Theodor W. Hänsch, Daniel König, Jörg P. Kotthaus, Jakob Reichel, and Philipp Treutlein, “Resonant Coupling of a Bose-Einstein Condensate to a Micromechanical Oscillator”, Phys. Rev. Lett. 104, 143002 (2010). Abstract.
[2] K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, “Strong coupling of a mechanical oscillator and a single atom”, Phys. Rev. Lett. 103, 063005 (2009). Abstract.
[3] L. Tian and P. Zoller, “Coupled Ion-Nanomechanical Systems”, Phys. Rev. Lett. 93, 266403 (2004). Abstract.
[4] S. Chu, “Cold atoms and quantum control”, Nature 416, 206 (2002). Abstract.
[5] A. D. O’Connell et al., “Quantum ground state and single-phonon control of a mechanical resonator”, Nature 464, 697 (2010). Abstract.

Everlasting Quantum Wave: Prediction of A New Form of Soliton in Ultracold Gases

Radha Balakrishnan [photo courtesy: Indian Academy of Sciences]

Solitary waves that run a long distance without losing their shape or dying out are a special class of waves called solitons. These everlasting waves are exotic enough, but theoreticians at the Joint Quantum Institute (JQI, a collaboration of the National Institute of Standards and Technology and the University of Maryland), and their colleagues from the Institute of Mathematical Sciences (India) and the George Mason University, now believe that there may be a new kind of soliton that’s even more special. Expected to be found in certain types of ultracold gases, the new soliton would not be just a low-temperature atomic curiosity, it also may provide profound insights into other physical systems, including the early universe.

Indubala Satija [photo courtesy: Joint Quantum Institute, NIST/U. Maryland]

Solitons can occur everywhere. In the 1830s, Scottish scientist John Scott Russell first identified them while riding along a narrow canal, where he saw a water wave maintaining its shape over long distances, instead of dying away. This “singular and beautiful” phenomenon, as Russell termed it, has since been observed, created and exploited in many systems, including light waves in optical-fiber telecommunications, the vibrational waves that sweep through atomic crystals, and even “atom waves” in Bose-Einstein condensates (BECs), an ultracold state of matter.

Atoms in BECs can join together to form single large waves that travel through the gas. The atom waves in BECs can even split up, interfere with one another, and cancel each other out. In BECs with weakly interacting atoms, this has resulted in observations of “dark solitons,” long-lasting waves that represent absences of atoms propagating through the gas, and “bright” solitons (those carrying actual matter).

Charles W. Clark [photo courtesy: Joint Quantum Institute, NIST/ U. Maryland]

By taking a new theoretical approach, the new work predicts a third, even more exotic “immortal” soliton—never before seen in any other physical system. This new soliton can occur in BECs made of “hard-core bosons”—atoms that repel each other strongly and thus interact intensely —organized in an egg-crate-like arrangement known as an “optical lattice.”

In 1990, one of the coauthors of the present work, Radha Balakrishnan of the Institute of Mathematical Sciences in India, wrote down the mathematical description of these new solitons, but considered her work merely to approximate the behavior of a BEC made of strongly interacting gas atoms. With the subsequent observations of BECs, the JQI researchers recently realized both that Balakrishnan’s equations provide an almost exact description of a BEC with strongly interacting atoms, and that this previously unknown type of soliton actually can exist. While all previously known solitons die down as their wave velocity approaches the speed of sound, this new soliton would survive, maintaining its wave height (amplitude) even at sonic speeds.

[Image credit: I. Satija et al., Joint Quantum Institute] A newly predicted “immortal” soliton (left) as compared to a conventional “dark” soliton (right). The horizontal axis depicts the width of the soliton wavefronts (bounded by yellow in the left panel and purple on the right panel, with different colors representing different wave heights). The vertical axis corresponds to the speed of the soliton as a fraction of the velocity of sound. The immortal soliton on the left maintains its shape right up to the sound barrier.

If the “immortal” soliton could be created to order, it could provide a new avenue for investigating the behavior of strongly interacting quantum systems, whose members include high-temperature superconductors and magnets. As atoms cooling into a BEC represent a phase transition (like water turning to ice), the new soliton could also serve as an important tool for better understanding phase transitions, even those that took place in the early universe as it expanded and cooled.

Reference
“Particle-hole asymmetry and brightening of solitons in a strongly repulsive Bose-Einstein condensate,”
R. Balakrishnan, I.I. Satija and C.W. Clark,
Physical Review Letters, vol. 103, p. 230403 (2009) Abstract.

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

Creation of ‘Synthetic Magnetic Fields’ for Neutral Atoms

Ian Spielman [photo courtesy: Joint Quantum Institute, University of Maryland]

The current (December 3) issue of the journal 'Nature' carries an article describing the creation of the so-called “synthetic” magnetic fields for ultracold gas atoms, in effect “tricking” neutral atoms into acting as if they are electrically charged particles subjected to a real magnetic field.

This important new capability in ultracold atomic gases is achieved by a team of researchers at the Joint Quantum Institute (JQI), a collaboration of the University of Maryland and the National Institute of Standards and Technology (NIST). The demonstration of this capability not only paves the way for exploring the complex natural phenomena involving charged particles in magnetic fields, but may also contribute to an exotic new form of quantum computing.

As researchers have become increasingly proficient at creating and manipulating gaseous collections of atoms near absolute zero, these ultracold gases have become ideal laboratories for studying the complex behavior of material systems. Unlike usual crystalline materials, they are free of obfuscating properties, such as impurity atoms, that exist in normal solids and liquids.

However, studying the effects of magnetic fields is problematic because the gases are made of neutral atoms and so do not respond to magnetic fields in the same way as charged particles do. So how would you simulate, for example, such important exotic phenomena as the quantum Hall effect, in which electrons can “divide” into quasiparticles carrying only a fraction of the electron’s electric charge?

The answer Ian Spielman and his colleagues came up with is a clever physical trick to make the neutral atoms behave in a way that is mathematically identical to how charged particles move in a magnetic field. A pair of laser beams illuminates an ultracold gas of rubidium atoms already in a collective state known as a Bose-Einstein condensate. The laser light ties the atoms' internal energy to their external (kinetic) energy, modifying the relationship between their energy and momentum. Simultaneously, the researchers expose the atoms to a real magnetic field that varies along a single direction, so that the alteration also varies along that direction.

A pair of laser beams (red arrows) impinges upon an ultracold gas cloud of rubidum atoms (green oval) to create synthetic magnetic fields (labeled Beff). (Inset) The beams, combined with an external magnetic field (not shown) cause the atoms to "feel" a rotational force; the swirling atoms create vortices in the gas [Image courtesy: JQI]

In a strange inversion, the laser-illuminated neutral atoms react to the varying magnetic field in a way that is mathematically equivalent to the way a charged particle responds to a uniform magnetic field. The neutral atoms experience a force in a direction perpendicular to both their direction of motion and the direction of the magnetic field gradient in the trap. By fooling the atoms in this fashion, the researchers created vortices in which the atoms swirl in whirlpool-like motions in the gas clouds. The vortices are the “smoking gun,” Spielman says, for the presence of synthetic magnetic fields.

A harbinger of the synthetic magnetic fields is the formation of vortices (spots). These spots, the number of which increases with increasing synthetic field, mark the points about which atoms swirled with a whirlpool-like motion. The measurement units in each panel indicate the size of the external magnetic field gradient applied to the gas of atoms, with larger external fields producing more vortices. [Image courtesy: JQI]

Previously, other researchers had physically spun gases of ultracold atoms to simulate the effects of magnetic fields, but rotating gases are unstable and tend to lose atoms at the highest rotation rates.

In their next step, the JQI researchers plan to partition a nearly spherical system of 20,000 rubidium atoms into a stack of about 100 two-dimensional “pancakes” and increase their currently observed 12 vortices to about 200 per-pancake. At a one-vortex-per-atom ratio, they could observe the quantum Hall effect and control it in unprecedented ways. In turn, they hope to coax atoms to behave like a class of quasiparticles known as “non-abelian anyons,” a required component of “topological quantum computing,” in which anyons dancing in the gas would perform logical operations based on the laws of quantum mechanics.

Reference
"Synthetic magnetic fields for ultracold neutral atoms"
Y.-J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto & I. B. Spielman.
Nature, 462, 628-632 (3 December, 2009). Abstract.

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

Bose-Einstein Condensation of Strontium

Figure 1: The SrBEC team. From left to right: Bo Huang, Meng Khoon Tey, Rudolf Grimm, Florian Schreck (Author), and Simon Stellmer



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




Author: Florian Schreck

Affiliation: Institut für Quantenoptik und Quanteninformation (IQOQI), Austria
Link to the 'Ultracold Atoms and Quantum Gases' Group >>

Atoms are particles as well as waves. The wave nature of atoms becomes evident when cooling a gas of bosonic atoms to extremely low temperatures. The de Broglie wavelength describing the atomic wave packets grows and as soon as it exceeds the interatomic spacing, the gas undergoes a phase-transition and enters a collective state of matter, known as Bose-Einstein condensate (BEC). This behavior was predicted in 1924 by Bose and Einstein and realized for the first time in 1995 in gases of alkali-metal atoms [1, 2, 3]. Research on these degenerate quantum gases has since grown strongly and has now connected to many other fields as, for example, condensed-matter physics, molecular physics and precision measurements.

Since then, ten elements have been Bose-condensed: all stable alkali-metal atoms and hydrogen, metastable helium, chromium, ytterbium [4] and very recently calcium [5]. Oftentimes new isotopes cooled to quantum degeneracy have, with their unique properties, opened the doors to the investigation of novel phenomena. Atoms with two electrons in their outer shell, as ytterbium and the alkaline-earth elements, have properties unlike any other of the condensed species: a non-magnetic ground-state (for bosonic isotopes), metastable states and a combination of broad and narrow linewidth optical transitions. This has made these elements, especially ytterbium and strontium, prime choices for neutral atom optical clocks. In addition, numerous proposals employ these properties to realize quantum simulation and computation schemes, mHz-linewidth lasers or to probe the time dependence of natural constants.

These applications either rely on or would benefit from the availability of quantum degenerate samples. Already ten years ago, strontium atoms have been cooled to near quantum degeneracy [6], but a BEC could not be reached. The problem resided in the last cooling stage used in all experiments that have produced degenerate quantum gases: evaporative cooling. This cooling process works by removing hot atoms from the sample and using elastic collisions to rethermalize the remaining gas at a lower temperature. For strontium evaporative cooling worked very badly: the most abundant isotope, ⁸⁸Sr with 83% abundance, essentially does not collide. ⁸⁶Sr with 10% abundance has the opposite problem: the atoms collide so strongly that often molecules are formed, releasing the molecular binding energy, which leads to heating and the loss of atoms. Sr has yet another bosonic isotope: ⁸⁴Sr with only 0.56% natural abundance. Apparently for this reason nobody had undertaken experiments using this isotope.

However, we had experience working with low abundance isotopes and took a closer look at ⁸⁴Sr. We asked Roman Ciuryło to calculate the scattering properties of ⁸⁴Sr by scaling the known properties of the abundant isotopes with the mass. Based on measurements by Thomas Killians group he deduced an elastic scattering cross section in the Goldilocks zone: neither too small nor too big. This was shortly afterwards confirmed by two other groups [7, 8]. Therefore we decided to make ⁸⁴Sr our main approach to Sr BEC.

To overcome the low natural abundance, a combination of Sr properties turned out to be very beneficial. To produce a sample of cold Sr atoms suitable for evaporative cooling, an atomic beam is slowed and then held and cooled in a magneto-optical trap (MOT) using laserlight near-resonant with a broad-linewidth transition. A small fraction of the atoms in the excited state of that transition will not decay back to the ground-state, but to a metastable state with a lifetime of several minutes. Atoms in this state are magnetic and can be trapped in the quadrupole magnetic field used for the MOT. Within 10 seconds we can accumulate about 100 million atoms in this state, overcoming the low natural abundance and giving us enough material for evaporative cooling.

Temperature and density achievable in a MOT depend on the linewidth of the transition used. Strontium has also a narrow-linewidth transition that is suitable for a MOT. It is too narrow to allow slowing of an atomic beam or capture of atoms from that beam, but it can be used to further cool the atoms accumulated in the metastable state (after optically pumping them back to the ground-state). The figure of merit for a cooling process with the goal to reach BEC is phase-space density, the product of density and the de Broglie wavelength cubed. The phase-transition to BEC will occur if the phase-space density exceeds 2.6. For alkali-metal atoms, only one MOT transition exists, which allows to obtain phase-space densities on the order of 10^-6. The combination of broad-linewidth and just perfectly sized narrow-linewidth transition in strontium allows to achieve remarkably high phase-space densities of 10^-2 already after the MOT stage. This means that only very little evaporative cooling is required to obtain quantum degeneracy.

For evaporative cooling, the atoms have to be held in a conservative potential. Atoms in the ground-state have no magnetic moment, so a magnetic trap can not be used. We confine them using a so-called optical dipole trap, which consists of two crossed infrared laser beams. About one million atoms are loaded into the crossing region after switching off the MOT. Evaporative cooling proceeds now by letting hot atoms escape from the trap and waiting for the remaining atoms to thermalize. To force evaporation to continue at ever lower temperatures, the potential depth is lowered over the course of a few seconds. We knew that the elastic scattering properties of ⁸⁴Sr would be ideal for evaporative cooling, but it was impossible to predict the inelastic scattering properties that can lead to detrimental atom loss and heating. To our great pleasure we discovered that inelastic processes were very weak. Evaporative cooling worked the first time we tested it and only minutes later we created the first Bose-Einstein condensate of strontium.

Figure 2: Density distribution of strontium atoms released from a trap. To the left a thermal sample is shown. Further cooling results in the appearance of a dense and cold Bose-Einstein condensate in the middle of the cloud. Finally the thermal component is too small to be detectable.

Figure 3: Expansion of a ⁸⁴Sr BEC from an elongated trap. The repulsion between the atoms leads to a faster expansion along the initially strongly confined directions. The sequence of images shows the temporal evolution in 5ms steps [Ref: Physical Review Letters, 103, 200401 (2009)]

Figure 2 shows images of the density distributions of clouds of ⁸⁴Sr atoms across the phase transition from a thermal cloud to a pure BEC. As soon as the phase-transition is crossed, a dense central peak appears, the BEC. Figure 3 highlights another property of the BEC: after release from the trap it expands fastest along the direction in which it was initially strongest confined leading to a disk-shaped density distribution, shown here from the side. Thermal atoms would expand isotropically and show a spherical density distribution.

About two weeks after we had achieved BEC of Sr [9], the group of Thomas Killian arrived at the same goal [10]. It is clear from both experiments that BEC of Sr is very robust. Simple scaling up of the volume of the optical dipole trap should result in BECs in excess of one million atoms. The two other species with two electrons in the outer shell that have been Bose-condensed, Yb and Ca, have so far only produced relatively small BECs of up to 6 X 10⁴ atoms. This puts Sr in a prime position for experiments with BECs of two-electron systems.

Using sympathetic cooling it should be possible to cool also the other Sr isotopes to quantum degeneracy. ⁸⁸Sr is nearly non-interacting, which would be useful for precision sensors, for example force sensors. The fermionic isotope ⁸⁷Sr has a nuclear magnetic moment, which can be used to store quantum information. It is at the heart of proposals for quantum computation and is the key to the study of a new class of many-body systems. Sr₂ molecules can be created and used to measure the stability of fundamental constants. Cooling of the alkali-metal rubidium is compatible with the scheme employed for Sr. SrRb ground-state molecules would possess both, an electric and a magnetic dipole moment. This can be used to design many-body systems with spin-dependent long range interactions.

It will be exciting to explore all the new possibilities opened up by the Bose-Einstein condensation of strontium.

References
[1] M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in dilute atomic vapor,” Science, vol. 269, pp. 198–201 (1995). Abstract.
[2] K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and
W. Ketterle, “Bose-einstein condensation in a gas of sodium atoms,”
Phys. Rev. Lett., vol. 75, pp. 3969–3973 (1995). Abstract.
[3] C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, “Evidence of bose-einstein condensation in an atomic gas with attractive interactions,” Phys.Rev. Lett., vol. 75, pp. 1687–1690 (1995). Abstract.
[4] Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, and Y. Takahashi, “Spin-singlet bose-einstein condensation of two-electron atoms,”
Phys. Rev. Lett., vol. 91, p.040404 (2003). Abstract.
[5] S. Kraft, F. Vogt, O. Appel, F. Riehle, and U. Sterr, “Bose-einstein condensation of alkaline earth atoms: ⁴⁰Ca,” Phys. Rev. Lett., vol. 103, p. 130401, 2009. Abstract.
[6] H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami, “Laser cooling of strontium atoms toward quantum degeneracy,” in Atomic Physics 17 (E. Arimondo, P. DeNatale, and M. Inguscio, eds.), pp. 382–396, American Institute of Physics, Woodbury (2001).
[7] A. Stein, H. Knöckel, and E. Tiemann, “Fourier-transform spectroscopy of Sr₂ and revised groundstate potential,” Phys. Rev. A, vol. 78, p.042508 (2008). Abstract.
[8] Y. N. Martinez de Escobar, P. G. Mickelson, P. Pellegrini, S. B. Nagel, A. Traverso, M. Yan, R. Côté, and T. C. Killian, “Two-photon photoassociative spectroscopy of ultracold ⁸⁸Sr,”
Phys.Rev. A, vol. 78, p.062708 (2008). Abstract.
[9] S. Stellmer, M. K. Tey, B. Huang, R. Grimm, and F. Schreck, “Bose-Einstein condensation of strontium,” Physical Review Letters, vol. 103, no. 20, p.200401 (2009). Abstract.
[10] Y. N. M. de Escobar, P. G. Mickelson, M. Yan, B. J. DeSalvo, S. B. Nagel, and T. C. Killian, “Bose-einstein condensation of ⁸⁴Sr,” Physical Review Letters, vol. 103, no. 20, p.200402 (2009). Abstract.

Finer Atomic Matchmaking by Radio Frequency Tuning

The image shows, in the sequence of green arrows, how a pair of ultracold gas atoms collides, briefly forms a molecule, and flies apart, in the presence of an external magnetic field (not shown) that influences this process. By adding RF radiation (lightning bolts) of the right frequency, the atoms can experience being in many different molecular states (red arrows), providing even more extensive and detailed control of the collision. The size of the yellow bursts indicate the amount of absorption/emission of RF radiation. [Image Credit: Eite Tiesinga, Joint Quantum Institute, University of Maryland/ National Institute of Standards and Technology]

In a paper accepted for publication in Physical Review A, a team of scientists at the Joint Quantum Institute (JQI) of the National Institute of Standards and Technology (NIST) and the University of Maryland have reported that properly tuned radio-frequency waves can influence how much the atoms attract or repel one another, opening up new ways to control their interactions.

While investigating mysterious data in ultracold gases of rubidium atoms, they found that the radio-frequency (RF) radiation could serve as a second "knob," in addition to the more traditionally used magnetic fields, for controlling how atoms in an ultracold gas interact. Just as it is easier to improve reception on a home radio by both electronically tuning the frequency on the receiver and mechanically moving the antenna, having two independent knobs for influencing the interactions in atomic gases could produce richer and more exotic arrangements of ultracold atoms than ever before.

Previous experiments with ultracold gases, including the creation of Bose-Einstein condensates, have controlled atoms by using a single knob—traditionally, magnetic fields. These fields can tune atoms to interact strongly or weakly with their neighbors, pair up into molecules, or even switch the interactions from attractive to repulsive. Adding a second control makes it possible to independently tune the interactions between atoms in different states or even between different types of atoms.

Such greater control could lead to even more exotic states of matter. A second knob, for example, may make it easier to create a weird three-atom arrangement known as an Efimov state, whereby two neutral atoms that ordinarily do not interact strongly with one another join together with a third atom under the right conditions [Read past 2Physics report on Efimov state]

For many years, researchers had hoped to use RF radiation as a second knob for atoms, but were limited by the high power required. The new work shows that, near magnetic field values that have a big effect on the interactions, significantly less RF power is required, and useful control is possible.

In the new work, the JQI/NIST team examined intriguing experimental data of trapped rubidium atoms taken by the group of David Hall at Amherst College in Massachusetts. This data showed that the RF radiation was an important factor in tuning the atomic collisions. To explain the complicated way in which the collisions varied with RF frequency and magnetic field, NIST theorist Thomas Hanna developed a simple model of the experimental arrangement.

"The model reconstructed the energy landscape of the rubidium atoms and explained how RF radiation was changing the atoms' interactions with one another. In addition to providing a roadmap for rubidium, this simplified theoretical approach could reveal how to use RF to control ultracold gases consisting of other atomic elements", Hanna says.

Reference
"Radio-frequency dressing of multiple Feshbach resonances"
A.M. Kaufman, R.P. Anderson, T.M. Hanna, E. Tiesinga, P.S. Julienne, and D.S. Hall,
To appear in Physical Review A.
Abstract: We demonstrate and theoretically analyze the dressing of several proximate Feshbach resonances in 87Rb using radiofrequency radiation (rf). We present accurate measurements and characterizations of the resonances, and the dramatic changes in scattering properties that can arise through the rf dressing. Our scattering theory analysis yields quantitative agreement with the experimental data. We also present a simple interpretation of our results in terms of rf-coupled bound states interacting with the collision threshold.

[We thank NIST for materials used in this posting]

Bose Gas in 2D Flatland and Mysteries of Superfluidity

Kristian Helmerson [photo courtesy: Joint Quantum Institute, University of Maryland]

In a paper accepted for publication in Physical Review Letters, a team of physicists led by Kristian Helmerson of Joint Quantum Institute [JQI, a partnership of National Institute of Standards and Technology (NIST) and the University of Maryland] presents some exciting aspects of physics happening in a 2D Flatland.

If physicists lived in Flatland—the fictional two-dimensional world invented by Edwin Abbott in his 1884 novel —some of their quantum physics experiments would turn out differently (not just thinner) than those in our world. The distinction has taken another step from speculative fiction to real-world puzzle with this paper reporting on a Flatland arrangement of ultracold gas atoms [1]. The new results, which don’t quite jibe with earlier Flatland experiments in Paris [2,3], might help clarify a strange property: “superfluidity.”

In three dimensions, cooling a gas of certain atoms to sufficiently low temperatures turns them into a Bose-Einstein condensate (BEC). As predicted in the 1920s (and first demonstrated in 1995) the once individualistic gas atoms begin to move as a single, coordinated entity. But back in 1970, theorists predicted that something different would happen in two dimensions: an ultracold gas of interacting atoms would undergo the analogous “Berezinskii, Kosterlitz and Thouless” (BKT) transition, in which atoms don’t quite move in lockstep as they do in a BEC, but mysteriously share some of a BEC’s properties, such as superfluidity, or frictionless flow.

In these new experiments, the team at JQI has achieved the latest experimental observation of the BKT transition. The JQI researchers trap and cool a micron-thick layer of sodium atoms, confined to move in only two dimensions. At higher temperatures, the atoms have normal “thermal” behavior in which they act as individual entities, but then as the temperature lowers, the gas transforms into a “quasi-condensate,” consisting of little islands each behaving like a tiny BEC.

[Image credit: Kristian Helmerson, JQI] A gas of atoms arranged in a single, flat layer ordinarily has ‘thermal’ behavior (left) in which the atoms act as individual entities. At lowered temperatures, the gas transforms into a ‘quasi-condensate‘ (middle) consisting of little islands (schematically represented as colored blobs) that fluctuate in time; within each island atoms act as a single coordinated entity. At lower temperatures still, the gas enters the superfluid ‘BKT’ phase (right): the islands start to coalesce and atoms can flow frictionlessly within the merged area.

By further lowering the temperature, the gas makes the transition to a BKT superfluid where the islands begin to merge into a sort of “United States” of superfluidity. In this situation, an atom can flow unimpeded between neighboring “states” since the borders of the former islands are not well defined, but one can tell that the atom is “not in Kansas anymore,” in contrast to a BEC where one cannot pinpoint the location of a particular atom anywhere in the gas.

When a group from Ecole Normale Supérieure (Paris) lowered the temperature of their 2-D gas in earlier experiments [2,3], they only saw a sharp transition from thermal behavior to a BKT superfluid, rather than the additional step of the non-superfluid quasi-condensate. But the Paris group used rubidium atoms, which are heavier and more strongly interacting, possibly exhibiting a qualitatively different behavior. These new results may cast light on superfluidity, which decades after its discovery still seems to hold new mysteries.

References
[1] "Observation of a 2D Bose-gas: From thermal to quasi-condensate to superfluid",
P. Cladé, C. Ryu, A. Ramanathan, K. Helmerson and W.D. Phillips, Physical Review Letters, accepted for publication [link will be added after it's published]. arXiv:0805.3519.
[2] "Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas", Zoran Hadzibabic, Peter Krüger, Marc Cheneau, Baptiste Battelier and Jean Dalibard, Nature 441, 1118 (2006). Abstract.
[3] "Critical Point of an Interacting Two-Dimensional Atomic Bose Gas",
Peter Krüger, Zoran Hadzibabic, and Jean Dalibard, Phys. Rev. Lett. 99, 040402 (2007). Abstract.

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

New Technique Probes Ultracold Atomic Gases

Deborah Jin [photo courtesy: JILA, Boulder, CO]

In a paper published in August 7th issue of the journal Nature, a team of physicists from JILA (link to Deborah Jin Group->), a joint institute of the National Institute of Standards and Technology (NIST) and the University of Colorado at Boulder, reported a new powerful technique that reveals hidden properties of ultracold atomic gases. The idea behind the technique originates from 'photoemission spectroscopy' which has been used for nearly a century in the study of materials and, specifically, for probing the energy of electrons in a material. The team of scientists led by Deborah Jin adapted this technique to study potassium atoms in an ultracold gas.

Photoemission spectroscopy is particularly powerful in revealing details of the pairing of electrons in high-temperature superconductors, which are solids that have zero resistance to electrical current at relatively high temperatures (but still below room temperature). The scientists at JILA study a very similar phenomenon: superfluidity (fluids that can flow with zero friction). Specifically, they study how atoms in a Fermi gas behave as they "cross over" from acting like a Bose Einstein Condensate (in which fermions pair up to form tightly bound molecules) to behaving like pairs of separated electrons in a superconductor.

In the crossover region, atoms in an ultracold gas exert very strong forces on each other, which masks their individual properties. To see the hidden behavior, JILA scientists apply a radio frequency field to a cloud of trapped, paired potassium atoms, ejecting a few atoms from the strongly interacting cloud. Then the laser trap is turned off so the gas can expand. Scientists make images and count the numbers of escaping atoms at different velocities. With this information, scientists can calculate the atoms' original energy states and momentum values back when they were inside the gas. Scientists then map the energy levels for all the original states of the atoms and can identify a particular pattern that shows the appearance of a large "energy gap," which represents the amount of energy needed to break apart a pair of atoms.

The new photoemission technique represents a huge jump in the information available to physicists who study ultracold gases. Traditionally, scientists could probe either the energy or momentum of these gases, not both. The new technique simultaneously probes the energy and momentum, allowing the scientists to study the microscopics involved in the pairing of two atoms.

"This technique is a clean probe of the microscopics in this system, and it allows us to see interesting things like a very large energy gap that seems to appear before the superfluid state," says group leader Deborah Jin. Ultimately, the JILA work studying superfluidity in atomic gases may one day help in understanding the energy gap that appears in high-temperature superconductors, which may have applications such as more efficient transmission of electricity across power grids. In addition, the new technique can be extended beyond the study of pairing to include, for example, the study of atoms trapped in crisscrossed "lattices" of laser light, a building block for some atomic clock and quantum computer designs.

Reference
"Using photoemission spectroscopy to probe a strongly interacting Fermi gas"
J. T. Stewart, J. P. Gaebler, D. S. Jin,
Nature, 454, p744-747 (7 August, 2008) Abstract.

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

Store Light Here and Retrieve It at a Distance

Lene Vestergaard Hau, Mallinckrodt Professor of Physics and of Applied Physics [Photo courtsey: Jay Penni Photography, Harvard Univ]

In Bose-Einstein condensates (BECs), atoms are cooled to such low temperatures that they all occupy the same quantum state, even though they may be physically apart from each other. Making use of such quantum mechanically indistinguishable microscopic particles, Lene Hau and colleagues from Harvard University have been able to imprint a coherent pulse of light on a collection of ultracold atoms -- and then retrieve the same light pulse from a second set of atoms that is some distance away.

"We demonstrate that we can stop a light pulse in a supercooled sodium cloud, store the data contained within it, and totally extinguish it, only to reincarnate the pulse in another cloud two-tenths of a millimeter away," announced Lene Hau. In a paper published in Feb 8 issue of 'Nature', Lene Hau and her co-authors, Naomi S. Ginsberg and Sean R. Garner, reported their spectacular finding that the light pulse can be revived, and its information transferred between the two clouds of sodium atoms (or, the Bose-Einstein condensates -- illuminated with a control laser and cooled to just billionths of a degree above absolute zero), by converting the original optical pulse into a traveling matter wave. The matter wave is a matter-copy of the original pulse, traveling at a leisurely 200 meters per hour. When the matter pulse enters the second of the supercooled clouds which is illuminated with a control laser, it is readily converted back into light.

The results of this experiment provide a powerful means of controlling optical information and certainly will lead a way to future directions of optical communication. It could also have applications in the developing fields of quantum information processing and quantum cryptography.

Reference:
"Coherent control of optical information with matter wave dynamics"
Naomi S. Ginsberg, Sean R. Garner and Lene Vestergaard Hau
Nature 445, 623-626 (8 February 2007) Link to Abstract

Background Reading
Wikipedia page on Bose-Einstein Condensate
BEC homepage, JILA, Colorado
2Physics past posting on BEC

Bose-Einstein condensate

About 80 years ago, based on previous work by the Indian physicist
Satyendra Nath Bose, Einstein proposed that if a gas of neutral atoms is
cooled to a low enough temperature, all atoms of the gas would fall into the
same quantum state. In other words, all of the million or billion atoms in
the gas would end up in the same place at the same time, a weird quantum
state dubbed a Bose-Einstein condensate.

The supercold atoms are created from a hot gas of neutral atoms that is
laser cooled, collected in a magneto-optic trap, cooled further by evaporation,
and then spun off into a magnetic trap for a few seconds of study before it
warms up and dissipates.

A team of physicists at UC Berkeley has created a Bose-Einstein condensate
of rubidium atoms and nudged it into a circular racetrack 2 millimeters
across, creating a particle storage ring analogous to the accelerator storage
rings of high energy physics. This ring, the first to contain a Bose-Einstein gas,
is full of cold particles at a temperature of only one-millionth of a degree
above absolute zero (which is -273 degree centigrade), traveling with
energies a billion trillion times less than the particles in a high-energy storage
ring [The atoms circled the racetrack at a speed of about 50 to 150 millimeters
per second, which is equal to an energy of about one nano-electron volt (eV)
per atom, or one billionth of an electron volt. High-energy particle accelerators
routinely bump particles to energies of a few tera-electron volts, or a trillion
eV - a billion trillion times more energetic than the cold rubidium atoms].

Though such slow-moving rubidium atoms would be useless for producing
the exotic collision particles that are the bread and butter of high-energy
accelerators, cold collisions of such atoms might reveal new quantum physics,
said Dan Stamper-Kurn, assistant professor of physics at UC Berkeley and
leader of the study. Their paper was accepted for publication by Physical
Review Letters last week.

Useful Sites:
http://www.colorado.edu/physics/2000/bec/index.html
http://en.wikipedia.org/wiki/Bose-Einstein_condensate