We derive the response function for a comoving, pointlike Unruh-DeWitt particle detector coupled to a complex scalar field $ϕ$, in the $(3+1)$-dimensional cosmological de Sitter spacetime. The field-detector coupling is taken to be proportional to $ϕ^{\dagger} ϕ$. We address both conformally invariant and massless minimally coupled scalar field theories, respectively in the conformal and the Bunch-Davies vacuum. The response function integral for the massless minimal complex scalar, not surprisingly, shows divergences and accordingly we use suitable regularisation scheme to find out well behaved results. The regularised result also contains a de Sitter symmetry breaking logarithm, growing with the cosmological time. Possibility of extension of these results with the so called de Sitter $α$-vacua is discussed. While we find no apparent problem in computing the response function for a real scalar in these vacua, a complex scalar field is shown to contain some possible ambiguities in the detector response. The case of the minimal and nearly massless scalar field theory is also briefly discussed.
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…
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-…
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 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…
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…
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…
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 …
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 …
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…
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…
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 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 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 discuss how to formulate a condition for choosing the vacuum state of a quantum scalar field on a timelike hyperplane in the general boundary formulation (GBF) using the coupling to an Unruh-DeWitt detector. We explicitly study the response of an Unruh-DeWitt detector for evanescent modes which occur naturally in quantum field theory in the presence of the equivalent of a dielectric boundary. We find that the physically correct vacuum state has to depend on the physical situation outside of the boundaries of the spacetime region considered. Thus it cannot be determined by general principles…
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…
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 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…
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…
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 …
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 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 firstly generalize the massive scalar propagator for planar gravitational waves propagating on Minkowski space obtained recently in Ref. [1]. We then use this propagator to study the response of a freely falling Unruh-DeWitt detector to a gravitational wave background. We find that a freely falling detector completely cancels the effect of the deformation of the invariant distance induced by the gravitational waves, such that the only effect comes from an increased average size of scalar field vacuum fluctuations, the origin of which can be traced back to the change of the surface in which …
We study a type of an Unruh-DeWitt-like detector based on a vector rather than scalar field. This detector has two energy states and produces Larmor radiation when there is no energy gap between them. This setup indicates that Larmor radiation and Unruh radiation are two counterparts of the same phenomenon. Larmor radiation is observed in the inertial frame, while Unruh radiation is observed in an accelerated frame. The accelerated observer sees that his detector absorbed a particle inside its own accelerated horizon, while the Larmor radiation is the companion particle which leaves the accele…
In the paper, the temperature associated with a dynamical spherically symmetric black hole or with a cosmological horizon is investigated from the point of view of a point-like detector. First, we briefly review the Hamilton-Jacobi tunneling method for a generic dynamical spherically symmetric space-time, and present two applications of the tunneling method. Then, we apply a well-known relativistic quantum theoretical technique, namely the Unruh-DeWitt detector formalism for a conformally coupled scalar field in a generic FRW space-time. As an application, for the generic static black hole cas…
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.
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…
We examine an Unruh-DeWitt particle detector that is coupled linearly to the scalar density of a massless Dirac field in Minkowski spacetimes of dimension $d\ge2$ and on the static Minkowski cylinder in spacetime dimension two, allowing the detector's motion to remain arbitrary and working to leading order in perturbation theory. In $d$-dimensional Minkowski, with the field in the usual Fock vacuum, we show that the detector's response is identical to that of a detector coupled linearly to a massless scalar field in $2d$-dimensional Minkowski. In the special case of uniform linear acceleration…
We demonstrate that the Unruh-DeWitt harmonic-oscillator detectors in (1+1) dimensions derivative-coupled with a massless scalar field can mimic the atom mirrors in free space. Without introducing the Dirichlet boundary condition to the field, the reflectivity of our detector/atom mirror is dynamically determined by the interaction of the detector's internal oscillator and the field. When the oscillator-field coupling is strong, a broad frequency range of the quantum field can be mostly reflected by the detector mirror at late times. Constructing a cavity model with two such detector mirrors, …
It is well-known that the $(1+1)$ dimensional Schwarzschild and spatially flat FLRW spacetimes are conformally flat. This work examines entanglement harvesting from the conformal field vacuums in these spacetimes between two Unruh-DeWitt detectors, moving along outgoing null trajectories. In $(1+1)$ dimensional Schwarzschild spacetime, we considered the Boulware and Unruh vacuums for our investigations. In this analysis, one observes that while entanglement harvesting is possible in $(1+1)$ dimensional Schwarzschild and $(1+3)$ dimensional de Sitter spacetimes, it is not possible in the $(1+1)…
Entanglement harvesting from the quantum field is a well-known fact that, in recent times, is being rigorously investigated further in flat and different curved backgrounds. The usually understood formulation studies the possibility of two uncorrelated Unruh-DeWitt detectors getting entangled over time due to the effects of quantum vacuum fluctuations. Our current work presents a thorough formulation to realize the entanglement harvesting from non-vacuum background fluctuations. In particular, we further consider single excitation field states and a pair of inertial detectors, respectively, in…
In the lack of a full-fledged theory of quantum gravity, I consider free, scalar, quantum fields on curved spacetimes to gain insight into the interaction between quantum and gravitational phenomena. I employ the Unruh-DeWitt detector approach to probe thermal, quantum effects on static, non-globally hyperbolic spacetimes. In this context, all physical observables depend on the choice of a boundary condition that cannot be singled-out, in general, without resorting to an experiment. Notwithstanding, the framework applied admits a large family of (Robin) boundary conditions and grants us physic…
Motivated by black hole physics, we define the Unruh state for a scalar field in de Sitter space. Like the Bunch-Davies state, the Unruh-de Sitter state appears thermal to a static observer. However, it breaks some of the symmetries of de Sitter space. We calculate the expectation value of the energy-momentum tensor in the Unruh-de Sitter state in two dimensions and find a non-vanishing flux of outgoing negative energy. Extrapolating the result to four dimensions, we argue that this backreacts on the initial de Sitter geometry semi-classically. Notably, we estimate that de Sitter space is dest…
We analyze correlations between pairs of particle detectors quadratically coupled to a real scalar field. We find that, while a single quadratically coupled detector presents no divergences, when one considers pairs of detectors there emerge unanticipated persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire from the field. We have characterized such divergences, discussed whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally we have fou…
It is well known that a receding mirror in Minkowski spacetime can model the formation of a black hole, producing Hawking-like radiation at late times. We ask what an observer would need to do to discern whether the radiation is fermionic or bosonic. Specialising to massless fields in 1+1 dimensions, we find that an Unruh-DeWitt detector accomplishes this: the late time transition rate of a detector coupled linearly to the scalar density of a spinor field is proportional to the Helmholtz free energy density of a fermionic thermal bath, hence showing a clear sign of Fermi-Dirac statistics, with…
We present novel methods to numerically address the problem of characterizing the response of particle detectors in curved spacetimes. These methods allow for the integration of the Wightman function, at least in principle, in rather general backgrounds. In particular we will use this tool to further understand the nature of conformal massless scalar Hawking radiation from a Schwarzschild black hole in anti-de Sitter space. We do that by studying an Unruh-DeWitt detector at rest above the horizon and in circular geodesic orbit. The method allows us to see that the response rate shows peaks at …
The model of Unruh-DeWitt detector coupled to the scalar field for finite time is studied. A systematic way of computing finite time corrections in various cases is suggested and nonperturbative effects like thermalization are discussed. It is shown in particular that adiabatic switching off the coupling between the detector and the thermal bath leaves non-vanishing corrections to the detector's levels distribution. Considering the two level detector as an information bearing degree of freedom encoding one bit of information, limits on external work for the detector's (de)couling in finite tim…
In this essay we examine the response of an Unruh-DeWitt detector (a quantum two-level system) to a gravitational wave background. The spectrum of the Unruh-Dewitt detector is of the same form as some scattering processes or three body decays such as muon-electron scattering or muon decay. Based on this similarity we propose that the Unruh-DeWitt detector response implies a "decay" or attenuation of gravitons, $G$, into photons, $γ$, via $G + G \rightarrow γ+ γ$ or $G \rightarrow γ+ γ+ G$. Over large distances such a decay/attenuation may have consequences in regard to the detection of gravita…
If an Unruh-DeWitt detector moves with a uniform acceleration in Fock-space vacuum, then the transition rate of the detector is proportional to the thermal spectrum. It is well known that the transition rate of the detector crucially depends on the two-point function along the detectors trajectory and in order to compute it the standard "$i ε$" regularization is used for Fock space. Numerically, we show here that the regulator $ε$ is generic in polymer quantization, the quantization method used in \emph{loop quantum gravity} with a finite value $ε\approx 2.16$, which leads to non-thermal spect…
We consider entanglement extraction into two two-level Unruh-DeWitt detectors from a vacuum of a neutral massless quantum scalar field in a four-dimensional spacetime, where the general monopole coupling to the scalar field is assumed. Based on the reduced density matrix of the two detectors derived within the perturbation theory, we show that the single copy of the entangled pair of the detectors can be utilized in quantum teleportation even when the detectors are separated acausally, while we observe no violation of the Bell-CHSH inequality. In the case of the Minkowski vacuum, in particular…
We study the decoherence and thermalization of an Unruh-DeWitt detector linearly coupled to the free massless scalar field in flat spacetime of arbitrary dimensions ($d\geq 2$). The initial state of the detector is chosen to be a pure state consisting of a linear superposition of ground and excited states, and we calculate the time evolution of reduced density matrix of the detector. Using perturbation method, we analytically derive the transition rate of the detector (the rate of change of the diagonal elements in the density matrix) and the decoherence rate (the rate of change of the off-dia…
We investigate a two-level Unruh-DeWitt detector coupled to a massless scalar field or its proper time derivative in $(1+1)$-dimensional Minkowski spacetime, in a quantum state whose correlation structure across the Rindler horizon mimics the stationary aspects of a firewall that Almheiri et al have argued to ensue in an evaporating black hole spacetime. Within first-order perturbation theory, we show that the detector's response on falling through the horizon is sudden but finite. The difference from the Minkowski vacuum response is proportional to $ω^{-2}\ln(|ω|)$ for the non-derivative dete…
In a quantum sense, vacuum is not an empty void but full of virtual particles (fields). It may have long-range properties, be altered, and even undergo phase transitions. It is suggested that long-range properties of a quantum vacuum may be probed by distributing matter over a large spatial volume. Here, we study a simplest example of such, i.e., two uniformly accelerated Unruh-DeWitt detectors which are spatially separated, and examine the inter-detector interaction energy arising from the coupling between the detectors and fluctuating fields to see if novel phenomena related to the long-rang…
We investigate entanglement harvesting in AdS$_4$. Applying the general results of [Phys. Rev. D 97, 125011 (2018)], we consider two scenarios: one where two particle detectors are geodesic, with equal redshift; and one where both are static, at unequal redshift. As expected, at large AdS length $L$, our results approximate flat space. However at smaller $L$ we observe non-trivial effects for various field boundary conditions. Furthermore, in the static case we observe a novel feature of the entanglement as a function of switching time delay, which we attribute to different (coordinate) freque…
