Published papers

© 2016, Springer Science+Business Media New York. We theoretically investigate the specific heat at constant volume CV and strong-coupling effects in a Fermi gas with p-wave interaction. In a 40K 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 CV 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.

© 2016, Springer Science+Business Media New York. 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 improves 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 6Li Fermi gas, our results would be useful for the study of strong-coupling physics associated with this quasi-long-range order.

We extend some of the authors’ previous work for a mass-balanced Bose–Fermi mixture to include effects of realistic mass imbalance in a Na– K and a Rb– 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 . 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 Na– K, as well as Rb– 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. 23 40 87 40 23 40 87 40 BEC

We investigate the photoemission-type spectrum in a cold Fermi gas which was recently measured by the JILA group. This quantity gives us very useful information about single-particle properties in the BCS-BEC crossover. In this paper, including pairing fluctuations within a T-matrix theory, as well as effects of a harmonic trap within the local density approximation, we show that spatially inhomogeneous pairing fluctuations due to the trap potential are an important key to understanding the observed spectrum. In the crossover region, while strong pairing fluctuations lead to the so-called pseudogap phenomenon in the trap center, such strong-coupling effects are found to be weak around the edge of the gas. Our results including this effect are shown to agree well with the recent photoemission data of the JILA group. © 2010 The American Physical Society.

We propose a mechanism of the semiconductive temperature dependence of the c-axis resistivity (ρc) in the normal state of high-Tc superconductors. We show that antiferromagnetic spin fluctuations in the CuO2-layer affect the temperature dependence of the Fermi surface shape and that they decrease (increase) the conductive carrier density (band mass) in the c-direction. Thus, when this effect dominates the temperature dependence of ρc, ρc increases at low temperatures. On the other hand, in the in-plane direction, the AF spin fluctuations do not affect the carrier density while they decrease the so-called k-mass at low temperatures. As a consequence, taking into account the damping rate which is caused by the electron-electron interaction, we obtain the in-plane resistivity (ρab) which decreases with decreasing temperature. Thus, the present mechanism can explain the semiconductive temperature dependence of ρc satisfying the metallic behavior of ρab.

© 2015 American Physical Society. We propose a theoretical idea to reach the p-wave superfluid phase in an ultracold Fermi gas. The key of our idea is that the pairing symmetry of a Fermi superfluid is fully dominated by the symmetry of the superfluid order parameter, which is essentially given by the product of a pair amplitude and a pairing interaction. Noting this, in our proposal, we first prepare a p-wave pair amplitude not by using a p-wave interaction, but by using the phenomenon that a p-wave pair amplitude is induced in an s-wave superfluid Fermi gas with antisymmetric spin-orbit interaction. In this case, although the system is still in the s-wave superfluid state with the s-wave superfluid order parameter, when one suddenly replaces the s-wave interaction by an appropriate p-wave one (which is possible in cold Fermi gases by using a Feshbach resonance technique), the product of the p-wave interaction and the p-wave pair amplitude that has already been prepared in the spin-orbit-coupled s-wave superfluid state immediately gives a finite p-wave superfluid order parameter. Thus, at least just after this manipulation, the system is in the p-wave superfluid state, being characterized by the artificially produced p-wave superfluid parameter. In this paper, to assess our idea, we evaluate the p-wave pair amplitude in a spin-orbit-coupled s-wave superfluid Fermi gas at T=0. We determine the region where a large p-wave pair amplitude is obtained in the phase diagram with respect to the strengths of the s-wave pairing interaction and the spin-orbit coupling. We also discuss the accessibility of this optimal region on the viewpoint of the superfluid phase transition temperature. Since the achievement of a p-wave superfluid Fermi gas is one of the most crucial issues in cold-atom physics, our proposal would be useful for this exciting challenge.

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. © Published under licence by IOP Publishing Ltd.

©2017 The Physical Society of Japan. 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 BEC . In the unitary regime at T 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 investigate the shear viscosity η 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 . We show that, while η diverges in both the weak-coupling BCS and strong-coupling BEC limits, it becomes small in the unitary regime. The minimum of η is obtained, not at the unitarity, but slightly in the strong-coupling BEC side. This deviation is consistent with the recent experiment on a Li Fermi gas. In the weak-coupling BCS regime, we also find that η exhibits anomalous temperature dependence near T , which is deeply related to the pseudogap phenomenon originating from strong pairing fluctuations. c c 6

We investigate the specific heat C 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 Nozières 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 in the weak-coupling regime, C is found to be sensitive to the uniaxial anisotropy in the strong-coupling regime. This originates from the population imbalance among pi-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 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. V V V 40

The dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential was analyzed. The frequency of this collective mode was not affected by an interaction between the atoms and was always equal to the trap frequency, according to Kohn's theorem. The effect of a Feshbach resonance and a condensate of the associated molecular bound states was also included. The dipole frequency was shown to depend on the strength of effective interaction associated with the Feshbach resonance, when the molecular bosons feel a different trap frequency from the Fermi atoms.

The effects of the trap potential and the on-site repulsion on the pairing correlation in the confined gas of Fermi atoms placed in the optical lattice were investigated using exact diagonalization method. It was found that the local Mott insulation core develops due to the strong repulsion and the singlet pairing correlation grows remotely between the core edges. It was also found that the 'Mott insulation core' appeared in the center of the trap, where each site was occupied by one atom. The results show that the superfluidity can locally develop at the surrounding of the Mott core.

We investigate the nuclear spin-lattice relaxation rate (T 1T)-1 in atomic-scale superconductor/magnet multilayered systems and discuss the discrepancy between two recent (T1T) -1 experiments on Ru in RuSr2YCu2O8. When the magnetic layers are in the antiferromagnetic state, (T 1T)-1 in the magnetic layers is shown to decrease with decreasing temperature due to the excitation gap associated with the magnetic ordering. The proximity effect of superconductivity on (T1T) -1 in the magnetic layer is negligibly small. Our result indicates that the temperature dependence of (T1T)-1 on Ru in RuSr2YCu2O8 likely originates from the antiferromagnetism in the RuO2 layers, but not from the superconductivity in the CuO2 layers. © 2003 The Physical Society of Japan.

We investigate nonmagnetic impurity effects on antiferromagnetic (AF) spin fluctuations in dx2-y2-wave superconductivity. We show that, far below the transition temperature (Tc), the low-energy AF spin fluctuations are enhanced by impurity scatterings in the unitarity limit owing to the formation of low-energy bound states around the impurities. As a result, the nuclear-spin lattice relaxation rate on Cu (1/(T1T)Cu) increases at low temperatures even below Tc. On the other hand, the enhancement of the AF spin fluctuations does not occur in the case of the Born scattering because of the absent of the bound states. The result in the unitarity limit can explain the anomalous increase of 1/(T1T)Cuwhich was recently observed in Zn-doped YBa2Cu4O8. © 2001 Elsevier Science B.V. All rights reserved.

We investigate a single impurity Anderson model in superconducting state focusing on the localized excited states induced around the impurity site with use of the numerical renormalization group method. Using this model, we present a unified treatment of electronic states around various kinds of impurities embedded in conventional s-wave superconductivity that have been investigated independently so far: (1) magnetic impurity, (2) nonmagnetic impurity with potential scattering, and (3) nonmagnetic impurity with resonance scattering. In the case of the symmetric Anderson model, we clarify how the localized excited state induced around (1) is transformed into the one induced around (3) with a decrease of the strength of the on-site Coulomb repulsion at the impurity site. On the other hand, in the case of the asymmetric Anderson model, we show how the bound state induced by the magnetic impurity disappears when the impurity is gradually transformed from (1) into (2) with an increase of the energy of the impurity level. We also clarify the region where competition between the Kondo effect and superconductivity dominates the properties of the ground and the localized excited states in the parameter space of the Anderson model. In this region, we show that the bound state energy is scaled well by the single parameter TK/Δ (TK: Kondo temperature, Δ: superconducting order parameter) as in the case of the antiferromagnetic s-d interaction in superconductivity.

© 2014 American Physical Society. We investigate the superfluid phase transition and single-particle excitations in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an unpolarized ultracold Fermi gas with mass imbalance (where two different species contributing to Cooper pairs have different atomic masses). In our recent paper [R. Hanai, Phys. Rev. A 88, 053621 (2013)PLRAAN1050-294710.1103/PhysRevA.88.053621], we showed that an extended T-matrix approximation (ETMA) can overcome the serious problem known in the ordinary (non-self-consistent) T-matrix approximation that it unphysically gives double-valued superfluid phase transition temperature Tc in the presence of mass imbalance. However, at the same time, the ETMA was also found to give the vanishing Tc in the weak-coupling and highly mass-imbalanced case. In this paper, we inspect the correctness of this ETMA result, using the self-consistent T-matrix approximation (SCTMA). We show that the vanishing Tc is an artifact of the ETMA, coming from an internal inconsistency of this theory. The superfluid phase transition actually always occurs, irrespective of the ratio of mass imbalance. We also apply the SCTMA to the pseudogap problem in a mass-imbalanced Fermi gas. We show that pairing fluctuations induce different pseudogap phenomena between the light component and heavy component. We also point out that a Li6-K40 mixture is a useful system for the realization of a heteropairing state, as well as for the study of component-dependent pseudogap phenomena.

We investigate strong-coupling properties of a trapped two-dimensional normal Fermi gas. Within the framework of a combined T-matrix theory with the local density approximation, we calculate the local density of states, as well as the photoemission spectrum, to see how two-dimensional pairing fluctuations affect these single-particle quantities. In the BCS (Bardeen-Cooper-Schrieffer)- BEC (Bose-Einstein condensation) crossover region, we show that the local density of states exhibits a dip structure in the trap center, which is more remarkable than the three-dimensional case. This pseudogap phenomenon is found to naturally lead to a double-peak structure in the photoemission spectrum. The peak-to-peak energy of the spectrum at p=0 agrees well with a recent experiment on a two-dimensional 40K Fermi gas. Since pairing fluctuations are sensitive to the dimensionality of a system, our results would be useful for the study of many-body physics in the BCS-BEC crossover regime of a two-dimensional Fermi gas. © 2013 American Physical Society.

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

We investigate tunneling properties of a bound pair of Fermi atoms in an optical lattice. Including a realistic cosine-shape optical lattice potential, we calculate the molecular wavefunction ψ. Starting from the weak-coupling regime, we show how ψ shrinks as one increases the strength of a pairing interaction between atoms. When the molecular size becomes comparable to the lattice constant in the intermediate coupling regime, we find from the spatial structure of ψ that the molecular tunneling between lattice sites is accompanied by virtual dissociation. This phenomenon is shown to be suppressed in the strong-coupling regime due to very strong binding energy. We point out that, while the molecular tunneling accompanied by virtual dissociation can be described by the Hubbard model, it cannot describe the molecular tunneling with no virtual dissociation in the strong-coupling regime. © 2009 IOP Publishing Ltd.

We investigate effects of pseudospin population imbalance on Mott phases in one-dimensional trapped two-component atomic Fermi gases loaded on optical lattices based on the repulsive Hubbard model in harmonic traps. By using the density-matrix renormalization-group method, we numerically calculate density profiles of each component and clarify the pseudospin magnetism. Consequently, we find that all the features from weakly imbalance to fully polarized cases are well described by S=1/2 antiferromagnetic Heisenberg chain under magnetic field. These results indicate that the Mott phases offer experimental stages for studying various interacting spin systems. © 2008 The American Physical Society.