Hetero pairing and component-dependent pseudogap phenomena in an ultracold Fermi gas with mass imbalance

We investigate the superfluid phase transition and single-particle excitations in the BCS (Bareen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas with mass imbalance. In our recent paper [R. Hanai, et. al., Phys. Rev. A 88, 053621 (2013)], we showed that an extended $T$-matrix approximation (ETMA) can overcome the serious problem known in the ordinary (non-self-consistent) $T$-matrix approximation that it unphysically gives double-valued superfluid phase transition temperature $T_{\rm c}$ in the presence of mass imbalance. However, at the same time, the ETMA was also found to give the vanishing $T_{\rm c}$ in the weak-coupling and highly mass-imbalanced case. In this paper, we inspect the correctness of this ETMA result, using the self-consistent $T$-matrix approximation (SCTMA). We show that the vanishing $T_{\rm c}$ is an artifact of the ETMA, coming from an internal inconsistency of this theory. The superfluid phase transition actually always occurs, irrespective of the ratio of mass imbalance. We also apply the SCTMA to the pseudogap problem in a mass-imbalanced Fermi gas. We show that pairing fluctuations induce different pseudogap phenomena between the the light component and heavy component. We also point out that a $^6$Li-$^{40}$K mixture is a useful system for the realization of a hetero pairing state, as well as for the study of component-dependent pseudogap phenomena.Comment: 27 pages, 14 figure

Spin susceptibility and effects of inhomogeneous strong pairing fluctuations in a trapped ultracold Fermi gas

We theoretically investigate magnetic properties of a unitary Fermi gas in a harmonic trap. Including strong pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a trap potential within the local density approximation (LDA), we calculate the local spin susceptibility $\chi(T,r)$ above the superfluid phase transition temperature $T_{\rm c}$. We show that the formation of preformed singlet Cooper pairs anomalously suppresses $\chi(T,r)$ in the trap center near $T_{\rm c}$. We also point out that, in the unitarity limit, the spin-gap temperature in a uniform Fermi gas can be evaluated from the observation of the spatial variation of $\chi(T,r)$. Since a real ultracold Fermi gas is always in a trap potential, our results would be useful for the study of how this spatial inhomogeneity affects thermodynamic properties of an ultracold Fermi gas in the BCS-BEC crossover region.Comment: 7 pages, 3 figures, Proceedings of QFS201

Strong-coupling corrections to spin susceptibility in the BCS-BEC crossover regime of a superfluid Fermi gas

We theoretically investigate the uniform spin susceptibility $\chi$ in the superfluid phase of an ultracold Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. In our previous paper [H. Tajima, {\it et. al.}, Phys. Rev. A {\bf 89}, 033617 (2014)], including pairing fluctuations within an extended $T$-matrix approximation (ETMA), we showed that strong pairing fluctuations cause the so-called spin-gap phenomenon, where $\chi$ is anomalously suppressed even in the normal state near the superfluid phase transition temperature $T_{\rm c}$. In this paper, we extend this work to the superfluid phase below $T_{\rm c}$, to clarify how this many-body phenomenon is affected by the superfluid order. From the comparison of the ETMA $\chi$ with the Yosida function describing the spin susceptibility in a weak-coupling BCS superfluid, we identify the region where pairing fluctuations crucially affect this magnetic quantity below $T_{\rm c}$ in the phase diagram with respect to the strength of a pairing interaction and the temperature. This spin-gap regime is found to be consistent with the previous pseudogap regime determined from the pseudogapped density of states. We also compare our results with a recent experiment on a $^6$Li Fermi gas. Since the spin susceptibility is sensitive to the formation of spin-singlet preformed pairs, our results would be useful for the study of pseudogap physics in an ultracold Fermi gas on the viewpoint of the spin degrees of freedom.Comment: 24 pages, 8 figure

Photoluminescence and gain/absorption spectra of a driven-dissipative electron-hole-photon condensate

We investigate theoretically nonequilibrium effects on photoluminescence and gain/absorption spectra of a driven-dissipative exciton-polariton condensate, by employing the combined Hartree-Fock-Bogoliubov theory with the generalized random phase approximation extended to the Keldysh formalism. Our calculated photoluminescence spectra is in semiquantitative agreement with experiments, where features such as a blue shift of the emission from the condensate, the appearance of the dispersionless feature of a diffusive Goldstone mode, and the suppression of the dispersive profile of the mode are obtained. We show that the nonequilibrium nature of the exciton-polariton condensate strongly suppresses the visibility of the Bogoliubov dispersion in the negative energy branch (ghost branch) in photoluminescence spectra. We also show that the trace of this branch can be captured as a hole burning effect in gain/absorption spectra. Our results indicate that the nonequilibrium nature of the exciton-polariton condensate strongly reduces quantum depletion, while a scattering channel to the ghost branch is still present.Comment: 25 pages, 21 figure

Non-equilibrium properties of a pumped-decaying Bose-condensed electron-hole gas in the BCS-BEC crossover region

We theoretically investigate a Bose-condensed exciton gas out of equilibrium. Within the framework of the combined BCS-Leggett strong-coupling theory with the non-equilibrium Keldysh formalism, we show how the Bose-Einstein condensation (BEC) of excitons is suppressed to eventually disappear, when the system is in the non-equilibrium steady state. The supply of electrons and holes from the bath is shown to induce quasi-particle excitations, leading to the partial occupation of the upper branch of Bogoliubov single-particle excitation spectrum. We also discuss how this quasi-particle induction is related to the suppression of exciton BEC, as well as the stability of the steady state.Comment: 7 pages, 2 figures, Proceedings of QFS-201

Spin Susceptibility and Strong Coupling Effects in an Ultracold Fermi Gas

We investigate magnetic properties and strong coupling corrections in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Within the framework of an extended $T$-matrix theory, we calculate the spin susceptibility $\chi$ above the superfluid phase transition temperature $T_{\rm c}$. In the crossover region, the formation of preformed Cooper pairs is shown to cause a non-monotonic temperature dependence of $\chi$, which is similar to the so-called spin-gap phenomenon observed in the under-doped regime of high-$T_{c}$ cuprates. From this behavior of $\chi$, we determine the spin-gap temperature as the temperature at which $\chi$ takes a maximum value, in the BCS-BEC crossover region. Since the spin susceptibility is sensitive to the formation of singlet Cooper pairs, our results would be useful in considering the temperature region where pairing fluctuations are important in the BCS-BEC crossover regime of an ultracold Fermi gas.Comment: 7 pages, 3 figures, proceedings of QFS-201

Pseudogap regime of a two-dimensional uniform Fermi gas

We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within a self-consistent $T$-matrix approximation, we determine the pseudogap temperature $T^*$ below which a dip appears in the density of states $\rho(\omega)$ around the Fermi level. Evaluating $T^*$, we identify the pseudogap region in the phase diagram of this system. We find that, while the observed BKT (Berezinskii-Kosterlitz-Thouless) transition temperature $T^{\rm exp}_{\rm BKT}$ in a $^6$Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in $\rho(\omega)$ at $T^{\rm exp}_{\rm BKT}$ still differs from a fully-gapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed $T^{\rm exp}_{\rm BKT}$ in the weak-coupling regime cannot be explained by the recent BKT theory which only includes phase fluctuations, our results may provide a hint about how to improve this BKT theory. Although $\rho(\omega)$ has not been measured in this system, we show that the assessment of our results is still possible by using the observable Tan's contact.Comment: 23 pages, 9 figure

Single-particle Excitations and Effects of Hetero-pairing Fluctuations in a Bose-Fermi Mixture with a Feshbach Resonance

We theoretically investigate normal-state properties of a gas mixture of single-component bosons and fermions with a hetero-nuclear Feshbach resonance. Including strong hetero-pairing fluctuations associated with the Feshbach resonance, we calculate single-particle density of states, as well as the spectral weight at various interaction strengths. For this purpose, we employ an improved T-matrix approximation (TMA), where the bare Bose Green's function in the non-selfconsistent TMA self-energy is modified so as to satisfy the Hugenholtz-Pines relation at the Bose-Einstein condensation (BEC) temperature $T_{\rm BEC}$. In the unitary regime at $T_{\rm BEC}$, we show that hetero-pairing fluctuations couple Fermi atomic excitations with Fermi molecular excitations, as well as with Bose atomic excitations. Although a similar coupling phenomenon by pairing fluctuations is known to give a pseudo-gapped density of states in the unitary regime of a two-component Fermi gas, such a dip structure is found to not appear even in the unitary limit of a Bose-Fermi mixture. It only appears in the strong-coupling regime. Instead, a spectral peak along the molecular dispersion appears in the spectral weight.We also clarify how this coupling phenomenon is seen in the Bose channel. Since a hetero-nuclear Feshbach resonance, as well as the formation of Bose-Fermi molecules, have been realized, our results would be useful for the study of strong-coupling properties of this unique quantum gas

Triplet pair amplitude in a trapped ss-wave superfluid Fermi gas with broken spin rotation symmetry

We investigate the possibility that the broken spatial inversion symmetry by a trap potential induces a spin-triplet Cooper-pair amplitude in an $s$-wave superfluid Fermi gas. Being based on symmetry considerations, we clarify that this phenomenon may occur, when a spin rotation symmetry of the system is also broken. We also numerically confirm that a triplet pair amplitude is really induced under this condition, using a simple model. Our results imply that this phenomenon is already present in a trapped $s$-wave superfluid Fermi gas with spin imbalance. As an interesting application of this phenomenon, we point out that one may produce a $p$-wave superfluid Fermi gas, by suddenly changing the $s$-wave pairing interaction to a $p$-wave one by using the Feshbach resonance technique. Since a Cooper pair is usually classified into the spin-singlet (and even-parity) state and the spin-triplet (and odd-parity) state, our results would be useful in considering how to mix them with each other in a superfluid Fermi gas. Such admixture has recently attracted much attention in the field of non-centrosymmetric superconductivity, so that our results would also contribute to the further development of this research field, on the viewpoint of cold Fermi gas physics.Comment: 26 pages, 8 figure

Strong Coupling Effects on the Specific Heat of an Ultracold Fermi Gas in the Unitarity Limit

We investigate strong-coupling corrections to the specific heat $C_V$ in the normal state of an ultracold Fermi gas in the BCS-BEC crossover region. A recent experiment on a $^6$Li unitary Fermi gas [M. J. H. Ku, {\it et. al.}, Science {\bf 335}, 563 (2012)] shows that $C_V$ is remarkably amplified near the superfluid phase transition temperature $T_{\rm c}$, being similar to the well-known $\lambda$-structure observed in liquid $^4$He. Including pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that strong pairing fluctuations are sufficient to explain the anomalous behavior of $C_V$ observed in a $^6$Li unitary Fermi gas near $T_{\rm c}$. We also show that there is no contribution from {\it stable} preformed Cooper pairs to $C_V$ at the unitarity. This indicates that the origin of the observed anomaly is fundamentally different from the case of liquid $^{4}$He, where {\it stable} $^4$He Bose atoms induce the $\lambda$-structure in $C_V$ near the superfluid instability. Instead, the origin is the suppression of the entropy $S$, near $T_{\rm c}$, due to the increase of {\it metastable} preformed Cooper pairs. Our results indicate that the specific heat is a useful quantity to study the effects of pairing fluctuations on the thermodynamic properties of an ultracold Fermi gas in the BCS-BEC crossover region.Comment: 7 pages, 3 figure