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Masao Hirokawa

Publications and source records attributed to Masao Hirokawa.

At least 19 recordsLinked to original sources
arXiv2026

Strong-coupling asymptotics for anisotropic Rabi model

The anisotropic quantum Rabi model provides a continuous interpolation between the quantum Rabi model and the Jaynes-Cummings model. In this paper, we study the norm-resolvent limit of the anisotropic quantum Rabi model as the coupling strength tends to infinity. After subtracting an explicit quadratic renormalization term, we identify the limiting Hamiltonian, which determines the asymptotic spectral structure of the model. Our result provides a unified description connecting the Jaynes-Cummings model and the full quantum Rabi model in the strong-coupling limit, thereby revealing the dominant role of the counter-rotating interaction.

math-ph↗
arXiv2026

Quantum Simulation of Energy Bifurcation and Z_2-Symmetry Restoration in Macroscopic Quantum Tunneling

Macroscopic quantum tunneling (MQT), a cornerstone of Leggett's program, is deeply linked with instanton physics, yet its experimental verification remains elusive. This Perspective demonstrates that the quantum Rabi model manifests observable, instanton-like effects via quantum simulation. In the MQT regime, qubit-boson interactions drive Polyakov's energy bifurcation, governing tunneling and spontaneous symmetry breaking. Mapping the quantum Rabi model onto an effective double-well potential reveals that while tunneling suppression induces spontaneous symmetry breaking, instanton-like contributions act to restore it. This mechanism enables experimental access to the classical Euclidean action of an effective instanton-like particle, offering a route to probe non-perturbative phenomena.

quant-ph↗
arXiv2023

A Model without Higgs Potential for Quantum Simulation of Radiative Mass-Enhancement in SUSY Breaking

We study a quantum-simulation model of a mass enhancement in the fermionic states, as well as in the bosonic ones, of the supersymmetric quantum mechanics. The bosonic and fermionic states are graded by a qubit. This model is so simple that it may be implemented as a quantum simulation of the mass enhancement taking place when supersymmetry (SUSY) is spontaneously broken. Here, our quantum simulation means the realization of the target quantum phenomenon with some quantum-information devices as a physical reality. The model describes how the quasi-particle consisting of the annihilation and creation of 1-mode scalar bosons eats the spin effect given by the X-gate, and how it acquires the mass enhancement in the fermionic states in the spontaneous SUSY breaking. Our model's interaction does not have any Higgs potential. Instead, the qubit acts as a substitute for the Higgs potential by the 2-level-system approximation of the double-well potential, and then, the spontaneous SUSY breaking takes place and the mass is enhanced.

quant-ph↗
arXiv2022

Can quantum Rabi model with A^2-term avoid no-go theorem for spontaneous SUSY breaking?

The hierarchy problem asks why the mass of the Higgs particle is so much lighter than the Planck-scale mass. Considering the interaction of the Higgs particle and an elementary particle in the Planck-scale, to cope with that big difference, the conventional calculation needs the help of an arbitrary, excessive fine-tuning, that is, the huge cancellation between the bare mass term and the quantum correction, without obeying a physical principle such as symmetry. Thus, it is often said to be unnatural. On the other hand, the theory of supersymmetry (SUSY) is a strong candidate naturally to solve the hierarchy problem. However, any sign of SUSY even for the quantum mechanics (QM) version had not been firmly, directly observed in the physical reality until Cai et al. reported the observation of N=2 SUSY and its spontaneous breaking in a trapped ion quantum simulator for the prototype model for SUSY QM. In this discussion, I derive a no-go theorem for the spontaneous SUSY breaking in the strong coupling limit for the quantum Rabi model with the A^2-term, and at the same time, I show another limit proposed in the scheme by Cai et al. can avoid the no-go theorem and take that model from the N=2 SUSY to its spontaneous breaking. I propose a theoretical method to observe how the effect of A^2-term appears in the spontaneous SUSY breaking.

quant-ph↗
arXiv2021

Concealing-Restoring System for Physical Layer Data Based on Stochastic Filtering Theory

We propose a concealing-restoring system (CRS) for data on physical layer of the OSI reference model. CRS conceals those data by disturbing them with some random noises, and restores the data from the concealed ones to the original ones by using the noise elimination based on a proper stochastic filtering theory. Although we introduced the outline of the almost linear version of CRS in our previous work [Fujii & Hirokawa, Math. Industry, Springer (2020)], we explain its details, and study its nonlinearization to improve the security of CRS in this paper.

cs.IT↗
arXiv2018

Schrodinger-Cat-Likeness in Adiabatic Approximation for Generalized Quantum Rabi Model without and with A^2-Term

We give a mathematical procedure to obtain the adiabatic approximation for the generalized quantum Rabi Hamiltonian both without and with a quadratic interaction. We consider the Hamiltonian as the energy of a model describing the interaction system of a two-level artificial atom and a one-mode microwave photon in circuit QED. In the case without the quadratic interaction, we show in the adiabatic approximation that whether each bare eigenstate forms a Schrodinger-cat-like entangled state or not depends on whether the energy bias of the atom is zero or non-zero, and then, the effect of the tunnel splitting of the atom is ignored. On the other hand, in the case with the quadratic interaction, we show in the adiabatic approximation that all the physical eigenstates obtained by the (meson) pair theory form individual Schrodinger-cat-like entangled states for every energy bias. We conclude that this fact comes from the effect of the tunnel splitting.

quant-ph↗
arXiv2016

A Mathematical Analysis of Dressed Photon in Ground State of Generalized Quantum Rabi Model Using Pair Theory

We consider the generalized quantum Rabi model with the so-called $A^{2}$-term in the light of the Hepp-Lieb-Preparata quantum phase transition. We investigate the dressed photon in its ground state when the atom-light coupling strength is in the deep-strong coupling regime. We show how the dressed photon appears in the ground state. We dedicate this paper to Pavel Exner and Herbert Spohn on the occasion of their 70th birthdays, and Klaus Hepp on the occasion of his 80th birthday.

quant-ph↗
arXiv2015

A duality between a dark state and a quasi-dark state

We consider the optomechanical system consisting of an atom-cavity system coupled with a mechanical resonator, and expand the notion of quasi-dark state to the optomechanical system. We theoretically prove that even if both the one-mode light of the cavity and the one-mode Bose field of the mechanical resonator interact with the atom, each of a dark state and a quasi-dark state has an individual chance to appear when an interaction between the one-mode light and the one-mode Bose field exists. We then come up with a duality between the dark state and the quasi-dark state.

quant-ph↗
arXiv2014

Spin-Boson Model through a Poisson-Driven Stochastic Process

We give a functional integral representation of the semigroup generated by the spin-boson Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a method of constructing Gibbs path measures indexed by the full real line which can be applied also to more general stochastic processes with jump discontinuities. Using these tools we then show existence and uniqueness of the ground state of the spin-boson, and analyze ground state properties. In particular, we prove super-exponential decay of the number of bosons, Gaussian decay of the field operators, derive expressions for the positive integer, fractional and exponential moments of the field operator, and discuss the field fluctuations in the ground state.

math-ph↗
arXiv2013

On the Coupling-Strength Growth of the Rabi Model in the Light of SUSYQM

We consider the coupling-strength growth of the Rabi model from the point of the view of SUSYQM. We show that the Rabi model takes the supersymmetric system to the spontaneous supersymmetry breaking as its coupling strength g grows lager from the case g=0 to the case g\approx\infty. We study a kind of chirality quantum phase transition in this process.

quant-ph↗
arXiv2013

A Mathematical Aspect of A Tunnel-Junction for Spintronic Qubit

We consider the Dirac particle living in the 1-dimensional configuration space with a junction for a spintronic qubit. We give concrete formulae explicitly showing the one-to-one correspondence between every self-adjoint extension of the minimal Dirac operator and the boundary condition of the wave functions of the Dirac particle. We then show that the boundary conditions are classified into two types: one of them is characterized by two parameters and the other is by three parameters. Then, we show that Benvegnu and Dabrowski's four-parameter family can actually be characterized by three parameters, concerned with the reflection, penetration, and phase factor.

quant-ph↗
arXiv2013

One-Dimensional Tunnel-Junction Formula for Schrodinger Particle

We handle all the self-adjoint extensions of the minimal Schroedinger operator for the non-relativistic electron living in the one-dimensional configuration space with a junction. We are interested in every boundary condition corresponding to the individual self-adjoint extension. Thus, we clarify all the types of those boundary conditions of the wave functions of the non-relativistic electron. We find a tunnel-junction formula for the non-relativistic electron passing through the junction. Using this tunnel-junction formula, we propose a mathematical possibility of a tunnel-junction device for qubit.

math-ph↗
arXiv2010

Role of a Phase Factor in the Boundary Condition of a One-Dimensional Junction

One-dimensional quantum systems can be experimentally studied in recent nano-technology like the carbon nanotube and the nanowire. We have considered the mathematical model of the one-dimensional Schrödinger particle with a junction and have analyzed the phase factor in the boundary condition of the junction. We have shown that the phase factor in the tunneling case appears in the situation of the non-adiabatic transition with the three energy levels in the exact WKB analysis.

quant-ph↗
arXiv2008

Dicke-Type Energy Level Crossings in Cavity-Induced Atom Cooling: Another Superradiant Cooling

This paper is devoted to energy-spectral analysis for the system of a two-level atom coupled with photons in a cavity. It is shown that the Dicke-type energy level crossings take place when the atom-cavity interaction of the system undergoes changes between the weak coupling regime and the strong one. Using the phenomenon of the crossings we develop the idea of cavity-induced atom cooling proposed by the group of Ritsch, and we lay mathematical foundations of a possible mechanism for another superradiant cooling in addition to that proposed by Domokos and Ritsch. The process of our superradiant cooling can function well by cavity decay and by control of the position of the atom, at least in (mathematical) theory, even if there is neither atomic absorption nor atomic emission of photons.

quant-ph↗
arXiv2007

Characterization of Infrared Catastrophe by The Carleman Operator and Its Singularity

This paper addresses some mathematical problems arising from the infrared (IR) catastrophe in quantum field theory. IR catastrophe is formulated and studied in operator theory, characterized by the Carleman operator. Non-existence of ground state under IR catastrophe is also investigated with the help of the characterization. The theory presented in this paper is applied to the Hamiltonian of the model describing a non-relativistic electron coupled with a quantum field of phonons or polaritons in the light of mathematics as well as solid state physics.

math-ph↗
arXiv2006

Stability of Formation of Large Bipolaron: Nonrelativistic Quantum Field Theory

We are concerned with the stability of formation of large bipolaron in a 3-dimensional (3D) crystal. This problem is considered in the framework of nonrelativistic quantum field theory. Thus, the Hamiltonian formalism, as Froehlich introduced, is employed to describe the bipolaron. We approach the problem by characterizing some sufficient or necessary conditions for the bipolaron being stable. This paper gives a full detail of the author's talks at ESI, RIMS, and St. Petersburg State Univ. in 2005.

cond-mat.other↗
arXiv2005

Infrared Catastrophe for Nelson's Model

We mathematically study the infrared catastrophe for the Hamiltonian of Nelson's model when it has the external potential in a general class. For the model, we prove the pull-through formula on ground states in operator theory first. Based on this formula, we show both non-existence of any ground state and divergence of the total number of soft bosons.

math-ph↗