BCS-BEC Crossover Regime Research Articles

Inhomogeneous Pseudogap Phenomenon in the BCS-BEC Crossover Regime of a Trapped Superfluid Fermi Gas

We investigate pseudogap phenomena in the unitarity limit of a trapped superfluid Fermi gas. Including effect of strong pairing fluctuations within a T-matrix approximation, as well as effects of a harmonic trap within the local density approximation (LDA), we calculate the local superfluid density of states below the superfluid phase transition temperature Tc. We show that the spatial region where single-particle excitations are dominated by the pseudogap may still exist even below Tc, due to inhomogeneous pairing fluctuations caused by the trap potential. From the temperature dependence of the pseudogapped density of states, we identify the pseudogap regime of the unitarity Fermi gas with respect to the temperature and spatial position. We also show that the combined T-matrix theory with the LDA can quantitatively explain the local pressure which was recently observed in the unitarity limit of a 6Li Fermi gas.

Coexistence of superfluid gap and pseudogap in the BCS-BEC crossover regime of a trapped Fermi gas belowTc

We investigate strong pairing fluctuations and effects of a harmonic trap in the superfluid phase of an ultracold Fermi gas. Including amplitude and phase fluctuations of the inhomogeneous superfluid order parameter $\Delta(r)$ in a trap within a combined $T$-matrix theory with the local density approximation, we examine local properties of single-particle excitations and a thermodynamic quantity in the BCS-BEC crossover region. Below the superfluid phase transition temperature $T_{\rm c}$, we show that inhomogeneous pairing fluctuations lead to a shell structure of the gas cloud in which the spatial region where the ordinary BCS-type superfluid density of states appears is surrounded by the region where the pseudogap associated with strong pairing fluctuations dominates single-particle excitations. The former spatial region enlarges to eventually cover the whole gas cloud far below $T_{\rm c}$. We also examine how this shell structure affects the photoemission spectrum, as well as the local pressure. Since a cold Fermi gas is always trapped in a harmonic potential, our results would be useful for the study of strong-coupling superfluid physics, including this realistic situation.

Spin susceptibility and fluctuation corrections in the BCS-BEC crossover regime of an ultracold Fermi gas

We investigate magnetic properties and effects of pairing fluctuations in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Recently, Liu and Hu, and Parish, pointed out that the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem is found to also exist in the ordinary non-self-consistent T-matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended T-matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a 6Li Fermi gas done by Sanner and co-workers. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature Tc, as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below Tc in the BCS-BEC crossover regime of cold Fermi gases.

Two-Dimensional Pseudogap Effects of an Ultracold Fermi Gas in the BCS-BEC Crossover Region

We investigate pseudogap phenomena originating from pairing fluctuations in the BCS-BEC crossover regime of a two-dimensional Fermi gas in a harmonic trap. Including pairing fluctuations within a $T$-matrix theory and effects of a trap within the local density approximation, we calculate the local density of states (LDOS) at the superfluid phase transition temperature $T_{\rm c}$. In the weak-coupling regime, we show that the pseudogap already appears in LDOS around the trap center. The spatial region where the pseudogap can be seen in LDOS becomes wider for a strong pairing interaction. We also discuss how the pseudogap affects the spectrum of the photoemission-type experiment developed by JILA group.

Erratum: Superfluid density of states and pseudogap phenomenon in the BCS-BEC crossover regime of a superfluid Fermi gas [Phys. Rev. A82, 043630 (2010)

Received 24 February 2012DOI:https://doi.org/10.1103/PhysRevA.85.039908©2012 American Physical Society

Pseudogap temperature and effects of a harmonic trap in the BCS-BEC crossover regime of an ultracold Fermi gas

We theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using a combined $T$-matrix theory with the local density approximation, we calculate strong-coupling corrections to single-particle local density of states (LDOS), as well as the single-particle local spectral weight (LSW). Starting from the superfluid phase transition temperature $T_{\rm c}$, we clarify how the pseudogap structures in these quantities disappear with increasing the temperature. As in the case of a uniform Fermi gas, LDOS and LSW give different pseudogap temperatures $T^*$ and $T^{**}$ at which the pseudogap structures in these quantities completely disappear. Determining $T^*$ and $T^{**}$ over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensate) crossover region, we identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also show that the so-called back-bending peak recently observed in the photoemission spectra by JILA group may be explained as an effect of pseudogap phenomenon in the trap center. Since strong pairing fluctuations, spatial inhomogeneity, and finite temperatures, are important keys in considering real cold Fermi gases, our results would be useful for clarifying normal state properties of this strongly interacting Fermi system.

Superfluid density of states and pseudogap phenomenon in the BCS-BEC crossover regime of a superfluid Fermi gas

We investigate single-particle excitations and strong-coupling effects in the BCS-BEC crossover regime of a superfluid Fermi gas. Including phase and amplitude fluctuations of the superfluid order parameter within a $T$-matrix theory, we calculate the superfluid density of states (DOS), as well as single-particle spectral weight, over the entire BCS-BEC crossover region below the superfluid transition temperature $T_{\rm c}$. We clarify how the pseudogap in the normal state evolves into the superfluid gap, as one passes through $T_{\rm c}$. While the pseudogap in DOS continuously evolves into the superfluid gap in the weak-coupling BCS regime, the superfluid gap in the crossover region is shown to appear in DOS after the pseudogap disappears below $T_{\rm c}$. In the phase diagram with respect to the temperature and interaction strength, we determine the region where strong pairing fluctuations dominate over single-particle properties of the system. Our results would be useful for the study of strong-coupling phenomena in the BCS-BEC crossover regime of a superfluid Fermi gas.

Photoemission spectrum and effect of inhomogeneous pairing fluctuations in the BCS-BEC crossover regime of an ultracold Fermi gas

We investigate the photoemission-type spectrum in a cold Fermi gas which was recently measured by JILA group [J. T. Stewart {\it et al}., Nature \textbf{454}, 744 (2008)]. This quantity gives us very useful information about single-particle properties in the BCS-BEC crossover. In this letter, including pairing fluctuations within a $T$-matrix theory, as well as effects of a harmonic trap within the local density approximation, we show that spatially inhomogeneous pairing fluctuations due to the trap potential is an important key to understand the observed spectrum. In the crossover region, while strong pairing fluctuations lead to the so-called pseudogap phenomenon in the trap center, such strong-coupling effects are found to be weak around the edge of the gas. Our results including this effect are shown to agree well with the recent photoemission data by JILA group.

Stability of Sarma phases in density imbalanced electron-hole bilayer systems

We study excitonic condensation in an electron-hole bilayer system with unequal layer densities at zero temperature. Using mean-field theory we solve the BCS gap equations numerically and investigate the effects of intra-layer interactions. We analyze the stability of the Sarma phase with $\bk,-\bk$ pairing by calculating the superfluid mass density and also by checking the compressibility matrix. We find that with bare Coulomb interactions the superfluid density is always positive in the Sarma phase, due to a peculiar momentum structure of the gap function originating from the singular behavior of the Coulomb potential at zero momentum and the presence of a sharp Fermi surface. Introducing a simple model for screening, we find that the superfluid density becomes negative in some regions of the phase diagram, corresponding to an instability towards a Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) type superfluid phase. Thus, intra-layer interaction and screening together can lead to a rich phase diagram in the BCS-BEC crossover regime in electron-hole bilayer systems.

Phenomenological Equation of State and Density Profiles of Strongly Interacting Trapped Superfluid Fermi Gases with Arbitrary Atom Numbers

We present a phenomenological equation of state (EOS), derive a nonlinear quantum hydrodynamical equation and investigate the density profiles of a trapped superfluid Fermi gas with arbitrary number of particles in the BCS-BEC crossover regime. The asymptotic behavior of the EOS exactly matches with its expansions in three limiting regimes: BCS, unitarity and BEC. By using this EOS, the quantum hydrodynamical equation is beyond mean-field version, valid in all interacting regimes and used for the unitarity regime specially. We take a Fetter-like trial wave function in generalized Thomas-Fermi approximation, solve the hydrodynamical equation and calculate the energy, chemical potential, sizes and profiles of the ground-state condensate in the BCS-BEC crossover regime. Our results agree well with the theoretical and experimental results.

Instability of superfluid Fermi gases induced by a rotonlike density mode in optical lattices

We study the stability of superfluid Fermi gases in deep optical lattices in the BCS--Bose-Einstein condensation (BEC) crossover at zero temperature. Within the tight-binding attractive Hubbard model, we calculate the spectrum of the low-energy Anderson-Bogoliubov (AB) mode as well as the single-particle excitations in the presence of superfluid flow in order to determine the critical velocities. To obtain the spectrum of the AB mode, we calculate the density response function in the generalized random-phase approximation applying the Green's function formalism developed by C\^ot\'e and Griffin to the Hubbard model. We find that the spectrum of the AB mode is separated from the particle-hole continuum having the characteristic rotonlike minimum at short wavelength due to the strong charge-density-wave fluctuations. The energy of the rotonlike minimum decreases with increasing the lattice velocity and it reaches zero at the critical velocity which is smaller than the pair-breaking velocity. This indicates that the superfluid state is energetically unstable due to the spontaneous emission of the short-wavelength rotonlike excitations of the AB mode instead due to pair breaking. We determine the critical velocities as functions of the interaction strength across the BCS-BEC crossover regime.

Pairing fluctuations and pseudogap effects in the BCS–BEC crossover regime of a superfluid Fermi gas

We study effects of strong pairing fluctuations on single-particle properties of a superfluid Fermi gas in the BCS–BEC crossover region. Including phase and amplitude fluctuations of the order parameter within the T-matrix approximation, we calculate the superfluid density of states below the superfluid phase transition temperature Tc. We show how the pseudogap appearing in the normal phase above Tc changes into the superfluid gap over the entire BCS–BEC crossover region, as one passes through Tc.

Inelastic Collisions of a Fermi Gas in the BEC-BCS Crossover

We measure inelastic three-body and two-body collisional decay rates for a two-component Fermi gas of 6Li, which are highly suppressed by the Pauli exclusion principle. Our measurements are made in the BEC-BCS crossover regime, near the two-body collisional (Feshbach) resonance. At high temperature (energy) the data show a dominant three-body decay process, which is studied as a function of bias magnetic field. At low energy, the data show a coexistence of two-body and three-body decay processes near and below the Feshbach resonance. Below resonance, the observed two-body inelastic decay can arise from molecule-atom and molecule-molecule collisions. We suggest that at and above resonance, an effective two-body decay rate arises from collisions between atoms and correlated (Cooper) pairs that can exist at sufficiently low temperature.

The quantum pressure correction to the excitation spectrum of the trapped superfluid Fermi gases in a BEC-BCS crossover

Using quantum hydrodynamic approaches, we study the quantum pressure correction to the collective excitation spectrum of the interacting trapped superfluid Fermi gases in the BEC-BCS crossover. Based on a phenomenological equation of state, we derive hydrodynamic equations of the system in the whole BEC-BCS crossover regime. Beyond the Thomas–Fermi approximation, expressions of the frequency corrections of collective modes for both spherical and axial symmetric traps excited in the BEC-BCS crossover are given explicitly. The corrections of the eigenfrequencies due to the quantum pressure and their dependence on the inverse interaction strength, anisotropic parameter and particle numbers of the condensate are discussed in detail.

Collective Excitations of Trapped Superfluid Fermi Gases in a BCS-BEC Crossover with Arbitrary Atom Numbers

We investigate the collective excitations of an axially-symmetric harmonically trapped superfluid Fermi gas in the BCS-BEC crossover, focusing on the dependence of the frequency of the collective modes on the atom number. Starting from a phenomenological equation of state valid for the whole BCS-BEC crossover regime and the time-dependent Gross-Pitaevskii equation of the condensed fermionic superfluid, we obtain analytically the chemical potential and ground-state wavefunction of the paired fermions with arbitrary atom numbers by use of variational method. We solve the generalized Bogoliubov-de Gennes equations numerically and discuss the properties of low-lying excitations when the system consists with Fermi atoms of several hundreds or thousands. Our numerical results reveal some new properties of the small system in the excited states.

Realization of a Strongly Interacting Bose-Fermi Mixture from a Two-Component Fermi Gas

We show the emergence of a strongly interacting Bose-Fermi mixture from a two-component Fermi mixture with population imbalance. By analyzing in situ density profiles of 6Li atoms in the BCS-BEC crossover regime, we identify a critical interaction strength, beyond which all minority atoms pair up with majority atoms and form a Bose condensate. This is the regime where the system can be effectively described as a boson-fermion mixture. We determine the dimer-fermion and dimer-dimer scattering lengths and beyond-mean-field contributions. Our study realizes a gedanken experiment of bosons immersed in a Fermi sea of one of their constituents, revealing the composite nature of the bosons.

Energetics and structural properties of trapped two-component Fermi gases

Using two different numerical methods, we study the behavior of two-component Fermi gases interacting through short-range $s$-wave interactions in a harmonic trap. A correlated Gaussian basis-set expansion technique is used to determine the energies and structural properties, i.e., the radial one-body densities and pair distribution functions, for small systems with either even or odd $N$, as functions of the $s$-wave scattering length and the mass ratio $\ensuremath{\kappa}$ of the two species. Particular emphasis is put on a discussion of the angular momentum of the system in the BEC-BCS crossover regime. At unitarity, the excitation spectrum of the four-particle system with total angular momentum $L=0$ is calculated as a function of the mass ratio $\ensuremath{\kappa}$. The results are analyzed from a hyperspherical perspective, which offers unique insight into the problem. Additionally, fixed-node diffusion Monte Carlo calculations are performed for equal-mass Fermi gases with up to $N=30$ atoms. We focus on the odd-even oscillations of the ground-state energy of the equal-mass unitary system having up to $N=30$ particles, which are related to the excitation gap of the system. Furthermore, we present a detailed analysis of the structural properties of these systems.

Superfluid density in the BCS–BEC crossover regime of a Fermi superfluid

We investigate the superfluid carrier density ρs in the BCS–BEC crossover regime of a Fermi superfluid at finite temperatures. Including pairing fluctuations within a Gaussian approximation, we calculate the superfluid order parameter, chemical potential, and ρs in a consistent manner in the whole BCS–BEC crossover region. In the weak-coupling BCS regime, the temperature dependence of ρs is dominated by single-particle excitations accompanied by thermal dissociation of Cooper pairs. In the strong-coupling BEC regime, we show that single-particle excitations become less dominant and thermal excitations of collective Bogoliubov mode become important for ρs. We clarify how the weak-coupling BCS result smoothly changes into the strong-coupling BEC result, as one increases the strength of a pairing interaction.

Imbalanced Superfluid Phase of a Trapped Fermi Gas in the BCS–BEC Crossover Regime

We theoretically investigate the ground state of trapped neutral fermions with population imbalance in the BCS–BEC crossover regime. On the basis of the single-channel Hamiltonian, we perform full numerical calculations of the Bogoliubov–de Gennes equation coupled with the regularized gap and number equations. The zero-temperature phase diagram in the crossover regime is presented, where the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing state governs the weak-coupling BCS region of a resonance. It is found that the FFLO oscillation vanishes in the BEC side, in which the system under population imbalance turns into a phase separation (PS) between locally binding superfluid and fully polarized spin domains. We also demonstrate numerical calculations with a large particle number O (10 5 ), comparable to that observed in recent experiments. The resulting density profile on a resonance yields the PS, which is in good agreement with the recent experiments, while the FFLO modulation exists in the pairing field. It is also proposed that the most favorable location for the detection of the FFLO oscillation is in the vicinity of the critical population imbalance in the weak coupling BCS regime, where the oscillation periodicity becomes much larger than the interparticle spacing. Finally, we analyze the radio-frequency (RF) spectroscopy in the imbalanced system. The clear difference in the RF spectroscopy between BCS and BEC sides reveals the structure of the pairing field and local “magnetization”.

Superfluid Density in the BCS-BEC Crossover Regime of a Two-Component Fermi Gas at Finite Temperatures

We investigate the superfluid carrier density ρs in the BCS-BEC crossover regime of a superfluid Fermi gas at finite temperatures. Including pairing fluctuations within the gaussian fluctuation approximation, we determine the superfluid order parameter Δ, Fermi chemical potential μ, as well as ρs, in a consistent manner. In the weak-coupling regime, the normal fluid density ρn≡ρ−ρs is dominated by quasi-particle excitations associated with the dissociation of Cooper pairs. As one approaches the BCS-BEC crossover regime, effects of pairing fluctuations on ρn become strong. In the strong-coupling BEC regime, ρn is shown to be dominated by Bogoliubov phonon in a molecular Bose superfluid.