Unruh-DeWitt Detector Research Articles

Gravitational wave signals in an Unruh–DeWitt detector

We firstly generalize the massive scalar propagator for planar gravitational waves propagating on Minkowski space obtained recently in van Haasteren and Prokopec (2022 arXiv:2204.12930 [gr-qc]). 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 the gravitational waves fluctuate. The effect originates from the quantum interference between propagation on off-shell detector’s trajectories which probe different spatial gravitational potential induced by the gravitational backreaction from gravitational waves, and it is therefore purely quantum. When resummed over classical graviton insertions, gravitational waves generate cuts on the imaginary axis of the complex -plane (where denotes the difference of proper times), and the discontinuity across these cuts is responsible for a continuum of energy transitions induced in the Unruh–DeWitt detector. Not surprisingly, we find that the detector’s transition rate is exponentially suppressed with increasing energy and the mass of the scalar field. What is surprising, however, is that the transition rate is a non-analytic function of the gravitational field strain. This means that, no matter how small is the gravitational field amplitude, expanding in powers of the gravitational field strain cannot approximate well the detector’s transition rate. We present numerical and approximate analytical results for the detector’s transition rate both for circularly polarized and for polarized monochromatic, unidirectional, gravitational waves.

Effective master equations for two accelerated qubits

We revisit the problem involving two constantly accelerating Unruh-DeWitt detectors using Open Effective Field Theory methods. We study the time evolution of the joint detector state using a Markovian approximation which differs from the standard one taken in the literature. We show that this Markovian limit already implies the complete positivity of the dynamical evolution map without invoking the rotating wave approximation (RWA), in contrast to standard derivations of open system master equations. By calculating explicitly the domain of validity of this Markovian approximation, we argue that the lack of complete positivity in the usual microscopic derivation stems from the (subtle) fact that the Redfield equation is used outside its domain of validity. We give two well-known cases studied in the literature that violate the validity of the Markovian approximation: (i) the ``stacked trajectory'' limit (when detector trajectories are taken to be on top of one another), and (ii) large gap-to-acceleration ratio. Since Markovian dynamics with or without RWA can lead to different qualitative predictions for entanglement dynamics, our work emphasizes the need to properly track the regime of validity of all approximations.

Unruh DeWitt probe of late time revival of quantum correlations in Friedmann spacetimes

Unruh DeWitt (UDW) 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 study the response rate of Unruh DeWitt detectors which interact with quantum fields in FRW spacetimes. We consider both conventionally as well as derivatively coupled Unruh DeWitt detectors. Particularly, we consider their interaction with massless scalar fields in FRW spacetimes and nearly massless scalar fields in de Sitter spacetime. We discuss how the term which gives rise to the infrared divergence in the massless limit in de Sitter spacetime manifests itself at the level of the response rate of these Unruh DeWitt detectors in a wide class of Friedmann spacetimes. In order to carry out this study, we make use of an equivalence that exists between massless scalar fields in FRW spacetimes with massive scalar fields in de Sitter spacetime. Further, we show that while the derivative coupling regulates the divergence appearing in de Sitter spacetime, it does not completely remove them in matter dominated universe. This gives rise to large transitions in the detector which can be used as a probe of setting up of large correlations in late time era of the universe as well. We also apply the results of these otherwise formal analyses to the coupling of hydrogen atoms with gravitational waves. We show that the coupling of hydrogen atoms with gravitational waves takes a form that is similar to derivatively coupled UDW detectors and hence has significant observational implications as a probe of late time revival of quantum correlators.

Physical significance of generalized boundary conditions: An Unruh-DeWitt detector viewpoint on [formula omitted

On PAdS2×S2, 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∈[0,π2]. 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 secondary solutions in a qualitatively different, and rather bizarre, fashion. Our results highlight once more the existence of a freedom in choosing boundary conditions at a timelike boundary which is often neglected, though it has a notable associated physical significance.

Steady-state entanglement for rotating Unruh-DeWitt detectors

The Unruh-DeWitt model of particle detector is widely used to probe quantum effects in noninertial frames and curved spacetimes. In this paper, we investigate the entanglement dynamics of a quantum system composed of two rotating Unruh-DeWitt detectors in interaction with a fluctuating massless scalar field in vacuum. We obtain the necessary and sufficient condition for the detectors to achieve steady-state entanglement, and systematically investigate the steady-state entanglement of two Unruh-DeWitt detectors rotating in coaxial orbits with the same orbital radius and angular velocity. When the separation between the detectors is vanishing, the detectors can obtain steady-state entanglement dependent on the initial state, as the detectors in uniform acceleration and static detectors in a thermal bath do. Remarkably, however, when the separation between the detectors is nonvanishing but small compared with the transition wavelength of detectors, the detectors can obtain steady-state entanglement irrespectively of what the initial state is. This is the unique phenomenon caused by the centripetal acceleration and is not present in the uniform acceleration case and the case of static detectors in a thermal bath.

Unruh-Fulling effect in nonlocal field theory: The role of Unruh decomposition

We investigate the Unruh-Fulling effect in a class of nonlocal field theories by examining both the number operator and Unruh-DeWitt detector methods. Unlike in previous literature, we use Unruh quantization to quantize the matter field. Such choice, as oppose to standard Minkowski decomposition, naturally incorporates the time translational invariance in the positive frequency Wightman function and thus captures the thermal equilibrium of the system. We analyze the Unruh-Fulling effect for a massless real scalar field in both the Lorentz noninvariant and Lorentz invariant nonlocal theories. In Lorentz noninvariant nonlocal theory, the expectation value of number operator and the response function of the detector are modified by an overall multiplicative factor. Whereas in Lorentz invariant nonlocal theory these quantities remain identical to those of the standard Unruh-Fulling effect. The temperature of the thermal bath remains unaltered for both the Lorentz noninvariant and Lorentz invariant nonlocal theories. Therefore, in terms of temperature, the nonlocal Unruh-Fulling effect is universal while it is derived via Unruh quantization, whereas the transition rate may be modified.

Berry Phase from the Entanglement of Future and Past Light Cones: Detecting the Timelike Unruh Effect.

The Unruh effect can not only arise out of the entanglement between modes of left and right Rindler wedges, but also between modes of future and past light cones. We explore the geometric phase resulting from this timelike entanglement between the future and past, showing that it can be captured in a simple Λ system. This provides an alternative paradigm to the Unruh-deWitt detector. The Unruh effect has not been experimentally verified because the accelerations needed to excite a response from Unruh-deWitt detectors are prohibitively large. We demonstrate that a stationary but time-dependent Λ-system detects the timelike Unruh effect with current technology.

Entanglement harvesting of inertially moving Unruh-DeWitt detectors in Minkowski spacetime

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 a massless scalar field vacuum in four-dimensional Minkowski spacetime. Working within the weak coupling approximation, we find that the negativity is a (nonelementary) 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 relative velocity, the harvested entanglement is inversely correlated with the detector energy gap (at sufficiently high values) and the distance of closest approach of two detectors.

Effect of spacetime dimensions on quantum entanglement between two uniformly accelerated atoms

We investigate the entanglement dynamics for a quantum system composed of two uniformly accelerated Unruh-DeWitt detectors in different spacetime dimensions. It is found that the range of parameters in which entanglement can be generated is shrunk and the amount of generated entanglement is also decreased with the increasing spacetime dimension, by calculating the evolution of two-atom states using the method for open quantum systems. We study the entanglement evolution between two accelerated atoms for different initial two-atom states, and the influence of corresponding spacetime dimensions for every initial state is discussed. When the spacetime dimensions increase, the change of entanglement becomes slower with time. The influence of spacetime dimensions on the change of entanglement also expands to the case of the massive field. The time delay for entanglement generation is shown in different spacetime dimensions. In particular, entanglement decreases more quickly with the increasing spacetime dimensions compared with that in the case of the massless field. The recently found anti-Unruh effect is discussed, and a novel and interesting phenomenon is found that the Unruh effect in small spacetime dimensions can become the anti-Unruh effect in large spacetime dimensions with the same parameters.

A little excitement across the horizon

We analyse numerically the transitions in an Unruh-DeWitt detector, coupled linearly to a massless scalar field, in radial infall in (3 + 1)-dimensional Schwarzschild spacetime. In the Hartle–Hawking and Unruh states, the transition probability attains a small local extremum near the horizon-crossing and is then moderately enhanced on approaching the singularity. In the Boulware state, the transition probability drops on approaching the horizon. The unexpected near-horizon extremum arises numerically from angular momentum superpositions, with a deeper physical explanation to be found.

Quantum teleportation with relativistic communication from first principles

In this work we provide a genuine relativistic quantum teleportation protocol whose classical communication component makes use of relativistic causal propagation of a quantum field. Consequently, the quantum teleportation is fully relativistic by construction. Our scheme is based on Unruh-DeWitt qubit detector model, where the quantum state being teleported is associated to an actual qubit rather than a field mode considered by Alsing and Milburn [PRL 91, 180404 (2003)]. We show that the existing works in (relativistic) quantum information, including good definitions of one-shot and asymptotic channel capacities, as well as algebraic formulation of quantum field theory, already provide us with all the necessary ingredients to construct fundamentally relativistic teleportation protocol in relatively straightforward manner.

Probing Lorentz-invariance-violation-induced nonthermal Unruh effect in quasi-two-dimensional dipolar condensates

The Unruh effect states an accelerated particle detector registers a thermal response when moving through the Minkowski vacuum, and its thermal feature is believed to be inseparable from Lorentz symmetry: Without the latter, the former disappears. Here we propose to observe analogue circular Unruh effect using an impurity atom in a quasi-two-dimensional Bose-Einstein condensate (BEC) with dominant dipole-dipole interactions between atoms or molecules in the ultracold gas. Quantum fluctuations in the condensate possess a Bogoliubov spectrum $\omega_{\mathbf k}=c_0|{\mathbf k}|f(\hbar\,c_0|{\mathbf k}|/M_\ast)$, working as an analogue Lorentz-violating quantum field with the Lorentz-breaking scale $M_\ast$, and the impurity acts as an effective Unruh-DeWitt detector thereof. When the detector travels close to the sound speed, observation of the Unruh effect in our quantum fluid platform becomes experimentally feasible. In particular, the deviation of the Bogoliubov spectrum from the Lorentz-invariant case is highly engineerable through the relative strength of the dipolar and contact interactions, and thus a viable laboratory tool is furnished to experimentally investigate whether the thermal characteristic of Unruh effect is robust to the breaking of Lorentz symmetry.

Entanglement harvesting from conformal vacuums between two Unruh-DeWitt detectors moving along null paths

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) dimensional de Sitter background for the same set of parameters when the detectors move along the same outgoing null trajectory. The qualitative results from the Boulware and the Unruh vacuums are alike. Furthermore, we observed that the concurrence depends on the distance d between the two null paths of the detectors periodically, and depending on the parameter values, there could be entanglement harvesting shadow points or regions. We also observe that the mutual information does not depend on d in (1 + 1) dimensional Schwarzschild and de Sitter spacetimes but periodically depends on it in (1 + 3) dimensional de Sitter background. We also provide elucidation on the origin of the harvested entanglement.

Probing long-range properties of vacuum altered by uniformly accelerating two spatially separated Unruh-DeWitt detectors

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-range properties emerge of a vacuum altered by uniformly accelerating two spatially separated detectors through it. Our results show that when the inter-detector separation is much larger than the thermal wavelength of the Unruh thermal bath, the inter-detector interaction displays a completely new behavior, which, as compared with that of the inertial detectors, is surprisingly exclusively acceleration-dependent, signaling a new phase of the vacuum in which its imprint as seen by two inertial observers seems to be completely wiped out. Moreover, we demonstrate that the inter-detector interaction in the near region can be significantly enhanced by the accelerated motion in certain circumstances, and with two Rydberg atoms as the detectors, the acceleration required for an experimentally detectable enhancement of the interaction energy can be 105 times smaller than that required for the detection of the Unruh effect.

Cavity Optimization for Unruh Effect at Small Accelerations.

One of the primary reasons behind the difficulty in observing the Unruh effect is that for achievable acceleration scales the finite temperature effects are significant only for the low frequency modes of the field. Since the density of field modes falls for small frequencies in free space, the field modes which are relevant for the thermal effects would be less in number to make an observably significant effect. In this Letter, we investigate the response of an Unruh-DeWitt detector coupled to a massless scalar field which is confined in a long cylindrical cavity. The density of field modes inside such a cavity shows a resonance structure, i.e., it rises abruptly for some specific cavity configurations. We show that an accelerating detector inside the cavity exhibits a nontrivial excitation and de-excitation rates for small accelerations around such resonance points. If the cavity parameters are adjusted to lie in a neighborhood of such resonance points, the (small) acceleration-induced emission rate can be made much larger than the already observable inertial emission rate. We comment on the possibilities of employing this detector-field-cavity system in the experimental realization of the Unruh effect, and argue that the necessity of extremely high acceleration can be traded off in favor of precision in cavity manufacturing for realizing noninertial field theoretic effects in laboratory settings.

Anti-Hawking phenomena around a rotating BTZ black hole

In both flat and curved spacetimes, there are weak and strong versions of the anti-Unruh/anti-Hawking effects, in which the Kubo-Martin-Schwinger field temperature is anticorrelated with the response of a detector and its inferred temperature. We investigate for the first time the effects on the weak and strong anti-Hawking effects for an Unruh-DeWitt detector orbiting a Banados-Teitelboim-Zanelli black hole in the corotating frame. We find that rotation can significantly amplify the strength of the weak anti-Hawking effect, whereas it can either amplify or reduce the strength of the strong anti-Hawking effect depending on boundary conditions. For the strong anti-Hawking effect, we find a nonmonotonic relationship between the angular momentum and detector temperature for each boundary condition. In addition, we note that the weak anti-Hawking effect is independent of a changing AdS length, while a longer AdS length increases the temperature range of the strong anti-Hawking effect.

The cost of building a wall for a fermion

We analyse the energy cost of building or demolishing a wall for a massless Dirac field in (1+1)-dimensional Minkowski spacetime and the response of an Unruh-DeWitt particle detector to the generated radiation. For any smoothly-evolving wall, both the field’s energy density and the detector’s response are finite. In the limit of rapid wall creation or demolition, the energy density displays a delta function squared divergence. By contrast, the response of an Unruh-DeWitt detector, evaluated within first-order perturbation theory, diverges only logarithmically in the duration of the wall evolution. The results add to the evidence that a localised matter system may not be as sensitive to the rapid wall creation as the local expectation values of field observables. This disparity has potential interest for quantum information preservation scenarios.

Entanglement harvesting between two inertial Unruh-DeWitt detectors from nonvacuum quantum fluctuations

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 $(1+1)$ and $(1+3)$ dimensions for this investigation. Our main observation asserts that entanglement harvesting is suppressed compared to the vacuum fluctuations in this situation. Our other observations confirm a non-zero individual detector transition probability in this background and vanishing entanglement harvesting for parallel co-moving detectors. We look into the characteristics of the harvested entanglement and discuss its dependence on different system parameters.

Entanglement harvesting of three Unruh-DeWitt detectors

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 larger spacelike separations from the other two than in the corresponding bipartite case. We also find that for small detector separations bipartite correlations become larger than tripartite ones, leading to an apparent violation of the Coffman-Kundu-Wootters (CKW) inequality. We show that this is not a consequence of our perturbative expansion but that it instead occurs because the harvesting qubits are in a mixed state.

Quantized mass-energy effects in an Unruh-DeWitt detector

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 dynamically evolving under a non-relativistic Hamiltonian. However, the processes of interest -- the absorption or emission of field particles -- necessarily change the detector's rest mass by the amount of energy of the absorbed or emitted field quanta. Neither of the above models can capture such effects. Here we incorporate the quantization of the detector's mass-energy into the Unruh-DeWitt model. We show that internal energy changes due to emission or absorption are relevant even in the lowest energy limit. Specifically, corrections to transition rates due to the detector's mass changing cannot be ignored unless the entire center of mass dynamics is also ignored. Our results imply that one cannot have a consistent model of the Unruh-DeWitt detector as a massive particle without including the mass-energy equivalence.