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Ultracold Atoms

Control of Single Neutral Atoms

The Cindy Regal group has developed a technique for preparing a single cold rubidium atom (87Rb) in its quantum-mechanical ground state. Such atoms can be arbitrarily manipulated for investigations of quantum simulation and quantum logic gates for future high-speed computers.

The process of trapping a single 87Rb atom begins with capturing a gas of approximately 1 million of these atoms. Then, the cloud is illuminated with a tightly focused beam of laser light that creates a tiny micro-sized trap called an optical tweezer. This process loads approximately 10 atoms into the tweezer.

However, when the atoms are illuminated inside the tweezer, they repeatedly collide, forming molecules, which are lost from the trap. If there was originally an even number of atoms in trap, then all the atoms escape as molecules. But, with an odd numbers of atoms, a single atom is left in the trap. This atom can then be detected and cooled to its quantum ground state.

This capability opened up a new field of research. The Regal group began working on trapping multiple single 87Rb atoms in optical tweezers to see if it is possible to observe quantum tunneling between different tweezers. Quantum tunneling is a phenomenon in which a tiny particle, such as an atom or electron, flows through an energy barrier that it would not be able to surmount according to the laws of classical physics.

The group recently observed tunneling between two optical tweezers (each containing a single 87Rb atom)—if the tweezers were brought close enough together for the atoms' wave functions to slightly overlap (~600 nm). Interestingly, tunneling resulted in both atoms unpredictably appearing in one or the other tweezer. After the experiment started, single atoms rarely reappeared as one atom in each of the tweezers! The group deduced that in a superposition of the wavefunctions of one atom in each tweezer, the wavefunctions interfered destructively, making that outcome improbable. 

In related work, the Regal group has started a project in collaboration with the Ana Maria Rey theory group to explore using laser light to create an effective magnetic field around a set of four single-trapped neutral atoms. The researchers want to see whether such a setup would allow individual atoms to move from one tweezer to another. The Rey group is also working with John Bollinger at NIST on a similar experiment with single-trapped ions.

In the future, single cold atoms may be placed near complicated optical patterns near surface such as a chip destined for a quantum computer. This placement should be possible because neutral atoms do not usually interact with their surroundings as do charged ions, which were the first single particles to be cooled and trapped.

Fundamental Techniques

Bose Einstein Condensation

Eric Cornell and former JILAn Carl Wieman began seminal 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.

JILA's ultracold research 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, quantum simulation, 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.

Seven JILA scientists investigate Bose-Einstein condensation (BEC). 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, Murray Holland, and Ana Maria Rey contribute theoretical analyses that help explain experimental findings and guide future investigations.

The Eric Cornell and Deborah Jin groups collaborate on on-going investigations of strongly interacting BECs. Recently they met the challenge of creating and characterizing an extremely strongly interacting BEC. Strongly interacting means the atoms act if they were puffed up in size until they rubbed against and slid by one another, just like molecules do in liquid water. In other words, the new strong interactions changed a quantum gas of 85Rb atoms into a quantum liquid. Thus, quantum liquids with controllable interactions have become a fascinating new field of study.

Before making a quantum liquid, the two groups charted new territory by using Feshbach physics to create a relatively strongly interacting BEC and probe it with Bragg spectroscopy. They consulted with the John 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. The comparison of experiments with theory has opened up a whole new direction in ultracold matter research.

For example, the two groups discovered irrefutable evidence for the contact in a BEC. Like pressure, volume, and temperature, the contact is an important property of ensembles of atoms. The contact is particularly important when the atoms interact with each other, since the contact is a measure of how likely it is that an atom in an ensemble is having a close encounter with another atom.

The contact had been predicted by Shina Tan of Georgia Tech in 2005 and seen experimentally in an ultracold gas of fermions by the Jin group in 2008. Since the contact hadn’t been predicted in a BEC, its discovery has stimulated research into strongly interacting BECs. In the process of finding the contact, the two groups also developed a fast, radio frequency-based contact spectroscopy for probing strongly interacting quantum gases. Contact spectroscopy promises to be a useful tool for the exploration of ultra cold quantum gases and liquids. The Jin and Cornell groups are using it to investigate BECs with even stronger interactions. 

The John Bohn and Murray Holland groups conduct theoretical studies of BEC and quantum Fermi gases. Bohn specializes in the study of magnetic atoms and polar molecules with dipole moments. For example, the Bohn group has investigated rotons in BECs. A roton is a strange type of quasi particle formed when strongly magnetic atoms or dipolar molecules come together and act like a different kind of particle. The roton is like a sound wave, with regions of low and high density. Its relationship between its wavelength is strange, however. When a roton’s wavelength gets small enough, its frequency stops growing; in fact it gets smaller. The onset of this oddball phenomenon coincides with the appearance of ripples associated with the drag on a laser probe as it traverses a dipolar BEC. A wide probe will also create vortices in the BEC. The Bohn group discovered that the orientation of dipoles in a superfluid determines whether a roton appears at all! Thus, ultracold superfluids consisting of dipolar atoms or molecules are not necessarily uniform in all directions. This work is leading to new studies on BECs made from more strongly interacting dipoles.

For his part, Holland has shown that 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 ultra cold atoms and atomic particles such as electrons in zero, one, or two dimensions is not yet well understood; and (5) atomtronics.

In an effort to discover practical applications of Bose-Einstein condensation, the Dana Anderson group has developed an atom interferometer and 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.

In one interferometer-related experiment, the Anderson and Cornell groups employed a model-free analysis technique to extract results from interferometry experiments on BECs. Statistical processing techniques were able to pinpoint correlations in large image sets, helping the researchers to uncover unbiased experimental results. By looking for correlations and relationships between pixels in a series of images, the researchers were able to “see” changes in the overall number of atoms, changes in three peaks in a momentum distribution, and changes in the fraction of atoms in the primary experimental signal.
The Anderson group is also working on second practical device that is in commercialization: a portable BEC system for atom chips. The complete working system easily fits on an average-sized rolling cart. Portable BEC technology has opened the door to using ultracold matter in gravity sensors, atomic clocks, inertial sensors, electric- and magnetic-field sensing as well as in space.

Key components of the new system include a two-chamber vacuum cell and an innovative chip design. The new vacuum cell was under development for more than a decade. The new, ultrahigh quality vacuum cell is 10–20 times smaller than its conventional counter parts. The now standardized cell also serves as the platform for the atom chip where the BECs are made.
The innovative atom chip was developed in a five-year collaboration between the Anderson group and CU’s Department of Mechanical Engineering, Teledyne Technologies, Inc., the Sarnoff Corporation, and Vescent Photonics. Although the collaboration’s microchip was not the first to incorporate a BEC, it makes a BEC faster than any comparable technology in the world.
In the portable system, the atom chip is 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 were miniaturized without sacrificing performance.

Degenerate Fermi Gases

Experimentalists Deborah Jin, Eric Cornell, and Jun Ye, together with theorists Murray Holland, and Ana Maria Rey investigate the physics of ultra cold 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 relies 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 ultra cold 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 anti ferromagnetism, superfluidity, and Bose-Fermi interactions. For instance, Ana Maria Rey is seeking a better understanding of the formation of Feshbach molecules in an optical lattice. She is working with professors from the University of Colorado to investigate the problem from the perspectives of both condensed-matter and atomic physics. Rey and her colleagues have developed a simple model that sheds light on the fundamental physics of the quantum behavior of sermonic atoms in a lattice in the presence of a Feshbach resonance.
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. 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 ultra cold Fermi gases.

In one experiment, the Jin group investigated the velocity spread of potassium atoms throughout the continuum from BEC to superfluidity. 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.

The Jin group introduced the technique of atom photoemission spectroscopy in 2008 to study a strongly interacting ultracold gas of 40K atoms in the crossover region. In this experiment, the researchers discovered an energy gap in their superfluid gas. The atom gas was filled with atom pairs dancing in sync even though they didn’t actually form molecules. The energy gap corresponded to the minimum energy required to break apart atoms back into single atoms. Its presence meant that researchers would have to add enough energy to the system to break apart the dancing pairs before it would be possible to excite either atom of a pair.

The original experiment was conducted at a temperature known as Tc, which is the point at which a superfluid forms. Theory predicted that atom pairs would act in sync below Tc, creating the energy gap. However, the same theory predicted that above Tc, no atom pairs would form and, thus, no energy gap would exist.

Interestingly, the prediction of the disappearance of the gap held true for all superconducting materials except high-temperature superconductors. There, researchers do see a gap above Tc. So, the researchers decided to see what would happen to the gap in an ultracold gas of 40K above Tc. And, sure enough, they observed a gap!

These results raised the question of what is similar about high-temperature superconductors and strongly interacting superfluid gases.

The degenerate Fermi gas 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.

In 2012, theorist Ana Maria Rey’s group investigated entanglement of quantum spin states in an ultracold gas of fermions. A recent study upended the conventional wisdom that it would take carefully tailored measurements or control schemes to entangle the quantum spin states of hundreds or thousands of atoms in an ultracold gas. The group discovered that entanglement evolves naturally in a gas of reactive fermions at relatively “warm” micro-Kelvin temperatures. Once the temperature rises to the point where fermions collide and react in pairs, atoms or molecules that don’t get knocked out of the experiment will be left entangled. These particles lose their individual identities as a result of being unable to collide. Fermions that behave this way include strontium (Sr) and ytterbium (Yb) atoms, which are used in atomic clocks, and molecules such as potassium-rubidium (KRb), which are used in JILA cold-molecule experiments.

In 2012, members of the Jin experimental group found a way to measure (for the first time) a type of abstract “surface” in a gas of ultracold atoms. Known as the Fermi surface, this boundary had been predicted in 1926 by Enrico Fermi and Paul Dirac, but not previously observed. Since then, physicists were unable to see the Fermi surface by looking at the speeds of a bunch of fermions. One difficult was that interactions between fermions wash out the Fermi Surface in systems other than ultracold gases.

However, confining ultracold gas clouds with light and magnetic fields causes variations in density in different parts of the cloud. These density variations wash out the sharp Fermi surface when the speed distributions are averaged over an entire ultracold gas cloud. To see the surface experimentally, the Jin group used two perpendicular laser beams to probe just the atoms near the center of an ultracold Fermi gas. The density inside the tiny “box” was uniform enough to reveal the Fermi surface in a speed distribution. Its location and sharpness allowed the researchers to determine both the average density and the temperature of the fermions inside the box.

The Jin group also conducts experiments probing superfluidity in ultracold Fermi gases. The group 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).

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 an 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.

Optical Lattices

Optical lattices consist of potential-energy wells created by the interference patterns of counterpropagating laser beams. Lattices can trap neutral atoms when particles begin flipping back and forth in response to the oscillating electric field of the lasers. They create 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 make it possible to study the motions of atoms in exquisite detail. They make it possible to explore chemical reactions in just one or two dimensions. They are also the basis for the neutral strontium optical atomic clock and the quantum simulator, which are both under development in the Ye labs.

Optical lattices are the focus of Ana Maria Rey group’s research on the 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,Rey has begun to explore the use of alkaline earth atoms, polar molecules, and trapped ions in optical lattices as quantum simulators of complex materials such as heavy fermions and transition metal oxides.

Transition metal oxides are predicted to exhibit entirely new properties such as colossal magnetoresistance, in which materials dramatically change their electrical resistance in the presence of a magnetic field. For their part, heavy fermion materials are metallic compounds in which, at low temperatures, conduction electrons behave as if their masses were a thousand times greater than normal because of strong interaction effects. To better understand heavy fermions, Rey is working on a way to simulate a condensed-matter model known as the Kondo lattice model, which is believed to be the simplest model that describes heavy fermion behavior. The simulation uses alkaline-earth atoms in two different electronic states that can experience different lattice potentials.
The Rey group is also interested in using artificial light crystals to study the generation and manipulation of entanglement in quantum systems. Rey is using her increasing understanding of quantum entanglement in optical lattices to help guide experiments in precision measurement and quantum information processing. For instance, optical lattices are at the heart of her and Jun Ye’s design of a quantum computer based on Sr atoms and of Ye’s Sr-lattice optical atomic clock.

In a related effort, 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.

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 fermonic alkaline earth atoms, including an investigation of their use in information processing. 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 such as liquids and solids.

Rey is investigating the interplay of the nuclear spin with two long-lived electronic states (or clock states) of Sr and other fermonic 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 as in many other kinds of atoms. 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 quantum magnetism.

An understanding of quantum magnetism and the super-exchange interactions that frequently give rise to quantum magnetism is at the heart of modern quantum science. Superexchange interactions are spin interactions between particles, such as electrons, that occur even when the particles don’t occupy the same position in space. The interactions are believed to play a significant role in high-temperature superconductivity. The control of super exchange interactions could also play an important role in the context of quantum information processing.

Rey, in collaboration with her colleagues, has developed a strategy for preparing, detecting, and controlling short-range super exchange interactions in an ultracold Bose gas loaded in arrays created via optical superlattices. She is now working on best ways to use alkaline earth atoms to achieve the very low temperatures required to observe long-range antiferromagnetic correlations in one, two- and three-dimensional lattices. Antiferromagnetic correlations appear when the spins of electrons in atoms in one part of a lattice become aligned in a regular pattern with neighboring spins (in a different part of the lattice) pointing in opposite directions.

Rey’s exploration of alkaline earth atoms is leading to a better understanding of quantum magnetism. Alkaline earth atoms can have a large nuclear spin. This spin can come in as many as 10 flavors. So many spin flavors make it more interesting to study quantum magnetism and the exotic states of matter that arise because of the competition between magnetic ordering and the frustration of this ordering due to particle interactions inside a lattice.
The Rey group has a predicted that many spin flavors can help to reach colder temperatures than the ones currently reachable with only two flavors. This theoretical prediction suggests that before too long, highly controlled alkaline-earth atoms may be cooled down below nano-Kelvin temperatures. At such temperatures, it should be possible to directly observe quantum magnetism and study spin ordering. It may also be possible to create antiferromagnets and spin liquids. In antiferromagnets, random magnetic flavors assume their preferred directions at temperatures below 1 nK. Spin liquids occur when interactions or geometrical factors frustrate the antiferromagnetic order, causing it to “melt.” In the resulting spin liquid, spins can fluctuate through different states even near a temperature of absolute zero! Spin liquid states have been long sought in condensed matter materials, but so far never found.

As a result of this and other theory work on alkaline earth atoms and quantum magnetism, the Rey group hopes to soon see a laboratory demonstration of a spin liquid of alkaline earth atoms. 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 spin liquids for the first time. And, the application of the rich many-body physics of alkaline earth atoms may one day shed light on condensed-matter systems that are not yet well understood.

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 temperature, 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, ultra cold 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 vortex generation via mechanical rotation of an atomic cloud  or with laser light. (Light can also mimic the effect of rotation.) Rey has studied ways to generate superpositions of BECs with opposite circulations in rotating-ring superlattices. In her work, she 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 quantum superpositions or "cat" states.  Cat states (named after Schrödinger’s cat) are special entangled states in which a large number of particles can be in a quantum superposition of two different states at the same time.

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.


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 traveling 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. 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.

In a closely related effort, the groups of Ana Maria Rey, Murray Holland, and Dana Anderson have teamed up to understand how to implement the photo refractive effect, which occurs in some crystals that change their refractive index in response to light. This effect is a key process in holography, a long-standing interest of Anderson. The team wants to implement holography with cold atoms in an optical lattice. The project started with Anderson’s vision of doing quantum signal processing with atoms. A natural candidate for making this idea work is an optical lattice, the physics of which is one of Rey’s specialties.

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