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We theoretically explore a promising route to achieve the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a spin-imbalanced ultracold Fermi gas. In the current stage of cold atom physics, search for this exotic Fermi superfluid is facing two serious difficulties: One is the desperate destruction of the FFLO long-range order by FFLO pairing fluctuations, which precludes entering the phase through a second-order transition, even in three dimension. The other is the fierce competition with the phase separation into the BCS (Bardeen-Cooper-Schrieffer) state and the spin-polarized normal state. Including strong FFLO pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that the anisotropy of Fermi surface introduced by an optical lattice makes the FFLO state stable against the paring fluctuations. This stabilized FFLO state is also found to be able to overcome the competition with the phase separation under a certain condition. Since the realization of unconventional Fermi superfluids is one of the most exciting challenges in cold atom physics, our results would contribute to the further development of this field., Comment: 15 pages, 9 figures

We theoretically investigate the isothermal compressibility $\kappa_{T}$ 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 (SCTMA), we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While $\kappa_T$ 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 $\kappa_T$ 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 multi-body correlations between Cooper-pair molecules., Comment: 30 pages, 13 figures

We develop a theory to describe the dynamics of a driven-dissipative many-body Fermi system, to pursue our proposal to realize exotic quantum states based on reservoir engineering. Our idea is to design the shape of a Fermi surface so as to have multiple Fermi edges, by properly attaching multiple reservoirs with different chemical potentials to a fermionic system. These emerged edges give rise to additional scattering channels that can destabilize the system into unconventional states, which is exemplified in this work by considering a driven-dissipative attractively interacting Fermi gas. By formulating a quantum kinetic equation using the Nambu-Keldysh Green's function technique, we explore nonequilibrium steady states in this system and assess their stability. We find that, in addition to the BCS-type isotropic pairing state, a Fulde-Ferrell-type anisotropic superfluid state being accompanied by Cooper pairs with non-zero center-of-mass momentum exists as a stable solution, even in the absence of a magnetic Zeeman field. Our result implies a great potential of realizing quantum matter beyond the equilibrium paradigm, by engineering the shape and topology of Fermi surfaces in both electronic and atomic systems., 23 pages, 11 figures

We theoretically investigate quantum conductance across a point contact between two strongly-interacting ultracold Fermi gases. We evaluate the tunneling current, taking into account pairing fluctuations in the Fermi gases within the framework of a combined strong-coupling T-matrix approximation with the Schwinger-Keldysh non-equilibrium formalism. We show that quasi-particle conductance is gradually suppressed, as one passes through the BCS–BEC crossover region from the weak-coupling side. On the other hand, with increasing the strength of a pairing interaction, the fluctuation-pair conductance is found to remarkably increase in the crossover region, which is followed by the suppression in the strong-coupling regime.

We theoretically investigate the thermodynamic stability of an ultracold Bose–Fermi mixture with a tunable inter-species interaction associated with a hetero-nuclear Feshbach resonance. To include hetero-pairing fluctuations, we employ an improved T-matrix approximation (iTMA), where all Bose Green’s functions involved in the self-energy are modified so as to satisfy the required gapless Bose excitations at the BEC phase transition. Using iTMA, we evaluate the compressibility matrix in the normal state, to examine the stability of the system against an effective Bose–Bose attraction, mediated by Fermi atoms. We clarify how the mechanical collapse of a Bose–Fermi mixture can be avoided by a direct Bose–Bose repulsive interaction. We also show that this thermodynamic instability cannot be captured by the ordinary non-self-consistent TMA, where the bare Bose Green’s function is used in the self-energy. Since the thermodynamic stability is crucial for the experimental realization of a resonant Bose–Fermi mixture, our results would contribute to the research for many-body properties of this system.

We study a non-equilibrium unitary Fermi gas, being coupled with two baths with different values of chemical potential. Extending a T-matrix approximation developed in equilibrium Fermi gases to the non-equilibrium steady state by using the Keldysh Green’s function technique, we examine the superfluid phase transition out of equilibrium. We also clarify non-equilibrium effects on the pseudogap phenomenon by strong pairing fluctuations.

We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction $-U_{\rm BF}0$, the density collapse is suppressed, and the BEC transition becomes possible. It is also suppressed by the formation of tightly bound Bose-Fermi molecules when the hetero-pairing interaction $-U_{\rm BF}$ is strong; however, since the system may be viewed as a molecular Fermi gas in this case, the BEC transition does not also occur. Since quantum gases involving Bose atoms are known to be sensitive to inter-particle correlations, our results would be useful for the study of many-body properties of a Bose-Fermi mixture in a stable manner, without facing the unwanted density collapse., 30 pages, 12 figures

We theoretically investigate superfluid properties of a two-band gas of $^{173}$Yb Fermi atoms with an orbital Feshbach resonance (OFR). To describe the BCS-BEC crossover region, we include superfluid fluctuations caused by inter-band and intra-band pairing interactions associated with OFR, by extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink to the two-band case below the superfluid phase transition temperature; however, effects of an experimentally inaccessible deep bound state are removed, to model a real $^{173}$Yb Fermi gas near OFR. We show that the condensate fraction in the upper closed channel gradually becomes smaller than that in the lower open channel, as one moves from the strong- to the weak-coupling regime, because the OFR-pairing mechanism tunes the interaction strengths by adjusting the energy difference between the two bands. However, even when the closed-channel band is much higher in energy than the open-channel band in the weak-coupling regime, the magnitude of the superfluid order parameter in the closed channel is found to be still comparable to that in the open channel. As the reason for this, we point out a pair-tunneling effect by the OFR-induced inter-band interaction. Besides these superfluid quantities, we also examine collective modes, such as the Goldstone mode, Schmid (Higgs) mode, as well as Leggett mode, to clarify how they appear in the spectral weights of pair-correlation functions in each band. Since the realization of a multi-band superfluid Fermi gas is a crucial issue in cold Fermi gas physics, our results would contribute to the basic understanding of this type of Fermi superfluid in the BCS-BEC crossover region., Comment: 31 pages, 10 figures

We extend some of the authors’ previous work for a mass-balanced Bose–Fermi mixture to include effects of realistic mass imbalance in a $$^{23}$$ Na– $$^{40}$$ K and a $$^{87}$$ Rb– $$^{40}$$ K mixtures. Including effects of pairing fluctuations within the framework of an improved T-matrix theory, we calculate the single-particle spectral weight (SW), as well as the photoemission spectrum (PES) in the unitary regime at the Bose–Einstein condensation temperature $$T_{\mathrm {BEC}}$$ . We show that the characteristic three-peak structure induced by paring fluctuations, being predicted in the mass-balanced case, remains to exist in SW even in the presence of mass difference. We also show that PES is a useful experimental method to observe this phenomenon in a $$^{23}$$ Na– $$^{40}$$ K, as well as $$^{87}$$ Rb– $$^{40}$$ K, Bose–Fermi mixtures. Since this strong-coupling phenomenon is qualitatively different from that in a two-component Fermi gas, our results would be useful in clarifying how the quantum statistics affects Bose and Fermi pairing phenomena in a two-component gas mixture.

We theoretically investigate the isothermal compressibility $$\kappa _{\mathrm{T}}$$ in the normal state of an ultracold Fermi gas with a tunable attractive interaction. We calculate this thermodynamic quantity by considering fluctuations in the Cooper channel, within the framework of the self-consistent T-matrix approximation (SCTMA). For comparison, we also evaluate this quantity in a “non”-self-consistent T-matrix approximation (TMA). We show that the calculated $$\kappa _{\mathrm{T}}$$ diverges at $$T_{\mathrm{c}}$$ in the BCS–BEC crossover region. On the other hand, such a singular behavior is absent when we deal with this quantity in SCTMA. We point out that the origin of this difference is the neglect of an effective inter-pair interaction in the former approximation. We also explicitly show how such an interaction is involved in the theory when one deals with pairing fluctuations in SCTMA. Our results indicate that the isothermal compressibility is a useful quantity in considering how preformed Cooper pairs interact with one another in the BCS–BEC crossover regime of an ultracold Fermi gas.

We measured missing mass spectrum of the ^{12}C(γ,p) reaction for the first time in coincidence with potential decay products from η^{'} bound nuclei. We tagged an (η+p) pair associated with the η^{'}N→ηN process in a nucleus. After applying kinematical selections to reduce backgrounds, no signal events were observed in the bound-state region. An upper limit of the signal cross section in the opening angle cosθ_{lab}^{ηp}

We theoretically assess the conjecture proposed by Kovtun, Son, and Starinets, stating that the ratio $\eta/s$ of the shear viscosity $\eta$ to the entropy density $s$ has the lower bound as $\eta/s\ge\hbar/(4\pi k_{\mathrm{B}})$. In the normal state of a mass-imbalanced ultracold Fermi gas, consistently including strong-coupling corrections to both $\eta$ and $s$ within the self-consistent $T$-matrix approximation, we evaluate $\eta/s$ over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, in the presence of mass imbalance. We find that $\eta/s$ achieves the minimum value $4.5\times \hbar/(4\pi k_{\mathrm{B}})$, not at the unitarity, but slightly in the BEC regime, $(k_{\mathrm{F}}a_s)^{-1}\simeq 0.4>0$ (where $a_s$ is the $s$-wave scattering length, and $k_{\mathrm{F}}$ is the Fermi momentum). In contract to the previous expectation, we find that this lower bound is almost independent of mass imbalance: Our results predict that all the mass-balanced $^6$Li-$^6$Li and $^{40}$K-$^{40}$K mixtures and the mass-imbalanced $^{40}$K-$^{161}$Dy mixture give almost the same lower bound of $\eta/s$. We also point out that the two quantum phenomena, Pauli blocking and bound-state formation, are crucial keys for the lower bound of $\eta/s$., Comment: 11 pages, 9 figures

We propose a configuration of a phased-array receiver with an on-chip built-in self-test (BIST) function. Detection errors caused by asymmetry of the passive circuit are eliminated using a symmetrical layout signal distributor in the BIST path. By composing the signal distributor in compact manner with a shielded circuit structure, the adverse effect on the main receiving circuit is suppressed. We tested a 28-GHz CMOS phased-array receiver chip. Using this chip's receiver BIST function, we demonstrated that the difference in characteristics of phase between array elements in a phased-array receiver can be ascertained.

We theoretically investigate the spin-dipole oscillation of a strongly interacting Fermi gas in a harmonic trap. By using a combined diagrammatic strong-coupling theory with a local density approximation and a sum rule approach, we clarify the temperature dependence of the spin-dipole frequency near the unitarity, which is deeply related to the spin susceptibility, as well as pairing correlations. While the spin-dipole frequency exactly coincides with the trap frequency in a non-interacting Fermi gas, it is shown to remarkably be enhanced in the superfluid state, because of the suppression of the spin degree of freedom due to the spin-singlet Cooper-pair formation. In strongly interacting Fermi gases, this enhancement occurs even above the superfluid phase transition temperature, due to the strong pairing correlations., 15 pages, 7 figures

We theoretically investigate the shear viscosity $$\eta $$ , as well as the entropy density s, in the normal state of an ultracold Fermi gas. Including pairing fluctuations within the framework of a T-matrix approximation, we calculate these quantities in the Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensation (BEC) crossover region. We also evaluate $$\eta / s$$ , to compare it with the lower bound of this ratio, conjectured by Kovtun, Son, and Starinets (KSS bound). In the weak-coupling BCS side, we show that the shear viscosity $$\eta $$ is remarkably suppressed near the superfluid phase transition temperature $$T_{\mathrm{c}}$$ , due to the so-called pseudogap phenomenon. In the strong-coupling BEC side, we find that, within the neglect of the vertex corrections, one cannot correctly describe $$\eta $$ . We also show that $$\eta / s$$ decreases with increasing the interaction strength, to become very close to the KSS bound, $$\hbar /4\pi k_{\mathrm{B}}$$ , on the BEC side.

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.

We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal phase. In the three-dimensional case, it has been shown that the so-called pseudogap phenomena can be well described by a (non-self-consistent) $T$-matrix approximation (TMA). In the two-dimensional case, while this strong coupling theory can explain the pseudogap phenomenon in the strong-coupling regime, it unphysically gives large pseudogap size in the crossover region, as well as in the weak-coupling regime. We show that this difficulty can be overcome when one improve TMA to include higher order pairing fluctuations within the framework of a self-consistent $T$-matrix approximation (SCTMA). The essence of this improvement is also explained. Since the observation of the BKT transition has recently been reported in a two-dimensional $^6$Li Fermi gas, our results would be useful for the study of strong-coupling physics associated with this quasi-long-range order., Comment: 7pages, 4 figures, Proceedings of QFS2016

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.

We theoretically investigate the specific heat at constant volume \(C_\mathrm{V}\) and strong-coupling effects in a Fermi gas with p-wave interaction. In a \(^{40}\)K Fermi gas, a uniaxial anisotropy of a p-wave interaction associated with a p-wave Feshbach resonance is expected as a result of the split of the p-wave Feshbach resonance by a dipole interaction. Including this, as well as pairing fluctuations, we show that \(C_\mathrm{V}\) is significantly affected by this anisotropy in the strong-coupling regime. We also discuss the physical origin of this effect. Our results would contribute to the further understanding of an ultracold p-wave Fermi gas.

We investigate superfluid phase transitions of asymmetric nuclear matter at finite temperature ($T$) and density ($\rho$) with a low proton fraction ($Y_{\rm p} \le 0.2$) which is relevant to the inner crust and outer core of neutron stars. A strong-coupling theory developed for two-component atomic Fermi gases is generalized to the four-component case and is applied to the system of spin-$1/2$ neutrons and protons. The empirical phase shifts of neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) interactions up to $k = 2$ ${\rm fm}^{-1}$ are described by multi-rank separable potentials. We show that (i) the critical temperature of the neutron superfluidity $T_{\rm c}^{\rm nn}$ at $Y_{\rm p}=0$ agrees well with Monte Carlo data at low densities and takes a maximum value $T_{\rm c}^{\rm nn}=1.68$ MeV at $\rho/\rho_0 = 0.14$ with $\rho_0=0.17$ fm$^{-3}$, (ii) the critical temperature of the proton superconductivity $T_{\rm c}^{\rm pp}$ for $Y_{\rm p} \le 0.2$ is substantially suppressed at low densities due to np-pairing fluctuations and starts to dominate over $T_{\rm c}^{\rm nn}$ only above $\rho/\rho_0 = 0.70$ $(0.77)$ for $Y_p =0.1$ $(0.2)$, and (iii) the deuteron condensation temperature $T_{\rm c}^{\rm d}$ is suppressed at $Y_{\rm p}\le 0.2$ due to the large mismatch of the two Fermi surfaces., Comment: 23 pages, 12 figures

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 endpoint 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., Revised version. 6 pages and 4 figures + 13 pages and 6 figures of Supplemental Material

We theoretically investigate strong-coupling properties of an ultracold Fermi gas in the BCS-BEC crossover regime in the non-equilibrium steady state, being coupled with two fermion baths. By developing a non-equilibrium strong-coupling theory based on the combined $T$-matrix approximation with the Keldysh Green's function technique, we show that the chemical potential bias applied by the two baths gives rise to the anomalous enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing fluctuations (although the system has no spin imbalance), resulting in the re-entrant behavior of the non-equilibrium superfluid phase transition in the BCS-unitary regime. These pairing fluctuations are also found to anomalously enhance the pseudogap phenomenon. Since various non-equilibrium phenomena have recently been measured in ultracold Fermi gases, our non-equilibrium strong-coupling theory would be useful to catch up this experimental development in this research field., Comment: 21pages,15figures

We theoretically investigate strong-coupling effects on specific heat at constant volume $C_{\rm V}$ in a superfluid Fermi gas with a tunable interaction associated with Feshbach resonance. Including fluctuations of the superfluid order parameter within the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we calculate the temperature dependence of $C_{\rm V}$ at the unitarity limit in the superfluid phase. We show that, in the low temperature region, $T^3$-behavior is shown in the temperature dependence of $C_{\rm V}$. This result indicates that the low-lying excitations are dominated by the gapless Goldstone mode, associated with the phase fluctuations of the superfluid order parameter. Since the Goldstone mode is one of the most fundamental phenomena in the Fermionic superfluidity, our results are useful for further understanding how the pairing fluctuations affects physical properties in the BCS-BEC crossover physics below the superfluid transition temperature., Comment: 8 pages, 4 figures

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 $n({\boldsymbol Q})$ of Cooper pairs in terms of the center of mass momentum ${\boldsymbol Q}$. In the strong-coupling regime, $n({\boldsymbol Q}=0)$ 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 $^6$Li Fermi gas [M. G. Ries, {\it et. al.}, Phys. Rev. Lett. {\bf 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., 7 pages, 4 figures, Proceedings of QFS2015

We review the BCS (Bardeen–Cooper–Schrieffer)–BEC (Bose–Einstein condensation) crossover phenomenon discussed in an ultracold Fermi atomic gas and a neutron superfluid in the low-density crust regime of a neutron star. A purpose of this paper is to show that these two very different atomic and nuclear systems can be closely related to each other from the viewpoint of this quantum many-body phenomenon. We explain how the BCS–BEC crossover is realized in the former atomic system by using the novel pairing mechanism called Feshbach resonance. We present a simple explanation for this crossover phenomenon to grasp the essence, as well as detailed microscopic theories that can cover the entire BCS–BEC crossover region. In the latter, we point out that the ordinary BCS theory already has the ability to describe the BCS–BEC crossover at T = 0 . At finite temperatures T > 0 , however, we need to go beyond this mean-field theory. Besides general aspects of the BCS–BEC crossover phenomenon, we also pick up special topics peculiar to each atomic gas and neutron fluid. The first one is the pseudogap phenomenon in the normal state of a Fermi atomic gas. The second one is the problem of non-zero effective range in an s -wave neutron superfluid.

We theoretically investigate the shear viscosity $\eta$ in the BCS-BEC crossover regime of an ultracold Fermi gas with a Feshbach resonance. Within the framework of the strong-coupling self-consistent $T$-matrix approximation, we examine how a strong pairing interaction associated with a Feshbach resonance affects this transport coefficient, in the normal state above the superfluid phase transition temperature $T_{\rm c}$. We show that, while $\eta$ diverges in both the weak-coupling BCS and strong-coupling BEC limits, it becomes small in the unitary regime. The minimum of $\eta$ is obtained, not at the unitarity, but slightly in the strong-coupling BEC side. This deviation is consistent with the recent experiment on a $^6$Li Fermi gas. In the weak-coupling BCS regime, we also find that $\eta$ exhibits anomalous temperature dependence near $T_{\rm c}$, which is deeply related to the pseudogap phenomenon originating form strong pairing fluctuations., Comment: 11pages, 10 figures

Differential cross sections and photon-beam asymmetries for the γ[over →]p→π^{-}Δ^{++}(1232) reaction have been measured for 0.7