論文

© 2016 American Physical Society. We investigate the specific heat at constant volume CV in the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensate (BCS-BEC)-crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature Tc. Within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while CV(TTc) in the unitary regime is remarkably enhanced by metastable preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived 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 Li6 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.

© 2015, Springer Science+Business Media New York. We investigate strong-coupling corrections to the specific heat (Formula presented.) in the normal state of an ultracold Fermi gas in the BCS–BEC crossover region. A recent experiment on a (Formula presented.) Li unitary Fermi gas (Ku et. al. in Science 335:563 2012) shows that (Formula presented.) is remarkably amplified near the superfluid phase transition temperature (Formula presented.) , being similar to the well-known (Formula presented.) -structure observed in liquid (Formula presented.) He. Including pairing fluctuations within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that strong pairing fluctuations are sufficient to explain the anomalous behavior of (Formula presented.) observed in a (Formula presented.) Li unitary Fermi gas near (Formula presented.). We also show that there is no contribution from stable preformed Cooper pairs to (Formula presented.) at the unitarity. This indicates that the origin of the observed anomaly is fundamentally different from the case of liquid (Formula presented.) He, where stable (Formula presented.) He Bose atoms induce the (Formula presented.) -structure in (Formula presented.) near the superfluid instability. Instead, the origin is the suppression of the entropy S, near (Formula presented.) , due to the increase of 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.

© 2015, Springer Science+Business Media New York. 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, as well as effects of a trap potential within the local density approximation, we calculate the local spin susceptibility (Formula presented.) above the superfluid phase transition temperature (Formula presented.). We show that the formation of preformed singlet Cooper pairs anomalously suppresses (Formula presented.) in the trap center near (Formula presented.). 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 (Formula presented.). 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.

© 2015, Springer Science+Business Media New York. We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal state. Including pairing fluctuations within the framework of a T-matrix approximation, we calculate the distribution function (Formula presented.) of Cooper pairs in terms of the center of mass momentum (Formula presented.). In the strong-coupling regime, (Formula presented.) is shown to exhibit a remarkable increase with decreasing the temperature in the low temperature region, which agrees well with the recent experiment on a two-dimensional (Formula presented.) Li Fermi gas (Ries et al. in Phys Rev Lett 114:230401, 2015). Our result indicates that the observed remarkable increase of the number of Cooper pairs with zero center of mass momentum can be explained without assuming the Berezinskii–Kosterlitz–Thouless (BKT) transition, when one properly includes pairing fluctuations that are enhanced by the low-dimensionality of the system. Since the BKT transition is a crucial topic in two-dimensional Fermi systems, our results would be useful for the study toward the realization of this quasi-long-range order in an ultracold Fermi gas.

© 2016, Springer Science+Business Media New York. We investigate the formation of rashbon bound states and strong-coupling effects in an ultracold Fermi gas with a spherical spin–orbit interaction, (Formula presented.) (where (Formula presented.) are Pauli matrices). Extending the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR) to include this spin–orbit coupling, we determine the superfluid phase transition temperature (Formula presented.) , as functions of the strength of a pairing interaction (Formula presented.) , as well as the spin–orbit coupling strength (Formula presented.). Evaluating poles of the NSR particle–particle scattering matrix describing fluctuations in the Cooper channel, we clarify the region where rashbon bound states dominate the superfluid phase transition in the (Formula presented.) – (Formula presented.) phase diagram. Since the antisymmetric spin–orbit interaction (Formula presented.) breaks the inversion symmetry of the system, rashbon bound states naturally have not only a spin-singlet and even-parity symmetry, but also a spin-triplet and odd-parity symmetry. Thus, our results would be also useful for the study of this parity-mixing effect in the BCS–BEC crossover regime of a spin–orbit coupled Fermi gas.

© 2016 American Physical Society. We extend our recent work [Y. Endo, Phys. Rev. A 92, 023610 (2015)]PLRAAN1050-294710.1103/PhysRevA.92.023610 for a parity-mixing effect in a model of two-dimensional lattice fermions to a realistic three-dimensional ultracold Fermi gas. Including effects of broken local spatial inversion symmetry by a trap potential within the framework of the real-space Bogoliubov-de Gennes theory at T=0, we point out that an odd-parity p-wave Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity) s-wave superfluid Fermi gas with spin imbalance. This indicates that when one suddenly changes the s-wave pairing interaction to an appropriate p-wave one by using a Feshbach technique in this case, a nonvanishing p-wave superfluid order parameter is immediately obtained, which is given by the product of the p-wave interaction and the p-wave pair amplitude that has already been induced in the spin-imbalanced s-wave superfluid Fermi gas. Thus, by definition, the system is in the p-wave superfluid state, at least just after this manipulation. Since the achievement of a p-wave superfluid state is one of the most exciting challenges in cold Fermi gas physics, our results may provide an alternative approach to this unconventional pairing state. In addition, since the parity-mixing effect cannot be explained as far as one deals with a trap potential in the local density approximation (LDA), it is considered as a crucial example which requires us to go beyond the LDA.

© 2017 American Physical Society. We theoretically present an economical and convenient way to study ground-state properties of a strongly interacting superfluid Fermi gas. Our strategy is that complicated strong-coupling calculations are used only to evaluate quantum fluctuation corrections to the chemical potential μ. Then, without any further strong-coupling calculations, we calculate the compressibility, sound velocity, internal energy, pressure, and Tan's contact, from the calculated μ without loss of accuracy, by using exact thermodynamic identities. Using a recent precise measurement of μ in a superfluid Li6 Fermi gas, we show that an extended T-matrix approximation (ETMA) is suitable for our purpose, especially in the BCS-unitary regime, where our results indicate that many-body corrections are dominated by superfluid fluctuations. Since precise determinations of physical quantities are not always easy in cold Fermi gas physics, our approach would greatly reduce experimental and theoretical efforts toward the understanding of ground-state properties of this strongly interacting Fermi system.

© 2017 American Physical Society. We theoretically investigate a spin-orbit-coupled s-wave superfluid Fermi gas, to examine the time evolution of the system, after an s-wave pairing interaction is replaced by a p-wave one at t=0. In our recent paper [T. Yamaguchi, D. Inotani, and Y. Ohashi, J. Phys. Soc. Jpn. 86, 013001 (2017)JUPSAU0031-901510.7566/JPSJ.86.013001], we proposed that this manipulation may realize a p-wave superfluid Fermi gas because the p-wave pair amplitude that is induced in the s-wave superfluid state by a parity-broken antisymmetric spin-orbit interaction gives a nonvanishing p-wave superfluid order parameter, immediately after the p-wave interaction is turned on. In this paper, using a time-dependent Bogoliubov-de Gennes theory, we assess this idea under various conditions with respect to the s-wave and p-wave interaction strengths, as well as the spin-orbit coupling strength. From these, we clarify that the momentum distribution of Fermi atoms in the initial s-wave state (t<0) is a key to produce a large p-wave superfluid order parameter. Since the realization of a p-wave superfluid state is one of the most exciting and difficult challenges in cold Fermi gas physics, our results may provide a possible way to accomplish this.

© 2017 American Physical Society. We theoretically investigate single-particle excitations in the BCS-BEC-crossover regime of an ultracold Fermi gas. Including strong pairing fluctuations within a T-matrix approximation, as well as effects of a harmonic trap potential in the local-density approximation, we calculate the local photoemission spectrum in the normal state. Recently, the JILA group measured this quantity in a K40 Fermi gas in order to examine homogeneous single-particle properties of this system. Comparing our results with this experiment, we show that this attempt indeed succeeds under JILA's experimental condition. However, we also find that the current local photoemission spectroscopy still has room for improvement in order to examine the pseudogap phenomenon predicted in the BCS-BEC-crossover region. Since ultracold Fermi gases are always in a trap, our results would be useful in applying this system to various homogeneous Fermi systems as a quantum simulator.

We theoretically investigate the isothermal compressibility κT in the normal state of an ultracold Fermi gas. Including pairing fluctuations, as well as preformed-pair formations, within the framework of the self-consistent T-matrix approximation, we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While κT in the weak-coupling BCS regime is dominated by Fermi atoms near the Fermi surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles in the strong-coupling BEC regime. In the latter region, besides a two-body molecular interaction, a three-body one is shown to sizably affect κT near the superfluid phase-transition temperature. Our results indicate that the strong-coupling BEC regime of an ultracold Fermi gas would provide a unique opportunity to study multibody correlations between Cooper-pair molecules.

© 2017, Springer Science+Business Media New York. We theoretically investigate the normal state properties of a Bose–Fermi mixture with a strong attractive interaction between Fermi and Bose atoms. We extend the ordinary T-matrix approximation (TMA) with respect to Bose–Fermi pairing fluctuations, to include the Hugenholtz–Pines’ relation for all Bose Green’s functions appearing in TMA self-energy diagrams. This extension is shown to be essentially important to correctly describe the physical properties of the Bose–Fermi mixture, especially near the Bose–Einstein condensation instability. Using this improved TMA, we clarify how the formation of composite fermions affects Bose and Fermi single-particle excitation spectra, over the entire interaction strength.

© 2017 American Physical Society. We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended T-matrix approximation, as well as effects of a harmonic trap in the local density approximation, we calculate the local spin susceptibility χt(r,T) in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover region. We show that pairing fluctuations cause nonmonotonic temperature dependence of χt(r,T). Although this behavior looks similar to the spin-gap phenomenon associated with pairing fluctuations in a uniform Fermi gas, the trapped case is found to also be influenced by the temperature-dependent density profile, in addition to pairing fluctuations. We demonstrate how to remove this extrinsic effect from χt(r,T), to study the interesting spin-gap phenomenon purely originating from pairing fluctuations. Since experiments in cold-atom physics are always done in a trap, our results would be useful for the assessment of preformed pair scenario, from the viewpoint of spin-gap phenomenon.

© 2017 American Physical Society. 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 to the nonequilibrium 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 antiparallel to θ(r) [where θ(r) is the phase of the condensate] in the BCS regime, both leading to dynamical instabilities of an exciton BEC. Our results suggest that a substantial region of the exciton-BEC phase in the phase diagram (in terms of the interaction strength and the decay rate) is unstable.

The understanding of physical properties of fermions in the unitary regime, where the s-wave scattering length in the collisional channel of particles is longer than both the interparticle distance and the size of the interaction potential, is a crucial issue for electron systems of high-temperature superconductivity, dilute nucleons in nuclei, and neutron stars. We experimentally determine various thermodynamic quantities of interacting two-component fermions at the zero-temperature limit from the BCS region to the unitarity limit. The obtained results are very accurate in the sense that the systematic error is within 4% in the unitary regime. Using this advantage, we can compare our data with various many-body theories. We find that an extended T-matrix approximation, which is a strong-coupling theory involving fluctuations in the Cooper channel, well reproduces our experimental results. We also find that the superfluid order parameter Δ calculated by solving the ordinary BCS gap equation with the chemical potential of interacting fermions is close to the binding energy of the paired fermions directly observed in a spectroscopic experiment and that obtained using a quantum Monte Carlo method.

© 2018 American Physical Society. We propose a theoretical idea to use an ultracold Fermi gas as a quantum simulator for the study of the low-density region of a neutron-star interior. Our idea is different from the standard quantum simulator that heads for perfect replication of another system, such as the Hubbard model discussed in high-Tc cuprates. Instead, we use the similarity between two systems and theoretically make up for the difference between them. That is, (1) we first show that the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR) can quantitatively explain the recent experiment on the equation of state (EoS) in a Li6 superfluid Fermi gas in the BCS (Bardeen-Cooper-Schrieffer) unitary limit far below the superfluid phase-transition temperature Tc. This region is considered to be very similar to the low-density region (crust regime) of a neutron star (where a nearly unitary s-wave neutron superfluid is expected). (2) We then theoretically compensate the difference that, while the effective range reff is negligibly small in a superfluid Li6 Fermi gas, it cannot be ignored (reff=2.7 fm) in a neutron star, by extending the NSR theory to include effects of reff. The calculated EoS when reff=2.7 fm is shown to agree well with the previous neutron-star EoS in the low-density region predicted in nuclear physics. Our idea indicates that an ultracold atomic gas may more flexibly be used as a quantum simulator for the study of other complicated quantum many-body systems, when we use not only the experimental high tunability, but also the recent theoretical development in this field. Since it is difficult to directly observe a neutron-star interior, our idea would provide a useful approach to the exploration for this mysterious astronomical object.

© 2018 American Physical Society. 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.

We propose a novel mechanism for a nonequilibrium phase transition in a U(1)-broken phase of an electron-hole-photon system, from a Bose-Einstein condensate of polaritons to a photon laser, induced by the non-Hermitian nature of the condensate. We show that a (uniform) steady state of the condensate can always be classified into two types, namely, arising either from lower or upper-branch polaritons. We prove (for a general model) and demonstrate (for a particular model of polaritons) that an exceptional point where the two types coalesce marks the end point of a first-order-like phase boundary between the two types, similar to a critical point in a liquid-gas phase transition. Since the phase transition found in this paper is not in general triggered by population inversion, our result implies that the second threshold observed in experiments is not necessarily a strong-to-weak-coupling transition, contrary to the widely believed understanding. Although our calculation mainly aims to clarify polariton physics, our discussion is applicable to general driven-dissipative condensates composed of two complex fields.