arXiv subjects

Katsuhiro Nakamura

Publications and source records attributed to Katsuhiro Nakamura.

At least 19 recordsLinked to original sources

arXiv2022

Fast-forward scaling theory

Speed is the key to further advances in technology. For example, quantum technologies, such as quantum computing, require fast manipulations of quantum systems in order to overcome the effect of decoherence. However, controlling the speed of quantum dynamics is often very difficult due to both the lack of a simple scaling property in the dynamics and the infinitely large parameter space to be explored. Therefore, protocols for speed control based on understanding on the dynamical properties of the system, such as non-trivial scaling property, are highly desirable. Fast-forward scaling theory (FFST) was originally developed to provide a way to accelerate, decelerate, stop and reverse the dynamics of quantum systems. FFST has been extended in order to accelerate quantum and classical adiabatic dynamics of various systems including cold atoms, internal state of molecules, spins and solid-state artificial atoms. This paper describes the basic concept of FFST and review the recent developments and its applications such as fast state-preparations, state protection and ion sorting. We introduce a method, called inter-trajectory travel, derived from FFST recently. We also point out the significance of deceleration in quantum technology.

quant-ph↗

arXiv2020

Fast forward approach to stochastic heat engine

The fast-forward (FF) scheme proposed by Masuda and Nakamura (\textit{Proc. R. Soc. A} \textbf{466}, 1135 (2010)) in the context of conservative quantum dynamics can reproduce a quasi-static dynamics in an arbitrarily short time. We apply the FF scheme to the classical stochastic Carnot-like heat engine which is driven by a Brownian particle coupled with a time-dependent harmonic potential and working between the high ($T_h$)- and low ($T_c$)-temperature heat reservoirs. Concentrating on the underdamped case where momentum degree of freedom is included, we find the explicit expressions for the FF protocols necessary to accelerate both the isothermal and thermally-adiabatic processes, and obtain the reversible and irreversible works. The irreversible work is shown to consist of two terms with one proportional to and the other inversely proportional to the friction coefficient. The optimal value of efficiency $η$ at the maximum power of this engine is found to be $η^*=\frac{1}{2} \left( 1+\frac{1}{2}\left(\frac{T_c}{T_h}\right)^{\frac{1}{2}} - \frac{5}{4}\frac{T_c}{T_h} +O\left(\left(\frac{T_c}{T_h}\right)^{\frac{3}{2}}\right)\right)$ and $η^*= 1- \left(\frac{T_c}{T_h}\right)^{\frac{1}{2}}$, respectively in the cases of strong and weak dissipation. The result is justified for a wide family of time scaling functions, making the FF protocols very flexible. We also revealed that the accelerated full cycle of the Carnot-like stochastic heat engine cannot be conceivable within the framework of the overdamped case, and the power and efficiency can be evaluated only when the momentum degree of freedom is taken into consideration.

cond-mat.stat-mech↗

arXiv2019

Fast-forward approach to adiabatic quantum dynamics of regular spin clusters: nature of geometry-dependent driving interactions

The fast forward scheme of adiabatic quantum dynamics is applied to finite regular spin clusters with various geometries and the nature of driving interactions is elucidated. The fast forward is the quasi-adiabatic dynamics guaranteed by regularization terms added to the reference Hamiltonian, followed by a rescaling of time with use of a large scaling factor. With help of the regularization terms consisting of pair-wise and 3-body interactions, we apply the proposed formula (Phys. Rev.A 96, 052106(2017)) to regular triangle and open linear chain for N = 3 spin systems, and to triangular pyramid, square, primary star graph and open linear chain for N = 4 spin systems. The geometry-induced symmetry greatly decreases the rank of coefficient matrix of the linear algebraic equation for regularization terms. Choosing a transverse Ising Hamiltonian as a reference, we find: (1) for N = 3 spin clusters, the driving interaction consists of only the geometry-dependent pairwise interactions and there is no need for the 3-body interaction; (2) for N = 4 spin clusters, the geometry-dependent pair-wise interactions again constitute major part of the driving interaction, whereas the universal 3-body interaction free from the geometry is necessary but plays a subsidiary role. Our scheme predicts the practical driving interaction in accelerating the adiabatic quantum dynamics of structured regular spin clusters.

quant-ph↗

arXiv2018

Fast forward of adiabatic spin dynamics of entangled states

We develop a scheme of fast forward of adiabatic spin dynamics of quantum entangled states. We settle the quasi-adiabatic dynamics by adding the regularization terms to the original Hamiltonian and then accelerate it with use of a large time-scaling factor. Assuming the experimentally-realizable candidate Hamiltonian consisting of the exchange interactions and magnetic field, we solved the regularization terms. These terms multiplied by the velocity function give rise to the state-dependent counter-diabatic terms. The scheme needs neither knowledge of full spectral properties of the system nor solving the initial and boundary value problem. Our fast forward Hamiltonian generates a variety of state-dependent counter-diabatic terms for each of adiabatic states, which can include the state-independent one. We highlight this fact by using minimum (two-spin) models for a simple transverse Ising model, quantum annealing and generation of entanglement.

quant-ph↗

arXiv2018

Quantum gas in the fast forward scheme of adiabatically expanding cavities: Force and equation of states

With use of the scheme of fast forward which realizes quasi-static or adiabatic dynamics in shortened time scale, we investigate a thermally-isolated ideal quantum gas confined in a rapidly dilating one-dimensional (1D) cavity with the time-dependent size $L=L(t)$. In the fast-forward variants of equation of states, i.e., Bernoulli's formula and Poisson's adiabatic equation, the force or 1D analog of pressure can be expressed as a function of the velocity ($\dot{L}$) and acceleration ($\ddot{L}$) of $L$ besides rapidly-changing state variables like effective temperature ($T$) and $L$ itself. The force is now a sum of nonadiabatic (NAD) and adiabatic contributions with the former caused by particles moving synchronously with kinetics of $L$ and the latter by ideal bulk particles insensitive to such a kinetics. The ratio of NAD and adiabatic contributions does not depend on the particle number ($N$) in the case of the soft-wall confinement, whereas such a ratio is controllable in the case of hard-wall confinement. We also reveal the condition when the NAD contribution overwhelms the adiabatic one and thoroughly changes the standard form of the equilibrium equation of states.

quant-ph↗

arXiv2017

Fast forward of adiabatic control of tunneling states

By developing the preceding work on the fast forward of transient phenomena of quantum tunneling by Khujakulov and Nakamura (Phys. Rev. {\bf A 93}, 022101 (2016) ), we propose a scheme of the exact fast forward of adiabatic control of stationary tunneling states with use of the electromagnetic field. The idea allows the acceleration of both the amplitude and phase of wave functions throughout the fast-forward time range. The scheme realizes the fast-forward observation of the transport coefficients under the adiabatically-changing barrier with the fixed energy of an incoming particle. As typical examples we choose systems with (1) Eckart's potential with tunable asymmetry and (2) double $δ$-function barriers under tunable relative height. We elucidate the driving electric field to guarantee the stationary tunneling state during a rapid change of the barrier and evaluate both the electric-field-induced temporary deviation of transport coefficients from their stationary values and the modulation of the phase of complex scattering coefficients

quant-ph↗

arXiv2016

Sine-Gordon solitons in networks: Scattering and transmission at vertices

We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws, such as energy and current conservation. Traveling wave solutions for star and tree graphs are obtained analytically in the form of kink, antikink and breather solitons for a special case. It is shown that these solutions provide reflectionless soliton transmission at the graph vertex. We find the sum rule for bond-dependent coefficients making the sine-Gordon equation embedded on the graph completely integrable. For the general case the problem is solved numerically and the vertex scattering is quantified. Applications of the obtained results to Josephson junction networks, DNA double helix and elastic fibre networks are discussed.

nlin.PS↗

arXiv2016

Dynamics of trapped interacting vortices in Bose-Einstein condensates: Role of breathing degree of freedom

With use of a variational principle, we investigate a role of breathing width degree of freedom in the effective theory of interacting vortices in a trapped single-component Bose-Einstein condensates in 2 dimensions under the strong repulsive cubic nonlinearity. As for the trial function, we choose a product of two vortex functions assuming a pair interaction and employ the amplitude form of each vortex function in the Padé approximation which accommodates a hallmark of the vortex core. We have obtained Lagrange equation for the interacting vortex-core coordinates coupled with the time-derivative of width and also its Hamilton formalism by having recourse to a non-standard Poisson bracket. By solving the Hamilton equation, we find rapid radial breathing oscillations superposed on the slower rotational motion of vortex cores, consistent with numerical solutions of Gross-Pitaevskii equation. In higher-energy states of 2 vortex systems, the breathing width degree of freedom plays role of a kicking in the kicked rotator and generates chaos with a structure of sea-urchin needles. Byproduct of the present variational approach includes: (1) the charge-dependent logarithmic inter-vortex interaction multiplied with a pre-factor which depends on the scalar product of a pair of core-position vectors; (2) the charge-independent short-range repulsive inter-vortex interaction and spring force.

nlin.CD↗

arXiv2016

Scheme for accelerating quantum tunneling dynamics

We propose a scheme of the exact fast-forwarding of standard quantum dynamics for a charged particle. The present idea allows the acceleration of both the amplitude and phase of the wave function throughout the fast-forward time range and is distinct from that of Masuda-Nakamura (e.g., Proc. R. Soc. A {\bf 466}, 1135 (2010)) which enabled acceleration of only the amplitude of the wave function on the way. We shall apply the proposed method to the quantum tunneling phenomena and obtain the electro-magnetic field to ensure the rapid penetration of wave functions through a tunneling barrier. Typical examples described here are: 1) an exponential wave packet passing through the delta-function barrier; 2) the opened Moshinsky shutter with a delta-function barrier just behind the shutter. We elucidate the tunneling current in the vicinity of the barrier and find the remarkable enhancement of the tunneling rate (: tunneling power) due to the fast-forwarding. In the case of a very high barrier, in particular, we present the asymptotic analysis and exhibit a suitable driving force to recover a recognizable tunneling current. The analysis is also carried out on the exact acceleration of macroscopic quantum tunneling with use of the nonlinear Schrödinger equation which accommodates a tunneling barrier.

quant-ph↗

arXiv2014

High-fidelity rapid ground-state loading of an ultracold gas into an optical lattice

A protocol is proposed for the rapid coherent loading of a Bose-Einstein condensate into the ground state of an optical lattice, without residual excitation associated with the breakdown of adiabaticity. The driving potential required to assist the rapid loading is derived using the fast forward technique, and generates the ground state in any desired short time. We propose an experimentally feasible loading scheme using a bichromatic lattice potential, which approximates the fast-forward driving potential with high fidelity.

cond-mat.quant-gas↗

arXiv2012

Bernoulli's formula and Poisson's equations for a confined quantum gas: Effects due to a moving piston

We study a nonequilibrium equation of states of an ideal quantum gas confined in the cavity under a moving piston with a small but finite velocity in the case that the cavity wall suddenly begins to move at time origin. Confining to the thermally-isolated process, quantum non-adiabatic (QNA) contribution to Poisson's adiabatic equations and to Bernoulli's formula which bridges the pressure and internal energy is elucidated. We carry out a statistical mean of the non-adiabatic (time-reversal-symmetric) force operator found in our preceding paper (K. Nakamura et al, Phys. Rev. E Vol.83, 041133, (2011)) in both the low-temperature quantum-mechanical and high temperature quasi-classical regimes. The QNA contribution, which is proportional to square of the piston's velocity and to inverse of the longitudinal size of the cavity, has a coefficient dependent on temperature, gas density and dimensionality of the cavity. The investigation is done for a unidirectionally-expanding 3-d rectangular parallelepiped cavity as well as its 1-d version. Its relevance in a realistic nano-scale heat engine is discussed.

cond-mat.quant-gas↗

arXiv2012

Dynamics of inertial vortices in multi-component Bose-Einstein condensates

With use of the nonlinear Schr{ö}dinger (or Gross-Pitaevskii) equation with strong repulsive cubic nonlinearity, dynamics of multi-component Bose-Einstein condensates (BECs) with a harmonic trap in 2 dimensions is investigated beyond the Thomas-Fermi regime. In the case when each component has a single vortex, we obtain an effective nonlinear dynamics for vortex cores (particles). The particles here acquire the inertia, in marked contrast to the standard theory of point vortices widely known in the usual hydrodynamics. The effective dynamics is equivalent to that of charged particles under a strong spring force and in the presence of Lorentz force with the uniform magnetic field. The inter-particle (vortex-vortex) interaction is singularly-repulsive and short-ranged with its magnitude decreasing with increasing distance of the center of mass from the trapping center. "Chaos in the three-body problem" in the three vortices system can be seen, which is not expected in the corresponding point vortices without inertia in 2 dimensions.

cond-mat.quant-gas↗

arXiv2010

Fast-forward of quantum adiabatic dynamics in electro-magnetic field

We show a method to accelerate quantum adiabatic dynamics of wavefunctions under electro-magnetic field by developing the previous theory (Masuda & Nakamura 2008 and 2010). Firstly we investigate the orbital dynamics of a charged particle. We derive the driving field which accelerates quantum adiabatic dynamics in order to obtain the final adiabatic states except for the spatially uniform phase such as the adiabatic phase in any desired short time. Fast-forward of adiabatic squeezing and transport in the electro-magnetic field is exhibited. Secondly we investigate spin dynamics under the magnetic field, showing the fast-forward of adiabatic spin inversion and of adiabatic dynamics in Landau-Zener model. The connection of the present framework with Kato-Berry's transitionless quantum driving is elucidated in Appendix.

cond-mat.mes-hall↗

arXiv2009

Fast-forward of adiabatic dynamics in quantum mechanics

We propose a way to accelerate adiabatic dynamics of wave functions in quantum mechanics to obtain a final adiabatic state except for the spatially uniform phase in any desired short time. We develop the previous theory of fast-forward (Masuda & Nakamura 2008) so as to derive a driving potential for the fast-forward of the adiabatic dynamics. A typical example is the fast-forward of adiabatic transport of a wave function which is the ideal transport in the sense that a stationary wave function is transported to an aimed position in any desired short time without leaving any disturbance at the final time of the fast-forward. As other important examples we show accelerated manipulations of wave functions such as their splitting and squeezing. The theory is also applicable to macroscopic quantum mechanics described by the nonlinear Schroedinger equation.

cond-mat.mes-hall↗

arXiv2008

Diffusion in the Markovian limit of the spatio-temporal colored noise

We explore the diffusion process in the non-Markovian spatio-temporal noise.%the escape rate problem in the non-Markovian spatio-temporal random noise. There is a non-trivial short memory regime, i.e., the Markovian limit characterized by a scaling relation between the spatial and temporal correlation lengths. In this regime, a Fokker-Planck equation is derived by expanding the trajectory around the systematic motion and the non-Markovian nature amounts to the systematic reduction of the potential. For a system with the potential barrier, this fact leads to the renormalization of both the barrier height and collisional prefactor in the Kramers escape rate, with the resultant rate showing a maximum at some scaling limit.

cond-mat.stat-mech↗

arXiv2007

Effects of an oscillating field on pattern formation in a ferromagnetic thin film: Analysis of patterns traveling at a low velocity

Magnetic domain patterns under an oscillating field is studied theoretically by using a simple Ising-like model. We propose two ways to investigate the effects of the oscillating field. The first one leads to a model in which rapidly oscillating terms are averaged out, and the model can explain the existence of the maximum amplitude of the field for the appearance of patterns. The second one leads to a model that includes the delay of the response to the field, and the model suggests the existence of a traveling pattern which moves very slowly compared with the time scale of the driving field.

cond-mat.other↗

arXiv2007

Field sweep rate dependence of magnetic domain patterns: Numerical simulations for a simple Ising-like model

We study magnetic domain patterns in ferromagnetic thin films by numerical simulations for a simple Ising-like model. Magnetic domain patterns after quench demonstrate various types of patterns depending on the field sweep rate and parameters of the model. How the domain patterns are formed is shown with use of the number of domains, the domain area, and domain area distributions as well as snapshots of domain patterns. Considering the proper time scale of the system, we propose a criterion for the structure of domain patterns.

cond-mat.other↗

arXiv2007

Dynamical stability for finite quantum spin chains against a time-periodic inhomogeneous perturbation

We investigate dynamical stability of the ground state against a time-periodic and spatially-inhomogeneous magnetic field for finite quantum XXZ spin chains. We use the survival probability as a measure of stability and demonstrate that it decays as $P(t) \propto t^{-1/2}$ under a certain condition. The dynamical properties should also be related to the level statistics of the XXZ spin chains with a constant spatially-inhomogeneous magnetic field. The level statistics depends on the anisotropy parameter and the field strength. We show how the survival probability depends on the anisotropy parameter, the strength and frequency of the field.

cond-mat.other↗