arXiv subjects

Yusuke Nishida

Publications and source records attributed to Yusuke Nishida.

At least 73 records · Page 4Linked to original sources

arXiv2012

Time dependent impurity in ultracold fermions: orthogonality catastrophe and beyond

Recent experimental realization of strongly imbalanced mixtures of ultracold atoms opens new possibilities for studying impurity dynamics in a controlled setting. We discuss how the techniques of atomic physics can be used to explore new regimes and manifestations of Anderson's orthogonality catastrophe (OC), which could not be accessed in solid state systems. We consider a system of impurity atoms localized by a strong optical lattice potential and immersed in a sea of itinerant Fermi atoms. Ramsey interference experiments with impurity atoms probe OC in the time domain, while radio-frequency (RF) spectroscopy probes OC in the frequency domain. The OC in such systems is universal for all times and is determined by the impurity scattering length and Fermi wave vector of itinerant fermions. We calculate the universal Ramsey response and RF absorption spectra. In addition to the standard power-law contribution, which corresponds to the excitation of multiple particle-hole pairs near the Fermi surface, we identify a novel contribution to OC that comes from exciting one extra particle from the bottom of the itinerant band. This gives rise to a non-analytic feature in the RF absorption spectra, which evolves into a true power-law singularity with universal exponent 1/4 at the unitarity. Furthermore, we discuss the manifestations of OC in spin-echo experiments, as well as in the energy counting statistic of the Fermi gas following a sudden quench of the impurity state. Finally, systems in which the itinerant fermions have two or more hyperfine states provide an even richer playground for studying non-equilibrium impurity physics, allowing one to explore non-equilibrium OC and to simulate quantum transport through nano-structures. This provides a useful connection between cold atomic systems and mesoscopic quantum transport.

cond-mat.quant-gas↗

arXiv2012

Probing strongly interacting atomic gases with energetic atoms

We investigate properties of an energetic atom propagating through strongly interacting atomic gases. The operator product expansion is used to systematically compute a quasiparticle energy and its scattering rate both in a spin-1/2 Fermi gas and in a spinless Bose gas. Reasonable agreement with recent quantum Monte Carlo simulations even at a relatively small momentum k/kF>1.5 indicates that our large-momentum expansions are valid in a wide range of momentum. We also study a differential scattering rate when a probe atom is shot into atomic gases. Because the number density and current density of the target atomic gas contribute to the forward scattering only, its contact density (measure of short-range pair correlation) gives the leading contribution to the backward scattering. Therefore, such an experiment can be used to measure the contact density and thus provides a new local probe of strongly interacting atomic gases.

cond-mat.quant-gas↗

arXiv2012

Pairing instabilities in quasi-two-dimensional Fermi gases

We study non-equilibrium dynamics of ultracold two-component Fermi gases in low-dimensional geometries after the interactions are quenched from weakly interacting to strongly interacting regime. We develop a T-matrix formalism that takes into account the interplay between Pauli blocking and tight confinement in low-dimensional geometries. We employ our formalism to study the formation of molecules in quasi-two-dimensional Fermi gases near Feshbach resonance and show that the rate at which molecules form depends strongly on the transverse confinement. Furthermore, Pauli blocking gives rise to a sizable correction to the binding energy of molecules.

cond-mat.quant-gas↗

arXiv2011

Liberating Efimov physics from three dimensions

When two particles attract via a resonant short-range interaction, three particles always form an infinite tower of bound states characterized by a discrete scaling symmetry. It has been considered that this Efimov effect exists only in three dimensions. Here we review how the Efimov physics can be liberated from three dimensions by considering two-body and three-body interactions in mixed dimensions and four-body interaction in one dimension. In such new systems, intriguing phenomena appear, such as confinement-induced Efimov effect, Bose-Fermi crossover in Efimov spectrum, and formation of interlayer Efimov trimers. Some of them are observable in ultracold atom experiments and we believe that this study significantly broadens our horizons of universal Efimov physics.

cond-mat.quant-gas↗

arXiv2011

Counting Majorana zero modes in superconductors

A counting formula for computing the number of (Majorana) zero modes bound to topological point defects is evaluated in a gradient expansion for systems with charge-conjugation symmetry. This semi-classical counting of zero modes is applied to some examples that include graphene and a chiral p-wave superconductor in two-dimensional space. In all cases, we explicitly relate the counting of zero modes to Chern numbers.

cond-mat.supr-con↗

arXiv2010

Confinement-induced p-wave resonances from s-wave interactions

We show that a purely s-wave interaction in three dimensions (3D) can induce higher partial-wave resonances in mixed dimensions. We develop two-body scattering theories in all three cases of 0D-3D, 1D-3D, and 2D-3D mixtures and determine the positions of higher partial-wave resonances in terms of the 3D s-wave scattering length assuming a harmonic confinement potential. We also compute the low-energy scattering parameters in the p-wave channel (scattering volume and effective momentum) that are necessary for the low-energy effective theory of the p-wave resonance. We point out that some of the resonances observed in the Florence group experiment [Phys. Rev. Lett. 104, 153202 (2010)] can be interpreted as the p-wave resonances in the 2D-3D mixed dimensions. Our study paves the way for a variety of physics, such as Anderson localization of matter waves under p-wave resonant scatterers.

cond-mat.quant-gas↗

arXiv2010

Universal four-component Fermi gas in one dimension

A four-component Fermi gas in one dimension with a short-range four-body interaction is shown to exhibit a one-dimensional analog of the BCS-BEC crossover. Its low-energy physics is governed by a Tomonaga-Luttinger liquid with three spin gaps. The spin gaps are exponentially small in the weak coupling (BCS) limit where they arise from the charge-density-wave instability, and become large in the strong coupling (BEC) limit because of the formation of tightly-bound tetramers. We investigate the ground-state energy, the sound velocity, and the gap spectrum in the BCS-BEC crossover and discuss exact relationships valid in our system. We also show that a one-dimensional analog of the Efimov effect occurs for five bosons while it is absent for fermions. Our work opens up a very rich new field of universal few-body and many-body physics in one dimension.

cond-mat.quant-gas↗

arXiv2010

Topological superconductors as nonrelativistic limits of Jackiw-Rossi and Jackiw-Rebbi models

We argue that the nonrelativistic Hamiltonian of p_x+ip_y superconductor in two dimensions can be derived from the relativistic Jackiw-Rossi model by taking the limit of large Zeeman magnetic field and chemical potential. In particular, the existence of a fermion zero mode bound to a vortex in the p_x+ip_y superconductor can be understood as a remnant of that in the Jackiw-Rossi model. In three dimensions, the nonrelativistic limit of the Jackiw-Rebbi model leads to a "p+is" superconductor in which spin-triplet p-wave and spin-singlet s-wave pairings coexist. The resulting Hamiltonian supports a fermion zero mode when the pairing gaps form a hedgehoglike structure. Our findings provide a unified view of fermion zero modes in relativistic (Dirac-type) and nonrelativistic (Schrödinger-type) superconductors.

cond-mat.supr-con↗

arXiv2010

Phases of a bilayer Fermi gas

We investigate a two-species Fermi gas in which one species is confined in two parallel layers and interacts with the other species in the three-dimensional space by a tunable short-range interaction. Based on the controlled weak coupling analysis and the exact three-body calculation, we show that the system has a rich phase diagram in the plane of the effective scattering length and the layer separation. Resulting phases include an interlayer s-wave pairing, an intralayer p-wave pairing, a dimer Bose-Einstein condensation, and a Fermi gas of stable Efimov-like trimers. Our system provides a widely applicable scheme to induce long-range interlayer correlations in ultracold atoms.

cond-mat.quant-gas↗

arXiv2010

Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories

We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the epsilon expansion technique based on a systematic expansion in terms of the dimensionality of space. We apply this technique to compute the thermodynamic quantities, the quasiparticle spectrum, and the critical temperature of UFG. We then discuss consequences of the scale and conformal invariance of UFG. We prove a correspondence between primary operators in nonrelativistic conformal field theories and energy eigenstates in a harmonic potential. We use this correspondence to compute energies of fermions at unitarity in a harmonic potential. The scale and conformal invariance together with the general coordinate invariance constrains the properties of UFG. We show the vanishing bulk viscosities of UFG and derive the low-energy effective Lagrangian for the superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic scaling and conformal symmetries that can be in principle realized in ultracold atom experiments.

cond-mat.quant-gas↗

arXiv2010

Is a color superconductor topological?

A fully gapped state of matter, whether insulator or superconductor, can be asked if it is topologically trivial or nontrivial. Here we investigate topological properties of superconducting Dirac fermions in 3D having a color superconductor as an application. In the chiral limit, when the pairing gap is parity even, the right-handed and left-handed sectors of the free space Hamiltonian have nontrivial topological charges with opposite signs. Accordingly, a vortex line in the superconductor supports localized gapless right-handed and left-handed fermions with the dispersion relations E=+/-vp_z (v is a parameter dependent velocity) and thus propagating in opposite directions along the vortex line. However, the presence of the fermion mass immediately opens up a mass gap for such localized fermions and the dispersion relations become E=+/-v(m^2+p_z^2)^(1/2). When the pairing gap is parity odd, the situation is qualitatively different. The right-handed and left-handed sectors of the free space Hamiltonian in the chiral limit have nontrivial topological charges with the same sign and therefore the presence of the small fermion mass does not open up a mass gap for the fermions localized around the vortex line. When the fermion mass is increased further, there is a topological phase transition at m=(μ^2+Δ^2)^(1/2) and the localized gapless fermions disappear. We also elucidate the existence of gapless surface fermions localized at a boundary when two phases with different topological charges are connected. A part of our results is relevant to the color superconductivity of quarks.

hep-ph↗

arXiv2009

Confinement-induced Efimov resonances in Fermi-Fermi mixtures

A Fermi-Fermi mixture of 40K and 6Li does not exhibit the Efimov effect in a free space, but the Efimov effect can be induced by confining only 40K in one dimension. Here the Efimov's three-body parameter is controlled by the confinement length. We show that the three-body recombination rate in such a system in the dilute limit has a characteristic logarithmic-periodic dependence on the effective scattering length with the scaling factor 22.0 and can be expressed by formulas similar to those for identical bosons in three dimensions. The ultracold mixture of 40K and 6Li in the 1D-3D mixed dimensions is thus a promising candidate to observe the Efimov physics in fermions.

cond-mat.other↗

arXiv2009

Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs

We propose to use a two-species Fermi gas with the interspecies s-wave Feshbach resonance to realize p-wave superfluidity in two dimensions. By confining one species of fermions in a two-dimensional plane immersed in the background three-dimensional Fermi sea of the other species, an attractive interaction is induced between two-dimensional fermions. We compute the pairing gap in the weak-coupling regime and show that it has the symmetry of p_x+ip_y. Because the magnitude of the pairing gap increases toward the unitarity limit, it is possible that the critical temperature for the p_x+ip_y-wave superfluidity becomes within experimental reach. The resulting system has a potential application to topological quantum computation using vortices with non-Abelian statistics. We also discuss aspects of our system in the unitarity limit as a "nonrelativistic defect conformal field theory (CFT)". The reduced Schrödinger algebra, operator-state correspondence, scaling dimensions of composite operators, and operator product expansions are investigated.

cond-mat.other↗

arXiv2009

Ground-state energy of the unitary Fermi gas from the epsilon expansion

We update the ground-state energy ratio of unitary Fermi gas to noninteracting Fermi gas (xi) from the epsilon expansion by including the next-to-next-to-leading-order (NNLO) term near two spatial dimensions. Interpolations of the NNLO epsilon expansions around four and two spatial dimensions with the use of Pade approximants give xi=0.360+/-0.020 in three dimensions with the uncertainty due to different interpolation functions. This value is consistent with the previous interpolations of the NLO epsilon expansions xi=0.377+/-0.014 in spite of the large NNLO corrections.

cond-mat.other↗

arXiv2009

Casimir interaction among heavy fermions in the BCS-BEC crossover

We investigate a two-species Fermi gas with a large mass ratio interacting by an interspecies short-range interaction. Using the Born-Oppenheimer approximation, we determine the interaction energy of two heavy fermions immersed in the Fermi sea of light fermions as a function of the s-wave scattering length. In the BCS limit, we recover the perturbative calculation of the effective interaction between heavy fermions. The p-wave projection of the effective interaction is attractive in the BCS limit while it turns out to be repulsive near the unitarity limit. We find that the p-wave attraction reaches its maximum between the BCS and unitarity limits, where the maximal p-wave pairing of heavy minority fermions is expected. We also investigate the case where the heavy fermions are confined in two dimensions and the p-wave attraction between them is found to be stronger than that in three dimensions.

cond-mat.other↗

arXiv2008

Universal Fermi gases in mixed dimensions

We investigate a two-species Fermi gas in which one species is confined in a two-dimensional plane (2D) or one-dimensional line (1D) while the other is free in the three-dimensional space (3D). We discuss the realization of such a system with the interspecies interaction tuned to resonance. When the mass ratio is in the range 0.0351<m_2D/m_3D<6.35 for the 2D-3D mixture or 0.00646<m_1D/m_3D<2.06 for the 1D-3D mixture, the resulting system is stable against the Efimov effect and has universal properties. We calculate key quantities in the many-body phase diagram. Other possible scale-invariant systems with short-range few-body interactions are also elucidated.

cond-mat.other↗

arXiv2008

Unitary Fermi gas in the epsilon expansion

We construct systematic expansions around four and two spatial dimensions for a Fermi gas near the unitarity limit. Near four spatial dimensions such a Fermi gas can be understood as a weakly-interacting system of fermionic and bosonic degrees of freedom. To the leading and next-to-leading orders in the expansion over ε=4-d, with d being the dimensionality of space, we determine the thermodynamic functions, the fermion quasiparticle spectrum, the critical polarizations, and the critical temperature as functions of the binding energy of the two-body state. We also show that the unitary Fermi gas near two spatial dimensions reduces to a weakly-interacting Fermi gas and calculate the thermodynamic functions and the fermion quasiparticle spectrum in the expansion over \barε=d-2. We discuss the matching of the two systematic expansions around four and two spatial dimensions in order to extract physical observables at d=3. We find good agreement of the results with those from recent Monte Carlo simulations.

cond-mat.other↗

arXiv2008

Renormalization group analysis of resonantly interacting anyons

We formulate a field theory for resonantly interacting anyons, that enables us to perform a perturbative calculation near the fermionic limit. We derive renormalization group equations for three-body and four-body couplings at one-loop order. In addition to two fixed points, we find a limit cycle behavior in the four-body coupling, which implies an infinite set of bound states in the four-anyon system.

hep-th↗