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Majorana-based topological qubits are expected to exploit the nonabelian braiding statistics of Majorana modes in topological superconductors to realize fault-tolerant topological quantum computation. Scalable qubit designs require several Majorana modes localized on quantum wires networks, with braiding operations relying on the presence of the groundstate degeneracy of the topologically nontrivial superconducting phase. However, this degeneracy is lifted due to the hybridization between Majorana modes localized at a finite distance. Here, we describe a braiding protocol in a trijunction where each branch consists of a lattice of Majorana modes overlapping at a finite distance. We find that the energy splitting between the groundstate and the lowest-energy state decreases exponentially with the number of Majorana modes if the system is in its topologically nontrivial regime. This result does not rely on the specific braiding geometry and on the details of the braiding scheme but is a consequence of the supersymmetry and nontrivial topology of the effective low-energy Hamiltonian describing the Majorana lattice., Comment: 6 pages, 3 figures, title changed, section order changed, references added, and other minor revisions

We theoretically discuss the non-Hermitian superfluid phase transition in one-dimensional two-component Fermi gases near the $p$-wave Feshbach resonance accompanied by the two-body loss associated with the dipolar relaxation. For the first time we point out that this system gives us an opportunity to explore the interplay among various non-trivial properties such as universal thermodynamics at divergent $p$-wave scattering length, topological phase transition at vanishing chemical potential, and non-Hermitian Bardeen-Cooper-Schrieffer(BCS) to Bose-Einstein condensate (BEC) transition, in a unified manner. In the BCS phase, the loss-induced superfluid-normal transition occurs when the exceptional point appears in the effective non-Hermitian Hamiltonian. In the BEC phase, the diffusive gapless mode can be regarded as a precursor of the instability of the superfluid state. Moreover, we show that the superfluid state is fragile against the two-body loss near the topological phase transition point., Comment: 7 pages, 5 figures

The interior of a neutron star is expected to be occupied by a neutron $^{3}P_{2}$ superfluid, which is the condensate of spin-triplet $p$-wave Cooper pairs of neutrons with total angular momentum $J=2$. Here we investigate the thermodynamic stability of $^{3}P_{2}$ superfluids in a neutron-star interior under a strong magnetic field. Using the theory incorporating the finite-size correction of the neutron Fermi surface, we show that the spin-polarized phases of $^{3}P_{2}$ superfluids, the magnetized biaxial nematic phase, and the ferromagnetic phase appear in high temperatures and high magnetic fields. These phases were missed in the previous studies using the quasiclassical approximation in which dispersions of neutrons are linearized around the Fermi surface. In particular, the ferromagnetic phase, which is the condensation of Cooper-paired neutrons with fully polarized spins, appears between the normal phase and the biaxial nematic phase and enlarges the thermodynamic stability of $^{3}P_{2}$ superfluids under strong magnetic fields. Furthermore, we present the augmented Ginzburg-Landau theory that incorporates the thermodynamic stability of spin-polarized $^{3}P_{2}$ superfluid phases.

The possibility of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a population imbalanced Fermi gas with a vortex is proposed. Employing the Bogoliubov-de-Gennes formalism we self-consistently determine the superfluid order parameter and the particle number density in the presence of a vortex. We find that as increasing population imbalance, the superfluid order parameter spatially oscillates around the vortex core in the radial direction, indicating that the FFLO state becomes stable. We find that the radial FFLO states cover a wide region of the phase diagram in the weak-coupling regime at $T=0$ in contrast to the conventional case without a vortex. We show that this inhomogeneous superfluidity can be detected as peak structures of the local polarization rate associated with the node structure of the superfluid order parameter. Since the vortex in the 3D Fermi gas with population imbalance has been already realized in experiments, our proposal is a promising candidate of the FFLO state in cold atom physics., Comment: 7 pages, 4 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.

In neutron star matter, there exist S01 superfluids in lower density in the crust while P23 superfluids are believed to exist at higher density deep inside the core. In the latter, depending on the temperature and magnetic field, either the uniaxial nematic phase, the D2-biaxial nematic phase, or the D4-biaxial nematic (D4-BN) phase appears. In this paper, we discuss a mixture of the S01 and P23 superfluids and find their coexistence. Adopting the loop expansion and the weak-coupling approximation for the interaction between two neutrons, we obtain the Ginzburg-Landau (GL) free energy in which both of the S01 and P23 condensates are taken into account by including the coupling terms between them. We analyze the GL free energy and obtain the phase diagram for the temperature and magnetic field. We find that the S01 superfluid excludes the P23 superfluid completely in the absence of magnetic field, they can coexist for weak magnetic fields, and the S01 superfluid is expelled by the P23 superfluid at strong magnetic fields, thereby proving the robustness of P23 superfluid against the magnetic field. We further show that the D4-BN phase covers the whole region of the P23 superfluidity as a result of the coupling term, in contrast to the case of a pure P23 superfluid studied before in which the D4-BN phase is realized only under strong magnetic fields. Thus, the D4-BN phase is topologically the most interesting phase, e.g., admitting half-quantized non-Abelian vortices relevant not only in magnetars but also in ordinary neutron stars.

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 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 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

We theoretically propose an idea to use an ultracold Fermi gas as a quantum simulator for the study of the neutron-star equation of state (EoS) in the low-density region. Our idea is different from the standard quantum simulator that heads for {\it perfect} replication of another system, such as a Hubbard model discussed in high-$T_{\rm c}$ cuprates. Instead, we use the {\it 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 Nozieres-Schmitt Rink (NSR) can quantitatively explain the recent EoS experiment on a $^6$Li superfluid Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)-unitary limit far below the superfluid phase transition temperature $T_{\rm c}$. 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 $r_{\rm eff}$ is negligibly small in a superfluid $^6$Li Fermi gas, it cannot be ignored ($r_{\rm eff}=2.7$ fm) in a neutron star, by extending the NSR theory to include effects of $r_{\rm eff}$. The calculated EoS when $r_{\rm eff}=2.7$ 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.

We theoretically investigate strong-coupling and finite temperature effects on the p-wave contacts, as well as the asymptotic behavior of the momentum distribution in large momentum region in a one-component Fermi gas with a tunable p-wave interaction. Including p-wave pairing fluctuations within a strong-coupling theory, we calculate the p-wave contacts above the superfluid transition temperature $T_{\rm c}$ from the adiabatic energy relations. We show that while the p-wave contacts related to the scattering volume monotonically increases with increasing the interaction strength, one related to the effective range non-monotonically depends on interaction strength and its sign changes in the intermediate-coupling regime. The non-monotonic interaction dependence of these quantities is shown to originate from the competition between the increase of the cutoff momentum and the decrease of the coupling constant of the p-wave interaction with increasing the effective range. We also analyze the asymptotic form of the momentum distribution in large momentum region. In contrast to the conventional s-wave case, we show that the asymptotic behavior cannot be completely described by only the p-wave contacts, and the extra terms, which is not related to the thermodynamic properties, appear. Furthermore, in high temperature region, we find that the extra terms dominate the sub-leading term of the large-momentum distribution. We also directly compare our results with the recent experimental measurement, by including the effects of a harmonic trap potential within the local density approximation. We show that our model explains the dependence on the interaction strength of the p-wave contacts., Comment: 26 pages, 12 figures

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)], 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 ($tl0$) 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.

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.

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 $\mu$. Then, without any further strong-coupling calculations, we calculate the compressibility, sound velocity, internal energy, pressure, and Tan's contact, from the calculated $\mu$ without loss of accuracy, by using exact thermodynamic identities. Using a recent precise measurement of $\mu$ in a superfluid $^6$Li 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., Comment: 12 pages, 5 figures, accepted by Physical Review A

We investigate the specific heat $C_V$ at constant volume and effects of uniaxial anisotropy of a $p$-wave attractive interaction in the normal state of an ultracold Fermi gas. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we evaluate this thermodynamic quantity as a function of temperature, in the whole interaction regime. While the uniaxial anisotropy is not crucial for $C_V$ in the weak-coupling regime, $C_V$ is found to be sensitive to the uniaxial anisotropy in the strong-coupling regime. This originates from the population imbalance among $p_i$-wave molecules ($i=x,y,z$), indicating that the specific heat is a useful observable to see which kinds of $p$-wave molecules dominantly exist in the strong-coupling regime when the $p$-wave interaction has uniaxial anisotropy. Using this strong point, we classify the strong-coupling regime into some characteristic regions. Since a $p$-wave pairing interaction with uniaxial anisotropy has been discovered in a $^{40}$K Fermi gas, our results would be useful in considering strong-coupling properties of a $p$-wave interacting Fermi gas, when the interaction is uniaxially anisotropic., Comment: 21 pages, 7 figures

We theoretically investigate single particle excitations in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-Condensation) 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, JILA group has measured this quantity in a $^{40}$K 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 the 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., Comment: 21 pages, 9 figures

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 figures

We theoretically investigate strong-coupling properties of an ultracold Fermi gas with an orbital Feshbach resonance (OFR). Including tunable pairing interaction associated with an OFR within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR), we examine the occupation of the closed channel. We show that, although the importance of the closed channel is characteristic of the system with an OFR, the occupation number of the closed channel is found to actually be very small at the superfluid phase transition temperature $T_{\rm c}$, in the whole BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, when we use the scattering parameters for an ultracold $^{173}$Yb Fermi gas. The occupation of the closed channel increases with increasing the temperature above $T_{\rm c}$, which is more remarkable for a stronger pairing interaction. We also present a prescription to remove effects of an experimentally inaccessible deep bound state from the NSR formalism, which we meet when we theoretically deal with a $^{173}$Yb Fermi gas with an OFR.

We theoretically investigate normal-state properties of a unitary Bose-Fermi mixture. Including strong hetero-pairing fluctuations, we evaluate the Bose and Fermi chemical potential, internal energy, pressure, entropy, as well as specific heat at constant volume $C_V$, within the framework of a combined strong-coupling theory with exact thermodynamic identities. We show that hetero-pairing fluctuations at the unitarity cause non-monotonic temperature dependence of $C_V$, being qualitatively different from the monotonic behavior of this quantity in the weak- and strong-coupling limit. On the other hand, such an anomalous behavior is not seen in the other quantities. Our results indicate that the specific heat $C_V$, which has recently become observable in cold atom physics, is a useful quantity for understanding strong-coupling aspects of this quantum system.

We theoretically propose an idea to realize a $p$-wave superfluid Fermi gas. To overcome the experimental difficulty that a $p$-wave pairing interaction to form $p$-wave Cooper pairs damages the system before the condensation growth, we first prepare a $p$-wave pair amplitude ($\Phi_{p}$) in a spin-orbit coupled $s$-wave superfluid Fermi gas, without any $p$-wave interaction. Then, by suddenly changing the $s$-wave interaction with a $p$-wave one ($U_{p}$) by using a Feshbach resonance, we reach the $p$-wave superfluid phase with the $p$-wave order parameter being symbolically written as $\Delta_{p}\sim U_{p}\Phi_{p}$. In this letter, we assess this scenario within the framework of a time-dependent Bogoliubov-de Gennes theory. Our results would contribute to the study toward the realization of unconventional pairing states in an ultracold Fermi gas.

We extend our recent work [Y. Endo et al., Phys. Rev. A 92, 023610 (2015)] 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 $p\text{-wave}$ Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity) $s\text{-wave}$ superfluid Fermi gas with spin imbalance. This indicates that when one suddenly changes the $s\text{-wave}$ pairing interaction to an appropriate $p\text{-wave}$ one by using a Feshbach technique in this case, a nonvanishing $p\text{-wave}$ superfluid order parameter is immediately obtained, which is given by the product of the $p\text{-wave}$ interaction and the $p\text{-wave}$ pair amplitude that has already been induced in the spin-imbalanced $s\text{-wave}$ superfluid Fermi gas. Thus, by definition, the system is in the $p\text{-wave}$ superfluid state, at least just after this manipulation. Since the achievement of a $p\text{-wave}$ 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.

We theoretically investigate photoemission spectrum (PES) in a 173Yb Fermi gas with a tunable pairing interaction associated with an orbital Feshbach resonance. Including the two-channel character ...

We investigate the center-of-mass momentum distribution $n_{\boldsymbol Q}$ of Cooper pairs and their first-order correlation function $g_1(r)$ in a strongly interacting two-dimensional Fermi gas. Recently, the BKT (Berezinskii-Kosterlitz-Thouless) transition was reported in a two-dimensional $^6$Li Fermi gas, based on (1) the observations of anomalous enhancement of $n_{{\boldsymbol Q}={\boldsymbol 0}}$ [M. G. Ries, et. al., Phys. Rev. Lett. 114, 230401 (2015)], as well as (2) a power-law behavior of $g_1(r)$ [P. A. Murthy, et. al., Phys. Rev. Lett. 115, 010401 (2015)]. However, including pairing fluctuations within a $T$-matrix approximation (TMA), we show that these results can still be explained as strong-coupling properties of a normal-state two-dimensional Fermi gas. Our results indicate the importance of further experimental observations, to definitely confirm the realization of the BKT transition in this system. Since the BKT transition has been realized in a two-dimensional ultracold Bose gas, our results would be useful for the achievement of this quasi-long range order in an ultracold Fermi gas.

We theoretically investigate the specific heat $C_V$ at constant volume in the normal state of a $p$-wave interacting Fermi gas. Including fluctuations in the $p$-wave Cooper channel within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we clarify how $C_V$ as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime, $C_V$ is shown to be enhanced by $p$-wave pairing fluctuations, near the superfluid phase transition temperature $T_{\rm c}$. Similar enhancement of $C_V(T\simeq T_{\rm c})$ is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of $p$-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the $p$-wave molecular Bose gas regime, and (3) the region between the two, where $p$-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a $p$-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above $T_{\rm c}$., Comment: 7 pages, 6 figures

We investigate the specific heat $C_V$ at constant volume in the normal state of a $p$-wave interacting Fermi gas. Including $p$-wave pairing fluctuations within the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that, in the weak-coupling side, $C_V$ exhibits a dip-hump behavior as a function of the temperature. While the dip is associated with the pseudogap phenomenon near $T_{\rm c}$, the hump structure is found to come from the suppression of Fermi quasiparticle scattering into a $p$-wave molecular state in the Fermi degenerate regime. Since the latter phenomenon does not occur in the ordinary $s$-wave interacting Fermi gas, it may be viewed as a characteristic phenomenon associated with a $p$-wave pairing interaction., Comment: 5 pages, 6 figures

We theoretically 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, below the superfluid phase transition temperature T c. Within the strong-coupling framework developed by Nozieres and Schmitt-Rink, we show that the temperature dependence of C V drastically changes as one passes through the crossover region, and is sensitive to strong fluctuations in the Cooper channel near the unitarity limit. We also compare our results to a recent experiment on a 6Li unitary Fermi gas. Since fluctuation effects are a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how the fermionic BCS superfluid changes into BEC with increasing the interaction strength, from the viewpoint of specific heat.

We investigate superfluid properties of a one-component Fermi gas with a uniaxially anisotropic $p$-wave pairing interaction, $U_x>U_y=U_z$ (where $U_i$ ($i=x,y,z)$ is a $p_i$-wave pairing interaction). This type of interaction is considered to be realized in a $^{40}$K Fermi gas. Including pairing fluctuations within a strong-coupling $T$-matrix theory, we determine the $p_x$-wave superfluid phase transition temperature $T^{p_x}_{\rm c}$, as well as the other phase transition temperature $T_{\rm c}^{p_x+ip_y}$ ($, Comment: 27 pages, 11 figures

We investigate the formation of rashbon bound states and strong-coupling effects in an ultracold Fermi gas with a spherical spin-orbit interaction, $H_{\rm so}=\lambda{\bf p}\cdot{\bf \sigma}$ (where ${\bf \sigma}=(\sigma_x,\sigma_y,\sigma_z)$ are Pauli matrices). Extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR) to include this spin-orbit coupling, we determine the superfluid phase transition temperature $T_{\rm c}$, as functions of the strength of a pairing interaction $U_s$, as well as the spin-orbit coupling strength $\lambda$. 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 $U_{s}$-$\lambda$ phase diagram. Since the antisymmetric spin-orbit interaction $H_{\rm so}$ 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., Comment: 7 pages, 3 figues, proceedings of the international symposium on Quantum Fluids and Solids QFS2015

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 figures

We present a superfluid theory of a polarized dipolar Fermi gas with an effective dipole-dipole pairing interaction. Treating each dipole as a molecule consisting of two atoms with opposite charges to each other, we show that the well-known ultraviolet divergence in the theory of dipolar Fermi superfluids can be eliminated without introducing any cutoff prescription. Using this cutoff-free superfluid theory, we discuss how the deformation of the Fermi surface coming from the anisotropic nature of the dipole-dipole interaction affects the superfluid order parameter at T = 0.

We theoretically propose a method to detect ±s-wave state in newly discovered Fe-pnictide superconductors, using ac Josephson current through a single-band superconductor/insulator/±s-wave superconductor ( S / I / ± S ) junction. We show that, because of the Riedel anomaly, the ac Josephson current vanishes at some values of biased voltage across the junction. This phenomenon does not occur without the sign difference of order parameters in the two band superconductor, so that the observation of the vanishing ac Josephson current would be a clear signature of ±s-wave pairing symmetry in Fe-pnictides.

We investigate single-particle properties of a mass-imbalanced Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. In the presence of mass imbalance, we point out that the ordinary $T$-matrix approximation, which has been extensively used to clarify various BCS-BEC crossover physics in the mass-balanced case, unphysically gives a double-valued solution in terms of the superfluid phase transition temperature $T_{\rm c}$ in the crossover region. To overcome this serious problem, we include higher order strong-coupling corrections beyond the $T$-matrix level. Using this extended $T$-matrix theory, we calculate single-particle excitations in the normal state above $T_{\rm c}$. The so-called pseudogap phenomena originating from pairing fluctuations are shown to be different between the light mass component and heavy mass component, which becomes more remarkable at higher temperatures. Since Fermi condensates with hetero-Cooper pairs have recently been discussed in various fields, such as exciton (polariton) condensates, as well as color superconductivity, our results would be useful for the further development of Fermi superfluid physics, beyond the conventional superfluid state with homo-Cooper pairs., 26 pages, 14 figures

We investigate superfluid properties and strong-coupling effects in a one-component Fermi gas with an anisotropic p-wave interaction. Within the framework of the Gaussian fluctuation theory, we determine the superfluid transition temperature $T_{\rm c}$, as well as the temperature $T_0$ at which the phase transition from the $p_x$-wave pairing state to the $p_x+ip_y$-wave state occurs below $T_{\rm c}$. We also show that while the anisotropy of the p-wave interaction enhances $T_{\rm c}$ in the strong-coupling regime, it suppresses $T_0$., 7 pages, 3 figures, proceedings of QFS 2012

We investigate the superfluid phase transition and effects of mass imbalance in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an cold Fermi gas. We point out that the Gaussian fluctuation theory developed by Nozi\`eres and Schmitt-Rink and the $T$-matrix theory, that are now widely used to study strong-coupling physics of cold Fermi gases, give unphysical results in the presence of mass imbalance. To overcome this problem, we extend the $T$-matrix theory to include higher-order pairing fluctuations. Using this, we examine how the mass imbalance affects the superfluid phase transition. Since the mass imbalance is an important key in various Fermi superfluids, such as $^{40}$K-$^6$Li Fermi gas mixture, exciton condensate, and color superconductivity in a dense quark matter, our results would be useful for the study of these recently developing superfluid systems., Comment: 7 pages, 4 figures, Proceedings of QFS-2012

An extension of the Ambegaokar-Baratoff relation to a superconductor-insulator-superconductor (SIS) Josephson junction with multiple tunneling channels is derived. Appling the resultant relation to a SIS Josephson junction formed by an iron-based (five-band) and a single-band Bardeen-Cooper-Schrieffer (BCS) type superconductors, a theoretical bound of the Josephson critical current ($I_{\rm c}$) multiplied by the resistance of the junction ($R_{\rm n}$) is given. We reveal that such a bound is useful for identifying the pairing symmetry of iron-pnictide superconductors. One finds that if a measured value of $I_{\rm c}R_{\rm n}$ is smaller than the bound then the symmetry is $\pm s$-wave, and otherwise $s$-wave without any sign changes. In addition, we stress that temperature dependence of $I_{\rm c}R_{\rm n}$ is sensitive to the difference of the gap functions from the BCS type gap formula in the above heterojunction., 7 pages, 6 figures

We theoretically propose a method to identify $\ifmmode\pm\else\textpm\fi{}s$-wave order parameter in recently discovered Fe-pnictide superconductors. Our idea uses the Riedel anomaly in ac-Josephson current through a $\text{SI}(\ifmmode\pm\else\textpm\fi{}\text{S})$ (single-band $s$-wave superconductor/insulator/$\ifmmode\pm\else\textpm\fi{}s$-wave two-band superconductor) junction. We show that the Riedel peak effect leads to vanishing ac-Josephson current at some values of biased voltage. This phenomenon does not occur in the case when the $\ifmmode\pm\else\textpm\fi{}s$-wave superconductor is replaced by a conventional $s$-wave one so that the observation of this vanishing Josephson current would be a clear signature of $\ifmmode\pm\else\textpm\fi{}s$-wave pairing state in Fe-pnictide superconductors.

We investigate pseudogap phenomena in an ultracold Fermi gas with a p-wave tunable pairing interaction. Including p-wave pairing fluctuations within a strong-coupling T-matrix theory, we calculate the single-particle density of states (DOS) above the superfluid transition temperature Tc. Starting from the weak-coupling regime, we show that, at first, a dip structure gradually appears to become remarkable in DOS with increasing the strength of the p-wave pairing interaction at Tc. However, this pseudogap structure again becomes less remarkable to eventually disappear, as one passes through the intermediate coupling regime to enter the strong-coupling region. This non-monotonic interaction dependence of the pseudogap is quite different from the s-wave case, where the pseudogap size simply increases with increasing a s-wave interaction strength. This difference is found to originate from the momentum dependence of the p-wave interaction. We also determine the pseudogap temperature below which the dip structure in DOS appears and identify the pseudogap regime in the phase diagram of a Fermi gas with respect to the temperature and p-wave interaction strength.