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We analyze the harvesting of entanglement and classical correlations from the quantum vacuum to particle detectors. We assess the impact on the detectors' harvesting ability of the spacetime dimensionality, the suddenness of the detectors' switching, their physical size and their internal energy structure. Our study reveals several interesting dependences on these parameters that can be used to optimize the harvesting of classical and quantum correlations. Furthermore, we find that, contrary to previous belief, smooth switching is much more efficient than sudden switching in order to harvest vacuum entanglement, especially when the detectors remain spacelike separated. Additionally, we show that the reported phenomenology of spacelike entanglement harvesting is not altered by subleading order perturbative corrections., Comment: 17 pages, 5 figures. RevTeX 4.1. V7: Added footnote for additional clarity, improved presentation and corrected a few minor typos

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 calculations with UDW detectors can be streamlined through the use of extended Feynman rules that include localized detector-field interactions.Our findings pave the way for the extension of previous studies of the Unruh and Hawking effects with UDW detectors, and provide new tools for studies in relativistic quantum information, for example, regarding relativistic quantum communication and studies of the entanglement structure of the fermionic vacuum., Comment: 49 pages, 25 figures. RevTex 4.1. V2: Minor updates to match published version

We find that a uniformly accelerated particle detector coupled to the vacuum can cool down as its acceleration increases, due to relativistic effects. We show that in (1+1)-dimensions, a detector coupled to the scalar field vacuum for finite timescales (but long enough to satisfy the KMS condition) has a KMS temperature that decreases with acceleration, in certain regimes. This contrasts with the heating that one would expect from the Unruh effect., Comment: 6 pages, 5 figures. RevTex 4.1. V2. Typos in the plots labeling corrected and plot rescaled. New discussion section added. Title changed

We analyze how pre-existing entanglement between two Unruh-DeWitt particle detectors evolves when one of the detectors falls through a Rindler firewall in (1+1)-dimensional Minkowski space. The firewall effect is minor and does not wash out the detector-detector entanglement, in some regimes even preserving the entanglement better than Minkowski vacuum. The absence of cataclysmic events should continue to hold for young black hole firewalls. A firewall's prospective ability to resolve the information paradox must hence hinge on its detailed gravitational structure, presently poorly understood., Comment: 5 pages, 3 figures. RevTeX 4.1. v2: Updated to match published version. Added references and clarifications, including new title

We show that the fluctuations of quantum fields as seen by late comoving observers are significantly influenced by the history of the early Universe, and therefore they transmit information about the nature of spacetime in timescales when quantum gravitational effects were non-negligible. We discuss how this may be observable even nowadays, and thus used to build falsifiability tests of quantum gravity theories., Comment: 3 pages. 2 Figures. Proceedings Theory Canada 9. Published in Canadian Journal of Physics. (http://www.nrcresearchpress.com/doi/abs/10.1139/cjp-2014-0567)

We analyze the implications of the violations of the strong Huygens principle in the transmission of information from the early universe to the current era via massless fields. We show that much more information reaches us through timelike channels (not mediated by real photons) than it is carried by rays of light, which are usually regarded as the only carriers of information., Comment: 5 pages, 2 figures. RevTeX 4.1. V2: Updated to match published version. Previous title "A glimpse of the early universe without real light" modified to match Physical Review Letters published version

The quantum Zeno effect is usually thought to require infinitely frequent and perfect projective measurements to freeze the dynamics of quantum states. We show that perfect freezing of quantum states can also be achieved by more realistic non-projective measurements performed at a finite frequency., Comment: 7 pages, 1 figure, RevTeX 4.1. v2: Updated to match published version

We review recent results regarding entanglement in quantum fields in cosmological spacetimes and related phenomena in flat spacetime such as the Unruh effect. We being with a summary of important results about field entanglement and the mathematics of Bogoliubov transformations that is very often used to describe it. We then discuss the Unruh-DeWitt detector model, which is a useful model of a generic local particle detector. This detector model has been successfully used as a tool to obtain many important results. In this context we discuss two specific types of these detectors: a qubit and a harmonic oscillator. The latter has recently been shown to have important applications when one wants to probe nonperturbative physics of detectors interacting with quantum fields. We then detail several recent advances in the study and application of these ideas, including echoes of the early universe, entanglement harvesting, and a nascent proposal for quantum seismology., Comment: 29 pages, 7 figures. Accepted in Classical and Quantum Gravity. Currently in press. (Special Issue focused on the topic of "Entanglement and Quantum Gravity")

We propose a quantum mechanical method of detecting weak vibrational disturbances inspired by the protocol of entanglement farming. We consider a setup where pairs of atoms in their ground state are successively sent through an optical cavity. It is known that in this way it is possible to drive that cavity toward a stable fixed-point state. Here we study how that fixed-point state depends on the time interval between pairs of atoms and on the distance between the cavity's mirrors. Taking advantage of an extremely precise resonance effect, we find that there are special values of these parameters where the fixed-point state is highly sensitive to perturbations, even harmonic vibrations with frequencies several orders of magnitude below the cavity's natural frequency. We propose that this sensitivity may be useful for high precision metrology., Comment: 10 pages, 5 figures. RevTeX 4.1

We show that the relativistic signatures on the transition probability of atoms moving through optical cavities are very sensitive to their spatial trajectory. This allows for the use of internal atomic degrees of freedom to measure small time-dependent perturbations in the proper acceleration of an atomic probe, or in the relative alignment of a beam of atoms and a cavity., Comment: 7 pages, 6 figures. RevTex 4.1. v2: Updated to match published version

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 certain characteristic frequencies, which correspond to the quasinormal modes (QNMs) of the space-time. It is in principle possible to apply these techniques to more complicated and interesting physical scenarios, e.g. geodesic infall or multiple detector entanglement evolution, or the study of the behaviour of quantum correlations in spacetimes with black hole horizons., Comment: 13 pages, 12 figures. RevTex 4.1. v2 Updated to published version

In this review article we revisit and spell out the details of previous work on how Berry phase can be used to construct a precision quantum thermometer. An important advantage of such a scheme is that there is no need for the thermometer to acquire thermal equilibrium with the sample. This reduces measurement times and avoids precision limitations. We also review how such methods can be used to detect the Unruh effect., Comment: 16 pages, 6 figures

We show that it is possible to use a massless field in the vacuum to communicate in such a way that the signal travels arbitrarily slower than the speed of light and such that no energy is transmitted from the sender to the receiver. Instead, the receiver has to supply a signal-dependent amount of work to switch his detector on and off. Because of that, this kind of communication without energy exchange may be called "Quantum Collect Calling". This type of communication is related to Casimir-like interactions and it is made possible by dimension ---and curvature--- dependent subtleties of Huygens' principle., Comment: Accepted in Physical Review Letters. RevTex 4.1, 5 pages, 2 figures. v3. Updated to match published version

We study the impact of the zero-mode of a quantum field on the evolution of a particle detector. For a massless scalar field in a periodic cavity, we show that the impact of the zero mode on the Unruh-DeWitt detector and its derivative-coupling generalisation is necessarily nonvanishing but can be made negligible in some limits, including those commonly occurring in non-relativistic quantum optics. For the derivative-coupling detector this can be accomplished by just tuning the zero mode's initial state, but the standard Unruh-DeWitt detector requires a more subtle and careful tuning. Applications include an inertial detector with arbitrary velocity, where we demonstrate the regularity of the ultrarelativistic limit, and a detector with uniform acceleration., Comment: 14 pages, 3 Figures. RevTex 4.1. v2: Added journal reference and minor edits to match published version

We harness general relativistic effects to gain quantum control on a stationary qubit in an optical cavity by controlling the non-inertial motion of a different probe atom. Furthermore, we show that by considering relativistic trajectories of the probe, we enhance the efficiency of the quantum control. We explore the possible use of these relativistic techniques to build universal quantum gates., Comment: 4 pages (+ 4 pages Appendix). 4 figures. RevTex 4.1

We exploit geometric properties of quantum states of light in optical cavities to carry out quantum non-demolition measurements. We generalize the 'mode invisibility' method to obtain information about the Wigner function of a squeezed coherent state in a non-destructive way. We also simplify the application of this non-demolition technique to measure single-photon and few-photon states., Comment: 14 pages, 10 figures. Revtex 4.1, V2: Updated to published version

Casimir-type forces, such as those between two neutral conducting plates, or between a sphere, atom or molecule and a plate have been widely studied and are becoming of increasing significance, for example, in nanotechnology. A key challenge is to better understand, from a fundamental microscopic approach, why the Casimir force is in some circumstances attractive and in others repulsive. Here, we study the Casimir-Polder forces experienced by small quantum systems such as atoms or molecules in an optical cavity. In order to make the problem more tractable, we work in a 1+1 dimensional setting, we take into account only the ground state and first excited state of the atom and we model the electromagnetic field as a scalar field with Dirichlet or Neumann boundary conditions. This allows us to determine the conditions for the Casimir force to be attractive or repulsive for individual atoms, namely through the interplay of paramagnetic and diamagnetic vacuum effects. We also study the microscopic-macroscopic transition, finding that as the number of atoms in the cavity is increased, the atoms start to affect the Casimir force exerted on the cavity walls similarly to a dielectric medium., Comment: 15 pages, 10 figures. Revtex 4.1. V2 Content extended and updated to match published version

We introduce a method to compute particle detector transition probability in spacetime regions of general curved spacetimes provided that the curvature is not above a maximum threshold. In particular we use this method to compare the response of two detectors, one in a spherically symmetric gravitational field and the other one in Rindler spacetime to compare the Unruh and Hawking effects: We study the vacuum response of a detector freely falling through a stationary cavity in a Schwarzschild background as compared with the response of an equivalently accelerated detector traveling through an inertial cavity in the absence of curvature. We find that as we set the cavity in further radiuses from the black hole, the thermal radiation measured by the detector approaches the quantity recorded by the detector in Rindler background showing in which way and at what scales the equivalent principle is recovered in the Hawking-Unruh effect. I.e. when the Hawking effect in a Schwarzschild background becomes equivalent to the Unruh effect in Rindler spacetime., Comment: 7 pages, 5 figures. RevTex 4.1

We propose a technique to probe the quantum state of light in an optical cavity without significantly altering it. We minimize the interaction of the probe with the field by arranging a setting where the largest contribution to the transition probability is cancelled. We show that we obtain a very good resolution to measure photon population differences between two given Fock states by means of atomic interferometry., Comment: 12 pages, 5 figures. RevTex 4.1. Added appendix with further mathematical detail. Updated to match published version

We propose a protocol by which entanglement can be extracted repeatedly from a quantum field. In analogy with prior work on entanglement harvesting, we call this protocol entanglement farming. It consists of successively sending pairs of unentangled particles through an optical cavity. Using non-perturbative Gaussian methods, we show that in certain generic circumstances this protocol drives the cavity field towards a non-thermal metastable state. This state of the cavity is such that successive pairs of unentangled particles sent through the cavity will reliably emerge significantly entangled. We calculate thermodynamic aspects of the harvesting process, such as energies and entropies, and also the long-term behavior beyond the few-mode approximation. Significant for possible experimental realizations is the fact that this entangling fixed point state of the cavity is reached largely independently of the initial state in which the cavity was prepared. Our results suggest that reliable entanglement farming on the basis of such a fixed point state should be possible also in various other experimental settings, namely with the to-be-entangled particles replaced by arbitrary qudits and with the cavity replaced by a suitable reservoir system., Comment: V2: Added Journal Reference. Title modified to match published version. 16 pages, 8 figures. RevTex 4.1

We identify a signature of quantum gravitational effects that survives from the early universe to the current era: Fluctuations of quantum fields as seen by comoving observers are significantly influenced by the history of the early universe. In particular we show how the existence (or not) of a quantum bounce leaves a trace in the background quantum noise that is not damped and would be non-negligible even nowadays. Furthermore, we estimate an upper bound for the typical energy and length scales where quantum effects are relevant. We discuss how this signature might be observed and therefore used to build falsifiability tests of quantum gravity theories., Comment: Revtex4.1. 2 Figures. V2: Content extended and edited to match published version

We explore the effects of different boundary conditions and coupling schemes on the response of a particle detector undergoing uniform acceleration in optical cavities. We analyze the thermalization properties of the accelerated detector via non-perturbative calculations. We prove non-perturbatively that if the switching process is smooth enough, the detector thermalizes to the Unruh temperature regardless of the boundary conditions and the form of the coupling considered., Comment: 9 pages, 3 figures. RevTex4. v2: minor update to match published version

We consider quantum signalling between two-level quantum systems in a cavity, in the pertubative regime of the earliest possible arrival times of the signal. We present two main results: First we find that, perhaps surprisingly, the analogue of amplitude modulated signalling (Alice using her energy eigenstates |g>, |e>, as in the Fermi problem) is generally sub-optimal for communication. Namely, e.g., phase modulated signalling (Alice using, e.g., |+>,|e>-states) overcomes the quantum noise already at a lower order in perturbation theory. Second, we study the effect of mode truncations that are commonly used in cavity QED on the modelling of the communication between two-level atoms. We show that, on general grounds, namely for causality to be preserved, the UV cutoff must scale at least polynomially with the desired accuracy of the predictions., Comment: RevTex 4.1. 15 pages, 7 figures. V2: extended version with extra detail. Some minor additional changes to match published version

We study bipartite quantum discord as a manifestation of a multipartite entanglement structure in the tripartite purified system. In particular, we find that bipartite quantum discord necessarily manifests itself in the presence of both bipartite and tripartite entanglement in the purification. This allows one to understand the asymmetry of quantum discord (between D[A,B] and D[B,A]) in terms of entanglement monogamy. As instructive special cases, we study discord for qubits and Gaussian states in detail. As a result of this we shed new light on a counterintuitive property of Gaussian states: the presence of classical correlations necessarily requires the presence of quantum correlations. Finally, our results also shed new light on a protocol for remote activation of entanglement by a third party., Comment: 8 pages, 3 figures. Revtex 4.1. V3: Upgraded and updated to published version

We develop a general formalism for a non-perturbative treatment of harmonic-oscillator particle detectors in relativistic quantum field theory using continuous-variables techniques. By means of this we forgo perturbation theory altogether and reduce the complete dynamics to a readily solvable set of first-order, linear differential equations. The formalism applies unchanged to a wide variety of physical setups, including arbitrary detector trajectories, any number of detectors, arbitrary time-dependent quadratic couplings, arbitrary Gaussian initial states, and a variety of background spacetimes. As a first set of concrete results, we prove non-perturbatively--and without invoking Bogoliubov transformations--that an accelerated detector in a cavity evolves to a state that is very nearly thermal with a temperature proportional to its acceleration, allowing us to discuss the universality of the Unruh effect. Additionally we quantitatively analyze the problems of considering single-mode approximations in cavity field theory and show the emergence of causal behaviour when we include a sufficiently large number of field modes in the analysis. Finally, we analyze how the harmonic particle detector can harvest entanglement from the vacuum. We also study the effect of noise in time dependent problems introduced by suddenly switching on the interaction versus ramping it up slowly (adiabatic activation)., Comment: v2: Updated bibliography to add Arxiv reference of citation to unpublished work. v3: Added Journal reference and minor updates to match published version. 19 pages, 5 figures, revtex 4.1

We show that particle detectors, such as 2-level atoms, in non-inertial motion (or in gravitational fields) could be used to build quantum gates for the processing of quantum information. Concretely, we show that through suitably chosen non-inertial trajectories of the detectors the interaction Hamiltonian's time dependence can be modulated to yield arbitrary rotations in the Bloch sphere due to relativistic quantum effects., Comment: Revtex4.1, 3 Figures. v2 Added journal reference and updated to published version

We present a completely localized solution to the problem of entanglement degradation in non-inertial frames. A two mode squeezed state is considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated), and a model of localized projective detection is used to study the amount of entanglement that they are able to extract from the initial state. The Unruh vacuum noise plays only a minor role in the degradation process. The dominant source of degradation is a mode mismatch between the mode of the squeezed state Rob observes and the mode he is able to detect from his accelerated frame. Leakage of the initial mode through Rob's horizon places a limit on his ability to fully measure the state, leading to an inevitable degradation of entanglement that even in principle cannot be corrected by changing the hardware design of his detector., Comment: 5 pages, 3 figures

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 of the smeared UdW interaction from QED first principles, then we analyze the spectral response of spatially smeared UdW detectors, and discuss the kind of spatial profiles which are useful for the study of relevant cases., Comment: 7 pages, 3 figures

Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 meters. In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ${\sim} 10^{-20}$ meters, up to that of hundreds of kilometers. Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective, as quantum communication technologies such as quantum key distribution advance into Space towards large distances, some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable., Comment: 34 pages, 9 figures. Journal version, modified to respond to numerous suggestions

We show that quantum field correlations in non-inertial frames are not as persistent as previously thought. We perform a simple calculation showing that the geometric discord, a measure of quantum correlations, does decay to zero in the infinite acceleration limit. This result is seen to be a natural and expected consequence of considering correlations in an infinite dimensional system, and it sheds doubt on the existence of useable quantum correlations in this regime. We contrast our results with previous research showing that the acceleration-induced degradation of quantum discord was not strong enough to extinguish discord in the large acceleration limit., Comment: 9 pages, revtex4, 2 figures. V2 Added journal reference and updated to published version

We analyse the evolution of the entanglement of a non-trivial initial quantum field state (which, for simplicity, has been taken to be a bipartite state made out of vacuum and the first excited state) when it undergoes a gravitational collapse. We carry out this analysis by generalising the tools developed to study entanglement behaviour in stationary scenarios and making them suitable to deal with dynamical spacetimes. We also discuss what kind of problems can be tackled using the formalism spelled out here as well as single out future avenues of research., Comment: 9 pages, 2 figures. v2: Added Journal reference and small changes to match published version

We develop a general technique to analyse the quantum effects of acceleration on realistic spatially-localised electromagnetic field states entangled in the polarization degree of freedom. We show that for this setting, quantum entanglement may build up as the acceleration increases, providing a clear signature of the quantum effects of relativistic acceleration., Comment: 5 pages, 3 figures

We study communication between an inertial observer and one of two causally-disconnected counter accelerating observers. We will restrict the quantum channel considering inertial-to-accelerated bipartite classical and quantum communication over different sets of Unruh modes (single-rail or dual-rail encoding). We find that the coherent information (and therefore, the amount of entanglement that can be generated via state merging protocol) in this strongly restricted channel presents some interesting monogamy properties between the inertial and only one of the accelerated observers if we take a fixed choice of the Unruh mode used in the channel. The optimization of the controllable parameters is also studied and we find that they deviate from the values usually employed in the literature., Comment: 7 pages, 6 figures

We review recent literature on the connection between quantum entanglement and cosmology, with an emphasis on the context of expanding universes. We discuss recent theoretical results reporting on the production of entanglement in quantum fields due to the expansion of the underlying spacetime. We explore how these results are affected by the statistics of the field (bosonic or fermionic), the type of expansion (de Sitter or asymptotically stationary), and the coupling to spacetime curvature (conformal or minimal). We then consider the extraction of entanglement from a quantum field by coupling to local detectors and how this procedure can be used to distinguish curvature from heating by their entanglement signature. We review the role played by quantum fluctuations in the early universe in nucleating the formation of galaxies and other cosmic structures through their conversion into classical density anisotropies during and after inflation. We report on current literature attempting to account for this transition in a rigorous way and discuss the importance of entanglement and decoherence in this process. We conclude with some prospects for further theoretical and experimental research in this area. These include extensions of current theoretical efforts, possible future observational pursuits, and experimental analogues that emulate these cosmic effects in a laboratory setting., Comment: 23 pages, 2 figures. v2 Added journal reference and minor changes to match the published version

We propose a scheme to study the effect of motion on measurements of a quantum field carried out by a finite-size detector. We introduce a model of projective detection of a localised field mode in an arbitrary reference frame. We apply it to extract vacuum entanglement by a pair of counter-accelerating detectors and to estimate the Unruh temperature of a single accelerated detector. The introduced method allows us to directly relate the observed effects with the instantaneous proper acceleration of the detector., Comment: 5 pages, 2 figures. v2 Significant increase in the detail level regarding the motivation of the detector model

We propose a realistic circuit QED experiment to test the extraction of past-future vacuum entanglement to a pair of superconducting qubits. The qubit P interacts with the quantum field along an open transmission line for an interval T_on and then, after a time-lapse T_off, the qubit F starts interacting for a time T_on in a symmetric fashion. After that, past-future quantum correlations will have transferred to the qubits, even if the qubits do not coexist at the same time. We show that this experiment can be realized with current technology and discuss its utility as a possible implementation of a quantum memory., Comment: 5 pages, 2 figures. v2: version accepted to Physical Review Letters. Title changed by editors