Unruh-DeWitt Hamiltonian couples a scalar field with a two-level atom serving as a particle detector model. Two such detectors held by different observers following general trajectories can be used to study entanglement behavior in quantum field theory. Lacking other methods, the unitary evolution must be studied perturbatively which is considerably time-consuming even to a low perturbative order. Here we completely solve the problem and present a simple algorithm for a perturbative calculation based on a solution of a system of linear Diophantine equations. The algorithm runs polynomially with the perturbative order. This should be contrasted with the number of perturbative contributions of the scalar phi^4 theory that is known to grow factorially. Speaking of the phi^4 model, a welcome collateral result is obtained to mechanically (almost mindlessly) calculate the interacting scalar phi^n theory without resorting to Feynman diagrams. We demonstrate it on a typical textbook example of two interacting fields for n=3,4.
Unruh-DeWitt Hamiltonian couples a scalar field with a two-level atom serving as a particle detector model. Two such detectors held by different observers following general trajectories can be used to study entanglement behavior in quantum field theory. Lacking other methods, the unitary evolution must be studied perturbatively which is considerably time-consuming even to a low perturbative order. Here we completely solve the problem and present a simple algorithm for a perturbative calculation based on a solution of a system of linear Diophantine equations. The algorithm runs polynomially with the perturbative order. This should be contrasted with the number of perturbative contributions of the scalar phi^4 theory that is known to grow factorially. Speaking of the phi^4 model, a welcome collateral result is obtained to mechanically (almost mindlessly) calculate the interacting scalar phi^n theory without resorting to Feynman diagrams. We demonstrate it on a typical textbook example of two interacting fields for n=3,4.
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 space-time, 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 find that entanglement usable in quantum teleportation is extracted due to the special relativistic effect when the detectors are in a relative inertial motion, while it is not when they are comoving inertially and the switching of the detectors is executed adiabatically at infinite past and future.
Abstract 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 about 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 this time delay is not affected by the temperature. Remarkably, the maximal concurrence of the quantum system generated during evolution may increase with acceleration for any inter-detector separation while that for static ones in a thermal bath decreases monotonically with temperature, and this can be considered as an anti-Unruh effect in terms of the entanglement generated.
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 is performed adiabatically enough at the asymptotic past and future. We consider the cases where the detectors are accelerated parallelly, antiparallelly, and in differently orientated directions. We show that entanglement is extracted if they are accelerated antiparallelly and the ratios of the excitation energy to the magnitude of the acceleration coincide between the two detectors. On the other hand, we find that the detectors are not entangled when the detectors are accelerated parallelly or in orientated directions. We discuss these results from the viewpoint of the energy conservation associated with the timelike boost Killing vector fields tangent to the worldlines of the detectors.
A bstract We study two accelerating Unruh-DeWitt detectors coupled linearly or quadratically with a scalar field, by using an approach different from previous ones. We use Rindler frame, and integrate over the spacetime coordinates before over the momenta. In this way, the divergent problem previously encountered is avoided. We show that entanglement between the detectors can be created by coupling with the field, and is divergent only in the limit that the two detectors coincide in spacetime. For linear coupling, entanglement increases monotonically with the decrease of acceleration, as previously found, while for quadratic coupling, entanglement behaves non-monotonically, as noted for the first time.
The setup in which two quantum systems, Alice and Bob, communicate using \nbosonic field quanta can be viewed as a prototype for wireless quantum communication. \nIn this thesis we focus on the most basic case, where Alice and Bob \nare modeled as Unruh-DeWitt detectors, i.e., as two-level quantum \nsystems that interact locally through a scalar quantum field. Our aim is to study how information propagation and entanglement generation between the two detectors are impacted by both relativity and by the unavoidable noise that is due to the quantum fluctuations of the field. \n \nWe start by studying information propagation between the two detectors. Concretely, we construct and study the information-theoretic quantum channel, ξ, i.e., the completely positive trace preserving map between the input density matrix ϱ, in which Alice prepares her detector for the emission, and the output density matrix ϱ '=ξ(ϱ) of Bob's detector at a later time. We confirm that the classical as well as the quantum channel capacity are strictly zero to all orders in perturbation theory for spacelike separations. \n \nWe then study entanglement generation between the two detectors. Specifically, we discuss how two Unruh-DeWitt detectors can extract entanglement from the vacuum. We show that the detectors can naturally and instantaneously become entangled through a Casimir-Polder effect. We then analyze the impact of various additions to this setup, such as the presence of a weak gravitational field, the presence of boundary conditions in the field, the presence of a weak classical potential, etc.
Unruh-deWitt detectors have been utilized widely as probes for quantum particles, entanglement and spacetime curvature. Here, we extend the standard treatment of an Unruh-deWitt detector interacting with a massless, scalar field to include the detector traveling in a quantum superposition of classical trajectories. We derive perturbative expressions for the final state of the detector, and show that it depends on field correlation functions evaluated locally along the individual trajectories, as well as nonlocally between the superposed trajectories. By applying our general approach to a detector traveling in a superposition of two uniformly accelerated trajectories, including those with equal and differing proper accelerations, we discover novel interference effects in the emission and absorption spectra. These effects can be traced to causal relations between the superposed trajectories. Finally, we show that in general, such a detector does not thermalize even if the superposed paths would individually yield the same thermal state.