Ultracold Atoms

JILAns Eric Cornell and Carl Wieman began their ground-breaking research in the field of ultracold matter in 1990. As described in The Wonderful World of Ultracold, this early work led to the Nobel Prize in Physics for both scientists. Today, the Institute continues its trendsetting research into ultracold atoms and molecules, seeking insights into superfluidity, superconductivity, quantum behavior control, the role of quantum processes in our everyday world, and the development of quantum devices.

Much ultracold research focuses on Bose-Einstein condensation, degenerate Fermi gases, the optical lattices formed when laser cooling causes atoms to become trapped in egg-cartonlike potential wells, and quantum simulations. JILA's ultracold research in these areas is characterized by a high degree of collaboration between experimentalists and theorists. This work is expected to offer new insights into many-body physics, the realization of exotic states of matter, superfluidity and superconductivity, the exquisite control of quantum processes, quantum computing, and the role of quantum processes in the macroscopic world. JILA scientists are actively exploring the connection between quantum mechanics and condensed matter physics, materials science, nuclear processes, and the dynamics that shape our Universe.

To enable physicists to explore uncharted territory in their quest to understand the laws that govern the Universe, James Thompson is looking for ways to use laser-cooled atoms to investigate new regimes in quantum physics. For instance, he wants to discover how to use the coherent control of cold atoms to extract more information about nature than is normally possible. Thompson uses lasers and magnetic fields to levitate atoms in vacuum and cool them to temperatures just a few millionths of a degree above absolute zero. By placing these ultracold atoms inside a high-finesse optical cavity to help control light-matter interactions, he believes he can reduce the effects of quantum noise that arises from the Heisenberg uncertainty principle. Thompson’s research impacts our understanding of how many-particle entanglement can both be generated and used as a resource.

Bose-Einstein Condensation

Seven JILA scientists investigate Bose- Einstein condensation. Eric Cornell and Deborah Jin head experimental groups engaged in these studies. Jun Ye and Dana Anderson contribute their expertise in atom optics, ultrafast optics, and precision measurement to the effort to define and understand this exotic form of matter. John Bohn, Chris Greene, Murray Holland, and Ana Maria Rey contribute theoretical analyses that help explain experimental findings and guide future investigations.

Eric Cornell and Deborah Jin are currently collaborating on an on-going investigation of strongly interacting Bose-Einstein condensates (BECs), a study that was originally initiated by Carl Wieman’s group. In 2001, Cornell and Wieman discovered one possibility for large attractive interactions: a condensate that shrinks and then explodes. Another possibility is behavior analogous to that of superfluid helium. If such dynamics were observed in strongly interacting BECs, it would help bridge the gap between the physics of superfluid liquids and ultracold atoms.

Recently, the Jin and Cornell groups charted new territory in the study of BEC. They used Feshbach physics to create a strongly interacting BEC and probe it with Bragg spectroscopy. First, the researchers changed the magnetic field around an ordinary BEC to create strong interactions among the atoms. Then they directed two red laser beams into the BEC from opposite sides of the condensate. The beams imparted energy and momentum to about 10% of the atoms. This energy and momentum then spread throughout the condensate via collisions. A picture taken of the whole condensate gave the researchers enough information to determine the BEC’s available energy and momentum states.

The Cornell and Jin groups consulted with the Bohn group to adapt theoretical descriptions of strongly interacting BECs for comparison with their experimental data. This comparison identified a need for a better theory describing the behavior of strongly interacting BECs. Older theories had ignored the tendency of strongly interacting BECs to form molecules, an assumption that appeared to be invalid in light of the new experiments. The comparison of the new experiments with theory has opened up a whole new direction in ultracold matter research. The experimentalists are currently looking for similarities between their strongly interacting BECs and superfluid liquid helium.

Theorist John Bohn has also collaborated with the Wieman, Jin, and Cornell groups to better understand the behavior of a mixture of two different rubidium isotopes during Bose-Einstein condensation. The experimentalists had observed the formation of alternating “bubbles” of 85Rb and 87Rb inside a cigar-shaped trap when repulsive interactions between the two isotopes predominated. Bohn’s group was able to simulate the formation of the bubbles and explain how the repulsive interactions of the different isotopes gave rise to the condensate bubbles.

Theorist Murray Holland conducts theoretical studies of Bose-Einstein condensation and quantum Fermi gases. He has shown that the theory of Bose-Einstein condensation is straightforward under conditions where atomic interactions are weak, but it fails rapidly as interactions strengthen. BECs with strongly interacting atoms resemble a variety of intriguing superfluids whose theoretical descriptions are complex and interesting. His research includes (1) electron resistance in strong magnetic fields at very low temperatures; (2) Fermi gas superfluidity; (3) Feshbach resonances in optical lattices; (4) resonances in systems with two or fewer dimensions, where the quantum behavior of ultracold atoms and atomic particles such as electrons in zero, one, or two dimensions is not yet well understood; and (5) atomtronics.

Holland's group has investigated whether a Bose-Einstein condensate could spontaneously escape from the trap in which it was created. The analysis explored how a many-body wave function like a BEC could theoretically tunnel out of a potential well (in a manner analogous to the escape of an atom or electron from a similar trap). The group discovered that quantum tunneling in a BEC should be observable on time scales of 10 ms to 10 s. However, even though BECs can tunnel through a potential barrier, the end result is different from that of single electrons, where the electron gets completely out of the potential well. With a BEC, three final states are possible: (1) All atoms in the BEC escape from the potential well; (2) Some atoms escape via tunneling, while others remain in the well; or (3) The entire BEC jumps over the top of the well and runs down the outside as a single ring soliton before breaking up into smaller bullets known as bright vortex solitons. The formation of the soliton(s) is high speed and violent, but entirely classical.

In an effort to discover practical applications of Bose-Einstein condensation, Dana Anderson is working on the development of an atom interferometer. His group has already completed a large and modular proof-of-concept experiment. It is an analog of the laser-based optical gyroscope used in airplane navigational systems. The atom interferometer will replace a laser with coherent atomic wave packets created and maintained in a BEC. Once it is perfected and scaled down to usable size, the atom interferometer should be three to four orders of magnitude more sensitive than its optical counterpart.

Recent work on the atom interferometer has focused on adapting the techniques of principal and independent component analysis to extract results from BEC interferometry experiments. These statistical processing techniques can rapidly determine the differential phase of the interferometer from large sets of images of interference patterns. Anderson anticipates that these tools may one day be useful for a variety of ultracold experiments.

Another practical device under development in Anderson's lab is a portable BEC system for atom chips. The system consists of an atom chip bonded to the top of a Pyrex cell with a magneto-optical trap inside. BECs of Rb atoms can be formed as fast as once every 2.65 seconds inside this tiny trap and transferred to the atom chip. The vacuum cell and pumping system for this BEC atom chip device have been miniaturized by the Anderson group without sacrifice of its performance.

The group is now working on integrating an atom Michelson interferometer into its atom-chip system and demonstrating rotation sensing. The group also plans to continue to simplify and miniaturize the ultracold atom components, with the goal of using atom-chip systems for the practical development of ultracold atom-based atomtronics devices, which mimic such semiconductor devices as diodes and transistors.

Anderson believes that the development of atomtronics as an engineering discipline will lead to robust, miniature, low-power and low-cost ultracold-atom devices for both military and civilian uses. These uses range from navigation, tunnel detection and magnetic field sensing to quantum communications, quantum information processing, and simulation of condensed-matter systems.

Degenerate Fermi Gases

Experimentalists Deborah Jin, Eric Cornell, and Jun Ye, together with theorists Murray Holland, Ana Maria Rey, and Chris Greene investigate the physics of ultracold degenerate Fermi gases. Studies are underway on the crossover region between BEC behavior, where fermion pairs form molecules, and the BCS (Bardeen-Cooper-Schrieffer) region where fermion pairs form superfluids. The characterization of this crossover region is increasingly relying on the use of Feshbach resonances. Feshbach resonances are specific values of the magnetic field where small changes in the field strength cause big changes in the behavior of the atoms in an ultracold gas. A powerful JILA collaboration is developing these resonances as tools for not only studying Fermi gases, but also BECs. The collaboration’s goal is to apply a broader understanding of Feshbach resonance physics to the investigation of antiferromagnetism, superfluidity, and Bose-Fermi interactions.

Since the mid 2000s, the Jin group has explored the link between BEC and superconductivity, which represent two ends of a continuum for quantum mechanical behavior. Since 2004, the group has studied the behavior of atoms in the BEC-BCS crossover, which is characterized by pairs of strongly interacting fermions. Changes in the magnetic field can induce these pairs to either behave more like molecules or more like Cooper pairs. The Jin group has used Feshbach resonances to characterize the crossover region and probe superfluidity in ultracold Fermi gases.

In one experiment, the Jin group investigated the velocity spread of potassium atoms throughout the continuum from BEC to superfluidity. Starting at the latter end, the researchers gradually decreased the magnetic field while monitoring changes in the velocity spread of the ultracold atoms. As shown in the figure, potassium atoms on the BCS side (the left side of the image) showed the least variation in velocity. The white, red, and yellow colors indicate a high density of atoms moving at the same velocity. By the time the researchers looked at the BCS-BEC crossover region (third from left), the atomic velocities were more spread out, with lower atom densities at one velocity, as evidenced by the green and light blue colors. Even as the atom pairs were getting much smaller, more pairs were forming. As the experimenters probed further toward the BEC end of the continuum, the velocities showed the broadest spread.

In a second experiment, the group measured the potential energy of an ultracold gas of potassium atoms in the BEC-BCS crossover and investigated the temperature dependence of this energy. An analysis of this work showed that ultracold Fermi gases made of different kinds of atoms behave consistently under similar conditions.

These experiments provided information for Murray Holland's group to evaluate the strengths and weaknesses of different crossover theories. The group has now developed a better understanding of crossover physics and a new theory that explains the quantum mechanical behavior of fermions in the crossover region. The theoretical and experimental collaboration between the Holland and Jin groups may one day help determine the quantum mechanical limits of designing high-temperature superconductors, whose properties resemble those of fermions in the crossover region.

Superfluidity

The Jin group conducts ongoing experiments to probe superfluidity in ultracold Fermi gases. The group recently took an important step towards creating superfluids of molecules whose atoms interact via p-waves. P-waves involve higher-order pairing of atoms in which the resulting molecules are rotating; such pairing contrasts with the more widely studied s-wave pairing in which the resulting molecules do not rotate. P-wave studies promise to expand the understanding of ultracold Fermi gases gained from s-wave-based studies of the BEC-BCS crossover. For instance, with p-waves, the group may be able to create a superfluid gas that involves higher-order pairing, akin to that found in superfluid helium (³He).

The group’s initial step toward creating a p-wave superfluid was the creation of p-wave pairs of fermionic potassium (⁴⁰K) atoms. The researchers used a p-wave Feshbach resonance to convert these atoms into quasi-bound p-wave K₂ molecules. By decreasing the magnetic field, they were able to change the quasi-bound molecules into real molecules. However, the p-wave molecules had a very short lifetime, posing a challenge to using them to produce fermionic p-wave condensates. The group is currently studying the interesting many-body effects of p-wave atom pairs and looking for clues of how to make a p-wave condensate.

In a related study, theorist Ana Maria Rey is exploring d-wave superfluidity in cold atoms. Her goal is the creation of superconductivity in optical lattices via a controlled preparation in smaller lattice configurations. She proposes to engineer d-wave superfluidity by first loading an array of plaquettes with cold fermions. A plaquette (shown here) is four lattice sites arranged in a square. It is the smallest system that exhibits d-wave symmetry. When loaded with four fermions, the ground state is d-wave symmetric; when loaded with only two fermions, the ground state is s-wave symmetric.

Plaquette arrays can be created via two-dimensional optical lattices. Rey suggests that a d-wave superfluid can be created by first weakly coupling d-wave symmetric plaquettes under conditions where such a superfluid could exist, and then increasing the coupling strength until the plaquettes melt. At this point the question becomes: Will the superfluid remain in the full two-dimensional lattice geometry?

In a separate approach to understanding superfluidity, the Jin group has found the first evidence of a strong experimental link between superfluidity in ultracold Fermi gases and superconductivity in metals. The group used photoemission spectroscopy, a technique that has been instrumental in revealing the properties of semiconductors, to study a strongly interacting system at the BEC-BCS crossover. At this crossover, an atom gas of ⁴⁰K became a superfluid, with nearly all the atoms paired up (one spin up and one spin down). Plus, the atom pairs were dancing in sync. The researchers sent a radio-frequency (rf) pulse into the atom cloud and turned off the laser trap holding the cloud. The low-momentum photons in the rf pulse transferred a small percentage of the atoms into another spin state. Even though these atoms were in the same place and traveling at the same velocity, they suddenly became invisible to their dance partners. The invisible dancers flew out of the trap and were easily imaged. The remaining correlated atom pairs continued to dance in sync, but in movements governed by the complicated physics of the system.

Using the energy and velocity of the escaping spin-flipped atoms, the researchers were able to determine the energy and velocity of the atoms when they were dancing in sync inside the ultracold atom cloud. In a similar fashion, condensed-matter physicists can deduce the position and velocity of surface electrons before they are knocked out by a ultraviolet (UV) photon.

The Jin group has also tested their powerful new spectroscopy tool on ultracold K2 molecules in the BCS-BEC crossover region. They found evidence of complex physics, including correlated pairing at a distance, thought to play a role in both superfluidity and superconductivity. The group is currently repeating these experiments at colder and colder temperatures to see if the new evidence holds up.

Bose-Fermi Interactions

The Jin group recently used an interspecies Feshbach resonance to induce ultracold atoms of ⁸⁷RB (bosons) and ⁴⁰K (fermions) to enter a quantum superposition of both being free atoms and being in a single, well-defined state known as a Feshbach molecule. The success of this experiment has given the group a new tool for probing the behavior of strongly interacting mixtures of bosons and fermions and the means for investigating the detailed physics of Feshbach resonances, which play a key role in Fermi gas superfluidity.

In related efforts, theorist Chris Greene is working on describing degenerate Fermi gases and BECs from the microscopic point of view. His goal is to develop and apply analytical methods to bridge the gap between the few-body physics that describes ultracold gases and condensates and the many-body physics that describes condensed-matter systems. As part of this effort, his group is investigating ultracold gases of lithium atoms, which have three spin components. The group is also analyzing strongly interacting ultracold Fermi gases to see whether there are conditions in which these gases would collapse and then explode, in a process known as a "Ferminova." The controversial Ferminova prediction is analogous to the Bosenova observed in 2001 by the Wieman group in an ultracold gas cloud of strongly interacting bosons (⁸⁵Rb atoms).

Optical Lattices

Optical lattices are potential wells created by the interference patterns of counterpropagating laser beams. These potential wells can trap neutral atoms, creating a system that resembles a crystal, with the atoms in optical lattices being analogous to electrons in solid-state crystals. Unlike naturally occurring crystals, however, these "artificial light crystals" are completely regular, without flaws. As such, they are an ideal quantum system where all parameters can be manipulated experimentally. They can be used to study effects that are difficult to observe in real crystals or other condensed matter systems.

Optical lattices are the focus of Ana Maria Rey’s research on fundamental properties of condensed matter. Her group’s goals are to use optical lattices to simulate, manipulate, and control novel states of matter such as quantum magnets, superfluids, insulators, and topological matter. Some of these states are difficult to investigate in ionic crystals or other complex condensed-matter environments, and cold atoms offer a unique laboratory for studying them. For example in cold atoms, it is possible to control the amount of disorder in a lattice and simulate (and better understand) the interplay between Anderson localization (a single particle phenomenon) and the Mott metal-insulator transition (which requires interactions between particles). In addition, Rey has begun to explore the use of alkaline earth atoms in optical lattices as quantum simulations of complex materials, such as transition metal oxides and heavy fermions, that appear in condensed matter physics.

Rey also uses artificial light crystals to probe both strongly correlated bosonic and fermionic systems and to study the generation and manipulation of entanglement in quantum systems. She plans to use quantum entanglement in precision measurement and quantum information processing. For instance, optical lattices are at the heart of Rey’s and Jun Ye’s design of a quantum computer based on Sr atoms and of Ye’s Sr-lattice optical atomic clock.

In related efforts, Deborah Jin and Murray Holland have conducted theoretical and experimental studies of optical lattices combined with Feshbach resonances. Together, they have developed new strategies for loading cold atoms into an optical lattice. Jin has used Feshbach resonances to study molecule formation in both two-dimensional and three-dimensional optical lattices and shown that a lattice enhances the efficiency of molecule production.

Holland and Rey are also modeling different aspects of the behavior of rotating optical lattices. Holland has also devised an optical-lattice-based quantum "laser" for the Sr-lattice optical atomic clock. The new device is expected to enhance the clock’s stability a hundredfold once it’s constructed in the laboratory.

Optical Atomic Clock

Since 2003, Jun Ye’s group has worked on the design, implementation, and enhancement of what is now the world’s most accurate and precise optical atomic clock based on neutral atoms. Currently, the clock neither gains nor loses a second in more than 200 million years. It is approximately three times more accurate than the nation’s primary time and frequency standard, the NIST-F1 cesium (Cs) fountain atomic clock. The new optical clock’s precision timekeeping mechanism is based on a narrow electronic transition in strontium (Sr) atoms held inside an optical lattice. Because this optical transition has a much higher frequency than the microwave clock transition in Cs, the clock has had the potential from its inception to be more accurate than the NIST-F1.

The first idea for optical atomic clocks based on neutral atoms inside optical lattices came from Hidetoshi Katori at the University of Tokyo in 2003. Ye’s group took this idea and ran with it, capitalizing on work already done in the lab on the cooling of Sr atoms. The group used high-precision spectroscopy to probe the electronic transitions in Sr, soon meeting the goal of identifying a transition that would work in the new clock.

The initial optical clock design used a variety of laser sources including a femtosecond comb and a diode laser stabilized with an optical cavity. The cavity, in turn, was locked to a narrow energy level transition in ultracold Sr atoms. The researchers soon determined that the clock transition they’d selected was not ideal for a next-generation optical atomic clock.

The group’s next step was to dream up a better scheme for the clock using a more stable electronic transition in Sr. The new design employed two lasers (and three atomic levels) to create a unique energy level transition that otherwise would not occur in nature. The new transition, which owes its existence to quantum interference, is very narrow and stable. Once the clock transition was identified, the group refined the optical lattice that would confine the Sr atoms in the new clock. The researchers created a one-dimensional “magic” wavelength optical lattice, which is a standing wave of far-infrared light. The lattice’s wavelength of 914 nm was magic because it has no net effect on the critical atomic transition at the heart of the Sr-lattice optical atomic clock.

With work on the optical lattice completed, the focus turned to the development of a superstable clock laser. As soon as the clock laser was assembled, the group built the first Sr-lattice optical clock in 2005. Within a year, the accuracy of the Sr-lattice optical atomic clock was just shy of that of the NIST-F1 Cs fountain clock. The clock team spent another year enhancing the performance of the clock.

The accuracy of the enhanced Sr-lattice clock was verified in a comparison (over a precise and accurate fiber optic link) with a comparable optical atomic clock based on neutral Ca atoms that was under development at NIST. This test confirmed that the Sr-lattice clock was more accurate than the NIST-F1 Cs fountain clock. The validation of the Sr-lattice clock’s accuracy has set the stage for another comparison – this time with the single-ion mercury optical atomic clock under development at NIST. The mercury-ion clock has thus far exhibited the highest accuracy ever measured. Preparation for this important test is ongoing.

As part of its efforts to enhance the performance of the Sr-lattice clock, the Ye group is studying the interactions among the Sr atoms themselves. The group recently identified frequency shifts in the clock caused by colliding fermions. Until these frequency shifts were measured, most physicists had assumed that there would be no such collisions when the Sr atoms were cooled to sufficiently low temperatures. This assumption was based on the laws of quantum mechanics, which mandate that identical fermions cannot get close enough to one another to actually collide.

After months of work, the researchers discovered that the interaction of their laser-based precision measurement technique with the optical lattice confining the Sr atoms was responsible for the measured frequency shifts. During measurements when a laser beam was focused on the (slightly curved) Sr atom-filled lattice, the atoms in the lattice transitioned to their excited states at slightly different rates. And, fermions in different superpositions of the ground and excited states are no longer identical; thus they can (and do) collide. The Ye group has now devised strategies to reduce, though not entirely eliminate, the number of atom-atom collisions and the resulting frequency shifts. Even so, the group still needs to improve the performance of their clock to measure up to the standard set by the mercury-ion clock. Theorist Murray Holland’s new quantum laser is critical for this performance enhancement.

The Ye group’s wildly successful implementation of the Sr lattice clock recently motivated theorist Ana Maria Rey to look for more applications of Sr and other alkaline earth atoms in optical lattices.

A New Quantum "Laser"

Theorist Murray Holland’s research has shown that the Ye group’s ultrastable laser isn’t stable enough to probe the clock transitions with the desired accuracy. To be the best it can be, the clock needs a laser that remains phase coherent a hundred times longer than the current clock laser.

Fortunately, the Holland group has come up with an innovative quantum device that can produce such long-lasting phase-coherent light — like a laser. However, the new quantum device is based on entirely different principles than a conventional laser. Its heart is a linear chain of neutral Sr atoms inside an optical lattice. The atoms will all dance in the same way exactly in phase when they are connected by a single "lasing" photon running around inside an optical cavity. As the lasing photon travels through the chain of Sr atoms, it "glues" the atoms together and locks them in phase. During this process, all the Sr atoms evolve into a coherent collective superposition of their ground and excited electronic states. This collective superposition causes each atom to oscillate like a spring, but because all the atoms are glued together, the entire chain of atoms extends and contracts in unison, as shown in the figure. This collective "superspring" loses energy by emitting coherent lasing photons, most of which exit the laser cavity.

The collective spring action of this innovative device permits the system to emit far more intense radiation than would occur with independent atoms. The collective emission is known as super-radiance. Because the new quantum device is a super-radiant system, its resulting power is about 10^-12 W, four orders of magnitude higher than if all the Sr atoms emitted their excess energy one at a time.

The power increase is just enough to make it technologically feasible for the Ye group to build the new quantum device for use with the Sr-lattice optical atomic clock. Once it’s built, the precision quantum laser will have a frequency linewidth of about .001 Hz, on the order of, or possibly even narrower than, the Sr lattice clock transition itself. Such performance, if verified in the laboratory, would improve the stability of the Sr lattice clock by at least a hundredfold.

Alkaline Earth Atoms In Optical Lattices

The precise control of cold Sr atoms achieved in the Ye group’s optical atomic clock experiments has inspired theorist Ana Maria Rey to take a closer look at new applications for fermionic alkaline earth atoms, including an investigation of their use in information processing. In addition, fermionic alkaline earth atoms, such as ⁸⁷Sr and ¹⁷¹Yb, can be loaded into optical lattices where they can be used as quantum simulators of phenomena found in condensed-matter systems.

Rey is investigating the interplay of the nuclear spin with the electronic variables in the clock states of Sr and other fermionic alkaline earth atoms. As opposed to alkali atoms, alkaline earth atoms have electronic and nuclear states that can be independently manipulated since they are not coupled by interactions between the nuclei and surrounding environments. An understanding of this interplay should open the door to a study of spin-orbital physics in the laboratory and lead to new insights into such systems as transition metal oxides and heavy fermion materials. For instance, transition metal oxides could exhibit entirely new properties such as colossal magnetoresistance, in which materials dramatically change their electrical resistance in the presence of a magnetic field. This kind of application of the rich many-body physics of alkaline earth atoms could shed light on condensed-matter systems that are not yet well understood.

Rey’s exploration of alkaline earth atoms is leading to a better understanding of quantum magnetism and superexchange interactions (spin interactions between particles, such as electrons, that occur even when the particles don’t occupy the same position in space). They are believed to play a significant role in high-temperature superconductivity. Superexchange interactions often lead to either antiferromagnetic ordering (in which the magnetic moments of adjacent atoms point in opposite directions), or ferromagnetic ordering (in which the magnetic moments of adjacent atoms point in the same direction, in spin ½ systems. Rey has already developed a proven strategy for preparing, detecting, and controlling short-range superexchange interactions in ultracold spinor bosons loaded in double-well arrays created via optical superlattices. She is now working to help experimentalists achieve the very low temperatures required for observing long-range antiferromagnetic correlations in two- or three-dimensional lattice geometry.

The control of superexchange interactions could also play an important role in the context of information processing. For instance, alkaline earth atoms have enhanced nuclear-spin symmetry (which means that if two alkaline earth atoms with different spins collide, no additional spin levels get populated as a result of the collision). This symmetry, when combined with superexchange interactions, could lead to a novel state of matter known as a chiral spin liquid that lacks magnetic order even at zero temperature. Among the possible types of chiral spin liquids there is one type in which the wave function changes by more than an overall phase upon exchange of excitations (i.e., this type exhibits non-Abelian statistics). As a result, the exchanges do not commute. Non-Abelian topological states have attracted significant attention recently because they could, in principle, be used for topologically protected quantum computation. Non-Abelian states can also exhibit such exotic properties as anyon excitations and fractional statistics. Anyons are two-dimensional (2D) particles with properties in between those of bosons and fermions, and fractional statistics are precise quantum mechanical descriptions of 2D states.

Physicists have looked for spin-liquid and non-Abelian behavior in condensed-matter systems, but have never seen it. Rey and her collaborators at CU (Michael Hemerle and Victor Gurarie) believe that alkaline earth atoms in an optical lattice are an ideal system for observing Abelian and non-Abelian chiral spin liquids for the first time.

Rotating Optical Lattices

Rotating BECs create vortices; the faster they spin, the greater the number of vortices. As more and more vortices appear, they arrange themselves into a crystal-like lattice structure. Eric Cornell has demonstrated these effects in the laboratory. He has also shown that condensates in a vortex array communicate with one another when atoms tunnel from one BEC to another. This tunneling somehow keeps all the BECs in the lattice coherent. However, this coherence can be destroyed by warmer temperatures, for reasons that are not yet understood at the fundamental level. Cornell wonders whether the observed temperature dependence of vortex formation takes place in the nebulous transition between the small, ultracold world where the laws of quantum mechanics predominate and the larger world explained by classical physics. The answer to this question awaits a new theory to explain atom-condensate collisions.

Theorists Murray Holland and Ana Maria Rey have undertaken a long-term project to model rapidly rotating vortices. Rey recently studied ways to generate macroscopic superpositions of BECs with opposite circulations in rotating-ring superlattices. In her work, she has found that because of their weak coupling to their environment and the ease with which they can be controlled, cold atoms in an optical lattice are ideal systems for generating macroscopic quantum superpositions and "cat" states. In quantum computing, cat states (named after Schrödinger’s cat) are special states in which extremely different qubits are in an equal superposition.

The Holland group has been focusing on the effect of the speed of rotation on rotating optical lattices. Holland says that, in principle, if the vortices rotate fast enough, the lattice could become unstable and melt. But before that can happen, his new theory predicts that the physics of the system will change dramatically as electrons are shorn from neutral atoms, creating a 2D highly correlated "sea" of electrons. This strongly correlated state would neither be a solid, nor a liquid, nor a gas. Though sometimes referred to as an "electron gas" in condensed-matter physics, this highly correlated state would actually be a new state of matter.

Electrons likely become strongly correlated in condensed-matter systems. However, from a theoretical point of view, correlated electrons are much easier to study in an optical lattice. There, experimentalists could control the efficiency of electron interactions by varying the strength of the optical lattice. If strongly correlated interactions actually develop in rapidly rotating BECs, then evidence of them should emerge in experiments. At present, however, there are significant technical barriers to such experiments that appear to be quite challenging to overcome.

Holland says that once these challenges are met, experimentalists should be able to see some very interesting physics in a strongly correlated ultracold system, including the observation of anyons, which are predicted to appear in strongly correlated 2D systems. Anyons are sort of a cross between the neighborly bosons, which can occupy the same quantum state at ultracold temperatures and the less friendly fermions, no two of which can occupy the same quantum state at ultracold temperatures. Anyons alternately take on characteristics of bosons or fermions, neither of which can exist as a separate particle in a strongly correlated 2D system.

Holland is currently exploring the relationship between electron behavior in cold-atom vortices and in condensed-matter systems.

Quantum Simulations

Ultracold atoms and molecules are an excellent model system for the study of quantum mechanics and systems in which the laws of quantum mechanics prevail. Ultracold atomic and molecular gases are much larger than nanoscale systems, making them easier to study. In Bose-Einstein condensates, for example, thousands of atoms collapse into a single one millimeter wave that is big enough for the eye to see. Degenerate Fermi gases, whose behaviors are entirely quantum mechanical, are large enough to see with an optical microscope, as are optical lattices. Optical lattices each contain a single large ultracold atom or molecule, with spacing between lattice sites on the order of 500–1000 nm. JILA scientists Eric Cornell, Jun Ye, Dana Anderson, and Deborah Jin study these systems to observe quantum behavior in action. Their insights promise to shed light on the behavior of electrons passing through the switch region of tiny transistors as well as on the dynamics of nanoscale biomolecules, materials, and electronic devices.

The study of ultracold atoms and molecules at JILA has already led to important theoretical insights into quantum computing and atomtronics devices, which are cold-atom analogs of such well-known electronics devices as batteries, wires, circuits, diodes, and transistors.

An Innovative Quantum Computer

Jun Ye and Ana Maria Rey are collaborating with Professor Peter Zoller at the Universität Innsbruck and scientists at Harvard University on developing a comprehensive theoretical framework for an optical-lattice quantum computer based on alkaline earth metals such as Sr. This choice dovetails with expertise already found in the Ye experimental group. During the development of the Sr-lattice optical atomic clock, for example, the group explored many aspects of neutral Sr atoms, including their cooling, electronic transitions, and behavior in an optical lattice. This deep understanding of lattice-based neutral Sr atoms is informing the collaborative theoretical studies. Thus far the "information-processing" collaboration has proposed solutions for the key problems of storing, addressing, and transporting qubits (information encoded on the nuclear spins of Sr atoms). It has also put forward the advantages of a computer design that would use (1) local processors (i.e., quantum registers) for maintaining coherence and (2) qubit-state-controlled quantum gates for managing communications between qubits.

Storage and Transport

Rey, Ye, and their colleagues have figured out how a Sr-based quantum computer could store qubits and have come up with a plan for communicating with individual atoms. They have also worked out a scheme for selecting a single atom, moving it to another location in an optical lattice to interact with another qubit, and then moving it back, all under coherent control. These solutions required two specially engineered optical lattices that specifically address the interactions of the Sr atoms with the trapping laser light.

The computer’s optical lattices would be created from two separate wavelengths of red light, both of which are long lived. One wavelength (689.2 nm) has no net effect on Sr atoms in their ground state, while the other (627 nm) has no net effect on Sr atoms in their electronically excited, but metastable, state. The 689.2 nm lattice would be the qubit "transport" lattice, and the 627 nm lattice would be the qubit "storage" lattice. The storage lattice would hold the qubits in their ground state. When a specific qubit (i.e., atom) needed to be transported, it could be excited with laser light into its metastable state and loaded into the 689.2 nm transport lattice, where its motion could be precisely controlled (again with laser light).

The system works because the electronic structure of Sr atoms allows the atoms to store and hide stable, coherent information. Because Sr atoms have two valence electrons, both their ground and metastable states are minimally affected by external magnetic fields. This insensitivity means that the robust nuclear spins of Sr atoms can form long-lasting qubits. Equally importantly, a third electronically excited state has a high sensitivity to magnetic fields. That means magnetic fields could be used to select a specific atom from the transport lattice for operations!

This is where the precision Sr atomic clock laser comes into the picture. The clock laser makes it possible to precisely detect, measure, or manipulate atoms in both the storage and transport lattices. The beauty of this laser is that it can accurately address one or more individual frequencies encoded on the qubits in the storage lattice, and, with the help of the third electronic state, transfer only those particular qubits into the transport lattice.

Coherence

Rey’s quantum computer theory offers a novel solution for maintaining coherence in an information-processing device. Rather than constantly monitoring and attempting to keep all the atoms in the computer resonantly coherent, her formulation would build the computer out of local processors, or quantum registers. In this formulation, each register would be a single Sr atom. However, the quantum register would consist of both the atom’s electronic transitions, which would function as communications qubits, and its nuclear spin states, which would store information. As one or more quantum registers performed the same calculation, they would need to remain coherent. However, the entire computer would not need to be in sync with them. The only circumstance in which every Sr atom (quantum register) would have to be in sync is one in which every quantum register were required for a particularly complex operation. Whether one, two, or many quantum registers were working together on a computation, the communications qubits would be responsible for maintaining coherence. This task is relatively simple within one atom. However, communication between two or more atoms requires a way for just the right atoms to become entangled. In other words, the computer requires quantum phase gates.

Entanglement

The new quantum computer requires entangled states for both communication and computation. Entanglement occurs when the quantum states of two or more atoms become linked together. A key challenge for Rey and Ye is the design of robust methods for not only generating entanglement between two specific atoms, but also developing methods to maintain entangled states for as long as they are required. Rey has already proposed a design that protects entangled states from local decoherence processes. She has used it for generating robust optical coherent states in optical lattices and trapped ions.

Computations

The movement of the storage and transport lattice relative to one another allows the computer to perform calculations with information retrieved by the clock laser from different parts of the storage lattice. Calculations are performed via quantum-gate operations, in which two atoms interact by becoming entangled in a single lattice site. Once the calculation is complete, the clock laser dumps the qubits back into the storage lattice.

Quantum Phase Gates

Quantum phase gates consist of double quantum wells, with Sr atoms on either side. Only atoms in the ground state with opposite spins can tunnel to the other side of the well and get entangled with the atom on the other side. This entanglement is only through the electronic degrees of freedom. The process doesn’t disturb the nuclear-spin linked qubits because only communications qubits (i.e., the electronic transitions) are sharing information. Thus communication between two atoms in a single lattice site does not result in the loss of any information; nor would it disturb the coherence of the computer in any way. Equally importantly, atoms not needed for a particular calculation would be unable to pass through the quantum gate.

A two-qubit gate, combined with single qubit rotations, is sufficient to perform a universal quantum computation. Single qubit rotations would be controlled by precision lasers capable of detecting and changing the state of any ground-state atom. The lasers would also manage communication between atoms by rotating the nuclear spin of a ground-state atom into a spin that allows it to tunnel through a quantum gate. The ability to control communication, together with the ability to measure and control the states of individual Sr atoms, are essential ingredients in the new quantum computer theory.

Recently, Rey and her collaborators did a theoretical study of using cold polar molecules to implement a controlled phase gate. The molecules could be in either 1D or 2D optical lattices, or they could become ordered in a crystalline structure because of long-range dipole interactions (a phenomenon known as a Wigner crystal). The two-dimensional systems appeared to offer better fidelity. Fidelity is also enhanced by the induction of a dipole moment in the ground and excited states of the molecules. So long as major sources of decoherence (i.e., nonsymmetric interactions and phonon dispersion in Wigner crystals) were adequately addressed, the system appears to be feasible for use in optical quantum information processing.

Atomtronics

Experimental physicist Dana Anderson and theorist Murray Holland are exploring ideas for "atomtronics" devices, which are cold-atom analogs of batteries, currents, resistors, transistors, and, eventually, amplifiers, oscillators, and logic gates. In theory, such devices have important theoretical advantages over conventional semiconductor-based electronics, including (1) superfluidity and superconductivity, (2) minimal thermal noise and instability, and (3) coherent flow. These characteristics suggest they could play important roles in quantum computing, nanoscale amplifiers, and precision sensors.

Atomtronics devices are based on strongly interacting ultracold Bose atomic gases in optical lattices. Here, light beams create and control currents made of flowing ultracold atoms. Anderson and Holland believe they can use such a current of atoms to build a host of electronics analogs, including batteries, circuits, diodes, amplifiers, and transistors. Eventually these atomtronics parts could be combined into an atomtronics computer. The circuits of such a computer would literally materialize as needed, made from little more than beams of light travelling through egg-carton-shaped wells of ultracold gas (optical lattices). Such a computer’s parts would be quite flexible, with the ability to reconfigure from data processing to data storage in response to a simple command. However, there is one major challenge for the design and operation of this amazing computer: It would have to operate at temperatures of just a few millionths of a degree above absolute zero.

Such incredibly low temperatures would confer unheard advantages on an atomtronics computer. For instance, magnetic fields could be used to tune the amount of force felt between atoms in the circuits, increasing either their repulsion or attraction. At the turn of a dial, researchers could turn an ultracold material made of light and atoms from a metal into an insulator — or even into a semiconductor. And, once you’ve made an ultracold semiconductor, you’re on the way to making ultracold atom analogs of electrical components. Holland has described how this works for batteries, circuits, diodes, and transistors.

In his scheme, a battery’s negative terminal would consist of a dense cloud of ultracold atoms trapped by laser beams. The positive terminal would consist of an optical trap, created by identical laser beams, but without the ultracold gas. This difference in atom density creates a chemical potential, analogous to the electrical potential created inside a battery. If the optical lattices holding the terminals of the battery are connected by a waveguide or series of empty wells in optical lattices, the "wires" will allow atoms to flow from a lattice site with lots of atoms to another with just a few atoms. For example, if the "wire" connecting the terminals is an optical lattice containing many empty wells, current flow will depend on the repulsive interactions inside the ultracold atom cloud in the negative terminal. As these interactions grow stronger, some atoms will tunnel into the wire and "hop" along the wire (by tunneling from well to well) all the way to the positive terminal of the battery. The depth of the wells determines how fast the "current" of atoms will travel. Shallower wells allow the atoms to tunnel through the wire faster. In contrast, increasing the height of an optical lattice slows atom currents.

The ability to control the current by raising or lowering the height of an optical lattice in a "wire" is analogous to a variable resistor in an electronic circuit. However, higher lattices don’t dissipate heat and cause power loss as do resistors. In addition, precisely adjusting the height of adjacent optical lattice sites and changing the number of atoms in those sites can create a "diode", which allows current flow in only one direction. In the most recent iteration of an atomtronics diode, Holland’s team exposes half of the wells in its optical lattice array to laser light of a slightly different frequency. This slight shift in energy is sufficient to keep the atoms flowing in one direction. Atoms at the high-energy end of the wire can easily tunnel through that region and continue along the wire even when they reach the low-energy region. However, current flow can’t happen in the opposite direction. Atoms starting at the low-energy end of the wire don’t have enough oomph to make the leap to the high-energy region. When the atoms fill up the low-energy half of the lattice, current flow stops. These atomtronics diodes are analogous to semiconductor diodes created by adjoining n-type and p-type semiconductors.

By aligning two atomtronics diodes back to back, one can make a simple atomtronics transistor. Although this transistor would be able to control a large current flow with a small current, it would also create a large negative gain. For this reason, Holland and his group have proposed a different design that uses three traps containing BECs in three spatially separated potential energy wells created with optical lattices. The wells (traps) are (1) a source well, (2) a gate well, and (3) a drain well, as shown in the figure. When the traps are brought close enough together to interact, the atoms in the source well can tunnel to the drain well only when the chemical potential of the gate well is roughly equal to that of the other two wells. Placing atoms in the gate well tunes its chemical potential.

Like its electronic counterpart, this transistor shows "switching" behavior; the ratio between the atoms in the drain and gate (i.e., the gain) becomes large only when a threshold number of atoms have accumulated in the gate well. This threshold value can also be changed by altering the steepness of the gate well and the phase of the BEC in the gate well. This more sophisticated atomtronics transistor can be used to amplify weak atomic signals.

Because atomtronics transistors would be the building blocks of different kinds of logic gates, it should be possible to assemble computer memory or microprocessor chips from atomtronics devices. In principle, one could build a complete ultracold computer from nothing more than light beams and atoms. Of course, an atomtronics computer would likely run more slowly than a counterpart based on electrons; atoms are not only heavier than electrons, but also move very slowly at ultracold temperatures.

Even so, the Holland group plans to build on the theoretical analysis of atomtronics devices with the development of a more complex theory of atomtronics and more straightforward calculation methods. In the meantime, Anderson is already exploring the implementation of atomtronics devices with miniature atom-chip devices. He believes that the inherently quantum mechanical nature of the BECs makes the devices incorporating them fundamentally interesting.