Cold Atoms Physics

Space-based experiments today can uniquely address important questions related to the fundamental laws of Nature. In particular, high-accuracy physics experiments in space can test relativistic gravity and probe the physics beyond the Standard Model; they can perform direct detection of gravitational waves and are naturally suited for precision investigations in cosmology and astroparticle physics. In addition, atomic physics has recently shown substantial progress in the development of optical clocks and atom interferometers. If placed in space, these instruments could turn into powerful high-resolution quantum sensors greatly benefiting fundamental physics. We discuss the current status of space-based research in fundamental physics, its discovery potential, and its importance for modern science. We offer a set of recommendations to be considered by the upcoming National Academy of Sciences' Decadal Survey in Astronomy and Astrophysics. In our opinion, the Decadal Survey shoul...

Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency standards. Accurate polarizabilities for the group I and II atoms and ions of the periodic table have recently become available by a variety of techniques. These include refined many-body perturbation theory and coupled-cluster calculations sometimes combined with precise experimental data for selected transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index measurements in microwave cavities, ab initio calculations of atomic structures using explicitly correlated wave functions, interferometry with atom beams, and velocity changes of laser cooled atoms induced by an electric field. This review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.

The term 'laser cooling' is applied to the use of optical means to cool the motional energies of either atoms and molecules, or micromirrors. In the literature, these two strands are kept largely separate; both, however suffer from severe limitations. Laser cooling of atoms and molecules largely relies on the internal level structure of the species being cooled. As a result, only a small number of elements and a tiny number of molecules can be cooled this way. In the case of micromirrors, the problem lies in the engineering of micromirrors that need to satisfy a large number of constraints-these include a high mechanical Q-factor, high reflectivity and very good optical quality, weak coupling to the substrate, etc.-in order to enable efficient cooling.

We study the dynamical localization of cold atoms in Fermi accelerator both in position space and in momentum space. We report the role of classical phase space in the development of dynamical localization phenomenon. We provide set of experimentally assessable parameters to perform this work in laboratory.

We investigate the interplay dynamics of a cavity QED system, where the two-level atoms are trapped in a
double-well potential, and the cavity mode, with a frequency largely detuned from the atomic level splitting, is
driven by a probe laser. The interaction between the center-of-mass motion of the atoms and the cavity mode
is induced by the position-dependent atom-field coupling. The dynamics of the system is characterized by two
distinct time scales, the inverse of the atomic interwell tunneling rate and the inverse of the cavity loss rate.
The system shows drastically different
quasisteady behaviors in the short- and long-time intervals, and the
detection of the statistics of atom number distribution from the transmission spectra is available only in the
short-time interval.

Since the first atom interferometry experiments in 1991, measurements of rotation through the Sagnac effect in open-area atom interferometers has been studied. These studies have demonstrated very high sensitivity which can compete with state-of-the-art optical Sagnac interferometers. Since the early 2000s, these developments have been motivated by possible applications in inertial guidance and geophysics. Most matter-wave interferometers that have been investigated
since then are based on two-photon Raman transitions for the manipulation of atomic wave packets. Results from the two most studied configurations, a space-domain interferometer
with atomic beams and a time-domain interferometer with cold atoms, are presented and compared. Finally, the latest generation of cold atom interferometers and their preliminary results are presented.

We introduce novel schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in [Phys. Rev. Lett. 98, 220503 (2007), quant-ph/0609149]. Our method makes use of tools from many-body physics -matrix product states, finitely correlated states or projected entangled pairs states -to show how measurements on entangled states can be viewed as processing quantum information. This work hence constitutes an instance where a quantum information problem -how to realize quantum computation -was approached using tools from many-body theory and not vice versa. We give a more detailed description of the setting, and present a large number of new examples. We find novel computational schemes, which differ from the original one-way computer for example in the way the randomness of measurement outcomes is handled. Also, schemes are presented where the logical qubits are no longer strictly localized on the resource state. Notably, we find a great flexibility in the properties of the universal resource states: They may for example exhibit non-vanishing long-range correlation functions or be locally arbitrarily close to a pure state. We discuss variants of Kitaev's toric code states as universal resources, and contrast this with situations where they can be efficiently classically simulated. This framework opens up a way of thinking of tailoring resource states to specific physical systems, such as cold atoms in optical lattices or linear optical systems.

We demonstrate a combined magneto-optical trap and imaging system that is suitable for the investigation of cold atoms near surfaces. In particular, we are able to trap atoms close to optically scattering surfaces and to image them with an excellent signal-to-noise ratio. We also demonstrate a simple magneto-optical atom cloud launching method. We anticipate that this system will be useful for a range of experimental studies of novel atom-surface interactions and atom trap miniaturization.

We present a new experimental system (the "atom-optics billiard") and demonstrate chaotic and regular dynamics of cold, optically trapped atoms. We show that the softness of the walls and additional optical potentials can be used to manipulate the structure of phase space.

We investigate the feasibility of simulating different model Hamiltonians used in high-temperature superconductivity. We briefly discuss the most common models and then focus on the simulation of the so-called t-J-U Hamiltonian using ultra-cold atoms in optical lattices. For this purpose, previous simulation schemes to realize the spin interaction term J are extended. We especially overcome the condition of a filling factor of exactly one, which otherwise would restrict the phase of the simulated system to a Mott-insulator. Using ultra-cold atoms in optical lattices allows simulation of the discussed models for a very wide range of parameters. The time needed to simulate the Hamiltonian is estimated and the accuracy of the simulation process is numerically investigated for small systems.

Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing topological insulators, known as quantum Hall states, violated time-reversal symmetry. However, the discovery of the quantum spin Hall effect demonstrated the existence of novel topological states not rooted in time-reversal violations. Here, we lay out an experiment to realize time-reversal topological insulators in ultra-cold atomic gases subjected to synthetic gauge fields in the near-field of an atom-chip. In particular, we introduce a feasible scheme to engineer sharp boundaries where the "edge states" are localized. Besides, this multi-band system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Due to their unprecedented controllability, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.

We describe two experimental tests of the Equivalence Principle that are based on frequency measurements between precision oscillators and/or highly accurate atomic frequency standards. Based on comparisons between the hyperfine frequencies of 87 Rb and 133 Cs in atomic fountains, the first experiment constrains the stability of fundamental constants. The second experiment is based on a comparison between a cryogenic sapphire oscillator and a hydrogen maser. It tests Local Lorentz Invariance. In both cases, we report recent results which improve significantly over previous experiments.

An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze the universal properties associated with the Efimov effect in three- and four-body systems. In this progress report, we will discuss recent results obtained within this framework and report on progress regarding the inclusion of higher order corrections associated with the finite range of the underlying interaction.

In this review, we discuss the impact of the development of lasers on ultracold atoms and molecules and their applications. After a brief historical review of laser cooling and Bose-Einstein condensation, we present important applications of ultra cold atoms, including time and frequency metrology, atom interferometry and inertial sensors, atom lasers, simulation of condensed matter systems, production and study of strongly correlated systems, and production of ultracold molecules.

Physical phenomena driven by topological properties, such as the quantum Hall effect, have the appealing feature to be robust with respect to external perturbations. Lately, a new class of materials has emerged manifesting their topological properties at room temperature and without the need of external magnetic fields. These topological insulators are band insulators with large spin-orbit interactions and exhibit the quantum spin-Hall (QSH) effect. Here we investigate the transition between QSH and normal insulating phases under topology deformations of a two-dimensional lattice. We demonstrate that the QSH phase present in the honeycomb lattice looses its robustness as the occupancy of extra lattice sites is allowed. Furthermore, we propose a method for verifying our predictions with fermionic cold atoms in optical lattices. In this context, the spin-orbit interaction is engineered via an appropriate synthetic gauge field.

We have modelled and used polarisation spectroscopy to lock a very compact, high-performance extended cavity diode 85 Ž X . laser system to the Rb F s 3 to F s 4 transition. The laser has a linewidth of 135 kHz. Using this system we have trapped and cooled 1.5 = 10 8 Rb atoms in a magneto-optical trap. Atoms remained continuously trapped in the MOT for several minutes. q

We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.

Strongly correlated quantum systems can exhibit exotic behaviour called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasiparticles with anyonic statistics and have been proposed as candidates for naturally error-free quantum computation. However, anyons have never been observed in nature directly. Here, we describe how to unambiguously detect and characterize such states in recently proposed spinlattice realizations using ultracold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by carrying out global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations.

We study spin 3/2 fermionic cold atoms with attractive interactions confined in a one-dimensional optical lattice. Using numerical techniques, we determine the phase diagram for a generic density. For the chosen parameters, one-particle excitations are gapped and the phase diagram is separated into two regions: one where the two-particle excitation gap is zero, and one where it is finite. In the first region, the two-body pairing fluctuations (BCS) compete with the density ones. In the other one, a molecular superfluid (MS) phase, in which bound-states of four particles form, competes with the density fluctuations. The properties of the transition line between these two regions is studied through the behavior of the entanglement entropy. The physical features of the various phases, comprising leading correlations, Friedel oscillations, and excitation spectra, are presented. To make the connection with experiments, the effect of a harmonic trap is taken into account. In particular, we emphasize the conditions under which the appealing MS phase can be realized, and how the phases could be probed by using the density profiles and the associated structure factor. Lastly, the consequences on the flux quantization of the different nature of the pairing in the BCS and MS phases are studied in a situation where the condensate is in a ring geometry.

A theoretical study of interacting bosons in a periodic optical lattice is presented. Instead of the commonly used tight-binding approach (applicable near the Mott insulating regime of the phase diagram), the present work starts from the exact single-particle states of bosons in a cubic optical lattice, satisfying the Mathieu equation, an approach that can be particularly useful at large boson fillings. The effects of short-range interactions are incorporated using a self-consistent Hartree- Fock approximation, and predictions for experimental observables such as the superfluid transition temperature, condensate fraction, and boson momentum distribution are presented.

Istituto Elettrotecnico Nazionale Galileo Ferraris (IEN), National and Physikalisch-Technische Bundesanstalt (PTB) operate cold-atom based primary frequency standards which are capable of realizing the SI second with a relative uncertainty of 1 × 10 −15 or even below. These institutes performed an intense comparison campaign of selected frequency references maintained in their laboratories during about 25 days in October/November 2004. Active hydrogen maser reference standards served as frequency references for the institutes' fountain frequency standards. Three techniques of frequency (and time) comparisons were employed. Two-way satellite time and frequency transfer (TWSTFT) was performed in an intensified measurement schedule of 12 equally spaced measurements per day. The data of dual-frequency geodetic Global Positioning System (GPS) receivers were processed to yield an ionosphere-free linear combination of the code observations from both GPS frequencies, typically referred to as GPS TAI P3 analysis. Last but not least, the same GPS raw data were separately processed, allowing GPS carrier-phase (GPS CP) based frequency comparisons to be made. These showed the lowest relative frequency instability at short averaging times of all the methods. The instability was at the level of 1 part in 10 15 at one-day averaging time using TWSTFT and GPS CP. The GPS TAI P3 analysis is capable of giving a similar quality of data after averaging over two days or longer. All techniques provided the same mean frequency difference between the standards involved within the 1σ measurement uncertainty of a few parts in 10 16 . The frequency differences between the three fountains of IEN (IEN-CsF1), NPL (NPL-CsF1) and OP (OP-FO2) were evaluated. Differences lower than the 1σ measurement uncertainty were observed between NPL and OP, whereas the IEN fountain deviated by about 2σ from the other two fountains.

Unexpected accelerator modes were recently observed experimentally for cold cesium atoms when driven in the presence of gravity. A detailed theoretical explanation of this quantum effect is presented here. The theory makes use of invariance properties of the system, that are similar to the ones of solids, leading to a separation into independent kicked rotor problems. The analytical solution makes use of a limit that is very similar to the semiclassical limit, but with a small parameter that is not Planck's constant, but rather the detuning from the frequency that is resonant in absence of gravity.

Invariant transformation for quantum mechanical systems is proposed. A cloaking of matter wave can be realized at given energy by designing the potential and effective mass of the matter waves in the cloaking region. The general conditions required for such a cloaking are determined and confirmed by both the wave and particle (classical) approaches. We show that it may be possible to construct such a cloaking system for cold atoms using optical lattices.

We have measured the frequency splitting between the (2S, F = 1/2) and (2S, F = 3/2) hyperfine sublevels in atomic deuterium by an optical differential method based on two-photon Doppler-free spectroscopy on a cold atomic beam. The result f (D) HFS (2S) = 40 924 454 Hz is the most precise value for this interval to date. In comparison to the previous radio-frequency measurement we have improved the accuracy by the factor of three. The specific combination of hyperfine frequency intervals for metastable-and ground states in deuterium atom D21 = 8f

We propose the novel combination of a laser guide and magnetic lens to transport a cold atomic cloud. We have modelled the loading and guiding of a launched cloud of cold atoms with the optical dipole force. We discuss the optimum strategy for loading typically 30 % of the atoms from a MOT and guiding them vertically through 22 cm. However, although the atoms are tightly confined transversely, thermal expansion in the propagation direction still results in a density loss of two orders of magnitude. By combining the laser guide with a single impulse from a magnetic lens we show one can actually increase the density of the guided atoms by a factor of 10.

The lateral Casimir-Polder force between an atom and a corrugated surface should allow one to study experimentally non trivial geometrical effects in quantum vacuum. Here, we derive the theoretical expression of this force in a scattering approach that accounts for the optical properties of the corrugated surface. We show that large corrections to the ``proximity force approximation'' could be measured using present-day technology with a Bose-Einstein condensate used as a vacuum field sensor.

We study the superfluid phase of the one-band attractive Hubbard model of fermions as a prototype of a strongly correlated s-wave fermion superfluid on a lattice. We show that the collective mode spectrum of this superfluid exhibits, in addition to the long wavelength sound mode, a sharp roton mode over a wide range of densities and interaction strengths. We compute the sound velocity and the roton gap within a generalized random phase approximation (GRPA) and show that the GRPA results are in good agreement, at strong coupling, with a spin wave analysis of the appropriate strong coupling pseudospin model. We also investigate, using this two-pronged approach, the breakdown of superfluidity in the presence of a supercurrent. We find that the superflow can break down at a critical flow momentum via several distinct mechanisms -depairing, Landau instabilities or dynamical instabilities -depending on the dimension, the interaction strength and the fermion density. The most interesting of these instabilities is a charge modulation dynamical instability which is distinct from previously studied dynamical instabilities of Bose superfluids. The charge order associated with this instability can be of two types: (i) a commensurate checkerboard modulation driven by softening of the roton mode at the Brillouin zone corner, or, (ii) an incommensurate density modulation arising from superflow-induced finite momentum pairing of Bogoliubov quasiparticles. We elucidate the dynamical phase diagram showing the critical flow momentum of the leading instability over a wide range of fermion densities and interaction strengths and point out implications of our results for experiments on cold atom fermion superfluids in an optical lattice.

We investigate the properties of the Lieb lattice, i.e a face-centered square lattice, subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar quantum Hall effect, which is a consequence of the single Dirac cone and the flat band characterizing the energy spectrum. Then we explore the effects of an intrinsic spin-orbit term -a non-Abelian gauge fieldand demonstrate the occurrence of the quantum spin Hall effect in this model. Besides, we obtain the relativistic Hamiltonian describing the Lieb lattice at low energy and derive the Landau levels in the presence of external Abelian and non-Abelian gauge fields. Finally, we describe concrete schemes for realizing these gauge fields with cold fermionic atoms trapped in an optical Lieb lattice. In particular, we provide a very efficient method to reproduce the intrinsic (Kane-Mele) spin-orbit term with assisted-tunneling schemes. Consequently, our model could be implemented in order to produce a variety of topological states with cold-atoms.

We report on an absolute frequency measurement of the hydrogen 1S-2S two-photon transition in a cold atomic beam with an accuracy of 1.8 parts in 10 14 . Our experimental result of 2 466 061 413 187 103(46) Hz has been obtained by phase coherent comparison of the hydrogen transition frequency with an atomic cesium fountain clock. Both frequencies are linked with a comb of laser frequencies emitted by a mode locked laser. 06.30.Ft, 06.20.Jr, 42.62.Fi The 1S-2S two-photon transition in atomic hydrogen has played a central role in the progress of high resolution laser spectroscopy and optical frequency metrology . It provides a cornerstone for the determination of fundamental constants such as the Rydberg constant, which has become the most precisely measured constant in physics, and the 1S-Lamb shift to yield the most stringent test of quantum electrodynamics in an atom .

We propose a new possibility to form ultracold molecules, via photoassociation of a pair of cold atoms into vibrational levels of the external well of an excited electronic state located at intermediate interatomic distance (≈ 20 Bohr radii), and embedded in the dissociation continuum above its dissociation limit. The existence of such a well is demonstrated by conventional free-free absorption spectroscopy at thermal energies. Estimation for cold atom photoassociation and cold molecule formation rates are obtained within a perturbative approach [Drag et al., IEEE J. Quant. Electr. 36, 1378], and are found observable for usual conditions of photoassociation experiments.

Cold atomic gases placed in optical lattices enable studies of simple condensed matter theory models with parameters that may be tuned relatively easily. When the optical potential is randomized (e.g. using laser speckle to create a random intensity distribution) one may be able to observe Anderson localization of matter waves for non-interacting bosons, the so-called Bose glass in the presence of interactions, as well as the Fermi glass or quantum spin glass for mixtures of fermions and bosons.

In the context of quantum chaos, both theory and numerical analysis predict large fluctuations of the tunneling transition probabilities when irregular dynamics is present at the classical level. Here we consider the nondissipative quantum evolution of cold atoms trapped in a time-dependent modulated periodic potential generated by two laser beams. We give some precise guidelines for the observation of chaos-assisted tunneling between invariant phase space structures paired by time-reversal symmetry.

In this work we provide a general methodology to directly measure topological order in cold atom systems. As an application we propose the realisation of a characteristic topological model, introduced by Haldane, using optical lattices loaded with fermionic atoms in two internal states. We demonstrate that time-of-flight measurements directly reveal the topological order of the system in the form of momentum space skyrmions. 03.65.Vf Different phases of matter can be distinguished by their symmetries. This information is usually captured by locally measurable order parameters that summarize the essential properties of the phase. Topological insulators are materials with symmetries that depend on the topology of the energy eigenstates of the system [1]. These materials are of interest because they give rise to robust spin transport effects with potential applications ranging from sensitive detectors to quantum computation [2, 3]. However, direct observation and measurement of topological order has been up to now impossible due to its non-local character. Instead, experiments have relied so far on indirect manifestations of this order, such as edge states and the quantization of conductivity.

In this work we present an optical lattice setup to realize a full Dirac Hamiltonian in 2+1 dimensions. We show how all possible external potentials coupled to the Dirac field can arise from perturbations of the existing couplings of the honeycomb lattice pattern. This greatly simplifies the proposed implementations, requiring only spatial modulations of the intensity of the laser beams to induce complex non-Abelian potentials. We finally suggest several experiments to observe the properties of the quantum field theory in the setup.

We demonstrate the feasibility of a novel microwave power standard based on the electromagnetic interaction with cold atoms. Under the effect of the radiation, the internal state populations will undergo a Rabi oscillation. The measurement of its frequency will allow the determination of the electromagnetic field strength.

We review the basic theory of matrix product states (MPS) as a numerical variational ansatz for time evolution, and present two methods to simulate finite temperature systems with MPS: the ancilla method and the minimally entangled typical thermal state method. A sample calculation with the Bose-Hubbard model is provided.

We explain the dynamics of cold atoms, initially trapped and cooled in a magneto-optic trap, in a monochromatic stationary standing electromagnetic wave field. In the large-detuning limit, the system is modeled as a nonlinear quantum pendulum. We show that the wavepacket evolution of the quantum particle probes parametric regimes in the quantum pendulum that support the classical period and quantum-mechanical revival and superrevival phenomena. Interestingly, complete reconstruction, in particular the parametric regime at quantum revival times, is independent of the potential height.

We developed a new experimental system (the “atom-optics billiard”) and demonstrated chaotic and regular dynamics of cold, optically trapped atoms. We show that the softness of the walls and additional optical potentials can be used to manipulate the structure of phase space.

In recent years, production of cold-atoms ensembles by magneto-optical trapping has become a widely used technique in spectroscopy, in atom interferometry, and metrology. In metrology cold atoms production provides an advanced technique to measure the hyperfine levels of the ground state of the Cs-133 atoms by vertical launching atoms while maintaining low temperatures, as low as 3x10-6 K over absolute zero, allowing the realization of the so called atomic fountain frequency standards and so providing a way to measure, with extremely high accuracy, the energy difference of the hyperfine levels of the ground state of the Cs-133 atom. With this ultra high resolution spectroscopy is possible to reproduce the definition of the time unit of the International System (SI), the second, with an accuracy of few parts in 10 15. In this work we present a brief review of the development of the atomic clocks and we focus on the manipulation of the Cs-133 atoms with light an its application on the reproduction of the time unit, the second, of the SI. We review the mechanisms of the interaction photon-atoms that allows the control of the atom´s internal and external degrees of freedom involved in the Cs-133 cooling. Finally we present the progress done in Mexico at the Centro Nacional de Metrología (CENAM) in the design, construction, and operation of atomic clocks using atoms manipulation with light.

Different quantum phases of hard-core boson induced by dipole-dipole interaction with varying angles of polarization are discussed in this work. We consider the two most influential leading terms with anisotropy due to the tilted polarization of the on-site boson in the square lattice. To ensure the concreteness of this truncation, we compare our phase diagrams, obtained numerically from cluster mean-field theory (CMFT) and infinite projected entangled-pair state (iPEPS), with that of the long-range interacting model from quantum Monte Carlo. Next, we focus on the case where the azimuthal angle is fixed to φ = π/4. Using the mean-field analysis where the quantum spin operators are replaced by c-numbers, we aim to search for the underlying phases, especially the supersolid. Our results show a competing scenario mainly between two ordered phases with different sizes of unit cell, where first-order transition takes place in between them. With the help of CMFT and variational iPEPS, the phase boundaries predicted by the mean-field theory are determined more precisely. Our discoveries elucidate the possible underlying supersolid phases which might be seen in the ultracold experiments with strongly dipolar atoms. Moreover, our results indicate that an effective triangular optical lattice can be realized by fine tuning the polarization of dipoles in a square lattice.

We explore the trap profiles of a two-dimensional atomic Fermi gas in the presence of a Rashba spin-orbit coupling and under an adiabatic rotation. We first consider a noninteracting gas and show that the competition between the effects of Rashba coupling on the local density of single-particle states and the Coriolis effects caused by rotation gives rise to a characteristic ring-shaped density profile that survives at experimentally accessible temperatures. Furthermore, Rashba splitting of the Landau levels gives the density profiles a ziggurat shape in the rapid-rotation limit. We then consider an interacting gas under the BCS mean-field approximation for local pairing, and study the pair-breaking mechanism that is induced by the Coriolis effects on superfluidity, where we calculate the critical rotation frequencies both for the onset of pair breaking and for the complete destruction of superfluidity in the system. In particular, by comparing the results of a fully-quantum-mechanical Bogoliubov–de Gennes approach with those of a semiclassical local-density approximation, we construct extensive phase diagrams for a wide range of parameter regimes in the trap where the aforementioned competition may, e.g., favor an outer normal edge that is completely phase separated from the central superfluid core by vacuum.

This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian. We discuss several aspects of the slow dynamics in driven systems and emphasize the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions. We also review recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis and discuss relaxation in integrable systems. Finally we overview key experiments probing quantum dynamics in cold atom systems and put them in the context of our current theoretical understanding.

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k×k matrices. The single-particle dynamics in the case of intense U(2) vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.

Superconductors are considered in view of applications to atom chip devices. The main features of magnetic traps based on superconducting wires in the Meissner and mixed states are discussed. The former state may mainly be interesting for improved atom optics, while in the latter, cold atoms may provide a probe of superconductor phenomena. The properties of a magnetic side guide based on a single superconducting strip wire placed in an external magnetic field are calculated analytically and numerically. In the mixed state of type II superconductors, inhomogeneous trapped magnetic flux, relaxation processes and noise caused by vortex motion are posing specific challenges for atom trapping.