Bose-Einstein Condensation Regime Research Articles

Enhanced critical temperature, pairing fluctuation effects, and BCS-BEC crossover in a two-band Fermi gas

We study the superfluid critical temperature in a two-band attractive Fermi system with strong pairing fluctuations associated with both interband and intraband couplings. We focus specifically on a configuration where the intraband coupling is varied from weak to strong in a shallow band coupled to a weakly-interacting deeper band. The whole crossover from the Bardeen-Cooper-Schrieffer (BCS) condensation of largely overlapping Cooper pairs to the Bose-Einstein condensation (BEC) of tightly bound molecules is covered by our analysis, which is based on the extension of the Nozi\`{e}res-Schmitt-Rink (NSR) approach to a two-band system. In comparison with the single-band case, we find a strong enhancement of the critical temperature, a significant reduction of the preformed pair region where pseudogap effects are expected, and the entanglement of two kinds of composite bosons in the strong-coupling BEC regime.

Nonequilibrium dynamics in the pump-probe spectroscopy of excitonic insulators

We study the nonequilibrium dynamics in the pump-probe spectroscopy of excitonic insulators using the spinless two-orbital model with phonon degrees of freedom in the time-dependent mean-field approximation. We introduce the pulse light as a time-dependent vector potential via the Peierls phase in the Hamiltonian. We find that, in the Bose-Einstein condensation regime where the normal state is semiconducting, the excitonic order is suppressed when the frequency of the pulse light is slightly larger than the band gap, while the order is enhanced when the frequency of the pulse is much larger than the band gap. We moreover find that the excitonic order is completely destroyed in the former situation if the intensity of the pulse is sufficiently strong. In the BCS regime where the normal state is semimetallic, we find that the excitonic order is always suppressed, irrespective of the frequency of the pulse light. The quasiparticle band structure and optical conductivity spectrum after the pumping are also calculated for the instantaneous states.

Critical Vortex Shedding in a Strongly Interacting Fermionic Superfluid.

We study the critical vortex shedding in a strongly interacting fermionic superfluid of ^{6}Li across the BEC-BCS crossover. By moving an optical obstacle in the sample and directly imaging the vortices after the time of flight, the critical velocity u_{vor} for vortex shedding is measured as a function of the obstacle travel distance L. The observed u_{vor} increases with decreasing L, where the rate of increase is the highest in the unitary regime. In the deep Bose-Einstein condensation regime, an empirical dissipation model well captures the dependence of u_{vor} on L, characterized by a constant value of η=-[d(1/u_{vor})/d(1/L)]. However, as the system is tuned across the resonance, a step increase of η develops about a characteristic distance L_{c} as L is increased, where L_{c} is comparable to the obstacle size. This bimodal behavior is strengthened as the system is tuned towards the BCS regime. We attribute this evolution of u_{vor} to the emergence of the underlying fermionic degree of freedom in the vortex-shedding dynamics of a Fermi condensate.

Quantum Spin Dynamics of Individual Neutral Impurities Coupled to a Bose-Einstein Condensate.

We report on spin dynamics of individual, localized neutral impurities immersed in a Bose-Einstein condensate. Single cesium atoms are transported into a cloud of rubidium atoms and thermalize with the bath, and the ensuing spin exchange between localized impurities with quasispin F_{i}=3 and bath atoms with F_{b}=1 is resolved. Comparing our data to numerical simulations of spin dynamics, we find that, for gas densities in the Bose-Einstein condensate regime, the dynamics is dominated by the condensed fraction of the cloud. We spatially resolve the density overlap of impurities and gas by the spin population of impurities. Finally, we trace the coherence of impurities prepared in a coherent superposition of internal states when coupled to a gas of different densities. For our choice of states, we show that, despite high bath densities and, thus, fast thermalization rates, the impurity coherence is not affected by the bath, realizing a regime of sympathetic cooling while maintaining internal state coherence. Our work paves the way toward the nondestructive probing of quantum many-body systems via localized impurities.

Super Efimovian expansions of superfluid Fermi gases in the BCS–BEC crossover

We study the super Efimovian expansions of a superfluid Fermi gas in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC), by using superfluid hydrodynamic equations with the equation of state fitting from the experimental data and a scaling approach. We find that in an isotropic trap, the super Efimovian expansion of the Fermi superfluid in the unitary limit is characterized by the double-log periodicity, while for an axially symmetric trap, the double-log periodicity only emerges in the longer direction for a large anisotropy of the trapping frequencies. Away from unitarity where the scale invariance is broken, the super Efimovian expansions of the superfluid Fermi gases deviate from the double-log oscillations. The oscillations in the BCS regime deviate upward from the double-log oscillations, whereas the oscillations in the BEC regime deviate downward and the deviation in the BEC limit is the most significant. This difference can be used to discriminate different superfluid regimes.

Effect of finite range interactions on roton mode softening in a multi-component BEC

We consider the Gross-Pitaevskii model of a Bose–Einstein Condensate (BEC) for single-component and multi-component BEC. The pseudopotential for s-wave scattering between atoms is taken to be of a width of the order of the s-wave scattering length. Such an interaction giving rise to a roton minimum in the spectrum of elementary excitations of a single-component BEC is well known. However, softening roton modes take us into the strongly interacting BEC regime where three body losses occur. We study the roton mode softening for a multi-component BEC. We show that by increasing the number of components of a multi-component BEC, the roton mode can be softened at a progressively lower value of the gas parameter (a3n), thus reducing the three body losses.

Shear Viscosity of Uniform Fermi Gases with Population Imbalance

The shear viscosity has been an important topic in ultracold Fermi gases, and it has served as a diagnostic of various theories. Due to the complicated phase structures of population-imbalanced (polarized) Fermi gases with tunable attraction, past works on the shear viscosity mainly focused on unpolarized Fermi gases. Here we investigate the shear viscosity of homogeneous, population-imbalanced Fermi superfluid at finite temperatures by a pairing fluctuation theory for thermodynamical quantities and a gauge-invariant linear response theory for transport coefficients. The Cooper pairs lead to the anomalous shear viscosity analogous to the shear viscosity. We derive an exact relation connecting certain thermodynamic quantities and transport coefficients at the mean-field level for polarized unitary Fermi superfluids. An approximate relation beyond mean-field is proposed and only exhibits mild deviations from our numerical results. In the unitary and Bose-Einstein condensation (BEC) regimes, the total shear viscosity increases with the polarization because the excess majority fermions cause gapless excitations acting like a normal fluid. Moreover, competition among the excess fermions, noncondensed pairs, and fermionic quasiparticles may lead to non-monotonic behavior of the ratio between the shear viscosity and relaxation time as the polarization increases.

Multicomponent Electron-Hole Superfluidity and the BCS-BEC Crossover in Double Bilayer Graphene.

Superfluidity in coupled electron-hole sheets of bilayer graphene is predicted here to be multicomponent because of the conduction and valence bands. We investigate the superfluid crossover properties as functions of the tunable carrier densities and the tunable energy band gap E_{g}. For small band gaps there is a significant boost in the two superfluid gaps, but the interaction-driven excitations from the valence to the conduction band can weaken the superfluidity, even blocking the system from entering the Bose-Einstein condensate (BEC) regime at low densities. At a given larger density, a band gap E_{g}∼80-120 meV can carry the system into the strong-pairing multiband BCS-BEC crossover regime, the optimal range for realization of high-T_{c} superfluidity.

Relaxation dynamics of a driven two-level system coupled to a Bose–Einstein condensate: application to quantum dot-dipolar exciton gas hybrid systems

We develop a microscopic theory for the relaxation dynamics of an optically pumped two-level system (TLS) coupled to a bath of weakly interacting Bose gas. Using Keldysh formalism and diagrammatic perturbation theory, expressions for the relaxation times of the TLS Rabi oscillations are derived when the boson bath is in the normal state and the Bose–Einstein condensate (BEC) state. We apply our general theory to consider an irradiated quantum dot coupled with a boson bath consisting of a two-dimensional dipolar exciton gas. When the bath is in the BEC regime, relaxation of the Rabi oscillations is due to both condensate and non-condensate fractions of the bath bosons for weak TLS-light coupling and pre dominantly due to the non-condensate fraction for strong TLS-light coupling. Our theory also shows that a phase transition of the bath from the normal to the BEC state strongly influences the relaxation rate of the TLS Rabi oscillations. The TLS relaxation rate is approximately independent of the pump field frequency and monotonically dependent on the field strength when the bath is in the low-temperature regime of the normal phase. Phase transition of the dipolar exciton gas leads to a non-monotonic dependence of the TLS relaxation rate on both the pump field frequency and field strength, providing a characteristic signature for the detection of BEC phase transition of the coupled dipolar exciton gas.

Dynamical instability of a driven-dissipative electron-hole condensate in the BCS-BEC crossover region

We present a stability analysis on a driven-dissipative electron-hole condensate in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-condensation)-crossover region. Extending the combined BCS-Leggett theory with the generalized random phase approximation (GRPA) to the non-equilibrium case by employing the Keldysh formalism, we show that the pumping-and-decay of carriers causes a depairing effect on excitons. This phenomenon gives rise to an attractive interaction between excitons in the BEC regime, as well as a supercurrent that anomalously flows anti-parallel to $\nabla \theta({\bf r})$ (where $\theta({\bf r})$ is the phase of the condensate) in the BCS regime, both leading to dynamical instabilities of an exciton-BEC. Our result suggests that substantial region of the exciton-BEC phase in the phase diagram (in terms of the interaction strength and the decay rate) is unstable.

Multiply Quantized Vortices in Fermionic Superfluids: Angular Momentum, Unpaired Fermions, and Spectral Asymmetry.

We compute the orbital angular momentum L_{z} of an s-wave paired superfluid in the presence of an axisymmetric multiply quantized vortex. For vortices with a winding number |k|>1, we find that in the weak-pairing BCS regime, L_{z} is significantly reduced from its value ℏNk/2 in the Bose-Einstein condensation (BEC) regime, where N is the total number of fermions. This deviation results from the presence of unpaired fermions in the BCS ground state, which arise as a consequence of spectral flow along the vortex subgap states. We support our results analytically and numerically by solving the Bogoliubov-de Gennes equations within the weak-pairing BCS regime.

Goldstone mode and pair-breaking excitations in atomic Fermi superfluids

Bragg spectroscopy shows the evolution of gapless Goldstone modes and single-particle-like excitations in an atomic Fermi superfluid as it crosses from a Bardeen–Cooper–Schrieffer superfluid to the Bose–Einstein condensate regime. Spontaneous symmetry breaking is a central paradigm of elementary particle physics1, magnetism2, superfluidity3 and superconductivity4. According to Goldstone’s theorem, phase transitions that break continuous symmetries lead to the existence of gapless excitations in the long-wavelength limit5. These Goldstone modes can become the dominant low-energy excitation, showing that symmetry breaking has a profound impact on the physical properties of matter. Here, we present a comprehensive study of the elementary excitations in a homogeneous strongly interacting Fermi gas through the crossover from a Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC) of molecules using two-photon Bragg spectroscopy. The spectra exhibit a discrete Goldstone mode, associated with the broken-symmetry superfluid phase, as well as pair-breaking single-particle excitations. Our techniques yield a direct determination of the superfluid pairing gap and speed of sound in close agreement with strong-coupling theories.

Screening masses of photons interacting with a two-species fermionic system in relativistic BCS–BEC crossover

We address the behavior of Debye and Meissner masses of photons in a condensate of fermion pairs in the presence of number density asymmetry. Our formalism applies to a two-species fermionic system with number density asymmetry in BCS–Bose–Einstein condensation (BEC)–relativistic BEC crossover and with variable rapidity. Our results recover the known results of the photon self-energy in the ultrarelativistic limit and the superfluid density in the nonrelativistic limit. We further consider the electromagnetic stability of the condensate and show that the Meissner mass squared can become negative in the weakly coupling BCS regime and the strongly coupling relativistic BEC regime. The electromagnetic instability is compared to the mechanical stability discussed in previous works.

Influence of quantum phase transition on spin transport in the quantum antiferromagnet in the honeycomb lattice

We use the SU(3) Schwinger boson theory to study the spin transport properties of the two-dimensional anisotropic frustrated Heisenberg model in a honeycomb lattice at T=0 with single ion anisotropy and third neighbor interactions. We have investigated the behavior of the spin conductivity for this model that presents exchange interactions J1, J2 and J3. We study the spin transport in the Bose–Einstein condensation regime where the bosons tz are condensed. Our results show an influence of the quantum phase transition point on the spin conductivity behavior. We also have made a diagrammatic expansion for the Green-function and did not obtain any significant change of the results.

Zero-Temperature Properties of a Strongly Interacting Superfluid Fermi Gas in the BCS–BEC Crossover Region

We investigate thermodynamic properties and effects of quantum fluctuations in the Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensation (BEC) crossover region of a superfluid Fermi gas in the low-temperature limit. Including strong-coupling corrections within the framework of an extended T-matrix approximation, we numerically compute the isothermal compressibility $$\chi _n$$ . While quantum fluctuation effects on $$\chi _n$$ in the strong-coupling BEC regime are explained by the quantum depletion due to a repulsive interaction between tightly bound molecules, effects of self-energy shift on the Fermi chemical potential are found to enhance $$\chi _n$$ in the weak-coupling BCS region. We also show that the calculated $$\chi _n$$ agrees well with the recent experiment on a $$^6$$ Li Fermi gas done from the weak-coupling region to the unitarity limit. Our result would be useful for the study of many-body quantum corrections in the BCS–BEC crossover region of a strongly interacting Fermi superfluid.

Quantum Fluctuations and Vortex-Antivortex Unbinding in the 2D Bcs-Bec Crossover

Very recently quasi two-dimensional (2D) systems made of attractive fermionic alkali-metal atoms with a widely tunable interaction due to Fano-Feshbach resonances have been realized. In this way it has been achieved the 2D crossover from the Bardeen-Cooper-Schrieffer regime of weakly-interacting Cooper pairs to the Bose-Einstein condensate regime strongly bound dimers. These experiments pave the way to the investigation of 2D strongly-interacting attractive fermions during the Berezinskii-Kosterlitz-Thouless (BKT) transition from a low-temperature superfluid phase characterized by quasi-condensation to a high-temperature normal phase, where vortex proliferation driven by quantum and thermal fluctuations completely destroys superfluidity. In this paper we discuss our preliminar theoretical results on the behavior of the BKT critical temperature across the crossover. Our microscopic calculations are based on functional integration taking into account renormalized Gaussian fluctuations and the crucial 2D effect of vortex-antivortex unbinding.

Effect of the particle-hole channel on BCS-Bose-Einstein condensation crossover in atomic Fermi gases.

BCS–Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel, and has attracted a lot of attention since the experimental realization of quantum degenerate atomic Fermi gases. Here we study the effect of the (often dropped) particle-hole channel on the zero T gap Δ(0), superfluid transition temperature Tc, the pseudogap at Tc, and the mean-field ratio 2Δ(0)/, from BCS through BEC regimes, using a pairing fluctuation theory which includes self-consistently the contributions of finite-momentum pairs and features a pseudogap in single particle excitation spectrum. Summing over the infinite particle-hole ladder diagrams, we find a complex dynamical structure for the particle-hole susceptibility χph, and conclude that neglecting the self-energy feedback causes a serious over-estimate of χph. While our result in the BCS limit agrees with Gor’kov et al., the particle-hole channel effect becomes more complex and pronounced in the crossover regime, where χph is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the BEC regime, the particle-hole channel contributions drop to zero. We predict a density dependence of the magnetic field at the Feshbach resonance, which can be used to quantify χph and test different theories.

Spin superfluidity in the anisotropic XY model in the triangular lattice

Abstract We use the SU(3) Schwinger׳s boson theory to study the spin transport properties in the two-dimensional anisotropic frustrated Heisenberg model in the triangular lattice at T=0. We have investigated the behavior of the spin conductivity for this model which presents an single-ion anisotropy. We study the spin transport in the Bose-Einstein condensation regime where we have that the tz bosons are condensed and the following condition is valid: 〈 t z 〉 = 〈 t z † 〉 = t . Our results show a metallic spin transport for ω > 0 and a superfluid spin transport in the limit of DC conductivity, ω → 0 , where σ ( ω ) tends to infinity in this limit of ω.

Spin conductivity of the two-dimensional anisotropic frustrated Heisenberg model in the honeycomb lattice

Abstract We use the SU(3) Schwinger׳s boson theory to study the spin transport properties of the two-dimensional anisotropic frustrated Heisenberg model in a honeycomb lattice at T=0. We have investigated the behavior of the spin conductivity for this model which presents a single-ion anisotropy and J1 and J2 exchange interactions. We study the spin transport in the Bose–Einstein condensation regime where we have that the tz bosons are condensed and the following condition is valid: 〈 t z 〉 = 〈 t z † 〉 = t . Our results show a metallic spin transport for ω > 0 and a superconductor spin transport in the limit of DC conductivity, ω → 0 , where σ ( ω ) tends to infinity in this limit of ω.

Specific heat and effects of pairing fluctuations in the BCS-BEC-crossover regime of an ultracold Fermi gas

We investigate the specific heat at constant volume $C_V$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature $T_{\rm c}$. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while $C_V(T\gesim T_{\rm c})$ in the unitary regime is remarkably enhanced by {\it metastable} preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived {\it stable} molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a $^6$Li unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas, to eventually become stable, as one passes through the BCS-BEC crossover region.