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Using spacetime Gaussian test functions, we find closed-form expressions for the smeared Wightman function, Feynman propagator, retarded and advanced Green's functions, causal propagator and symmetric propagator of a massless scalar field in the vacuum of Minkowski spacetime. We apply our results to localized quantum systems which interact with a quantum field in Gaussian spacetime regions and study different relativistic quantum information protocols. In the protocol of entanglement harvesting, we find a closed-form expression for the entanglement that can be acquired by probes which interact in Gaussian spacetime regions and obtain asymptotic results for the protocol. We also revisit the case of two gapless detectors and show that the detectors can become entangled if there is two-way signalling between their interaction regions, providing closed-form expressions for the detectors' final state., Comment: 15 pages, 4 figures, 1 appendix. Revtex 4-2. v3 updated to match published version

We study the protocol of entanglement harvesting when the particle detectors that harvest entanglement from the field are replaced by fully relativistic quantum field theories. We show that two localized modes of the quantum field theories are able to harvest the same amount of leading order entanglement as two non-relativistic particle detectors, thus implying that QFT probes can generally harvest more entanglement than particle detectors. These results legitimize the use of particle detectors to study entanglement harvesting regardless of their internally non-relativistic nature., Comment: 17 pages, 3 figures. RevTeX 4.2. v2: Updated to match published version

It is well known that the experience of a linearly accelerated observer with acceleration $a$, interacting with a massless scalar field in its vacuum state in $3+1$ Minkowski spacetime, is identical to that of a static observer interacting with a massless scalar field in a thermal state of temperature $a/2\pi$ in $3+1$ Minkowski spacetime. We study the robustness of this duality by comparing an observer undergoing circular motion in a thermal bath with an observer that undergoes circular motion around a linearly accelerated trajectory. We find that in most regimes, observers in these two cases experience the field in different ways, and are generally able to tell the difference between the two cases by measuring observables localized along their trajectories., Comment: 19 pages, 3 figures. v2: sections 2 and 6 expanded after referee comments. v3: typos corrected. v4: added post-publication note

We present a fully relativistic model for localized probes in quantum field theory. Furthermore, we show that it is possible to obtain particle detector models from localized quantum field theories that interact with a free quantum field. In particular, a particle detector model is obtained when one traces out over inaccessible degrees of freedom of the localized field. This gives rise to a particle detector model, that is, a quantum degree of freedom that couples to a free field theory in an extended region of spacetime. Moreover, we show that the predictions of traditional particle detector models and fully relativistic localized fields completely coincide to leading order in perturbation theory., Comment: 10 pages, 2 appendices. V2: Updated to match published version

We present a duality between a particle detector model coupled to the amplitude of a scalar field and coupled to the field's derivative in the limit of large energy gaps. We show that the results of the models can be mapped to each other in a one-to-one fashion modulo a rescaling by the detector's gap. Our analysis is valid for arbitrary scalar fields in curved spacetimes, and requires minimal assumptions regarding the detectors. The duality also applies to the case where more than one detector is coupled to the field. This shows that many examples of entanglement harvesting with amplitude coupled UDW detectors give exactly the same result as derivative coupled detectors that interact with the field in the same region of spacetime., Comment: 9 pages, 3 figures + appendix

By considering a misaligned (asymptotically uniform) magnetic field in the background of a rotating black hole, we uncover a possibility for a highly non-trivial motion of Carrollian particles on the black hole horizon that is characterized by a time-dependent velocity field and reminds us (because of its latitudinal oscillations) of a 'monarch butterfly migration'., Comment: 6 pages, 3 figures

We revisit the motion of massless particles with anyonic spin in the horizon of Kerr-Newman geometry. As recently shown, such particles can move within the horizon of the black hole due to the coupling of charges associated with a two-parametric central extension of the two-dimensional Carroll group to the magnetic field generated by the black hole-the so-called "anyonic spin-Hall effect." We show that the previously computed magnetic field is not invariant under Carroll diffeomorphisms and find another result which respects these symmetries of the horizon. We also consider a more astrophysically relevant case of a (weakly charged) rotating back hole placed in a uniform magnetic field, which could, for instance, be induced by the surrounding plasma. We show that a qualitatively similar magnetic field assisted anyonic spin-Hall effect takes place, even in the absence of black hole rotation. The theoretical possibility of a motion induced by a magnetic monopole is also studied.

We write the curvature of spacetime in terms of the excitation probability of particle detectors ultra-rapidly coupled to a quantum field. More precisely, we provide an expansion for the excitation probability of a smeared UDW detector delta-coupled to a real scalar quantum field in a curved background. Using a short distance expansion for the Wightman function, we express the excitation probability of a detector as the transition probability in Minkowski spacetime plus correction terms written as a function of the curvature tensors and the detector size. Comparing the excitation probability in curved spacetimes with its flat analog, we are able to express the components of the Ricci and Riemann curvature tensors as a function of physically measurable excitation probabilities of different shaped detectors., Comment: 7 pages + 3 appendices

We write the curvature of spacetime in terms of the excitation probability of particle detectors ultra-rapidly coupled to a quantum field. More precisely, we provide an expansion for the excitation probability of a smeared UDW detector delta-coupled to a real scalar quantum field in a curved background. Using a short distance expansion for the Wightman function, we express the excitation probability of a detector as the transition probability in Minkowski spacetime plus correction terms written as a function of the curvature tensors and the detector size. Comparing the excitation probability in curved spacetimes with its flat analog, we are able to express the components of the Ricci and Riemann curvature tensors as a function of physically measurable excitation probabilities of different shaped detectors., Comment: 7 pages + 3 appendices

We analyze the differences between relativistic fields with or without quantum degrees of freedom in relativistic quantum information protocols. We classify the regimes where the existence of quantum degrees of freedom is necessary to explain the phenomenology of interacting quantum systems. We also identify the precise regimes where quantum fields can be well approximated by quantum-controlled classical fields in relativistic quantum information protocols. Our results can be useful to discern which features are fundamentally different in classical and quantum field theory., Comment: 16 pages + appendix, 9 figures. V3: Updated examples

We revisit the motion of massless particles with anyonic spin in the horizon of Kerr--Newman geometry. As recently shown, such particles can move within the horizon of the black hole due to the coupling of charges associated with a 2-parametric central extension of the 2-dimensional Carroll group to the magnetic field generated by the black hole -- the so called "anyonic spin-Hall effect". We show that the previously computed magnetic field is not invariant under Carroll diffeomorphisms and find another result which respects these symmetries of the horizon. We also consider a more astrophysically relevant case of a (weakly charged) rotating back hole placed in a uniform magnetic field, which could, for instance, be induced by the surrounding plasma. We show that a qualitatively similar magnetic field assisted anyonic spin-Hall effect takes place, even in the absence of black hole rotation. The theoretical possibility of a motion induced by a magnetic monopole is also studied., Comment: 8 pages, 3 figures

We study how quantum systems can harvest entanglement from the quantum degrees of freedom of the gravitational field. Concretely, we describe in detail the interaction of non-relativistic quantum systems with linearized quantum gravity, and explore how two spacelike separated probes can harvest entanglement from the gravitational field in this context. We provide estimates for the harvested entanglement for realistic probes which can be experimentally relevant in the future, since entanglement harvesting experiments can provide evidence for the existence of quantum degrees of freedom of gravity., Comment: 18 pages + appendices, 16 figures, revTex 4.2. V2: updated to match published version

We revisit the Bose-Marletto-Vedral (BMV) table-top experimental proposal - which aims to witness quantum gravity using gravity mediated entanglement - analyzing the role of locality in the experiment. We first carry out a fully quantum modelling of the interaction of matter and gravity and then show in what way gravity mediated entanglement in the BMV experiment could be accounted for without appealing to quantum degrees of freedom of the gravitational field. We discuss what assumptions are needed in order to interpret the current BMV experiment proposals as a proof of quantum gravity, and also identify the modifications that a BMV-like experiment could have in order to serve as proof of quantum gravity without having to assume the existence of a local mediators in the gravitational field., Comment: 5 pages + appendices, 1 figure. V5: updated to match published version

We investigate the protocol of entanglement harvesting, where two spacelike separated particle detectors extract quantum correlations from a quantum field. Specifically, we analyze the role of the mass of the field and the energy gap of the detectors in the protocol. Perhaps surprisingly, we find that there are regimes in which the entanglement harvested can increase with the mass of the field by decreasing the noise experienced by the detectors. Finally, we study the optimal relationship between the gap of the detectors and the other parameters of the setting that maximizes the entanglement harvested, showing that a small mass can improve the protocol even in this case., Comment: 15 pages, 15 figures. RevTex 4.1

In this manuscript we provide a consistent way of describing a localized non-relativistic quantum system undergoing a timelike trajectory in a background curved spacetime. Namely, using Fermi normal coordinates, we identify an inner product and canonically conjugate position and momentum operators defined in the rest space of the trajectory for each value of its proper time. This framework then naturally provides a recipe for mapping a quantum theory defined in a non-relativistic background to a theory around a timelike trajectory in curved spacetimes. This is done by reinterpreting the position and momentum operators and by introducing a local redshift factor to the Hamiltonian, which gives rise to new dynamics due to the curvature of spacetime and the acceleration of the trajectory. We then apply our formalism to particle detector models, that is, to the case where the non-relativistic quantum system is coupled to a quantum field in a curved background. This allows one to write a general definition for particle detector models which is able to recover the previous models in the literature. Our framework also allows one to estimate the regime of validity of these models, characterizing the situations where particle detectors can be used to accurately probe quantum fields., Comment: 16 pages, 3 figures, v3 added clarification after Eq. (41)

We provide a setup by which one can recover the geometry of spacetime from local measurements of quantum particle detectors coupled to a quantum field. Concretely, we show how one can recover the field's correlation function from measurements on the detectors. Then, we are able to recover the invariant spacetime interval from the measurement outcomes, and hence reconstruct a notion of spacetime metric. This suggest that quantum particle detectors are the experimentally accessible devices that could replace the classical 'rulers' and 'clocks' of general relativity., Comment: 19 pages, 10 Figures, 2 Appendices. RevTeX 4.2. V3: added a picture illustrating the setup

We explore entanglement harvesting with particle detectors that couple linearly to non-Hermitian fields. Specifically, we analyze the case of particle detectors coupled to a complex scalar quantum field and to a spin 1/2 fermionic field. We find that the complex scalar model can be a good approximation for the fermionic model in the protocol of entanglement harvesting when the mass of the field is sufficiently large compared to the inverse interaction time. Moreover, we show that by taking advantage of the U(1) degree of freedom of a complex detector it is possible to increase the harvested negativity by up to two orders of magnitude when compared to the case of a real detector., Comment: 24 pages, 18 Figures, 3 Appendices. RevTeX 4.1. V4: Updated to match published version

We study the thermalization of smeared particle detectors that couple locally to $any$ operator in a quantum field theory in curved spacetimes. We show that if the field state satisfies the KMS condition with inverse temperature $\beta$ with respect to the detector's local notion of time evolution, reasonable assumptions ensure that the probe thermalizes to the temperature $1/\beta$ in the limit of long interaction times. Our method also imposes bounds on the size of the system with respect to its proper acceleration and spacetime curvature in order to accurately probe the KMS temperature of the field. We then apply this formalism to a uniformly accelerated detector probing the Minkowski vacuum of any CPT symmetric quantum field theory, and show that the detector thermalizes to the Unruh temperature, independently of the operator it couples to. This exemplifies yet again the robustness of the Unruh effect, even when arbitrary smeared detectors are used to probe general operators in a quantum field theory., Comment: revtex4-1, 10 pages + appendices. Version 2: fixed minor typos and added a short discussion regarding experimental implementability

We show that gravitons with energy $E<\Omega$, where $\Omega$ is the energy gap a localized non-relativistic system, can be detected by finite-time interactions with a detector. Our detector is based on a quadrupole moment interaction between the hydrogen atom and the gravitational field in the linearized approximation. In this model, the external agent responsible for switching the interaction on an off inputs energy into the system, which creates a non-zero excitation probability even when the field is in the vacuum state. However, when the gravitational field is in a one-particle state with angular momentum, we obtain excitations due to the field's particle content. These detector excitations are then associated with the detection of gravitons. We also discuss a possible physical realization of our model where the electromagnetic field plays the role of the external agent., Comment: revtex 4-1, 7 pages, 2 figures

We analyze families of particle detector models that linearly couple to different kinds of fermionic and bosonic fields. We also study the response of these detectors to particle and anti-particle excitations of the field. We propose a simple linear complex scalar particle detector model that captures the fundamental features of fermionic field detectors similarly to how the Unruh-DeWitt model captures the features of the light matter interaction. We also discuss why we do not need to limit ourselves to quadratic models commonly employed in past literature. Namely, we provide a physically motivated mechanism that restores U(1) symmetry in these linear complex models., Comment: 30 pages, 5 Appendices, 3 figures. RevTeX 4.1

We provide a setup by which one can recover the geometry of spacetime from local measurements of quantum particle detectors coupled to a quantum field. Concretely, we show how one can recover the field's correlation function from measurements on the detectors. Then, we are able to recover the invariant spacetime interval from the measurement outcomes, and hence reconstruct a notion of spacetime metric. This suggest that quantum particle detectors are the experimentally accessible devices that could replace the classical 'rulers' and 'clocks' of general relativity., Comment: 19 pages, 10 Figures, 2 Appendices. RevTeX 4.2. V3: added a picture illustrating the setup

We explore entanglement harvesting with particle detectors that couple linearly to non-Hermitian fields. Specifically, we analyze the case of particle detectors coupled to a complex scalar quantum field and to a spin 1/2 fermionic field. We find that the complex scalar model can be a good approximation for the fermionic model in the protocol of entanglement harvesting when the mass of the field is sufficiently large compared to the inverse interaction time. Moreover, we show that by taking advantage of the U(1) degree of freedom of a complex detector it is possible to increase the harvested negativity by up to two orders of magnitude when compared to the case of a real detector., Comment: 24 pages, 18 Figures, 3 Appendices. RevTeX 4.1. V4: Updated to match published version

We study the thermalization of smeared particle detectors that couple locally to $any$ operator in a quantum field theory in curved spacetimes. We show that if the field state satisfies the KMS condition with inverse temperature $\beta$ with respect to the detector's local notion of time evolution, reasonable assumptions ensure that the probe thermalizes to the temperature $1/\beta$ in the limit of long interaction times. Our method also imposes bounds on the size of the system with respect to its proper acceleration and spacetime curvature in order to accurately probe the KMS temperature of the field. We then apply this formalism to a uniformly accelerated detector probing the Minkowski vacuum of any CPT symmetric quantum field theory, and show that the detector thermalizes to the Unruh temperature, independently of the operator it couples to. This exemplifies yet again the robustness of the Unruh effect, even when arbitrary smeared detectors are used to probe general operators in a quantum field theory., Comment: revtex4-1, 10 pages + appendices. Version 2: fixed minor typos and added a short discussion regarding experimental implementability

We show that gravitons with energy $E<\Omega$, where $\Omega$ is the energy gap a localized non-relativistic system, can be detected by finite-time interactions with a detector. Our detector is based on a quadrupole moment interaction between the hydrogen atom and the gravitational field in the linearized approximation. In this model, the external agent responsible for switching the interaction on an off inputs energy into the system, which creates a non-zero excitation probability even when the field is in the vacuum state. However, when the gravitational field is in a one-particle state with angular momentum, we obtain excitations due to the field's particle content. These detector excitations are then associated with the detection of gravitons. We also discuss a possible physical realization of our model where the electromagnetic field plays the role of the external agent., Comment: revtex 4-1, 7 pages, 2 figures

We analyze families of particle detector models that linearly couple to different kinds of fermionic and bosonic fields. We also study the response of these detectors to particle and anti-particle excitations of the field. We propose a simple linear complex scalar particle detector model that captures the fundamental features of fermionic field detectors similarly to how the Unruh-DeWitt model captures the features of the light matter interaction. We also discuss why we do not need to limit ourselves to quadratic models commonly employed in past literature. Namely, we provide a physically motivated mechanism that restores U(1) symmetry in these linear complex models., Comment: 30 pages, 5 Appendices, 3 figures. RevTeX 4.1

We reduce Dirac's spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and curvature around the center of mass of the system, generalizing the results of [Phys. Rev. D 22, 1922]. Under a non-relativistic approximation, one obtains a quantum description in a Hilbert space of complex wavefunctions defined in the rest space of the system. The wavefunction of the particle then evolves according to a modified Schr\"odinger equation associated with a symmetric Hamiltonian. When compared to the standard Schr\"odinger equation for a wavefunction, we obtain corrections in terms of the acceleration of the system's center of mass and curvature of spacetime along its trajectory. In summary, we provide a formalism for the use of a complex wavefunction to describe a localized quantum particle in curved spacetimes., Comment: 26 pages, 1 figure. RevTeX 4.1. V4. Added a more detailed explanation in Appendix C and fixed minor typos

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 detector model whose associated line defect is related to the derivative of a Wilson line. This is another instance where nonlocal operators in gauge theories can be interpreted as physical probes for quantum fields., Comment: 28 pages, 3 figures. V2 updated to match published version

We present a model for the coupling of non-relativistic quantum systems with a linearized gravitational field from a Lagrangian formulation. The coupling strongly resembles the light-matter interaction models that are known to be well approximated by the Unruh-DeWitt detector model for interactions with quantum fields. We then apply our model to linearized quantum gravity, which allows us to propose a detector based setup that can in principle probe the quantum nature of the gravitational field., Comment: 8 pages, 1 figure

We show that the predictions of spatially smeared particle detectors coupled to quantum fields are not generally covariant outside the pointlike limit. This lack of covariance manifests itself as an ambiguity in the time-ordering operation. We analyze how the breakdown of covariance affects typical detector models in quantum field theory such as the Unruh-DeWitt model. Specifically, we show how the violations of covariance depend on the state of the detectors-field system, the shape and state of motion of the detectors, and the spacetime geometry. Furthermore, we provide the tools to explicitly evaluate the magnitude of the violation, and identify the regimes where the predictions of smeared detectors are either exactly or approximately covariant in perturbative analyses., Comment: 12 pages. RevTeX 4.1. V2. Corrected minor typos

We propose a fully covariant model for smeared particle detectors in quantum field theory in curved spacetimes. We show how effects related to accelerated motion of the detector and the curvature of spacetime influence the way different observers assign an interaction Hamiltonian between the detector and the field. The fully covariant formulation explicitly leaves the physical predictions of the theory invariant under general coordinate transformations, hence providing a description of particle detector models (e.g., Unruh-DeWitt detectors, models for the light-matter interaction, etc) that is suitable for arbitrary trajectories in general spacetime backgrounds., Comment: 9 pages, 1 page of Appendix. RevTeX 4.1. V2: Updated to match published version

We analyze the problem of neutrino oscillations via a fermionic particle detector model inspired by the physics of the Fermi theory of weak interactions. The model naturally leads to a description of emission and absorption of neutrinos in terms of localized two-level systems. By explicitly including source and detector as part of the dynamics, the formalism is shown to recover the standard results for neutrino oscillations without mention to "flavor states", which are ill defined in quantum field theory. This illustrates how particle detector models provide a powerful theoretical tool to approach the measurement issue in quantum field theory and emphasizes that the notion of flavor states, although sometimes useful, must not play any crucial role in neutrino phenomenology., Comment: 10 pages, 3 figures. V2 updated to match published version

We present a model for the coupling of non-relativistic quantum systems with a linearized gravitational field from a Lagrangian formulation. The coupling strongly resembles the light-matter interaction models that are known to be well approximated by the Unruh-DeWitt detector model for interactions with quantum fields. We then apply our model to linearized quantum gravity, which allows us to propose a detector based setup that can in principle probe the quantum nature of the gravitational field., Comment: 8 pages, 1 figure

We propose a fully covariant model for smeared particle detectors in quantum field theory in curved spacetimes. We show how effects related to accelerated motion of the detector and the curvature of spacetime influence the way different observers assign an interaction Hamiltonian between the detector and the field. The fully covariant formulation explicitly leaves the physical predictions of the theory invariant under general coordinate transformations, hence providing a description of particle detector models (e.g., Unruh-DeWitt detectors, models for the light-matter interaction, etc) that is suitable for arbitrary trajectories in general spacetime backgrounds., Comment: 9 pages, 1 page of Appendix. RevTeX 4.1. V2: Updated to match published version

We analyze the problem of neutrino oscillations via a fermionic particle detector model inspired by the physics of the Fermi theory of weak interactions. The model naturally leads to a description of emission and absorption of neutrinos in terms of localized two-level systems. By explicitly including source and detector as part of the dynamics, the formalism is shown to recover the standard results for neutrino oscillations without mention to "flavor states", which are ill defined in quantum field theory. This illustrates how particle detector models provide a powerful theoretical tool to approach the measurement issue in quantum field theory and emphasizes that the notion of flavor states, although sometimes useful, must not play any crucial role in neutrino phenomenology., Comment: 10 pages, 3 figures. V2 updated to match published version