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Entanglement Harvesting with Moving Mirrors in $(1+1)$ Dimensions

Wan Cong, Erickson Tjoa, Robert B. Mann

Published Oct 16, 2018• 0 citations
OpenAlex

Abstract

We study the phenomenon of entanglement extraction from the vacuum of a massless scalar field in $(1+1)$ dimensional spacetime in presence of a moving Dirichlet boundary condition, i.e. mirror spacetime, using two inertial Unruh-DeWitt detectors. We consider a variety of non-trivial trajectories for these accelerating mirrors and find (1) an entanglement inhibition phenomenon similar to that recently seen for black holes, as well as (2) trajectory-independent entanglement enhancement in some regimes. We show that the qualitative result obtained is the same for both linear and derivative couplings of the detector with the field.

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Entanglement Harvesting with Moving Mirrors in (1+1)(1+1)(1+1) Dimensions
We study the phenomenon of entanglement extraction from the vacuum of a massless scalar field in (1+1)(1+1)(1+1) dimensional spacetime in presence of a moving Dirichlet boundary condition, i.e. mirror spacetime, using two inertial Unruh-DeWitt detectors. We consider a variety of non-trivial trajectories for these accelerating mirrors and find (1) an entanglement inhibition phenomenon similar to that recently seen for black holes, as well as (2) trajectory-independent entanglement enhancement in some regimes. We show that the qualitative result obtained is the same for both linear and derivative couplings of the detector with the field.
Abstract We study the phenomenon of entanglement extraction from the vacuum of a massless scalar field in (1 + 1) dimensional spacetime in presence of a moving Dirichlet boundary condition, i.e. mirror spacetime, using two inertial Unruh-DeWitt detectors. We consider a variety of non-trivial trajectories for these accelerating mirrors and find (1) an entanglement inhibition phenomenon similar to that recently seen for black holes, as well as (2) trajectory-independent entanglement enhancement in some regimes. We show that the qualitative result obtained is the same for both linear and derivative couplings of the detector with the field.
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.
Abstract 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.
We explore entanglement harvesting using two Unruh-DeWitt (UDW) detectors linearly coupled to the scalar density of a massless spin-1/21/21/2 field in 1+11+11+1 Schwarzschild spacetime. We consider different vacua, including the Boulware, Hartle-Hawking-Israel (HHI), and Unruh vacua, and investigate various configurations of detector trajectories. We find that the transition rate of the static UDW detector exhibits the expected Planckian behavior in the HHI state, while the Unruh state leads to the Helmholtz free energy density of a fermionic thermal bath. We demonstrate that the near-horizon entanglement properties for static detectors in the HHI state have similar behavior to those in Minkowski vacua for uniformly accelerated detectors in Rindler spacetime. We further consider a different interaction Hamiltonian which breaks local Lorentz symmetry and find that the transition rate of the static detector still exhibits Planckian behavior in the HHI state, while in the Unruh state, it leads to the Helmholtz free energy density of a bosonic or fermionic thermal bath corresponding to the static or conformal 2-bein in interaction, respectively. We observe that the anti-Hawking effect enhances the entanglement between the two detectors while the gravitational redshift and Hawking radiation decrease it. In particular, due to the presence of the anti-Hawking effect, the mutual information and concurrence near the event horizon can be non-zero even for static detectors with static 2-bein, which is in contrast with the case of the scalar field. Conclusions are discussed.
A bstract The effect of black holes on entanglement harvesting has been of considerable interest over the past decade. Research involving stationary Unruh-DeWitt (UDW) detectors near a (2+1)-dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole has uncovered phenomena such as entanglement shadows, entanglement amplification through black hole rotation, and differences between bipartite and tripartite entanglement. For a (1+1)-dimensional Schwarzschild black hole, it has been shown that two infalling UDW detectors can harvest entanglement from the scalar quantum vacuum even when separated by an event horizon. In this paper, we calculate the mutual information between two UDW detectors coupled to a massless quantum scalar field, with the detectors starting at rest and falling radially into a non-rotating (2+1)-dimensional BTZ black hole. The trajectory of the detectors includes regions where both detectors are switched on outside of the horizon; where one detector is switched on inside of the horizon while the other switches on outside; and where both detectors switch on inside of the horizon. We investigate different black hole masses, detector energy gaps, widths and temporal separations of the detector switching functions, and field boundary conditions. We find that black holes — even the simplest kind having constant curvature — significantly affect the correlation properties of quantum fields in the vacuum state. These correlations, both outside and inside the horizon, can be mapped out by infalling detectors.
We carry out the first investigation of the entanglement and mutual information harvesting protocols for detectors freely falling into a black hole. Working in (1+11+11+1)-dimensional Schwarzschild black hole spacetime, we consider two pointlike Unruh-DeWitt detectors in different combinations of free-falling and static trajectories. Employing a generalization of relative velocity suitable for curved spacetimes, we find that the amount of correlations extracted from the black hole vacuum, at least outside the near-horizon regime, is largely kinematic in origin (i.e., it is mostly due to the relative velocities of the detectors). Second, correlations can be harvested purely from the black hole vacuum even when the detectors are causally disconnected by the event horizon. Finally, we show that the previously known `entanglement shadow' near the horizon is indeed absent for the case of two free-falling-detectors, since their relative gravitational redshift remains finite as the horizon is crossed, in accordance with the equivalence principle.