arXiv subjects

Makoto Yamashita

Publications and source records attributed to Makoto Yamashita.

At least 91 records · Page 5Linked to original sources

arXiv2012

A construction of finite index C*-algebra inclusions from free actions of compact quantum groups

Given an action of a compact quantum group on a unital C*-algebra, one can amplify the action with an adjoint representation of the quantum group on a finite dimensional matrix algebra, and consider the resulting inclusion of fixed point algebras. We show that this inclusion is a finite index inclusion of C*-algebras when the quantum group acts freely. We show that two natural definitions for a quantum group to act freely, namely the Ellwood condition and the saturatedness condition, are equivalent.

math.OA↗

arXiv2012

The second-order reduced density matrix method and the two-dimensional Hubbard model

The second-order reduced density matrix method (the RDM method) has performed well in determining energies and properties of atomic and molecular systems, achieving coupled-cluster singles and doubles with perturbative triples (CC SD(T)) accuracy without using the wave-function. One question that arises is how well does the RDM method perform with the same conditions that result in CCSD(T) accuracy in the strong correlation limit. The simplest and a theoretically important model for strongly correlated electronic systems is the Hubbard model. In this paper, we establish the utility of the RDM method when employing the $P$, $Q$, $G$, $T1$ and $T2^\prime$ conditions in the two-dimension al Hubbard model case and we conduct a thorough study applying the $4\times 4$ Hubbard model employing a coefficients. Within the Hubbard Hamilt onian we found that even in the intermediate setting, where $U/t$ is between 4 and 10, the $P$, $Q$, $G$, $T1$ and $T2^\prime$ conditions re produced good ground state energies.

cond-mat.str-el↗

arXiv2012

Mott Transition and Spin Structures of Spin-1 Bosons in Two-Dimensional Optical Lattice at Unit Filling

We study the ground state properties of spin-1 bosons in a two-dimensional optical lattice, by applying a variational Monte Carlo method to the S=1 Bose-Hubbard model on a square lattice at unit filling. A doublon-holon binding factor introduced in the trial state provides a noticeable improvement in the variational energy over the conventional Gutzwiller wave function and allows us to deal effectively with the inter-site correlations of particle densities and spins. We systematically show how spin-dependent interactions modify the superfluid-Mott insulator transitions in the S=1 Bose-Hubbard model due to the interplay between the density and spin fluctuations of bosons. Furthermore, regarding the magnetic phases in the Mott region, the calculated spin structure factor elucidates the emergence of nematic and ferromagnetic spin orders for antiferromagnetic ($U_2>0$) and ferromagnetic ($U_2<0$) couplings, respectively.

cond-mat.quant-gas↗

arXiv2011

Index character associated to the projective Dirac operator

We calculate the equivariant index formula for an infinite dimensional Clifford module canonically associated to any Riemannian manifold. It encompasses the fractional index formula of the projective Dirac operator by Mathai--Melrose--Singer.

math.KT↗

arXiv2011

On subfactors arising from asymptotic representations of symmetric groups

We consider the infinite symmetric group and its infinite index subgroup given as the stabilizer subgroup of one element under the natural action on a countable set. This inclusion of discrete groups induces a hyperfinite subfactor for each finite factorial representation of the larger group. We compute subfactor invariants of this construction in terms of the Thoma parameter.

math.OA↗

arXiv2010

Interaction and filling induced quantum phases of dual Mott insulators of bosons and fermions

Many-body effects are at the very heart of diverse phenomena found in condensed-matter physics. One striking example is the Mott insulator phase where conductivity is suppressed as a result of a strong repulsive interaction. Advances in cold atom physics have led to the realization of the Mott insulating phases of atoms in an optical lattice, mimicking the corresponding condensed matter systems. Here, we explore an exotic strongly-correlated system of Interacting Dual Mott Insulators of bosons and fermions. We reveal that an inter-species interaction between bosons and fermions drastically modifies each Mott insulator, causing effects that include melting, generation of composite particles, an anti-correlated phase, and complete phase-separation. Comparisons between the experimental results and numerical simulations indicate intrinsic adiabatic heating and cooling for the attractively and repulsively interacting dual Mott Insulators, respectively.

cond-mat.quant-gas↗

arXiv2010

Connes-Landi Deformation of Spectral Triples

We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic $K$-theoretic invariants independent of the deformation parameter.

math.OA↗

arXiv2010

Time-of-flight imaging method to observe signatures of antiferromagnetically ordered states of fermionic atoms in an optical lattice

We propose a simple method to detect the antiferromagnetic (AF) state of fermionic atoms in an optical lattice by combining a time-of-flight (TOF) imaging method and a Feshbach resonance. In this scheme, the nontrivial dynamics of fermionic atoms during the imaging process works as a probe with respect to the breaking of the translational symmetry in the AF state. Precise numerical simulations demonstrate that the characteristic oscillatory dynamics induced by the scattering process that transfers an AF ordering vector appears in TOF images, which can be easily observed experimentally.

cond-mat.quant-gas↗

arXiv2010

Thermodynamic properties of two-component fermionic atoms trapped in a two-dimensional optical lattice

We study the finite temperature properties of two-component fermionic atoms trapped in a two-dimensional optical lattice. We apply the self-energy functional approach to the two-dimensional Hubbard model with a harmonic trapping potential, and systematically investigate the thermodynamic properties of this system. We find that entropy and grand potential provide evidence of a crossover between the Mott insulating and metallic phases at certain temperatures. In addition, we find that entropy exhibits a cusp-like anomaly at lower temperatures, suggesting a second or higher order antiferromagnetic transition. We estimate the antiferromagnetic transition temperatures, and clarify how the trapping potential affects this magnetic transition.

cond-mat.quant-gas↗

arXiv2009

Nonadiabatic Dynamics of Ultracold Fermions in Optical Superlattices

We study the time-dependent dynamical properties of two-component ultracold fermions in a one-dimensional optical superlattice by applying the adaptive time-dependent density matrix renormalization group to a repulsive Hubbard model with an alternating superlattice potential. We clarify how the time evolution of local quantities occurs when the superlattice potential is suddenly changed to a normal one. For a Mott-type insulating state at quarter filling, the time evolution exhibits a profile similar to that expected for bosonic atoms, where correlation effects are less important. On the other hand, for a band-type insulating state at half filling, the strong repulsive interaction induces an unusual pairing of fermions, resulting in some striking properties in time evolution, such as a paired fermion co-tunneling process and the suppression of local spin moments. We further address the effect of a confining potential, which causes spatial confinement of the paired fermions.

cond-mat.quant-gas↗

arXiv2006

Fermionic atoms trapped in one-dimensional optical superlattice with harmonic confinement

We study the ground-state properties of spin-1/2 fermionic atoms confined in a one-dimensional optical superlattice with harmonic confinement by using the density matrix renormalization group method. For this purpose, we consider an ionic Hubbard model that has superlattice potentials with 2-site periodicity. We find that several different types of insulating regimes coexist even if the number of atoms at each site is not an integer, but its average within the unit cell is an integer or half integer. This is contrasted to the coexisting phase of the metallic and Mott-insulating regimes known for the ordinary Hubbard model in an optical lattice. The phase characteristics are elucidated by investigating the profiles of the atom density, the local density/spin fluctuations, the double occupation probability and the spin correlations in detail.

cond-mat.stat-mech↗

arXiv2005

Gutzwiller study of spin-1 bosons in an optical lattice under a magnetic field

We study spin-1 bosons in an optical lattice under a magnetic field by the Gutzwiller approximation. Our results thus obtained join the discontinuous phase boundary curves obtained by perturbative studies through a first-order transition. On the phase boundary curve, we also find a peculiar cusp structure originating from the degeneracy between different spin Mott states under a magnetic field. The magnetic field dependence of both fluctuation in the total number of bosons and the spin magnetization clarifies that the superfluid phase is divided into two regions reflecting the coexisting first- and second-order superfluid transitions.

cond-mat.other↗

arXiv2005

Bose-Hubbard model with attractive interactions

We consider the Bose-Hubbard model of atoms in an optical lattice potential when the atom-atom interactions are attractive. If the lowest energy lattice sites are degenerate (such as in the homogeneous case), then, at a critical value of the interaction strength, a phase-coherent condensate becomes unstable to a quantum superposition such that the number distribution of each of the degenerate sites becomes double peaked. In the limit when the interaction dominates, the superposition becomes macroscopic and has the form $|ψ>\propto\sum_{j} e^{iϕ_{j}}\hat{b}^{\dagger N}_{j}|{\rm vac}>$, where $N$ is the total number of atoms and the sum ranges over the energy-degenerate sites.

cond-mat.stat-mech↗

arXiv2005

Maximal entanglement of two spinor Bose-Einstein condensates

Starting with two weakly-coupled anti-ferromagnetic spinor condensates, we show that by changing the sign of the coefficient of the spin interaction, $U_{2}$, via an optically-induced Feshbach resonance one can create an entangled state consisting of two anti-correlated ferromagnetic condensates. This state is maximally entangled and a generalization of the Bell state from two anti-correlated spin-1/2 particles to two anti-correlated spin$-N/2$ atomic samples, where $N$ is the total number of atoms.

cond-mat.stat-mech↗

arXiv2004

Efficient rapid production of a Bose-Einstein condensate by overcoming serious three-body loss

We report the efficient production of a large Bose-Einstein condensate in $^{87}$Rb atoms. This is achieved by quickly reducing the radio-frequency of the magnetic field at a rate of -96.8 kHz/s during the final stage of evaporative cooling, and we have produced a condensate with ${(2.2 \pm 0.1) \times 10^{6}}$ atoms against a serious three-body recombination loss. We observed the dependence of the cooling efficiency on the rate at which the truncated energy changes by measuring the condensate growth for three kinds of radio-frequency sweep. The experimental results quantitatively agree with calculations based on the quantum kinetic theory of a Bose gas.

cond-mat.other↗

arXiv2004

On-demand single-photon state generation via nonlinear absorption

We propose a method for producing on-demand single-photon states based on collision-induced exchanges of photons and unbalanced linear absorption between two single-mode light fields. These two effects result in an effective nonlinear absorption of photons in one of the modes, which can lead to single photon states. A quantum nonlinear attenuator based on such a mechanism can absorb photons in a normal input light pulse and terminate the absorption at a single-photon state. Because the output light pulses containing single photons preserve the properties of the input pulses, we expect this method to be a means for building a highly controllable single photon source.

quant-ph↗

arXiv2003

Stabilization of the number of Bose-Einstein condensed atoms in evaporative cooling via three-body recombination loss

The dynamics of evaporative cooling of magnetically trapped $^{87}$Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. We carried out the quantitative calculations of the time evolution of conventional evaporative cooling where the frequency of the radio-frequency magnetic field is swept exponentially. This "exponential-sweep cooling" is known to become inefficient at the final stage of the cooling process due to a serious three-body recombination loss. We precisely examine how the growth of a Bose-Einstein condensate depends on the experimental parameters of evaporative cooling, such as the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. It is shown that three-body recombination drastically depletes the trapped $^{87}$Rb atoms as the system approaches the quantum degenerate region and the number of condensed atoms finally becomes insensitive to these experimental parameters. This result indicates that the final number of condensed atoms is well stabilized by a large nonlinear three-body loss against the fluctuations of experimental conditions in evaporative cooling.

cond-mat.stat-mech↗

arXiv2002

Optimization of evaporative cooling towards a large number of Bose-Einstein condensed atoms

We study the optimization of evaporative cooling in trapped bosonic atoms on the basis of quantum kinetic theory of a Bose gas. The optimized cooling trajectory for $^{87}$Rb atoms indicates that the acceleration of evaporative cooling around the transition point of Bose-Einstein condensation is very effective against loss of trapped atoms caused by three-body recombination. The number of condensed atoms is largely enhanced by the optimization, more than two orders of magnitude in our present calculation using relevant experimental parameters, as compared with the typical value given by the conventional evaporative cooling where the frequency of radio-frequency magnetic field is swept exponentially. In addition to this optimized cooling, it is also shown that highly efficient evaporative cooling can be achieved by an initial exponential and then a rapid linear sweep of frequency.

cond-mat.stat-mech↗