We note that massless fields within the future and past light cone may be quantized as independent systems. We show that the vacuum is an entangled state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. We describe a detector which exhibits a thermal response to the vacuum when switched on at t = 0. The feasibility of experimentally detecting this effect is discussed.PACS numbers: 03.70.+k, 03.65.Ud A basic and far-reaching property of the quantum vacuum is that it is an entangled state -a fact underlying an impressive number of theoretical insights and predictions [1]. In the case of flat Minkowski spacetime, this is typically shown in the context of the Unruh effect [2,3]. There, the vacuum state of the field can be written as an entangled state between two sets of modes, respectively spanning two space-time wedges, known as the Rindler wedges (see Fig. 1). A uniformly accelerated observer sees only one set of Rindler modes. The tracing out of the unobserved Rindler modes leads to the prediction that such an accelerated observer sees a thermalized vacuum. Having been predicted over 30 years ago, the Unruh effect remains unobserved.Here, our main result is to demonstrate that precisely the same entanglement exists between the fields within the future and past light cone (F and P, respectively) as between the left and right Rindler wedges (L and R), and that the Unruh effect can be mapped onto an equivalent vacuum thermal effect for an inertial observer constrained to interact with the field in only the future or the past. We will demonstrate this result for a scalar field in 2-d spacetime, though the result is general for massless fields. Dimensional analysis suggests that observation of this effect may be within range of current technology. This paper is organized as follows: We first note that massless fields in F and P may be quantized as independent systems, and then describe our coordinatization of spacetime, and the mode functions living in each quadrant. We then express the state of the Minkowski vacuum restricted to F and P in terms of these modes, and note entanglement. An Unruh-DeWitt detector is then described, which shows a thermal response to these modes in F (or P), and a related prediction of Martinetti and Rovelli [4] is interpreted in light of this result. The feasibility of an experimental observation of this effect is discussed, based on dimensional analysis. We then offer some conclusions.Past/future commutator and independent systems: The concept of entanglement between the left and right Rindler wedges rests on the fact that the fields within may be quantized as independent systems. This is expressed through the vanishing of the Pauli-Jordan function, i∆(x − y) = [φ(x),φ † (y)] for spacelike intervals. This general feature holds for both massive and massless fields.In the case of massless fields, however, the PauliJordan function ∆(x − y) vanishes for all but lightlike intervals, (x − y) 2 = 0 [5]. In particular, it vanishes for...

Recently, it has been shown that the massless quantum vacuum state contains entanglement between timelike separated regions of spacetime, in addition to the entanglement between the spacelike separated regions usually considered. Here, we show that timelike entanglement can be extracted from the Minkowski vacuum and converted into ordinary entanglement between two inertial, two-state detectors at the same spatial location -- one coupled to the field in the past and the other coupled to the field in the future. The procedure used here demonstrates a clear time correlation as a requirement for extraction, e.g. if the past detector was active at a quarter to 12:00, then the future detector must wait to become active at precisely a quarter past 12:00 in order to achieve entanglement.Comment: 8 pages, 3 figure

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We propose a new experimental testbed that uses ions in the collective ground state of a static trap for studying the analog of quantum-field effects in cosmological spacetimes, including the Gibbons-Hawking effect for a single detector in de Sitter spacetime, as well as the possibility of modeling inflationary structure formation and the entanglement signature of de Sitter spacetime. To date, proposals for using trapped ions in analog gravity experiments have simulated the effect of gravity on the field modes by directly manipulating the ions' motion. In contrast, by associating laboratory time with conformal time in the simulated universe, we can encode the full effect of curvature in the modulation of the laser used to couple the ions' vibrational motion and electronic states. This model simplifies the experimental requirements for modeling the analog of an expanding universe using trapped ions and enlarges the validity of the ion-trap analogy to a wide range of interesting cases.