arXiv subjects

Bei-Lok Hu

Publications and source records attributed to Bei-Lok Hu.

At least 19 recordsLinked to original sources

arXiv2026

Quantum optomechanics with arbitrary mirror displacement: nonlinear Langevin equation with non-Markovian back-action noises

Quantum optomechanics (QOM) explores the interaction between a quantum field, often confined in a cavity, and the quantum motion of mirrors, membranes or material media, usually assumed slow enough with negligible particle production, which is the central concern of dynamical Casimir effects, and a drive laser field for effective control. This rapidly developing field has a wide range of applications, from quantum sensing to the detection of gravitational waves. Because the opto-mechanical coupling is nonlinear, most theoretical investigations assume that the amplitude of mirror motion $x$ remains small. Recent years saw several papers treating $x^2, x^3$ orders in the mirror displacement. In our work we take a different route, deploying the functional perturbative method presented in [1] and enriched in [2], applicable for sufficiently weak opto-mechanical couplings. With this we can treat arbitrary displacement of the mirror, not just at a higher order in a power series expansion in $x$. We first derive the influence action of the quantum field and its non-Markovian noises back-reacting on the moving mirror with self-consistency. From it we derive a nonlinear Langevin equation driven by these back-action noises from the quantum field. We then show how results from our general modeling and treatment can be linked with the models and the Langevin equations presented in the literature, starting with the popular radiation pressure $Nx$ coupling, with $N$ the photon number, up to the recent $x^3$ order results. We hope this new approach and the results presented here can provide useful theoretical support for high precision QOM experimentation in the future.

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arXiv2026

Quantum Optomechanics with Imperfect Mirrors and Casimir-Polder Effect of Atoms with Different Dynamic Polarizabilities: A Unified Treatment via a Microscopic Model

This work aims at bringing the microphysics model of quantum optomechanics (QOM) proposed in [1] and developed in [2, 3] one step closer to be applicable to realistic experimental conditions, specifically, for imperfect mirrors, and for real materials. The atom/mirror-oscillator-field (AMOF) model features an internal degree of freedom for a mirror or an atom whose interaction with a quantum field determines the transmission functions of a mirror or the dynamic polarizability of an atom. We study three problems with this model: 1) An imperfect mirror moving in a cavity field, comparing results from the AMOF model with the boundary condition methods; 2) We analyze how well the dynamic polarizability derived from the AMOF model fits the tabulated data at different frequencies. 3) Combining these two parts we analyze the quantum fluctuations induced Casimir-Polder energy between a dilute atom space and a wall. We examine how well we can use the three constituent parameters of the idf oscillator in the AMOF model to match with published results on a meta-stable He* atom near a Au plate and found excellent agreements. These examples show that the AMOF model not only has a sound theoretical structure, because it is based on the microphysics dynamics of the basic constituents, it also has good practical values because it can produce accurate results for certain real materials.

quant-ph↗

arXiv2026

Vacuum viscosity and relativistic inertia: Motion of a massive object with charged internal degrees of freedom interacting with a classical field

Our present investigation into a rather rudimentary problem is motivated by two classes of problems studied since the 70's, cosmological particle creation and its more accessible analog, the dynamical Casimir effect on the one hand, and quantum friction a neutral atom moving along a dielectric surface would experience, on the other. The backreaction effects of produced particles being able to isotropize the expansion of the universe, or to slow down the moving mirror can be understood via the concept of vacuum viscosity arising from fluctuations of the quantum field. We want to track down the origin of this effect by asking the question whether a moving massive $M$ object with a charged internal degrees of freedom $\chi$ interacting with a free unbounded classical field $\phi$ at zero temperature would experience a viscous force, similar to the said precedents. Adopting a microphysics model for optomechanics which can treat the unequal tripartite $\chi$-$\phi$-$M$ interactions, we first perform a nonrelativistic calculation, which seems perfectly legitimate considering the needs of atomic physics, and found the answer to be yes, but a relativistic covariant calculation says no. We identify where the nonrelativistic framework is defective. The resolution of this latent yet real conflict is technically nontrivial but physically quite inspirational. It results in added enriched contents to Newton's first and second laws when the principles of special relativity are enforced, and rules to follow to get the correct nonrelativistic answer

quant-ph↗

arXiv2026

Relativistic single-electron wavepacket in quantum electromagnetic fields II: Quantum radiation emitted by a uniformly accelerated electron

We compute the quantum radiation emitted by wavepackets of relativistic single electrons, both at rest and undergoing uniform acceleration in the Minkowski vacuum of the electromagnetic field. We find that the cubic terms in the original nonlinear action of electrodynamics should be considered in obtaining the quantum radiation to the leading order. We show that the quantum radiation from a single-electron wavepacket at rest vanishes exactly. For a uniformly accelerated electron, the quantum radiated power has secular growth in the long-time regime. We demonstrate that this secular growth has a classical interpretation, and argue that the resummed quantum radiation at late times would not diverge. Regarding experimental proposals for the detection of the Unruh effect from the quantum radiation in the `blind spots' of classical radiation we ascertain that quantum corrections in the two blind spots are fully contributed by the transverse deviation correlators, where the dominant contributions are irrelevant to the Unruh effect in electron microscopes.

hep-th↗

arXiv2026

Quantum Brownian motion with non-Gaussian noises: Fluctuation-Dissipation Relation and nonlinear Langevin equation

Building upon the work of Hu, Paz, and Zhang [1,2] on open quantum systems we consider the quantum Brownian motion (QBM) model with one oscillator (position variable $x$) as the system, {\it nonlinearly} coupled to an environment of $N$ harmonic oscillators (with mass $m_n$, natural frequency $\omega_n$, position $q_n$ and momentum $p_n$ variables) in the form $\sum_{n}\left(v_{n1}(x)q_{n}^{k}+v_{n2}(x)p_{n}^{l}\right)$ where $k, l$ are integers (the present work only considers the $k=l=2$ cases). The vertex functions $v_{n1}, v_{n2} $ are of the form $v_{n1}=\lambda C_{n1} f(x), v_{n2}(x)=-\lambda\,C_{n2}m_{n}^{-2}\omega_{n}^{-2}f(x)$ where $C_{n1,2}$ are the coupling constants with the $n$th oscillator, $f(x)$ is any arbitrary function of $x$, and $\lambda$ is a dimensionless constant. Employing the closed-time-path formalism the influence action $S_{IF}$ is calculated using a perturbative expansion in $\lambda$. It is possible to identify the terms in $S_{IF}$ quadratic or higher in $\Delta(s)\equiv f(x_{+}(s))-f(x_{-}(s))$ to constitute the noise kernel, while terms linear in $\Delta$ to that of the dissipation kernel. The non-Gaussian noise kernel gives rise to non-zero three-point correlation function of the corresponding stochastic force. The pathway presented here should be useful for the exploration of \textit{non-Gaussian properties of systems nonlinearly coupled with their environments}; examples in early universe cosmology and in quantum optomechanics (QOM) are mentioned. A modified fluctuation-dissipation relation (FDR) is also established, which ensures the consistency of the model and the accuracy of results even at higher perturbative orders. Another result of significance is the derivation of a nonlinear Langevin equation which is expected to be useful for many open quantum system applications.

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arXiv2025

Atom-Field-Medium Interactions III: Quantum Field-mediated Entanglement between Two Atoms near a Conducting Surface

This third paper in this series continues the investigation of atom-field interactions in the presence of a conductor or a dielectric medium, focusing on quantum information related basic issues such as decoherence and entanglement. Here we consider the entanglement between two atoms with internal degrees of freedom modeled by a harmonic oscillator, with varying separations between them and varying distances between them and a conducting surface. These are configurations familiar in the Casimir-Polder effect, but the behavior of atom-surface entanglement is quite different from the well-studied behavior of field-induced forces. For one, while the attractive force between an atom and a conducting surface increases as they come closer, the entanglement between the atom and the quantum field actually decreases as the atom gets closer to the conductor, as shown in \cite{Rong,AFD2}. We show how different factors play out, ranging from the coupling between the atoms and the field to the coupling between the atoms, going beyond the weak coupling restrictions often found necessary in the literature. Gathering our results for the entanglement dependence on each variable concerned, we can provide a spatial topography of quantum entanglement, thus enabling a visualized understanding of the behavior of quantum field-mediated entanglement. In particular we can quantify the definition of a three-dimensional \textit{entanglement domain} between the two atoms, how it varies with their coupling, their separation and their distances from the conducting surface, and for practical applications, how to exercise effective control of the entanglement between two atoms by changing these parameters. Our findings are expected to be useful for studies of atom-field-medium interactions in vacuum and surface physics.

quant-ph↗

arXiv2025

Non-Markovian Quantum Master and Fokker-Planck Equation for Gravitational Systems and Gravitational Decoherence

A quantum master equation describing the stochastic dynamics of a quantum massive system interacting with a quantum gravitational field is useful for the investigation of quantum gravitational and quantum informational issues such as the quantum nature of gravity, gravity-induced entanglement and gravitational decoherence. Studies of the decoherence of quantum systems by an electromagnetic field shows that a lower temperature environment is more conducive to successful quantum information processing experiments. Likewise, the quantum nature of (perturbative) gravity is far better revealed at lower temperatures than high, minimizing the corruptive effects of thermal noise. In this work, generalizing earlier results of the Markovian ABH master equation [1,2] which is valid only for high temperatures, we derive a non-Markovian quantum master equation for the reduced density matrix, and the associated Fokker-Planck equation for the Wigner distribution function, for the stochastic dynamics of two masses following quantum trajectories, interacting with a graviton field, including the effects of graviton noise, valid for all temperatures. We follow the influence functional approach exemplified in the derivation of the non-Markovian Hu-Paz-Zhang master equation [62,64] for quantum Brownian motion. We find that in the low temperature limit, the off-diagonal elements of the reduced density matrix decrease in time logarithmically for the zero temperature part and quadratically in time for the temperature-dependent part, which is distinctly different from the Markovian case. We end with a summary of our findings and a discussion on how this problem studied here is related to the quantum stochastic equation derived in [77] for gravitational self force studies, and to quantum optomechanics where experimental observation of gravitational decoherence and entanglement may be implemented.

gr-qc↗

arXiv2025

Atom-Field-Medium Interactions II: Covariance Matrix Dynamics for $N$ Harmonic Atoms in a Dielectric-Altered Quantum Field and Effects of Dielectric on Atom-Field Entanglement

We continue our investigation of multi-partite open quantum systems comprising layers of structure using the atom-field-medium interactions as a familiarly important example. Same as in Paper I~\cite{HH24} we consider a system of $N$ harmonic oscillators, modeling the internal degrees of freedom (idf) of $N$ neutral atoms interacting with a scalar quantum field altered by the presence of a dielectric medium. Different from Paper I, which uses the graded influence action formalism, here, taking advantage of the Gaussian nature of our extended system's interactions, we use the quantum Langevin equation method to calculate the time evolution of the covariance matrix elements of the quantum correlation functions of the idfs of the $N$ system-atoms in a dielectric-altered quantum field. The covariance matrix is particularly useful for extracting quantum informational properties of a Gaussian system related to quantum correlations, such as quantum entanglement. As an illustration of the method we calculate the entanglement between one system atom and the ambient quantum field outside the dielectric half-space, measured by the purity function and the von Neumann entropy. We highlight one somewhat peculiar feature in our results and one important technical issue: The special feature refers to the non-monotonic behavior of the purity function when the atom is positioned very close to the dielectric surface. By deriving the Robertson-Schrödinger function and displaying a similar qualitative behavior under these conditions we attribute this novelty to a manifestation of the uncertainty relation. The technical issue refers to the order-reduction scheme to remove the third time derivative term in the Langevin equation for the idfs of the atom. We point out the inconsistencies in the traditional treatments and propose a new consistent scheme of order reduction for Gaussian open systems.

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arXiv2024

Foundational Issues in Dynamical Casimir Effect and Analogue Features in Cosmological Particle Creation

Moving mirrors as analogue sources of Hawking radiation from black holes have been explored extensively, less so with cosmological particle creation (CPC), even though the analogy between dynamical Casimir effect (DCE) and CPC based on the mechanism of parametric amplification of quantum field fluctuations has also been known for a long time. This `perspective' essay intends to convey some of the rigor and thoroughness of quantum field theory in curved spacetime, which serves as the theoretical foundation of CPC, to DCE, which enjoys a variety of active experimental explorations. We have selected out seven issues of relevance to address, starting from the naively simple ones, e.g., why should one be bothered with `curved' spacetime when performing a laboratory experiment in ostensibly flat space, to foundational theoretical ones, such as the frequent appearance of nonlocal dissipation in the system dynamics induced by colored noises in its field environment, the existence of quantum Lenz law and fluctuation-dissipation relations in the backreaction effects of DCE emission on the moving atom/mirror or the source, and the construction of a microphysics model to account for the dynamical responses of a mirror or medium. The strengthening of theoretical ground for DCE is useful not only for improving conceptual clarity but needed for the development of proof of concept type of future experimental designs for DCE. Results from DCE experiments in turn will enrich our understanding of quantum field effects in the early universe because they are, in the spirit of analogue gravity, our best hopes for the verification of these fundamental processes.

hep-th↗

arXiv2024

Atom-Field-Medium Interactions I: Graded Influence Actions for $N$ Harmonic Atoms in a Dielectric-Altered Quantum Field

This series of papers has two broader aims: 1) Construct a theory for multi-partite open quantum systems comprising several layers of structure with self-consistent back-actions. Develop the graded influence action formalism \cite{BehHu10,BH11} to account for the influences of successive sub-layers on the dynamics of the variables of interest. 2) Apply these methods to the study of atom-field-medium interactions and highlight their merits over conventional methods. We consider a system of $N$ harmonic oscillators, modeling the internal degrees of freedom (idf) of $N$ neutral atoms (A), interacting with a quantum field (F), scalar here, for simplicity, altered by the presence of a dielectric medium (M). In this paper we use the coarse-grained and stochastic effective actions in the influence functional formalism to derive the stochastic equations for the reduced density matrices of the dynamical variables in the successive layers of structure. The word `graded' refers to the specific ordering of the coarse-graining procedures. Three layers of coarse-graining are performed, firstly, integrating over the common bath of the dielectric oscillators results not only in the appearance of necessary dissipative properties of the dielectric but also essential nuanced features such as nonMarkovian spatial correlations in the dielectric. Secondly, integrating over the medium variables as a whole results in a dielectric-modified quantum field, the influence of the medium on the quantum field manifesting through a frequency-dependent permittivity function. Finally, integrating over this dielectric-altered quantum field which interacts with the idfs of the atoms yields an influence action. From it we obtain the stochastic equation of motion which describes the nonequilibrium stochastic dynamics of the idf of the atoms interacting with a dielectric medium-modified quantum field.

hep-th↗

arXiv2024

Graviton physics: Quantum field theory of gravitons, graviton noise and gravitational decoherence -- a concise tutorial

The detection of gravitational waves in 2015 ushered in a new era of gravitational wave astronomy capable of probing into the strong field dynamics of black holes and neutron stars. It has opened up an exciting new window for laboratory and space tests of Einstein's theory of classical general relativity. In recent years there are two interesting proposals aimed at revealing the quantum natures of perturbative gravity: 1) theoretical predictions in how graviton noise from the early universe after the vacuum of the gravitational field was strongly squeezed by inflationary expansion; 2) experimental proposals using the quantum entanglement between two masses each in a superposition state. The first proposal invokes the stochastic properties of quantum fields, the second invokes a key concept of quantum information. An equally basic and interesting idea is to ask whether and how gravity might be responsible for a quantum system becoming classical in appearance, known as gravitational decoherence. Decoherence due to gravity is of special interest because gravity is universal. This is an important issue in macroscopic quantum phenomena. To fully appreciate these exciting developments requires a working knowledge in classical GR, QF theory and QI plus some familiarity with stochastic processes, namely, noise in quantum fields. Traditionally a new researcher may be conversant in one or two of these four subjects: GR, QFT, QI, SP, depending on his/her background. This tutorial attempts to provide the necessary connections between them, helping an engaging reader from any one of these four subjects to leapfrog to the frontier of these interdisciplinary research topics. Here we shall treat the three topics listed in the title, save gravitational entanglement, because its nature and implications proclaimed in relation to quantum gravity still contain many controversial elements.

hep-th↗

arXiv2024

Heat capacity and quantum compressibility of dynamical spacetimes with thermal particle creation

This work continues the investigation in two recent papers on the quantum thermodynamics of spacetimes, 1) placing what was studied in [1] for thermal quantum fields in the context of early universe cosmology, and 2) extending the considerations of vacuum compressibility of dynamical spaces treated in [2] to dynamical spacetimes with thermal quantum fields. We begin with a warning that thermal equilibrium condition is not guaranteed to exist or maintained in a dynamical setting and thus finite temperature quantum field theory in cosmological spacetimes needs more careful considerations than what is often described in textbooks. A full description requires nonequilibrium quantum field theory in dynamical spacetimes using `in-in' techniques. A more manageable subclass of dynamics is where thermal equilibrium conditions are established at both the beginning and the end of evolution are both well defined. Here we shall assume an in-vacuum state. It has been shown that if the intervening dynamics has an initial period of exponential expansion, such as in inflationary cosmology, particles created from the parametric amplification of the vacuum fluctuations in the initial vacuum will have a thermal spectrum measured at the out-state. Under these conditions finite temperature field theory can be applied to calculate the quantum thermodynamic quantities. Here we consider a massive conformal scalar field in a closed four-dimensional Friedmann-Lemaitre-Robertson-Walker universe based on the simple analytically solvable Bernard-Duncan model. We calculate the energy density of particles created from an in-vacuum and derive the partition function. From the free energy we then derive the heat capacity and the quantum compressibility of the spacetimes with thermal particle creation. We end with some discussions and suggestions for further work in this program of studies.

hep-th↗

arXiv2024

Relativistic single-electron wavepacket in quantum electromagnetic fields: Quantum coherence, correlations, and the Unruh effect

Conventional formulation of QED since the 50s works very well for stationary states and for scattering problems, but with newly arisen challenges from the 80s on, where real time evolution of particles in a nonequilibrium setting are required, and quantum features such as coherence, dissipation, correlation and entanglement in a system interacting with its quantum field environment are sought after, new ways to formulate QED suitable for these purposes beckon. In this paper we present a linearized effective theory using a Gaussian wavepacket description of a charged relativistic particle coupled to quantum electromagnetic fields to study the interplay between single electrons and quantum fields in free space, at a scale well below the Schwinger limit. The proper values of the regulators in our effective theory are determined from the data of individual experiments, and will be time-dependent in the laboratory frame if the single electrons are accelerated. Using this new theoretical tool, we address the issues of decoherence of flying electrons in free space and the impact of Unruh effect on the electrons. Our result suggests that vacuum fluctuations may be a major source of blurring the interference pattern in electron microscopes. For a single electron accelerated in a uniform electric field, we identify the Unruh effect in the two-point correlators of the deviations from the electron's classical trajectory. From our calculations we also bring out some subtleties, involving the bosonic versus fermionic spectral functions.

hep-th↗

arXiv2023

Dynamical Vacuum Compressibility of Space

This paper continues the investigation initiated in arXiv:2204.08634 into the quantum thermodynamic properties of space by deriving the vacuum compressibility of a variety of dynamical spacetimes containing massive and massless conformally coupled quantum fields. The quantum processes studied here include particle creation, Casimir effect, and the trace anomaly. The spaces include $S^2, S^3$, and $T^3$ with prescribed time evolution and $S^1$, where the temporal developments are backreaction determined. Vacuum compressibility belongs to the same group of quantum thermodynamic / mechanical response functions as vacuum viscosity, a concept first proposed in 1970 by Zel'dovich for capturing the effects of vacuum particle production on the dynamics of the early universe, made precise by rigorous work of many authors in the following decade using quantum field theory in curved spacetime methodologies and semiclassical gravity theory for treating backreaction effects. Various subtleties in understanding the behavior of the vacuum energies of quantum field origins, negative pressures and novel complicated features of dynamical compressibility are discussed.

gr-qc↗

arXiv2023

Optomechanical Backreaction of Quantum Field Processes in Dynamical Casimir Effect

Dynamical Casimir effect (DCE) and cosmological particle creation (CPC) share the same underlying physical mechanism, that of parametric amplification of vacuum fluctuations in the quantum field by an expanding universe or by a fast moving boundary. Backreaction of cosmological particle creation at the Planck time has been shown to play a significant role in the isotropization and homogenization of the early universe. Understanding the backreaction effects of quantum field processes in DCE is the goal of this work. We present analyses of quantum field processes in two model systems: in 1+1D, a ring with time-dependent radius, and in 3+1D, a symmetric rectangular conducting box with one moving side. In both cases the time-dependence of the radius or the length is determined solely by the backreaction of particle creation and related effects, there is no external agent. We find that for 1+1D, the only quantum field effect due to the trace anomaly tends to accelerate the contraction of the ring over and above that due to the attractive force in the static Casimir effect. For the rectangular box the expansion or contraction is slowed down compared to that due to the static Casimir effect. Our findings comply with what is known as the quantum Lenz law, found in cosmological backreaction problems: the backreaction works in the direction of opposing further changes, which means the suppression of particle creation and a slow down of the system dynamics. In conclusion we suggest two related classes of problems of theoretical significance for further investigations.

quant-ph↗

arXiv2023

Fluctuations-Induced Quantum Radiation and Reaction from an Atom in a Squeezed Quantum Field

In this third of a series on quantum radiation, we explore the feasibility of using the memories kept in a quantum field to decipher certain information about the early universe. As a model study, we let a massless quantum field be subjected to a parametric process for a finite time interval such that the mode frequency of the field transits from one constant value to another. This configuration mimics a statically-bounded universe, but not a continuously evolving one. The field squeezed by this process should contain information of the process itself. If an atom is coupled to the field after the parametric process, its response will depend on the squeezing, and any quantum radiation emitted by the atom will carry this information away so that an observer at a much later time may still identify it. Our analyses show that 1) a remote observer cannot measure the generated squeezing via the radiation energy flux from the atom because the net radiation energy flux is canceled. However, 2) there is a chance to identify squeezing by measuring the constant radiation energy density at late times. The only restriction is that this energy density is of the near-field nature. The second part of this paper focuses on 3) the dependence of squeezing on the functional form of the parametric process. Via several examples we demonstrate that the behavior of squeezing reflect essential properties of the parametric process. In fact, striking features may show up in complicated processes involving various scales. These analyses allow us to establish the connection between properties of a squeezed quantum field and the parametric process which does the squeezing. Therefore, 4) one can construct templates to reconstitute the unknown parametric processes from the data of measurable quantities subjected to squeezing. In a sequel paper these results will be applied to a study of quantum radiations in cosmology.

quant-ph↗

arXiv2023

Towards a Field-Theory based Relativistic Quantum Information

We present our program for the development of quantum informational concepts in relativistic systems in terms of the unequal-time correlation functions of quantum fields. We employ two formalisms that provide the basis for further developments. (i) The Quantum Temporal Probabilities (QTP) Method for quantum field measurements and (ii) the Closed- Time-Path (CTP) formalism for causal time evolutions. We present the main ideas of QTP and show how it relates to the CTP formalism, allowing one to express concepts of measurement theory in terms of path-integrals. We also present many links of our program to non-equilibrium quantum field theories. Details can be found in a recent paper by the authors (arxiv:2208.03696).

quant-ph↗

arXiv2023

Quantum Field Theory based Quantum Information: Measurements and Correlations

This is the first in a series of papers aiming to develop a relativistic quantum information theory in terms of unequal-time correlation functions in quantum field theory. In this work, we highlight two formalisms which together can provide a useful theoretical platform suitable for further developments: 1) Quantum field measurements using the Quantum Temporal Probabilities (QTP) method; 2) Closed-Time-Path (CTP) formalism for causal time evolutions. QTP incorporates the detector into the quantum description, while emphasising that the records of measurement are macroscopic, and they can be expressed in terms of classical spacetime coordinates. We first present a new, elementary derivation of the QTP formulas for the probabilities of n measurement events. We then demonstrate the relation of QTP with the Closed-Time-Path formalism, by writing an explicit formula that relates the associated generating functionals. We exploit the path integral representation of the CTP formalism, in order to express the measured probabilities in terms of path integrals. After this, we provide some simple applications of the QTP formalism. In particular, we show how Unruh-DeWitt detector models and Glauber's photodetection theory appear as limiting cases . Finally, with quantum correlation being the pivotal notion in relativistic quantum information and measurements, we highlight the role played by the CTP two-particle irreducible effective action which enables one to tap into the resources of non-equilibrium quantum field theory for our stated purpose.

quant-ph↗