Published papers

Nonequilibrium properties of a normal metal-superconductor-normal metal (NSN) junction are theoretically investigated under an external magnetic field. When a bias voltage is applied between the normal-metal leads, the confined superconductor is driven out of equilibrium, resulting in a nonequilibrium quasiparticle distribution function having a two-step structure. Using the nonequilibrium Green's function technique, a comprehensive phase diagram of the nonequilibrium superconductor is determined. This analysis reveals that the interplay between Zeeman-split energy bands and the nonequilibrium distribution function gives rise to a rich phase structure. Notably, it is found that superconductivity destroyed by a strong external magnetic field revives by applying the bias voltage. This reentrant phenomenon is shown to originate from four effective “Fermi surfaces” that result from the combination of Zeeman-split energy bands and the two-step structure in the nonequilibrium distribution function. These results demonstrate the possibility of controlling quantum states of matter through the combined engineering of energy band structures and distribution functions.

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 Bardeen - Cooper - Schrieffer-type isotropic pairing state, a Fulde-Ferrell-type anisotropic superfluid state being accompanied by Cooper pairs with nonzero 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.

We study pseudogap behaviors of ultracold Fermi gases in the BCS-BEC crossover region. We calculate the density of states (DOS), as well as the single-particle spectral weight, above the superfluid transition temperature T c including pairing fluctuations within a T-matrix approximation. We find that DOS exhibits a pseudogap structure in the BCS-BEC crossover region, which is most remarkable near the unitarity limit. We determine the pseudogap temperature T * at which the pseudogap structure in DOS disappears. We also introduce another temperature T** at which the BCS-like double-peak structure disappears in the spectral weight. While one finds T* >T** in the BCS regime, T ** becomes higher than T* in the crossover and BEC regime. We also determine the pseudogap region in the phase diagram in terms of temperature and pairing interaction. © 2009 Springer Science+Business Media, LLC.

This article deals with the shear viscosity and effects of inter-particle correlations from the viewpoint of the hierarchical structure of matter. Although the change in hierarchical levels, which means that one kind of dominant degrees of freedom transitions into another, does not necessarily accompany the phase transition, and then we cannot expect a clear boundary between them in general, we propose that the shear viscosity is a useful probe to detect it: the shear viscosity takes a minimum around the boundary of the change in hierarchies. The minimum of the shear viscosity itself has attracted much attention and has widely been investigated from various research fields, ranging from low-energy condensed matter physics to high-energy nuclear physics, due to the so-called Kovtun–Son–Starinets (KSS) conjecture (which predicts the existence of a universal lower bound (KSS bound) of this quantity). We discuss a viscosity minimum and the KSS bound in two examples: quark matter in high-energy physics and an ultracold Fermi gas in low-energy physics.

This review article deals with the role of quantum clusters in the hierarchical structure of quantum many-body systems, especially focusing on a two-component spin-1/2 ultracold Fermi gas. Quantum clusters, which are loosely bound states with both atomic and molecular properties, play a key role in hierarchical transitions. We explain how an atom-molecule transition continuously occurs by using a Feshbach resonance. We also explain how this hierarchy is reflected in the so-called BCS-BEC crossover phase diagram, where a normal Fermi gas phase and a normal Bose gas phase form a hierarchy structure, and the pseudogap phase appears between them as an intermediate “semi-hierarchy.” The crossover region is shown to be conveniently determined by using the specific heat at constant volume, as well as the spin susceptibility. We also point out that the isothermal compressibility is a useful quantity to see how an atomic interaction gives rise to an intermolecular one. Future experiments on thermodynamic quantities would be crucial for the assessment of these theoretical results, as well as the further understanding of hierarchical many-body systems.

We propose a novel spin density wave (SDW) state as a possible mechanism of the anomalous antiferromagnetism, the so called micromagnetism, in URu2Si2 below 17.5 K. In this new SDW, the electron-hole pair amplitude changes its sign in the momentum space as in the case of the unconventional superconductivity. It is shown that this state can be realized in an extended Hubbard model within the mean field theory. We also examine some characteristic properties of this SDW to compare with the experimental results. All these properties well explain the unsolved problem of the micromagnetism. © 1998 The American Physical Society.

We investigate the uniform spin susceptibility χs in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Including pairing fluctuations within the framework of an extended T-matrix approximation, we show that χs exhibits nonmonotonic temperature dependence in the normal state. In particular, χs is suppressed near the superfluid phase transition temperature Tc due to strong pairing fluctuations. To characterize this anomalous behavior, we introduce the spin-gap temperature Ts as the temperature at which χs takes a maximum value. Determining Ts in the whole BCS-BEC crossover region, we identify the spin-gap regime in the phase diagram of a Fermi gas in terms of the temperature and the strength of a pairing interaction. We also clarify how the spin-gap phenomenon is related to the pseudogap phenomenon appearing in the single-particle density of states. Our results indicate that an ultracold Fermi gas in the BCS-BEC crossover region is a very useful system to examine the pseudogap phenomenon and the spin-gap phenomenon in a unified manner. © 2014 American Physical Society.

We investigate the tunneling properties of collective excitations in the ferromagnetic phase of a spin-1 spinor Bose-Einstein condensate (BEC). In addition to the Bogoliubov mode, this superfluid phase has two spin excitations, namely, the gapless transverse spin wave and the quadrupolar mode with a finite excitation gap. In the mean-field theory at T=0, we examine how these collective modes tunnel through a barrier potential that couples to the local density of particles. In the presence of supercurrent with a finite momentum q, while the Bogoliubov mode shows the so-called anomalous tunneling behavior (which is characterized by perfect transmission) in the low-energy limit, the transverse spin wave transmits perfectly only when the momentum k of this mode coincides with ±q. At k=±q, the wave function of this spin wave has the same form as the condensate wave function in the current-carrying state, so that the mechanism of this perfect transmission is found to be the same as tunneling of the supercurrent. Using this fact, the perfect transmission of the spin wave is proved for a generic barrier potential. We show that such perfect transmission does not occur in the quadrupolar mode. Further, we consider the effects of potentials breaking U(1) and spin-rotation symmetries on the transmission properties of excitations. Our results would be useful for understanding excitation properties of spinor BEC's, as well as the anomalous tunneling phenomenon in Bose superfluids. © 2011 American Physical Society.

We investigate the tunneling properties of a bound pair of Fermi atoms in an optical lattice, comparing with results obtained in an attractive Hubbard model. In the strong-coupling regime of the Hubbard model, it has been predicted that the motion of a bound pair between lattice sites is accompanied by virtual dissociation. To explore the possibility of this interesting phenomenon in an optical lattice, we calculate the molecular wave function in a cosine-shaped periodic potential. We show that the molecular tunneling accompanied by dissociation occurs in the intermediate-coupling regime of the optical-lattice system. In the strong-coupling regime, in contrast to the prediction in the Hubbard model, the bound pair is shown to tunnel through the lattice potential without dissociation. As a result, the magnitude of the molecular band mass M remains finite even in the strong-coupling limit, which is in contrast to the diverging molecular mass in the case of the Hubbard model. Including this finite value of the molecular band mass, we evaluate the superfluid phase transition temperature Tc in the Bose-Einstein-condensate limit of the optical-lattice system, where the Hubbard model gives Tc =0 due to the diverging molecular mass. © 2008 The American Physical Society.

In order to study the vortex core electronic structure in high-T c superconductors, we examine 1-D Hubbard model with trap potential by using the density matrix renormalization group method. Instead of directly treating the vortex, the approach mimics the carrier density depression inside the vortex core via the trap potential and exactly calculate strong correlation effects on the depressed region. Consequently, we find that the Mott state emerges in the central region and the metallic edge surrounds the Mott region. Furthermore, when adding spin imbalance, the calculations reveal that a local antiferromagnetic order covers the Mott state region, and moreover, the antiferromagnetic order modulates with a long periodicity. We expect that these results closely relate to the vortex core electronic structure while their calculation results can be directly compared with atomic Fermi gases loaded on an optical lattice. © 2008 Elsevier B.V. All rights reserved.

High-Tc cuprate and MgB2 superconductors are recognized as intermediate or strong coupling superconductors. In such a non-weak regime, the vortex core structure is an interesting issue, since the vortex dissipation is expected to be anomalously reduced due to large level distance between localized core states. In this paper, we systematically clarify the vortex core structure based on the fermion-boson model which can cover a full coupling range from weak BCS to strong BEC superconductors. The mean-field calculations on the model reveal that the distances between the low-lying core levels expand and the low-lying states finally disappear when changing the coupling from weak BCS to strong BEC regime. This result suggests that the strong coupling makes the vortex motion non-dissipative. © 2006 Elsevier B.V. All rights reserved.

In atomic Fermi gases, the pairing character changes from BCS-like to BEC-like when decreasing the threshold energy of the Feshbach resonance. With this crossover, the system enters a strong-coupling regime through the population enhancement of diatom molecules, i.e., tightly bound Cooper pair, and the vortex structure shows much different features in contrast to the well-known core structure in BCS superfluid. In this paper, we study the structure of a single quantized vortex by numerically solving the generalized Bogoliubov-de Gennes equation derived from the boson-fermion model and clarify how the vortex structure changes with the crossover from BCS to BEC. As a result of numerical calculations, we find that the presence of the diatom molecular condensate enhances the matter density depletion inside the vortex core in the crossover regime and the Caroli-de Gennes-Matricon (CdGM) quasi-particle branch almost diminishes in BEC regime. © 2005 Elsevier B.V. All rights reserved.

© 2015 American Physical Society. We investigate the possibility that the broken spatial inversion symmetry caused by a trap potential induces a spin-triplet Cooper pair amplitude in an s-wave superfluid Fermi gas. 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 actually 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 a spin-singlet (and even-parity) state and a 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 an admixture has recently attracted much attention in the field of noncentrosymmetric superconductivity, so that our results would also contribute to the further development of this research field, from the viewpoint of cold Fermi gas physics.

In order to examine how the vortex core changes its structure when approaching BEC from BCS regime in superfluid fermion-atom gasses we make a systematic numerical study for the core structure of a singly quantized vortex, solving numerically the generalized Bogoliubov-de Gennes equation derived from the fermion-boson model. Numerical calculations reveal that the vortex core can be well characterized by two length scales based on the spatial variation of the fermionic gap functions and those scales show distinctive differences between the BCS and BEC regimes. © 2007 Elsevier B.V. All rights reserved.

© 2016, Springer Science+Business Media New York. 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 χn. While quantum fluctuation effects on χn 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 χn in the weak-coupling BCS region. We also show that the calculated χn agrees well with the recent experiment on a 6Li 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 discuss an idea to realize a spontaneous current in a superfluid Fermi gas. When a polarized Fermi superfluid (NN, where Nσ is the number of atoms in the hyperfine state described by pseudospin σ=) is loaded onto a ring-shaped trap with a weak potential barrier, some excess atoms (ΔN=N-N) are localized around the barrier. As shown in our previous paper, this polarized potential barrier works as a π junction in the sense that the superfluid order parameter changes its sign across the barrier. Because of this, the phase of the superfluid order parameter outside the junction is shown to be twisted by π along the ring, which naturally leads to a circulating supercurrent. While the ordinary supercurrent state is obtained as a metastable state, this spontaneous current state is shown to be more stable than the case with no current. Our results indicate that localized excess atoms would be useful for the manipulation of the superfluid order parameter in cold Fermi gases. © 2011 American Physical Society.

We theoretically investigate a possible spontaneous current state in a polarized superfluid Fermi gas confined in a toroidal trap. When one puts a weak nonmagnetic potential barrier in this system, this barrier is known to be magnetized in the sense that some of excess ↑-spin atoms are localized around it (where the ↑-spin describes the majority component of the polarized Fermi gas). Using this unique property, we show that this magnetized barrier, or the pseudo-ferromagnetic junction, induces a spontaneous current circulating along the toroidal trap. While the ordinary supercurrent state appears as a metastable state, this spontaneous current state is realized as the most stable state, originating from the phase twist of the superfluid order parameter by the magnetized potential barrier. © Published under licence by IOP Publishing Ltd.

The plasma oscillation in a superconductor is investigated for the case when the plasma energy is smaller than the superconducting gap. We show that the plasma energy has a temperature dependence in dirty superconductors. When the strength of the impurity scattering exceeds a critical value, the plasma disappears at the transition temperature (Formula presented) as observed in high-(Formula presented) cuprates (Formula presented) We also study the coupling of the plasma with the Carlson-Goldman (CG) mode in a dirty superconductor. A pole analysis show that the coupling occurs just below (Formula presented) However, even in this situation, we find that two different modelike peak structures can be still observed in the spectra of the density-density correlation function (Formula presented) and the structure function of the pair field susceptibility (Formula presented) The peak in (Formula presented) is located at a finite energy at (Formula presented) corresponding to the low-frequency plasma, while the CG mode with a linear dispersion is found in (Formula presented) © 1999 The American Physical Society.

© Published under licence by IOP Publishing Ltd. We investigate magnetic properties of a strongly interacting ultracold Fermi gas. Within the framework of an extended T-matrix approximation, we calculate the spin susceptibility χ in the unitarity limit. We show that effects of pairing fluctuations on this magnetic quantity are quite different in between the normal state and the superfluid phase. In the normal state, pairing fluctuations cause spin-gap phenomenon near the superfluid phase transition temperature Tc, where χ is anomalously suppressed. In the superfluid phase, on the other hand, the ordinary suppression of χ by the BCS energy gap is weakened by pairing fluctuations, because they induce finite density of states inside the gap. Our results indicate that the spin susceptibility is a useful quantity for the study of pairing fluctuations in the BCS-BEC crossover regime of an ultracold Fermi gas.