Alkaline-earth and ytterbium cold atomic gases make it possible to simulate SU(N)-symmetric fermionic systems in a very controlled fashion. Such a high symmetry is expected to give rise to a variety of novel phenomena ranging from molecular Luttinger liquids to (symmetry- protected) topological phases. We review some of the phases that can be stabilized in a one dimensional lattice. The physics of this multicomponent Fermi gas turns out to be much richer and more exotic than in the standard SU(2) case. For N > 2, the phase diagram is quite rich already in the case of the single-band model, including a molecular Luttinger liquid (with dominant superfluid instability in the N-particle channel) for incommensurate fillings, as well as various Mott-insulating phases occurring at commensurate fillings. Particular attention will be paid to the cases with additional orbital degree of freedom (which is accessible experimentally either by taking into account two atomic states or by putting atoms in the p-band levels). We introduce two microscopic models which are relevant for these cases and discuss their symmetries and strong coupling limits. More intriguing phase diagrams are then presented including, for instance, symmetry protected topological phases characterized by non-trivial edge states.
We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributi…
We study a two-component Fermi gas that is so strongly polarized that it remains normal fluid at zero temperature. We calculate the occupation numbers within the particle-particle random-phase approximation, which is similar to the Nozieres-Schmitt-Rink approach. We show that the Luttinger theorem is fulfilled in this approach. We also study the change of the chemical potentials which allows us to extract, in the limit of extreme polarization, the polaron energy.
We investigate one dimensional attractive Fermi gases in spin-dependent optical lattices. We show that three-body bound states - "trimers" - exist as soon as the two tunneling rates are different. We calculate the binding energy and the effective mass of a single trimer. We then show numerically that for finite and commensurate densities $n_\uparrow=n_\downarrow/2$ an energy gap appears, implying that the gas is a one-component Luttinger liquid of trimers with suppressed superfluid ordering. The boundaries of this novel phase are given. We discuss experimental situations to test our prediction…
Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate-like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly-interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a $^{87}$Rb condensate in a 2D lattice potential. The dynamical structure factor of the system …
Tomonaga-Luttinger liquid theory for one-dimensional attractive Fermi gases
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新院）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文系）；Department of Quantum Matter Physics, University of Geneva（日内瓦大学量子物质物理系）；Hefei National Laboratory（合肥国家实验室）；Department of Fundamental and Theoretical Physics, Research School of Physics, Australian National University（澳大利亚国立大学物理研究学院基础与理论物理系）
A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multi-component strongly attractive fermionic atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal multi-component Tomonaga-Luttinger liquid (TLL) phases are thus determined. For linear Zeeman splitting, the physics of the gapless phase at low temperatures belongs to the universality class of a two-component asymmetric TLL corresponding to spin-neutral N-atom composites and spin-(N-1)/2 single atoms. The equation of states is also obtained to open up the study of mu…
We study one dimensional fermionic and bosonic gases with repulsive power-law interactions $1/|x|^β$, with $β>1$, in the framework of Tomonaga-Luttinger liquid (LL) theory. We obtain an accurate analytical expression linking the LL parameter to the microscopic Hamiltonian, for arbitrary $β$ and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the LL unstable towards the formation of a cascade of lattice solids with fractional filling, thus forming a "Luttinger staircase". Several of these quantum phases and phase transitions are realized …
Recent experiments with ultra-cold atoms have demonstrated the possibility of realizing experimentally fermionic superfluids with imbalanced spin populations. We discuss how these developments have shed a new light on a half- century old open problem in condensed matter physics, and raised new interrogations of their own.
For ultra-cold atomic gases close to the critical temperature, there is a divergent correlation behavior within the critical regime. This divergent correlation behavior is the cornerstone of the universal behavior within the critical regime, e.g. the universal critical exponent for the same class with very different physical systems. It is still quite challenging to observe this divergent correlation behavior in experiments with ultra-cold atomic gases. Here we consider theoretically the interference effect of the critical atomic Bose gas by a Kapitza-Dirac scattering. We find that the Kapitza…
We reexamine how quantum density fluctuations in condensates of ultra-cold fermi gases lead to fluctuations in phonon times-of-flight, an effect that increases as density is reduced. We suggest that these effects should be measurable in pancake-like (two-dimensional) condensates on their release from their confining optical traps, providing their initial (width/thickness) aspect ratio is suitably large.
We study the equilibrium current density profiles of harmonically trapped ultra-cold Fermi gases in quantum Hall-like states that appear when the quasi-two-dimensional trap is set in fast rotation. The density profile of the gas (in the rotating reference frame) consists of incompressible strips of constant quantized density separated by compressible regions in which the density varies. Remarkably, we find that the atomic currents flow in opposite directions in the compressible and incompressible regions -- a prediction that should be amenable to experimental verification.
We study the behavior of excitations in the tilted one-dimensional Bose-Hubbard model. In the phase with broken symmetry, fundamental excitations are domain-walls which show fractional statistics. Using perturbation theory, we derive an analytic model for the time evolution of these fractional excitations, and demonstrate the existence of a repulsively bound state above a critical center of mass momentum. The validity of the perturbative analysis is confirmed by the use of t- DMRG simulations. These findings open the path for experimental detection of fractional particles in cold atomic gases.
We propose a spin-dependent optical lattice potential that realizes a three-dimensional antiferromagnetic topological insulator in a gas of cold, two-state fermions such as alkaline earths, as well as a model that describes the tight-binding limit of this potential. We discuss the physically observable responses of the gas that can verify the presence of this phase. We also point out how this model can be used to obtain two-dimensional flat bands with nonzero Chern number.
A cold gas of particles with anisotropic interactions of general form, due to a polarizing field, is studied. Special cases are atoms or molecules with dipole-dipole or quadrupole-quadrupole interactions. It is shown that the angular dependence of an observable on the direction of the polarizing field is largely determined by symmetry. For a gas in a confined quasi two-dimensional geometry, the effective interaction is calculated in general form. Some examples of dipole and quadrupole gases are considered. It is concluded that when anisotropic forces are studied in a general manner, one can ob…
The emergent phases of strongly correlated spin-1/2 Fermi gases of Rydberg dressed atoms in a one dimensional optical lattice are theoretically investigated. At weak coupling a bosonization description is used to demonstrate the ability to drive alternating quantum phase transitions between distinct Luttinger liquids. At strong coupling the ground state develops non-trivial phase separation exhibiting Luttinger liquid ''puddles'' separated by magnetic domain walls due to the interplay of the incommensurate filling and the Rydberg core length scale. These phases can be detected in ultracold gas…
We examine the effect of quantum fluctuations in a tunable cold Fermi gas on the propagation of phonons. We show that these fluctuations can be interpreted as inducing a stochastic (acoustic) space-time. The variation in times of flight induced by this stochastic behaviour can be significant in the transition region between BEC and BCS regimes.
To realize non-Abelian s-wave topological superfluid (TS) of cold Fermi gases, generally a Zeeman magnetic field larger than superfluid pairing gap is necessary. In this paper we find that using an anisotropic and spin-dependent optical lattice (ASDOL) to trap gases, a new non-Abelian TS phase appears, in contrast to an isotropic and spin-independent optical lattice. A characteristic of this new non-Abelian TS is that Zeeman magnetic field can be smaller than the superfluid pairing gap. By self-consistently solving pairing gap equation and considering the competition against normal state and p…
We derive the dynamical structure factor for an inhomogeneous Tomonaga-Luttinger liquid as can be formed in a confined strongly interacting one-dimensional gas. In view of current experimental progress in the field, we provide a simple analytic expression for the light-scattering cross section, requiring only the knowledge of the density dependence of the ground-state energy, as they can be extracted e.g. from exact or Quantum Monte Carlo techniques, and a Thomas-Fermi description. We apply the result to the case of one-dimensional quantum bosonic gases with dipolar interaction in a harmonic t…
The superfluid phases in the resonant dipolar Fermi gases are investigated by the standard mean-field theory. In contrast to the crossover from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid in the Fermi gases with the isotropic interactions, the resonant dipolar interaction leads to two completely different BEC phases of the tight-binding Fermi molecules on both sides of the resonance, which are characterized by two order parameters with the distinct internal symmetries. We point that near the resonance, the two competitive phases can coexist, and an emergent r…
We review the physics of one-dimensional interacting bosonic systems. Beginning with results from exactly solvable models and computational approaches, we introduce the concept of bosonic Tomonaga-Luttinger Liquids relevant for one-dimension, and compare it with Bose-Einstein condensates existing in dimensions higher than one. We discuss the effects of various perturbations on the Tomonaga-Luttinger liquid state as well as extensions to multicomponent and out of equilibrium situations. Finally, we review the experimental systems that can be described in terms of models of interacting bosons in…
Ultra-cold atomic gases provide new chance to study the universal critical behavior of phase transition. We study theoretically the matter wave interference for ultra-cold Bose gases in the critical regime. We demonstrate that the interference in the momentum distribution can be used to extract the correlation in the Bose gas. A simple relation between the interference visibility and the correlation length is found and used to interpret the pioneering experiment about the critical behavior of dilute Bose gases [Science {\bf 315}, 1556 (2007)]. Our theory paves the way to experimentally study v…
We show that the essential properties of a Feshbach resonance in cold atomic gases can be tuned by dressing the atomic states in different scattering channels through inter-channel couplings. Such a scheme can be readily implemented in the orbital Feshbach resonance of alkaline-earth-like atoms by coupling hyperfine states in the clock-state manifolds. Using $^{173}$Yb atoms as an example, we find that both the resonance position and the two-body bound-state energy depend sensitively on the inter-channel coupling strength, which offers control parameters in tuning the inter-atomic interactions…
We consider a quasi-one-dimensional model of a two-component Fermi gas at zero temperature on one, two and three-leg attractive-U Hubbard ladders. We construct the grand canonical phase diagram of a two-component spin-polarized gas. We find that the structure of the phase diagram of the attractive-U Hubbard model for two and three leg ladders significantly differs q from the structure of the phase diagram of a single chain. We argue that the single chain model is a special case, and that multichain ladders display qualitative features of the 1D-to-3D crossover, observed in experiments with tra…
Exact calculation of the condensate fraction in multi-dimensional inhomogeneous interacting Bose systems which do not possess continuous symmetries is a difficult computational problem. We have developed an iterative procedure which allows to calculate the condensate fraction as well as the corresponding eigenfunction of the one-body density matrix. We successfully validate this procedure in diffusion Monte Carlo simulations of a Bose gas in an optical lattice at zero temperature. We also discuss relation between different criteria used for testing coherence in cold Bose systems, such as fract…
The position and momentum space information entropies of weakly interacting trapped atomic Bose-Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems contain $N$ atoms confined in a $D(\le 3)$-dimensional harmonic trap has a universal form as $ S_t^{(D)} = N(a D - b \ln N) $, where $a \simeq 2.332$ and $b = 2$ for interacting bosonic systems and $a \simeq 1.982$ and $b = 1$ for ideal fermionic systems. These results obey the entropic uncert…
We address recent spin transport experiments in ultracold unitary Fermi gases. We provide a theoretical understanding for how the measured temperature dependence of the spin diffusivity at low $T$ can disagree with the expected behavior of a Fermi liquid (FL) while the spin susceptiblity(following the experimental protocols) is consistent with a Fermi liquid picture. We show that the experimental protocols for extracting $χ_s$ are based on a FL presumption; relaxing this leads to consistency within (but not proof of) a pseudogap-based approach. Our tranport calculations yield insight into the …
We theoretically investigate the localization properties of a spin-orbit coupled spin-1/2 particle moving in a one-dimensional quasiperiodic potential, which can be experimentally implemented using cold atoms trapped in a quasiperiodic optical lattice potential and external laser fields. We present the phase diagram in the parameter space of the disorder strength and those related to the spin-orbit coupling. The phase diagram is verified via multifractal analysis of the atomic wavefunctions and the numerical simulation of diffusion dynamics. We found that spin-orbit coupling can lead to the sp…
We present a thorough study of the thermodynamics of a one-dimensional repulsive Bose gas, focusing in particular on corrections beyond the Luttinger-liquid description. We compute the chemical potential, the pressure and the contact, as a function of temperature and gas parameter with exact thermal Bethe-Ansatz. In addition, we provide interpretations of the main features in the analytically tractable regimes, based on a variety of approaches (Bogoliubov, hard-core, Sommerfeld and virial). The beyond Luttinger-liquid thermodynamic effects are found to be non-monotonic as a function of gas par…
We investigate thermodynamics and quantum criticality of strongly attractive Fermi gases confined in a one-dimensional (1D) harmonic trap. Finite temperature density profiles, entropy, compressibility and susceptibility of the trapped gas are studied using analytic results for the thermodynamics within the local density approximation. We demonstrate that current experiments are capable of measuring universal Tomonaga-Luttinger liquid physics and quantum criticality of 1D strongly interacting Fermi gases. The results provide insights on recent measurements of key features of the phase diagram o…
We study the energy deposition in a one dimensional interacting quantum system with a point like potential modulated in amplitude. The point like potential at position $x=0$ has a constant part and a small oscillation in time with a frequency $ω$. We use bosonization, renormalization group and linear response theory to calculate the corresponding energy deposition. It exhibits a power law behavior as a function of the frequency that reflects the Tomonaga-Luttinger liquid (TLL) nature of the system. Depending on the interactions in the system, characterized by the TLL parameter $K$ of the syste…
We discuss the equilibrium properties of dilute Bose gases using a non-perturbative formalism based on auxiliary fields related to the normal and anomalous densities. We show analytically that for a dilute Bose gas of weakly-interacting particles at zero temperature, the leading-order auxiliary field (LOAF) approximation leads to well-known analytical results. Close to the critical point the LOAF predictions are the same as those obtained using an effective field theory in the large-N approximation. We also report analytical approximations for the LOAF results in the unitarity limit, which com…
We investigate the Zel'dovich effect in the context of ultra-cold, harmonically trapped quantum gases. We suggest that currently available experimental techniques in cold-atoms research offer an exciting opportunity for a direct observation of the Zel'dovich effect without the difficulties imposed by conventional condensed matter and nuclear physics studies. We also demonstrate an interesting scaling symmetry in the level rearragements which has heretofore gone unnoticed.
We systematically study ground state properties of fermionic dipolar gases in a planar array of one-dimensional potential tubes for an arbitrary orientation of dipole moments. Using the Luttinger liquid theory with the generalized Bogoliubov transformation, we calculate the elementary excitations and the Luttinger scaling exponents for various relevant quantum orders. The complete quantum phase diagrams for arbitrary polar angle of the dipole moment is obtained, including charge density wave, p-wave superfluid, inter-tube gauge-phase density wave, and inter-tube s-wave superfluid, where the la…
The transport dynamics of a quenched Luttinger liquid tunnel-coupled to a fermionic reservoir is investigated. In the transient dynamics, we show that for a sudden quench of the electron interaction universal power-law decay in time of the tunneling current occurs, ascribed to the presence of entangled compound excitations created by the quench. In sharp contrast to the usual non universal power-law behavior of a zero-temperature non-quenched Luttinger liquid, the steady state tunneling current is ohmic and can be explained in terms of an effective quench-activated heating of the system. Our s…
One of the most remarkable results of quantum mechanics is the fact that many-body quantum systems may exhibit phase transitions even at zero temperature. Quantum fluctuations, deeply rooted in Heisenberg's uncertainty principle, and not thermal fluctuations, drive the system from one phase to another. Typically, the relative strength of two competing terms in the system's Hamiltonian is changed across a finite critical value. A well-known example is the Mott-Hubbard quantum phase transition from a superfluid to an insulating phase, which has been observed for weakly interacting bosonic atomic…
The coupling of weak light fields to Rydberg states of atoms under conditions of electromagnetically induced transparency (EIT) leads to the formation of Rydberg polaritons which are quasi-particles with tunable effective mass and long-range interactions. Confined to one spatial dimension their low energy physics is that of a moving-frame Luttinger liquid which due to the long-range character of the repulsive interaction can form a Wigner crystal. We calculate the Luttinger $K$ parameter using density-matrix renormalization group (DMRG) simulations and find that under typical slow-light condit…
It was shown [Chin. Phys. Lett. 28, 020503 (2011)] that at zero temperature the ground state of the one-dimensional (1D) $w$-component Fermi gas coincides with that of the spinless Bose gas in the limit $ω\to \infty$. This behaviour was experimentally evidenced through a quasi-1D tightly trapping ultracold ${}^{173}$Yb atoms in the recent paper [Nature Physics 10, 198 (2014)]. However, understanding of low temperature behaviour of the Fermi gases with a repulsive interaction acquires spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnet…
The experimental realization of quantum degenerate cold Fermi gases with large hyperfine spins opens up a new opportunity for exotic many-body physics.
We consider response function and spin evolution in spin-orbit coupled cold atomic gases in a synthetic gauge magnetic field influencing solely the orbital motion of atoms. We demonstrate that various regimes of spin-orbit coupling strength, magnetic field, and disorder can be treated within a single approach based on the representation of atomic motion in terms of auxiliary collective classical trajectories. Our approach allows for a unified description of fermionic and bosonic gases.
We suggest that collective oscillation frequencies of cold trapped gases can be used to test predictions from quantum many-body physics. Our motivation lies both in rigid experimental tests of theoretical calculations and a possible improvement of measurements of particle number, chemical potential or temperature. We calculate the effects of interaction, dimensionality and thermal fluctuations on the collective modes of a dilute Bose gas in the hydrodynamic limit. The underlying equation of state is provided by non-perturbative Functional Renormalization Group or by Lee--Yang theory. The spect…
We study the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the rotation symmetry is spontaneously broken, in population imbalanced fermion gases. The superfluid gases at near T=0 are investigated on the basis of the Bogoliubov-de Gennes (BdG) equation. We find that the angular FFLO state is stabilized in the gases confined in the toroidal trap, but not in the harmonic trap. We discuss the mechanism of the angular FFLO state based on the self-one-dimensionalization of the superfluid gas.
The response of cold atom gases to small periodic phase modulation of an optical lattice is discussed. For bosonic gases, the energy absorption rate is given, within linear response theory, by imaginary part of the current correlation function. For fermionic gases in a strong lattice potential, the same correlation function can be probed via the production rate double occupancy. The phase modulation gives thus direct access to the conductivity of the system, as function of the modulation frequency. We give an example of application in the case of one dimensional bosons at zero temperature and …
We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum systems. We first revisit homogeneous anyonic gases with point-wise interactions. In the harmonic Luttinger liquid expansion of the one-particle density matrix for finite interaction strength, the non-universal field amplitudes were not yet known. We extract them from the Bethe Ansatz formula for the field form factors, providing an exact asymptotic expansio…
We consider diffusion of a cold Fermi gas in the presence of a random optical speckle potential. The evolution of the initial atomic cloud in space and time is discussed. Analytical and numerical results are presented in various regimes. Diffusion of a Bose-Einstein condensate is also briefly discussed and similarity with the Fermi gas case is pointed out.
Cold gas experiments can be tuned to achieve strongly-interacting regimes such as that of low-density neutron matter found in neutron-stars' crusts. We report $T$=0 diffusion Monte Carlo results (i) for the ground state of both spin-1/2 fermions with short-range interactions and low-density neutron matter in a cylindrical container, and (ii) properties of these systems with a vortex line excitation. We calculate the equation of state for cold atoms and low-density neutron matter in the bulk systems, and we contrast it to our results in the cylindrical container. We compute the vortex line exci…
We investigate the zero-temperature phases of bosonic and fermionic gases confined to one dimension and interacting via a class of finite-range soft-shoulder potentials (i.e. soft-core potentials with an additional hard-core onsite interaction). Using a combination of analytical and numerical methods, we demonstrate the stabilization of critical quantum liquids with qualitatively new features with respect to the Tomonaga-Luttinger liquid paradigm. These features result from frustration and cluster formation in the corresponding classical ground-state. Characteristic signatures of these liquids…
In these notes of six lectures on selected topics in the theory of cold, dilute Bose gases, presented at the 5th Warsaw School of Statistical Physics in June 2013, the following topics are discussed: 1) The concept of BEC, 2) the ground state energy of a dilute Bose gas with short range interactions, 3) Gross-Pitaevskii theory and BEC in trapped gases, 4) Bose gases in rotating traps and quantized vortices, and 5) strongly correlated phases in the lowest Landau level generated by rapid rotation.
Ultracold quantum gases offer unique possibilities to study interacting many-body quantum systems. Probing and manipulating such systems with ever increasing degree of control requires novel experimental techniques. Scanning electron microscopy is a high resolution technique which can be used for in situ imaging, single site addressing in optical lattices and precision density engineering. Here, we review recent advances and achievements obtained with this technique and discuss future perspectives.
This article reviews some recent developments for new cooling technologies in the fields of condensed matter physics and cold gases, both from an experimental and theoretical point of view. The main idea is to make use of distinct many-body interactions of the system to be cooled which can be some cooling stage or the material of interest itself, as is the case in cold gases. For condensed matter systems, we discuss magnetic cooling schemes based on a large magnetocaloric effect as a result of a nearby quantum phase transition and consider effects of geometrical frustration. For ultracold gase…
Within the context of Hartree-Fock-Bogoliubov theory, we study the behavior of superfluid Fermi systems when they pass from a small to a large container. Such systems can be now realized thanks to recent progress in experimental techniques. It will allow to better understand pairing properties at overflow and in general in rapidly varying external potentials.
We simulate ultra-cold interacting Bosons in quasi-one-dimensional, incommensurate optical lattices. In the tight-binding limit, these lattices have pseudo-random on-site energies and thus can potentially lead to Anderson localization. We explore the parameter regimes that lead to Anderson localization and investigate the role of repulsive interactions, harmonic confinement and finite temperature. We find that interactions can obscure the exponential localization characteristic of Anderson localization, thus impeding the direct observation of this phenomenon when interactions are present.
Dynamics of interacting cold atomic gases have recently become a focus of both experimental and theoretical studies. Often cold atom systems show hydrodynamic behavior and support the propagation of nonlinear dispersive waves. Although this propagation depends on many details of the system, a great insight can be obtained in the rather universal limit of weak nonlinearity, dispersion and dissipation (WNDD). In this limit, using a reductive perturbation method we map some of the hydrodynamic models relevant to cold atoms to well known chiral one-dimensional equations such as KdV, Burgers, KdV-B…
We study the quantum dynamics of a one-dimensional SU(3)-symmetric system of cold atoms in the presence of two-body losses. We exploit the representation theory of SU(3), the so-called eightfold way, as a scheme to organize the dark states of the dissipative dynamics in terms of generalized Dicke states and show how they are dynamically approached, both in the weakly- and and strongly-interacting and dissipative regimes. Our results are relevant for a wide class of alkaline-earth(-like) gases experiments, paving the way to the dissipative preparation and exploitation of generalized Dicke state…
We consider a cold two-species atomic Fermi gas confined in a trap. We combine the Hermitian coupling between the states (we assume them to be the states with different spins) with the Cooper pairing of atoms with these different spins. This opens up a new prospect for investigation of interplay between various phenomena involving Raman coupling (e.g., atom lasers, dark-state polaritons) and effects caused by Cooper pairing of particles (e.g., superfluidity). We have obtained a threshold of transition from oscillatory to amplifying behavior of matter waves.
We study the thermodynamic properties of a 2D array of coupled one-dimensional Bose gases. The system is realized with ultracold bosonic atoms loaded in the potential tubes of a two-dimensional optical lattice. For negligible coupling strength, each tube is an independent weakly interacting 1D Bose gas featuring Tomonaga Luttinger liquid behavior. By decreasing the lattice depth, we increase the coupling strength between the 1D gases and allow for the phase transition into a 3D condensate. We extract the phase diagram for such a system and compare our results with theoretical predictions. Due …
We study an effect of rotation on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of two component Fermi superfluid gases in a toroidal trap. We investigate a stability of the FFLO states in the quasi-one-dimensional regime on the basis of the Bogoliubov-de Gennes equation. We find that two novel FFLO phases, i.e., the half quantum vortex state and the intermediate state of Fulde-Ferrell (FF) state and Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half quantum vortex state is shown in both T-P plane and T-…
We present a scanning probe microscopy technique for spatially resolving transport in cold atomic gases, in close analogy with scanning gate microscopy in semiconductor physics. The conductance of a quantum point contact connected to two atomic reservoirs is measured in the presence of a tightly focused laser beam acting as a local perturbation that can be precisely positioned in space. By scanning its position and recording the subsequent variations of conductance, we retrieve a high-resolution map of transport through a quantum point contact. We demonstrate a spatial resolution comparable to…
