Bose-Einstein Condensation Regime Research Articles

Effect of the site dilution on spin transport in the two-dimensional biquadratic Heisenberg model

We use the SU(3) Schwinger's boson theory to study the spin transport in the biquadratic Heisenberg chains in a square lattice with a distribution of non-magnetic impurities on the lattice. We verify the influence of the site dilution in the Ac and Dc spin conductivities of this model in the Bose–Einstein condensation regime in which the bosons t are condensed. Our results show that the decreasing of the gap Δ with −β suffers a change for different concentrations x of non-magnetic impurities, however the point (in the −β axis) where the gap cancels does not change with x. Therefore, the size of the region ω, where the spin conductivity goes to zero decreases with the increase of x until the point where x=0.5, where the size of this region tends to zero.

Analytical solitonlike solutions and the dynamics of ultracold Fermi gases in a time-dependent three-dimensional harmonic potential

We present a theoretical study of solitonlike solutions and their dynamics of ultracold superfluid Fermi gases trapped in a time-dependent three-dimensional (3D) harmonic potential with gain or loss. The 3D analytical solitonlike solutions are obtained without introducing any additional integrability constraints used elsewhere. The propagation of both bright- and dark-soliton-like solutions is investigated. We show that the amplitudes of dark-soliton-like solutions exhibit periodic oscillation, whereas those of the bright-soliton-like ones do not show such behavior. Moreover, we highlight that the oscillation periods of dark-soliton-like solutions predicted by our approach are matched very well with those observed in a recent experiment carried out by Yefsah etal. [T. Yefsah, A. T. Sommer, M. J. H. Ku, L. W. Cheuk, W. Ji, W. S. Bakr, and M. W. Zwierlein, Nature (London) 499, 426 (2013)NATUAS0028-083610.1038/nature12338] in both Bose-Einstein condensation and unitarity regimes.

Orbital angular momentum and spectral flow in two-dimensional chiral superfluids.

We study the orbital angular momentum (OAM) L_{z} in two-dimensional chiral (p_{x}+ip_{y})^{ν}-wave superfluids (SFs) of N fermions on a disk at zero temperature, in terms of spectral asymmetry and spectral flow. It is shown that L_{z}=νN/2 for any integer ν, in the Bose-Einstein condensation regime. In contrast, in the BCS limit, while the OAM is L_{z}=N/2 for the p+ip-wave SF, for chiral SFs with ν≥2, the OAM is remarkably suppressed as L_{z}=N×O(Δ_{0}/ϵ_{F})≪N, where Δ_{0} is the gap amplitude and ϵ_{F} is the Fermi energy. We demonstrate that the difference between the p+ip-wave SF and the other chiral SFs in the BCS regimes originates from the nature of edge modes and related depairing effects.

Dynamics of spatial coherence and momentum distribution of polaritons in a semiconductor microcavity under conditions of Bose-Einstein condensation

The dynamics of spatial coherence and momentum distribution of polaritons in the regime of Bose-Einstein condensation in a GaAs microcavity with embedded quantum wells under nonresonant excitation with picosecond laser pulses are investigated. It is shown that the establishment of the condensate coherence is accompanied by narrowing of the polariton momentum distribution. At the same time, at sufficiently high excitation densities, there is significant qualitative discrepancy between the dynamic behavior of the width of the polariton momentum distribution determined from direct measurements and that calculated from the spatial distribution of coherence. This discrepancy is observed at the fast initial stage of the polariton system kinetics and, apparently, results from the strong spatial nonuniformity of the phase of the condensate wavefunction, which equilibrates on a much longer time scale.

Thermalization and breakdown of thermalization in photon condensates

We examine in detail the mechanisms behind thermalization and Bose-Einstein condensation (BEC) of a gas of photons in a dye-filled microcavity. We derive a microscopic quantum model, based on that of a standard laser, and show how this model can reproduce the behavior of recent experiments. Using the rate-equation approximation of this model, we show how a thermal distribution of photons arises. We go on to describe how the nonequilibrium effects in our model can cause thermalization to break down as one moves away from the experimental parameter values. In particular, we examine the effects of changing cavity length, and of altering the vibrational spectrum of the dye molecules. We are able to identify two measures which quantify whether the system is in thermal equilibrium. Using these, we plot ``phase diagrams'' distinguishing BEC and standard lasing regimes. Going beyond the rate-equation approximation, our quantum model allows us to investigate both the second-order coherence ${g}^{(2)}$ and the linewidth of the emission from the cavity. We show how the linewidth collapses as the system transitions to a Bose condensed state, and compare the results to the Schawlow-Townes linewidth.

Scattering length of composite bosons in the three-dimensional BCS-BEC crossover

We study the zero-temperature grand potential of a three-dimensional superfluid made of ultracold fermionic alkali-metal atoms in the BCS-BEC crossover. In particular, we analyze the zero-point energy of both fermionic single-particle excitations and bosonic collective excitations. The bosonic elementary excitations, which are crucial to obtain a reliable equation of state in the Bose-Einstein condensate regime, are obtained with a low-momentum expansion up to the forth order of the quadratic (Gaussian) action of the fluctuating pairing field. By performing a cutoff regularization and renormalization of Gaussian fluctuations, we find that the scattering length ${a}_{B}$ of composite bosons, bound states of fermionic pairs, is given by ${a}_{B}=(2/3)\phantom{\rule{4pt}{0ex}}{a}_{F}$, where ${a}_{F}$ is the scattering length of fermions.

Critical velocity in the BEC-BCS crossover.

We map out the critical velocity in the crossover from Bose-Einstein condensation to Bardeen-Cooper-Schrieffer superfluidity with ultracold ^{6}Li gases. A small attractive potential is dragged along lines of constant column density. The rate of the induced heating increases steeply above a critical velocity v_{c}. In the same samples, we measure the speed of sound v_{s} by exciting density waves and compare the results to the measured values of v_{c}. We perform numerical simulations in the Bose-Einstein condensation regime and find very good agreement, validating the approach. In the strongly correlated regime our measurements of v_{c} provide a testing ground for theoretical approaches.

Superradiant phase transition of Fermi gases in a cavity across a Feshbach resonance

We consider the superradiant phase transition of a two-component Fermi gas in a cavity across a Feshbach resonance. It is known that quantum statistics plays a crucial role for the superradiant phase transition in atomic gases; in contrast to bosons, in a Fermi gas this transition exhibits strong density dependence. We show that across a Feshbach resonance, while the two-component Fermi gas passes through the BEC-BCS crossover, the superradiant phase transition undergoes a corresponding crossover from a fermionic behavior on the weakly interacting BCS side, to a bosonic behavior on the molecular Bose-Einstein condensate (BEC) side. This intricate statistics crossover makes the superradiance maximally enhanced either in the unitary regime for low densities, in the BCS regime for moderate densities close to Fermi surface nesting, or in the BEC regime for high densities.

Excitonic Bose-Einstein condensation inTa2NiSe5above room temperature

We show that finite temperature variational cluster approximation (VCA) calculations on an extended Falicov-Kimball model can reproduce angle-resolved photoemission spectroscopy (ARPES) results on Ta2NiSe5 across a semiconductor-to-semiconductor structural phase transition at 325 K. We demonstrate that the characteristic temperature dependence of the flat-top valence band observed by ARPES is reproduced by the VCA calculation on the realistic model for an excitonic insulator only when the strong excitonic fluctuation is taken into account. The present calculations indicate that Ta2NiSe5 falls in the Bose-Einstein condensation regime of the excitonic insulator state.

Heavy solitons in a fermionic superfluid

Solitons-solitary waves that maintain their shape as they propagate-occur as water waves in narrow canals, as light pulses in optical fibres and as quantum mechanical matter waves in superfluids and superconductors. Their highly nonlinear and localized nature makes them very sensitive probes of the medium in which they propagate. Here we create long-lived solitons in a strongly interacting superfluid of fermionic atoms and directly observe their motion. As the interactions are tuned from the regime of Bose-Einstein condensation of tightly bound molecules towards the Bardeen-Cooper-Schrieffer limit of long-range Cooper pairs, the solitons' effective mass increases markedly, to more than 200 times their bare mass, signalling strong quantum fluctuations. This mass enhancement is more than 50 times larger than the theoretically predicted value. Our work provides a benchmark for theories of non-equilibrium dynamics of strongly interacting fermions.

Bose–Einstein condensation in the three-sphere and in the infinite slab: Analytical results

We study the finite size effects on Bose–Einstein condensation (BEC) of an ideal non-relativistic Bose gas in the three-sphere (spatial section of the Einstein universe) and in a partially finite box which is infinite in two of the spatial directions (infinite slab). Using the framework of grand-canonical statistics, we consider the number of particles, the condensate fraction and the specific heat. After obtaining asymptotic expansions for large system size, which are valid throughout the BEC regime, we describe analytically how the thermodynamic limit behaviour is approached. In particular, in the critical region of the BEC transition, we express the chemical potential and the specific heat as simple explicit functions of the temperature, highlighting the effects of finite size. These effects are seen to be different for the two different geometries. We also consider the Bose gas in a one-dimensional box, a system which does not possess BEC in the sense of a phase transition even in the infinite volume limit.

Exotic phase separation and phase diagrams of a Fermi-Fermi mixture in a trap at finite temperature

The pairing and superfluid phenomena in a two-component Fermi gas can be strongly affected by the population and mass imbalances. Here we present phase diagrams of atomic Fermi gases as they undergo BCS--Bose-Einstein condensation (BEC) crossover with population and mass imbalances, using a pairing fluctuation theory. We focus on the finite temperature and trap effects, with an emphasis on the mixture of $^{6}$Li and $^{40}$K atoms. We show that there exist exotic types of phase separation in the BEC regime as well as sandwich-like shell structures at low temperature with superfluid or pseudogapped normal state in the central shell in the BCS and unitary regimes, especially when the light species is the majority. Such a sandwich-like shell structure appear when the mass imbalance increases beyond certain threshold. Our result is relevant to future experiments on the $^6$Li--$^{40}$K mixture and possibly other Fermi-Fermi mixtures.

Tunneling manipulation of superfluid Fermi gas in the adiabatic condition

In the adiabatic limit, we study Rosen–Zener transition of superfluid Fermi gas in a double well potential. We find that s-wave scattering length of the system can affect the quantum transition dramatically. At certain regime the complete population transfer between two wells is observed. On the contrary, the quantum transition could be completely blocked in other regime. We have derived analytical expressions for the transition probability. We also find that, in the adiabatic limit, the population difference between two modes always oscillates around its corresponding fixed point during Rosen–Zener transition process. The difference between population imbalance and the corresponding fixed point decreases with the adiabatic condition becomes stronger. The numerical simulation show a power law relation between them. It is verified by the Rosen–Zener transition for superfluid Fermi gas in the limited cases of both deep Bose-Einstein condensate regime and unitarity regime.

Ultracold Fermi gas in a single-mode cavity: Cavity-mediated interaction and BCS-BEC evolution

We propose that the evolution of superfluidity from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime can be realized using ultracold Fermi gas coupled to a single-mode cavity. By the functional integral formalism, we derive an effective atom-only action, which mimics the two-component Fermi gas with tunable two-body interaction. First, we address the features of the cavity-mediated interaction. We find that the matter-light coupling creates an effective $s$-wave scattering whose sign and amplitude are controlled by parameters of the cavity. Second, we discuss the fermionic superfluidity on the mean-field level, including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, and dissociation temperature. It is shown that by varying the atom-cavity detuning, a BCS to BEC crossover occurs. In addition, the influences of the atomic collaborative effect and external pumping field on the pairing correlation are also studied.

THE EFFECTS OF THE BEYOND MEAN FIELD CORRECTIONS OF FERMI SUPERFLUID GAS IN A DOUBLE-WELL POTENTIAL

By considering the contribution of the higher-order term representing the lowest approximation of beyond mean field corrections, we investigate a superfluid Fermi gas confined in a double-well potential in Bose–Einstein Condensation (BEC) side of the Bardeen–Cooper–Schrieffer (BCS) to BEC crossover. Two limited cases of deep BEC regime and BEC regime of BCS–BEC crossover, corresponding to the two-body scattering length a sc is small enough and large enough, respectively. We derive a simple two-mode model that could depict the dynamics effectively. With making thorough analysis on the two-mode model and its corresponding classical Hamiltonian, we find that the Josephson oscillation or self-trapping phenomenon could emerge at certain parameters. We find three kinds of the phase states: Josephson oscillation (JO), oscillating-phase-type self-trapping (OPTST) and running-phase-type self-trapping (RPTST). The dependence of these three phase states on the dimensionless interaction parameter y = 1/(kFa sc ) and the initial system energy are given in this paper.

Nonequilibrium damping of the collective motion of homogeneous cold Fermi condensates with Feshbach resonances

Collisionless damping of a condensate of cold Fermi atoms, whose scattering is controlled by a Feshbach resonance, is explored throughout the BCS and Bose-Einstein condensate (BEC) regimes when small perturbations on its phase and amplitude modes are turned on to drive the system slightly out of equilibrium. Using a one-loop effective action, we first recreate the known result that for a broad resonance the amplitude of the condensate decays as ${t}^{\ensuremath{-}1/2}$ at late times in the BCS regime, whereas it decays as ${t}^{\ensuremath{-}3/2}$ in the BEC regime. We then examine the case of an idealized narrow resonance, and find that this collective mode decays as ${t}^{\ensuremath{-}3/2}$ throughout both the BCS and BEC regimes. Although this seems to contradict earlier results that damping is identical for both broad and narrow resonances, the breakdown of the narrow resonance limit restores this universal behavior. More measurably, the phase perturbation may give a shift on the saturated value to which the collective amplitude mode decays, which vanishes only in the deep BCS regime when the phase and amplitude modes are decoupled.

The self-trapping of superfluid Fermi gases in the Bose-Einstein condensation regime and in unitarity

In the mean-field theory and two-mode approximation, we study the self-trapping of superfluid Fermi gases in the BEC regime and in unitarity by observing the evolution of the population imbalance with time and the variation of the average of population imbalance with several non-linear interaction parameters. The high-frequency modulations of both the symmetric double-well potential and the potential well are studied. The boundary conditions of the self-trapping and non-self-trapping are given. We find that high-frequency modulation in a certain range of modulation can make the self-trapping phenomenon easier to achieve. Finally, we study the influence of the initial value on self-trapping, and find that the increase of the absolute of the initial value can make the self-trapping more conducive to the realization.

Dark solitons in a Gross–Pitaevskii equation with a power-law nonlinearity: application to ultracold Fermi gases near the Bose–Einstein condensation regime

In this work, we consider a model of a defocusing nonlinear Schrödinger equation with a variable nonlinearity exponent. This is motivated by the study of a superfluid Fermi gas in the Bose–Einstein condensation (BEC)–Bardeen–Cooper–Schrieffer crossover. In particular, we focus on the relevant mean-field model in the regime from BEC to unitarity and especially consider the modification of the nearly black soliton oscillation frequency due to the variation in the nonlinearity exponent in a harmonic trapping potential. The analytical expressions given as a function of the relevant nonlinearity exponent are corroborated by numerical computations and also extended past the BEC limit.

Auxiliary field formalism for dilute fermionic atom gases with tunable interactions

We develop the auxiliary field formalism corresponding to a dilute system of spin-1/2 fermions. This theory represents the Fermi counterpart of the BEC theory developed recently by F. Cooper et al. [Phys. Rev. Lett. 105, 240402 (2010)] to describe a dilute gas of Bose particles. Assuming tunable interactions, this formalism is appropriate for the study of the crossover from the regime of Bardeen-Cooper-Schriffer (BCS) pairing to the regime of Bose-Einstein condensation (BEC) in ultracold fermionic atom gases. We show that when applied to the Fermi case at zero temperature, the leading-order auxiliary field (LOAF) approximation gives the same equations as those obtained in the standard BCS variational picture. At finite temperature, LOAF leads to the theory discussed by by Sa de Melo, Randeria, and Engelbrecht [Phys. Rev. Lett. 71, 3202(1993); Phys. Rev. B 55, 15153(1997)]. As such, LOAF provides a unified framework to study the interacting Fermi gas. The mean-field results discussed here can be systematically improved upon by calculating the one-particle irreducible (1-PI) action corrections, order by order.

Evolution from Bardeen–Cooper–Schrieffer to Bose–Einstein condensate superfluidity in the presence of disorder

We describe the effects of disorder on the critical temperature of s-wave superfluids from the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein condensate (BEC) regime, with direct application to ultracold fermions. We use the functional integral method and the replica technique to study Gaussian correlated disorder due to impurities, and we discuss how this system can be generated experimentally. In the absence of disorder, the BCS regime is characterized by pair breaking and phase coherence temperature scales that are essentially the same, allowing strong correlations between the amplitude and phase of the order parameter for superfluidity. As non-pair-breaking disorder is introduced, the largely overlapping Cooper pairs seek to maintain phase coherence such that the critical temperature remains essentially unchanged, and Anderson's theorem is satisfied. However, in the BEC regime, the pair breaking and phase coherence temperature scales are very different such that non-pair-breaking disorder can dramatically affect phase coherence, and thus the critical temperature, without the requirement of breaking tightly bound fermion pairs simultaneously. In this case, Anderson's theorem does not apply, and the critical temperature can be more easily reduced in comparison to the BCS limit. Lastly, we find that the superfluid is more robust against disorder in the intermediate region near unitarity between the two regimes.