We consider the response of an Unruh-DeWitt detector near an extremal charged black hole, modeling the near-horizon region of this extremal spacetime by the Bertotti-Robinson spacetime. The advantage of employing the Bertotti-Robinson limit is that the two-point functions for a massless scalar field are obtainable in closed form for the field in a number of quantum states of interest. We consider the detector coupled to a massless field in both the Boulware vacuum state and arbitrary thermal states, including the Hartle-Hawking state, and analyse the detector's response for a broad range of trajectories. Particular attention is paid to the thermalization of the detector, the anti-Unruh and anti-Hawking effect.
Applying the techniques of light-front quantization to quantize a scalar field in a monochromatic gravitational wave background, we manage to investigate the response of the Unruh-DeWitt detector coupled to a scalar field in the presence of a gravitational wave for the two cases moving along a free-falling trajectory and a constant-accelerating trajectory. The transition rate of the Unruh-DeWitt detector, in both cases, is different from the result with no gravitational wave, and the leading-order correction due to the gravitational wave survives the long-wavelength limit that formally takes t…
Response of a circularly rotating Unrh-DeWitt detector to the Minkowski vacuum is investigated. What the detector observes depends on the surface (three volume) to define it by the Hamiltonian. Detectors in the past literature were defined on a surface of a constant Minkowski time, and this is the reason why rotating detectors investigated so far resister particles. No particle is detected by a detector defined by the Hamiltonian on a surface normal to the detector's orbit, in agreement with the global analysis of vacua. A detector with drift motion superposed on the linear acceleration is als…
We examine the Unruh-DeWitt particle detector coupled to a scalar field in an arbitrary Hadamard state in four-dimensional curved spacetime. Using smooth switching functions to turn on and off the interaction, we obtain a regulator-free integral formula for the total excitation probability, and we show that an instantaneous transition rate can be recovered in a suitable limit. Previous results in Minkowski space are recovered as a special case. As applications, we consider an inertial detector in the Rindler vacuum and a detector at rest in a static Newtonian gravitational field. Gravitational…
In a flat spacetime with one spatial dimension compactified, inertial reference frames are not all equivalent, but there are the preferred ones. This paper investigates the nonequivalence of inertial frames and also that of uniformly accelerated frames in connection with the response of the Unruh-DeWitt detector coupled to a massless scalar field. The detector's transition rates of both excitation and de-excitation are studied in depth for three different cases: (i) the detector moving at an arbitrary constant velocity, (ii) moving with a constant acceleration in the compact direction, and (ii…
Unruh deWitt detectors are important constructs in studying the dynamics of quantum fields in any geometric background. Curvature also plays an important role in setting up the correlations of a quantum field in a given spacetime. For instance, massless fields are known to have large correlations in de Sitter space as well as in certain class of Friedmann-Robertson-Walker (FRW) universes. However, some of the correlations are secular in nature while some are dynamic and spacetime dependent. An Unruh deWitt detector responds to such divergences differently in different spacetimes. In this work,…
We analyse the response of an arbitrarily-accelerated Unruh-DeWitt detector coupled to a massless scalar field in Minkowski spacetimes of dimensions up to six, working within first-order perturbation theory and assuming a smooth switch-on and switch-off. We express the total transition probability as a manifestly finite and regulator-free integral formula. In the sharp switching limit, the transition probability diverges in dimensions greater than three but the transition rate remains finite up to dimension five. In dimension six, the transition rate remains finite in the sharp switching limit…
In this paper, we investigate the quantum correlations and coherence of two accelerating Unruh-deWitt detectors coupled to a scalar field in 3 + 1 Minkowski space-time. We show that the entanglement is completely destroyed in the limit of infinite acceleration while the local quantum uncertainty and l1-norm of coherence remain nonzero. In addition, we also highlight the role of Unruh temperature and energy spacing of detectors on quantum correlations for different choices of initial states.
We have shown the classical correspondence of Unruh effect in the classical relativistic electron theory in our previous work (gr-qc/0105051). Here we demonstrate the analogy between the classical relativistic electron theory and the classical Unruh-DeWitt type monopole detector theory. The field configuration generated by a uniformly accelerated detector is worked out. The classical correspondence of Unruh effect for scalar fields is shown by calculating the modified energy density for the scalar field around the detector. We conclude that a classical monopole detector cannot find any evidenc…
We generalize the Unruh-DeWitt detector model to second quantization. We illustrate this model by applying it to an excited particle in a superposition of relativistic velocities. We calculate, to first order, how its decay depends on whether its superposition of velocities is coherent or incoherent. Further, we generalize the framework of quantum reference frames to allow transformations to the rest frames of second-quantized Unruh DeWitt detectors. As an application, we show how to transform into the rest frame of a decaying particle that, in the laboratory frame, is in a linear superpositio…
We propose a method for simulating an Unruh-DeWitt detector, coupled to a 1+1-dimensional massless scalar field, with a suitably-engineered $χ^{(2)}$ nonlinear interaction. In this simulation, the parameter playing the role of the detector acceleration is played by the relative inverse-group-velocity gradient inside the nonlinear material. We identify experimental parameters that tune the detector energy gap, acceleration, and switching function. This system can simulate time-dependent acceleration, time-dependent detector energy gaps, and non-vacuum initial detector-field states. Furthermore,…
In this contribution we describe some interesting interplay between quantum theory, general relativity and thermodynamics. In order to highlight the connection between these theories, we describe two approaches that allow to calculate thermal features as perceived by different observers in curved spacetimes: the tunnelling method and the Unruh-DeWitt detector. In this context, the semi-classical tunnelling approach is applied to the issue of Hawking radiation and allows the calculation of the horizon temperature in a wide variety of scenarios. The Unruh-DeWitt model is instead a quantum field-…
Two entangled two-level Unruh-DeWitt detectors, which are in rest, spontaneously loose entanglement when at least any one of them is not isolated from the environment quantum fields. For eternal interaction between the detectors and environment, the spontaneous emission from the detectors' exited states and vacuum fluctuations of field influence this negative effect. Consequently, it suggests that two entangled qubits become less communicated during their free-fall towards the black hole horizon.
We study, in the framework of open quantum systems, the entanglement dynamics for a quantum system composed of two uniformly accelerated Unruh-Dewitt detectors interacting with a bath of massive scalar fields in the Minkowski vacuum. We find that the entanglement evolution for the quantum system coupled with massive fields is always slower compared with that of the one coupled with massless fields, and this time-delay effect brought by the field being massive can however be counteracted by a large enough acceleration, in contrast to the case of a static quantum system in a thermal bath, where …
If an Unruh-DeWitt detector operates for an infinite proper time along the trajectory of a uniformly accelerated observer in Fock space then induced transition rate of the detector is proportional to Planck distribution. For a realistic detector which operates only for a finite period, the instantaneous transition rate contains both transient and non-transient terms. In particular, the non-transient term contains a residue evaluated at the pole of the two-point function. We show here by considering a massless scalar field that unlike in Fock quantization, the short-distance two-point function …
Applications of Unruh-Fulling (UF) effect are well studied in literature via the interaction of Unruh-DeWitt (UD) detector and {\it single} scalar field. In this work, we investigate a toy model, where the detector is interacting {\it simultaneously} with the {\it multiple} scalar fields. Our study reveals that the transition rate of the system significantly depends on the acceleration of the detector and the number of scalar fields ($n$). For $n\gg1$, there exists a {\it critical acceleration}, beyond which the transition rate becomes drastically high than the accelerations below the critical…
We prove a nonperturbative duality concerning the dynamics of harmonic-oscillator-type Unruh-DeWitt detectors in curved spacetimes. Concretely, using the Takagi transformation we show that the action of a harmonic oscillator Unruh-DeWitt detector with one frequency in a spacetime is equal to that of a detector with a different frequency in a conformally related spacetime. As an example, we show that the dynamics of simple stationary detectors in flat spacetime is dual to that of detectors in a cosmological scenario. The nonperturbative duality enables us to investigate entanglement harvesting …
We investigate the effects of relative motion on entanglement harvesting by considering a pair of Unruh-Dewitt detectors moving at arbitrary, but independent and constant velocities, both linearly interacting with the vacuum scalar field. Working within the weak coupling approximation, we find that the Negativity is a (non-elementary) function of the relative velocity of the detectors, as well as their energy gaps and minimal separation. We find parameter regions where Negativity increases with velocity up to a maximum and then decreases, reaching zero at some sublight velocity. At any given r…
Unruh-deWitt detectors have been utilised widely as probes for quantum particles, entanglement and spacetime curvature. Here, we extend the standard treatment of an Unruh-deWitt detector interacting with a massless, scalar field to include the detector travelling in a quantum superposition of classical trajectories. We derive perturbative expressions for the final state of the detector, and show that it depends on field correlation functions evaluated locally along the individual trajectories, as well as non-locally between the superposed trajectories. By applying our general approach to a det…
The Unruh effect can be correctly treated only by using the Minkowski quantization and a model of a "particle" detector, not by using the Rindler quantization. The energy produced by a detector accelerated only for a short time can be much larger than the energy needed to change the velocity of the detector. Although the measuring process lasts an infinite time, the production of the energy can be qualitatively explained by a time-energy uncertainty relation.
We analyse within first-order perturbation theory the instantaneous transition rate of an accelerated Unruh-DeWitt particle detector whose coupling to a massless scalar field on four-dimensional Minkowski space is regularised by a spatial profile. For the Lorentzian profile introduced by Schlicht, the zero size limit is computed explicitly and expressed as a manifestly finite integral formula that no longer involves regulators or limits. The same transition rate is obtained for an arbitrary profile of compact support under a modified definition of spatial smearing. Consequences for the asympto…
We find the response function and the transition rate for an Unruh-DeWitt detector interacting with a conformal scalar field in global two-dimensional anti--de Sitter (AdS) spacetime with different boundary conditions at its conformal infinities. We calculate the particle energy spectrum as seen by subcritical accelerated detectors and discuss how it depends on the choice of the boundary condition. We show that, despite this nontrivial dependence on the boundary conditions, the limit when the AdS length scale tends to zero is well defined and leads to the well-known results of 1+1 Minkowski sp…
Particle detector models such as the Unruh-deWitt detector are widely used in relativistic quantum information and field theory to probe the global features of spacetime and quantum fields. These detectors are typically modelled as coupling locally to the field along a classical worldline. In this paper, we utilize a recent framework which enables us to prepare the detector in a quantum-controlled superposition of trajectories, and study its response to the field in finite-temperature Minkowski spacetime and an expanding de Sitter universe. Unlike a detector on a classical path which cannot di…
We examine an Unruh-DeWitt particle detector which couples linearly to the scalar density of a massless Dirac field on the static cylindrical quotient of the (1+1)-dimensional Minkowski spacetime, allowing the detector's motion to remain arbitrary and working to leading order in perturbation theory. We show that the detector's response distinguishes the periodic and antiperiodic spin structures, and the zero mode that is present for periodic spinors contributes to the response by a state-dependent but well defined and controllable amount.
We examine an Unruh-DeWitt particle detector coupled to a scalar field in three-dimensional curved spacetime, within first-order perturbation theory. We first obtain a causal and manifestly regular expression for the instantaneous transition rate in an arbitrary Hadamard state. We then specialise to the Bañados-Teitelboim-Zanelli black hole and to a massless conformally coupled field in the Hartle-Hawking vacuum. A co-rotating detector responds thermally in the expected local Hawking temperature, while a freely-falling detector shows no evidence of thermality in regimes that we are able to pro…
Quantum radiated energy flux emitted by an Unruh-DeWitt (UD) detector, with the internal harmonic oscillator coupled to a massless scalar field, in linear oscillatory motion in (3+1) dimensional Minkowski space is studied by numerical methods. Our results show that quantum interference can indeed suppress the signal of the Unruh effect if the averaged proper acceleration is sufficiently low, but not in the regime with high averaged acceleration and short oscillatory cycle. While the averaged radiated energy flux over a cycle is always positive as guaranteed by the quantum inequalities, an obse…
In this paper we deal with several issues regarding the localization properties of the Unruh-DeWitt (UdW) detector model. Since its original formulation as a pointlike detector, the UdW model has been used to study extensively the physics of quantum fields in presence of accelerations or curved backgrounds. Natural extensions of it have tried to take into account the spatial profile of such detectors, but all of them have met a series of problems in their spectral response which render them useless to study some of the most interesting physical scenarios. In this paper we provide a derivation …
A simple but powerful particle detector model consists of a two-level system coupled to a field, where the detected particles are the field excitations. This is known as the Unruh-DeWitt detector. Research using this model has often focused on either a completely classical description of the external degrees of freedom of the detector, or a full field-theoretic treatment, where the detector itself is described as a field. Recently there has been much interest in quantum aspects of the detector's center of mass -- either described as moving in superposition along semiclassical trajectories, or …
The transition probability in first-order perturbation theory for an Unruh-DeWitt detector coupled to a massless scalar field in Minkowski space is calculated. It has been shown recently that the conventional $iε$ regularisation prescription for the correlation function leads to non-Lorentz invariant results for the transition rate, and a different regularisation, involving spatial smearing of the field, has been advocated to replace it. We show that the non-Lorentz invariance arises solely from the assumption of sudden switch-on and switch-off of the detector, and that when the model includes…
Since quantum field theories do not possess proper position observables, Unruh-DeWitt detector models serve as a key theoretical tool for extracting localized spatio-temporal information from quantum fields. Most studies have been limited, however, to Unruh-DeWitt (UDW) detectors that are coupled linearly to a scalar bosonic field. Here, we investigate UDW detector models that probe fermionic as well as bosonic fields through both linear and quadratic couplings. In particular, we present a renormalization method that cures persistent divergencies of prior models. We then show how perturbative …
We analyze a tripartite entanglement harvesting protocol with three Unruh-DeWitt detectors adiabatically interacting with a quantum scalar field. We consider linear, equilateral triangular, and scalene triangular configurations for the detectors. We find that, under the same parameters, more entanglement can be extracted in the linear configuration than the equilateral one, consistent with single instantaneous switching results. No bipartite entanglement is required to harvest tripartite entanglement. Furthermore, we find that tripartite entanglement can be harvested even if one detector is at…
The Unruh effect refers to the thermal fluctuations a detector experiences while undergoing linear motion with uniform acceleration in a Minkowski vacuum. This thermality can be demonstrated by tracing the vacuum state of the field over the modes beyond the accelerated detector's event horizon. However, the event horizon is well-defined only if the detector moves with eternal uniform linear acceleration. This idealized condition cannot be fulfilled in realistic situations when the motion unavoidably involves periods of non-uniform acceleration. Many experimental proposals to test the Unruh eff…
On $\text{AdS}_2 \times \mathbb{S}^2$, we construct the two-point correlation functions for the ground and thermal states of a real Klein-Gordon field admitting generalized $(γ,v)$-boundary conditions. We follow the prescription recently outlined in [1] for two different choices of secondary solutions. For each of them, we obtain a family of admissible boundary conditions parametrized by $γ\in\left[0,\fracπ{2}\right]$. We study how they affect the response of a static Unruh-DeWitt detector. The latter not only perceives variations of $γ$, but also distinguishes between the two families of seco…
We study the effects of motion for an Unruh-DeWitt detector, modeled as a two-level system, on the amount of coherence extracted, when it interacts with a massless scalar coherent field in 1+1 Minkowski spacetime. We observe that compared to a detector at rest, for certain values of the initial energy of the field and the interaction duration, the amount is larger for both a detector moving with a constant speed or uniform acceleration. This "swelling" of coherence, which becomes more intense for increasing values of velocity or acceleration, is mostly observed for short durations, when the en…
Quantum radiated power emitted by an Unruh-DeWitt (UD) detector in linear oscillatory motion in (3+1)D Minkowski space, with the internal harmonic oscillator minimally coupled to a massless scalar field, is obtained non-perturbatively by numerical method. The signal of the Unruh-like effect experienced by the detector is found to be pronounced in quantum radiation in the highly non-equilibrium regime with high averaged acceleration and short oscillatory cycle, and the signal would be greatly suppressed by quantum interference when the averaged proper acceleration is sufficiently low. An observ…
We study the response of a rotating monopole detector that is coupled to a massless scalar field which is described by a non-linear dispersion relation in flat spacetime. Since it does not seem to be possible to evaluate the response of the rotating detector analytically, we resort to numerical computations. Interestingly, unlike the case of the uniformly accelerated detector that has been considered recently, we find that defining the transition probability rate of the rotating detector poses no difficulties. Further, we show that the response of the rotating detector can be computed {\it exa…
We study the response of a static Unruh-DeWitt detector outside an exotic compact object (ECO) with a general reflective boundary condition in 3+1 dimensions. The horizonless ECO, whose boundary is extremely close to the would-be event horizon, acts as a black hole mimicker. We find that the response rate is notably distinct from the black hole case, even when the ECO boundary is perfectly absorbing. For a (partially) reflective ECO boundary, we find resonance structures in the response rate that depend on the different locations of the ECO boundary and those of the detector. We provide a deta…
We analyse the response and thermal behaviour of an Unruh-DeWitt detector as it travels through cosmological spacetimes, with special reference to the question of how to define surface gravity and temperature in dynamical spacetimes. Working within the quantum field theory on curved spacetime approximation, we consider a detector as it travels along geodesic and accelerated Kodama trajectories in de Sitter and asymptotically de Sitter FLRW spacetimes. By modelling the temperature of the detector using the detailed-balance form of the Kubo--Martin--Schwinger (KMS) conditions as it thermalises, …
We consider a pair of two-level Unruh-DeWitt detectors accelerated uniformly in the Minkowski vacuum of a massless neutral scalar field, and analyze, within the perturbation theory, the entanglement extracted from the vacuum into the Unruh-DeWitt detectors when the switching of the detectors are performed adiabatically enough at the asymptotic past and future. We consider the cases where the detectors are accelerated parallelly, anti-parallelly, and in differently orientated directions. We show that entanglement is extracted if they are accelerated anti-parallelly and the ratios of the excitat…
We study the late-time asymptotic state of a stationary Unruh-DeWitt detector interacting with a field in a thermal state. We work in an open system framework, where the field plays the role of an environment for the detector. The long-time interaction between the detector and the field is modelled with the aid of a one-parameter family of switching functions that turn on and off the interaction Hamiltonian between the two subsystems, such that the long-time interaction limit is reached as the family parameter goes to infinity. In such limit, we show that if the field is in a Kubo-Martin-Schwi…
Boundary-induced corrections to the response of an Unruh-DeWitt detector outside a compact star with Robin surface conditions
Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Kimyo International University in Tashkent（塔什干化学国际大学）；School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）
We examine an Unruh-DeWitt particle detector coupled to a scalar field in three-dimensional curved spacetime. We first obtain a regulator-free expression for the transition probability in an arbitrary Hadamard state, working within first-order perturbation theory and assuming smooth switching, and we show that both the transition probability and the instantaneous transition rate remain well defined in the sharp switching limit. We then analyse a detector coupled to a massless conformally coupled field in the Hartle-Hawking vacua on the Banados-Teitelboim-Zanelli black hole, under both transpar…
We analyze the response of an Unruh-DeWitt detector moving along an unbounded spatial trajectory in a two-dimensional spatial plane with constant independent magnitudes of both the four-acceleration and of a timelike proper time derivative of the four-accelration. In a Fermi-Walker frame moving with the detector, the direction of the acceleration rotates at a constant rate around a great circle. This is the motion of a charge in a uniform electric field when in the frame of the charge there is both an electric and a magnetic field. We compare the response of this detector to a detector moving …
We show that a particle detector can distinguish the $\mathbb{RP}^3$ geon from the Schwarzschild black hole, even though they differ only by a topological identification beyond the event horizon. This shows that the detector can read out information about the non-local structure even when separated from the non-locality by an event horizon. Our analysis of the dependence of the transition on the detector gap is novel, and in principle presents an interesting observational signal.
We derive the master equation that completely determines the time evolution of the density matrix of the Unruh-DeWitt detector in an arbitrary background geometry. We apply the equation to reveal a nonequilibrium thermodynamic character of de Sitter space. This generalizes an earlier study on the thermodynamic property of the Bunch-Davies vacuum that an Unruh-DeWitt detector staying in the Poincare patch and interacting with a scalar field in the Bunch-Davies vacuum behaves as if it is in a thermal bath of finite temperature. In this paper, instead of the Bunch-Davies vacuum, we consider a cla…
We investigate the transition probability of a Unruh-deWitt particle detector evolving in flat space and in a wormhole spacetime, in various scenarios. In Minkowski space, we look at the response of the detector on trajectories having discontinuities and rapid variations, as well as the effect of finite-time coupling. It is found that these features induce spurious oscillations in the probability and rate of transition. At large times the oscillations are damped and the probability tends to a constant value. Next, we look at the response of an inertial detector on a radial trajectory that pass…
Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic quantum information (RQI). We formulate the Unruh-DeWitt (UDW) particle detector model in terms of the path integral formalism. The formulation is able to recover the results of the model in general globally hyperbolic spacetimes and for arbitrary detector trajectories. Integrating out the detector's degrees of freedom yields a line defect that allows one to express the transition probability in terms of Feynman diagrams. Inspired by the light-matter interaction, we propose a gauge invariant det…
We analyse the response function of an Unruh--DeWitt detector moving with time-dependent acceleration along a one-dimensional trajectory in Minkowski spacetime. To extract the physics of the process, we propose an adiabatic expansion of this response function. This expansion is also a useful tool for computing the click rate of detectors in general trajectories. The expansion is done in powers of the time derivatives of the acceleration (jerk, snap, and higher derivatives). At the lowest order, we recover a Planckian spectrum with temperature proportional to the acceleration of the detector at…
We study the dynamics of an Unruh-DeWitt detector interacting with a massless scalar field in an arbitrary static spherically symmetric spacetimes whose metric is characterised by a single metric function $f(r)$. In order to obtain clean physical insights, we employ the derivative coupling variant of the Unruh-DeWitt model in (1+1) dimensions where powerful conformal techniques enable closed-form expressions for the vacuum two-point functions. Due to the generality of the formalism, we will be able to study a very general class of static spherically symmetric (SSS) background. We pick three ex…
In the present paper, Unruh--DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh--DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW …
