arXiv subjects

Jen-Tsung Hsiang

Publications and source records attributed to Jen-Tsung Hsiang.

At least 19 recordsLinked to original sources

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 $χ$ interacting with a free unbounded classical field $ϕ$ 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 $χ$-$ϕ$-$M$ 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↗

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

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.

quant-ph↗

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↗

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

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↗

arXiv2022

Hot entanglement? -- Parametrically coupled quantum oscillators in two heat baths: instability, squeezing and driving

Entanglement being a foundational cornerstone of quantum sciences and the primary resource in quantum information processing, understanding its dynamical evolution in realistic conditions is essential. Unfortunately, numerous model studies show that degradation of entanglement from a quantum system's environment, especially thermal noise, is almost unavoidable. Thus the appellation `hot entanglement' appears like a contradiction, until Galve et al [Phys. Rev. Lett. \textbf{105} 180501 (2010)] announced that entanglement can be kept at high temperatures if one considers a quantum system with time-dependent coupling between the two parties, each interacting with its individual bath. With the goal of understanding the sustenance of entanglement at high temperatures, working with the same model and set up as Galve et al, namely, parametrically-driven coupled harmonic oscillators interacting with their own Markovian baths, this work probes into the feasibility of `hot entanglement' from three aspects listed in the subtitle. Our findings show that 1) hot entanglement functions only in the unstable regimes, 2) instability is a necessary but not sufficient condition, and 3) the power intake required by the drive operating in the unstable regime to sustain entanglement increases exponentially. The last factor indicates that hot entanglement under this modeling is theoretically untenable and its actual implementation likely unattainable.

quant-ph↗

arXiv2022

NonMarkovian Abraham--Lorentz--Dirac Equation: Radiation Reaction without Pathology

Motion of a point charge emitting radiation in an electromagnetic field obeys the Abraham-Lorenz-Dirac (ALD) equation, with the effects of radiation reaction or self-force incorporated. This class of equations describing backreaction, including also the equations for gravitational self-force or Einstein's equation for cosmology driven by trace anomaly, contain third-order derivative terms. They are known to have pathologies like the possession of runaway solutions, causality violation in pre-acceleration and the need for an extra second-order derivative initial condition. In our current program we reexamine this old problem from the perspective of non-Markovian dynamics in open systems, applied earlier to backreaction problems in the early universe. Here we consider a harmonic atom coupled to a scalar field, which acts effectively like a supra-Ohmic environment, as in scalar electrodynamics. Our analysis shows that a) there is no need for specifying a second derivative for the initial condition; b) there is no pre-acceleration. These undesirable features in conventional treatments arise from an inconsistent Markovian assumption: these equations were regarded as Markovian ab initio, not as a limit of the backreaction-imbued non-Markovian equation of motion. If one starts with the full non-Markovian dynamical equation and takes the proper Markovian limit judiciously, no harms are done. Finally, c) There is no causal relation between the higher-derivative term in the equation of motion and the existence of runaway solutions. If the charge has an effective size greater than this critical value, its dynamics is stable. When this reasonable condition is met, radiation reaction understood and treated correctly in the non-Ohmic non-Markovian dynamics still obeys a third-order derivative equation, but it does not require a second derivative initial condition, and there is no pre-acceleration.

hep-th↗

arXiv2022

Entanglement dynamics of coupled quantum oscillators in independent nonMarkovian baths

This work strives to better understand how the entanglement in an open quantum system, here represented by two coupled Brownian oscillators, is affected by a nonMarkovian environment (with memories), here represented by two independent baths each oscillator separately interacts with. We consider two settings, a `symmetric' configuration wherein the parameters of both oscillators and their baths are identical, and an `asymmetric' configuration wherein they are different, in particular, a `hybrid' configuration, where one of the two coupled oscillators interacts with a nonMarkovian bath and the other with a Markovian bath. We ask two groups of questions: Q1) Which time regime does the bath's nonMarkovianity benefit the system's entanglement most? The answers we get from detailed numerical studies suggest that A1) For an initially entangled pair of oscillators, we see that in the intermediate time range, the duration of entanglement is proportional to the memory time, and it lasts a fraction of the relaxation time, but at late times when the dynamics reaches a steady state, the value of the symplectic eigenvalue of the partially transposed covariance matrix barely benefit from the bath nonMarkovianity. For the second group of questions: Q2)Can the memory of one nonMarkovian bath be passed on to another Markovian bath? And if so, does this memory transfer help to sustain the system's entanglement dynamics? Our results from numerical studies of the asymmetric hybrid configuration indicate that A2) A system with a short memory time can acquire improvement when it is coupled to another system with a long memory time, but, at a cost of the latter. The sustainability of the bipartite entanglement is determined by the party which breaks off entanglement most easily.

quant-ph↗

arXiv2022

Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation-Dissipation Inequalities

Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium current. In this initial stage of our research program, our goal is to provide the quantum theoretical basis of TURs using microphysics models of linear open quantum systems where it is possible to obtain exact solutions. In paper [Dong \textit{et al.}, Entropy {\bf 24}, 870 (2022)], we show how TURs are rooted in the quantum uncertainty principles and the fluctuation-dissipation inequalities (FDI) under fully nonequilibrium conditions. In this paper, we shift our attention from the quantum basis to the thermal manifests. Using a microscopic model for the bath's spectral density in quantum Brownian motion studies, we formulate a ``thermal'' FDI in the quantum nonequilibrium dynamics which is valid at high temperatures. This brings the quantum TURs we derive here to the classical domain and can thus be compared with some popular forms of TURs. In the thermal-energy-dominated regimes, our FDIs provide better estimates on the uncertainty of thermodynamic quantities. Our treatment includes full back-action from the environment onto the system. As a concrete example of the generalized current, we examine the energy flux or power entering the Brownian particle and find an exact expression of the corresponding current-current correlations. In so doing, we show that the statistical properties of the bath and the causality of the system+bath interaction both enter into the TURs obeyed by the thermodynamic quantities.

cond-mat.stat-mech↗

arXiv2022

Quantum Thermodynamic Uncertainties in Nonequilibrium Systems from Robertson-Schrödinger Relations

Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of thermodynamic quantities in nonequilibrium systems to their quantum origins, namely, to the quantum uncertainty principles. Our results enable us to make this categorical statement: For Gaussian systems, thermodynamic functions are functionals of the Robertson-Schrodinger uncertainty function, which is always non-negative for quantum systems, but not necessarily so for classical systems. Here, quantum refers to noncommutativity of the canonical operator pairs. From the nonequilibrium free energy[1], we succeeded in deriving several inequalities between certain thermodynamic quantities. They assume the same forms as those in conventional thermodynamics, but these are nonequilibrium in nature and they hold for all times and at strong coupling. In addition we show that a fluctuation-dissipation inequality exists at all times in the nonequilibrium dynamics of the system. For nonequilibrium systems which relax to an equilibrium state at late times, this fluctuation-dissipation inequality leads to the Robertson-Schrodinger uncertainty principle with the help of the Cauchy-Schwarz inequality. This work provides the microscopic quantum basis to certain important thermodynamic properties of macroscopic nonequilibrium systems.

cond-mat.stat-mech↗

arXiv2022

Quantum Capacity and Vacuum Compressibility of Spacetime: Thermal Fields

An important yet perplexing result from work in the 90s and 00s is the near-unity value of the ratio of fluctuations in the vacuum energy density of quantum fields to the mean in a collection of generic spacetimes. This was done by way of calculating the noise kernels which are the correlators of the stress-energy tensor of quantum fields. In this paper we revisit this issue via a quantum thermodynamics approach, by calculating two quintessential thermodynamic quantities: the heat capacity and the quantum compressibility of some model geometries filled with a quantum field at high and low temperatures. This is because heat capacity at constant volume gives a measure of the fluctuations of the energy density to the mean. When this ratio approaches or exceeds unity, the validity of the canonical distribution is called into question. Likewise, a system's compressibility at constant pressure is a criterion for the validity of grand canonical ensemble. We derive the free energy density and, from it, obtain the expressions for these two thermodynamic quantities for thermal and quantum fields in 2d Casimir space, 2d Einstein cylinder and 4d ($S^1 \times S^3$ ) Einstein universe. To examine the dependence on the dimensionality of space, for completeness, we have also derived these thermodynamic quantities for the Einstein universes with even-spatial dimensions: $S^1 \times S^2$ and $S^1 \times S^4$. With this array of spacetimes we can investigate the thermodynamic stability of quantum matter fields in them and make some qualitative observations on the compatibility condition for the co-existence between quantum fields and spacetimes, a fundamental issue in the quantum and gravitation conundrum.

gr-qc↗

arXiv2022

Quantum Radiation and Dissipation in Relation to Classical Radiation and Radiation Reaction

This work continues the investigation of radiation phenomena from atom-field interactions, extending our earlier study of quantum radiation from a stationary atom's internal degree of freedom, modeled by a harmonic oscillator, to the emittance of classical radiation. By assuming that the atom interacts with a quantum scalar field initially in a coherent state, we show how a stochastic component of the internal dynamics of the atom arises from the vacuum fluctuations of the field, resulting in the emittance of quantum radiation, whose reaction induces quantum dissipation in the internal dynamics. We also show how the deterministic mean field drives the internal classical mean component to emit classical radiation and receive classical radiation reaction. Both components are statistically distinct and fully decoupled. It is clearly seen that the effects of the vacuum fluctuations of the field are matched with those of quantum radiation reaction, not with classical radiation reaction, as the folklore goes. In contrast to the quantum component of the atom's internal dynamics, which always equilibrates, the relaxation dynamics of the classical component largely depends on the late-time behavior of the mean field. For the values of the parameters defining the coherent state of the field much greater than unity, if the mean field remains periodic, then the internal dynamics of the atom will appear classical and periodic. If the mean field diminishes with time, then the classical component of the atom's internal dynamics subsides but the quantum component will abide and dynamically equilibrate. This also explains why quantum radiation from a stationary atom is not observed, and a probe located far away only sees classical radiation. Our analysis therefore paints a continuum landscape starting from vacuum fluctuations in the quantum field to classical radiation and radiation reaction.

hep-th↗

arXiv2022

Fluctuation-Dissipation Relation for a Quantum Brownian Oscillator in a Parametrically Squeezed Thermal Field

In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh-DeWitt detector, coupled to a nonequilibrium, nonstationary quantum field and inquire whether a fluctuation-dissipation relation can exist after/if it approaches equilibration. This is a nontrivial issue since a squeezed bath field cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. B) The field is initially in a thermal state, but subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is met in cosmology and dynamical Casimir effect. The squeezing in the bath in both types of processes will affect the oscillator's nonequilibrium evolution. We show that at late times it approaches equilibration, which warrants the existence of an FDR. The trait of squeezing is marked by the oscillator's effective equilibrium temperature, and the factor in the FDR is only related to the stationary component of bath's noise kernel. Setting C) is more subtle: A finite system-bath coupling strength can set the oscillator in a squeezed state even the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium systems.

quant-ph↗

arXiv2022

Dynamical Response of an Unruh-DeWitt Detector in a Quantum Field over the History of the Universe

In this work we ask how an Unruh-DeWitt (UD) detector with harmonic oscillator internal degrees of freedom $Q$ measuring an evolving quantum matter field $Φ(\bm{x}, t)$ in an expanding universe with scale factor $a(t)$ responds. We investigate the detector's response which contains non-Markovian information about the quantum field squeezed by the dynamical spacetime. The challenge is in the memory effects accumulated over the evolutionary history. We first consider a detector $W$, the `\textsl{Witness}', which co-existed and evolved with the quantum field from the beginning. We derive a nonMarkovian quantum Langevin equation for the detector's $Q$ by integrating over the squeezed quantum field. The solution of this integro-differential equation would answer our question, in principle, but very challenging, in practice. Striking a compromise, we then ask, to what extent can a detector $D$ introduced at late times, called the `\textsl{Detective}', decipher past memories. This situation corresponds to many cosmological experiments today probing specific stages in the past, such as COBE targeting activities at the surface of last scattering. Somewhat surprisingly we show that it is possible to retrieve to some degree certain global physical quantities, such as the resultant squeezing, particles created, quantum coherence and correlations. The reason is because the quantum field has all the fine-grained information from the beginning in how it was driven by the cosmic dynamics $a(t)$. How long the details of past history can persist in the quantum field depends on the memory time. The fact that a squeezed field cannot come to complete equilibrium under constant driving, as in an evolving spacetime, actually helps to retain the memory. We discuss interesting features and potentials of this `\textit{archaeological}' perspective toward cosmological issues.

gr-qc↗