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arXiv:1003.0720 · Physical Review Letters

Entanglement between the Future and the Past in the Quantum Vacuum

S. Jay Olson, Timothy C. Ralph

Published Mar 17, 2011• 121 citations
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Abstract

We note that massless fields within the future and past light cone may be quantized as independent systems. The vacuum is shown to be a nonseparable state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. This leads to a notion of timelike entanglement. We describe an inertial detector which exhibits a thermal response to the vacuum when switched on at t=0, due to this property. The feasibility of detecting this effect is discussed, with natural experimental parameters appearing at the scale of 100 GHz.

DOI
10.1103/physrevlett.106.110404

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We note that massless fields within the future and past light cone may be quantized as independent systems. The vacuum is shown to be a nonseparable state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. This leads to a notion of timelike entanglement. We describe an inertial detector which exhibits a thermal response to the vacuum when switched on at t=0, due to this property. The feasibility of detecting this effect is discussed, with natural experimental parameters appearing at the scale of 100 GHz.
An intriguing property of the massless quantum vacuum state is that it contains entanglement between both spacelike and timelike separated regions of space-time. The implications of timelike entanglement and its connection to standard entanglement, however, are unexplored. Here we show that timelike entanglement can be extracted from the massless Minkowski vacuum and converted into standard entanglement ``at a given time'' 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 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.
The Unruh effect can not only arise out of the entanglement between modes of left and right Rindler wedges, but also between modes of future and past light cones. We explore the geometric phase resulting from this timelike entanglement between the future and past, showing that it can be captured in a simple Λ\LambdaΛ-system. This provides an alternative paradigm to the Unruh-deWitt detector. The Unruh effect has not been experimentally verified because the accelerations needed to excite a response from Unruh-deWitt detectors are prohibitively large. We demonstrate that a stationary but time-dependent Λ\LambdaΛ-system detects the timelike Unruh effect with current technology.
The Unruh effect can not only arise out of the entanglement between modes of left and right Rindler wedges, but also between modes of future and past light cones. We explore the geometric phase resulting from this timelike entanglement between the future and past, showing that it can be captured in a simple Λ system. This provides an alternative paradigm to the Unruh-deWitt detector. The Unruh effect has not been experimentally verified because the accelerations needed to excite a response from Unruh-deWitt detectors are prohibitively large. We demonstrate that a stationary but time-dependent Λ-system detects the timelike Unruh effect with current technology.
We demonstrate that the future and left Rindler wedges of Minkowski spacetime are entangled, leading to the Unruh effect. Similarly, the past and right Rindler wedges are also entangled. We propose a protocol to extract this entanglement using two two-state detectors located in the past and right Rindler wedges. By scaling the detector transition frequencies inversely with Minkowski time, entanglement from the quantum field is transferred to the detectors, suggesting they may support quantum teleportation via the vacuum. Our protocol can be implemented with current quantum systems, such as flux-tunable transmon qubits. This research provides new insights into the entanglement properties of spacetime and hints at practical applications for secure quantum information transfer using the vacuum state of a quantum field.
The Unruh effect predicts that an accelerating observer perceives the Minkowski vacuum as a thermal bath, yet direct detection remains experimentally inaccessible. Its timelike counterpart, arising from the entanglement of massless fields between the future and past light cones, offers a more feasible route but requires a detector whose transition frequency follows a specific conformal-time scaling. We propose and analyze a practical implementation of such a detector using superconducting fluxonium circuits, which naturally provide two quasi-degenerate ground states and a tunable excited state, forming an effective ΛΛΛ-system. By modulating the excited-state transition frequency in Minkowski time, the detector accumulates a geometric phase associated with the timelike Unruh effect. Open-system simulations predict ∼10%\sim 10\%∼10% shift in the ground-state population within 530530530 ns, representing a three-order-of-magnitude sensitivity enhancement over two-level Unruh-DeWitt detectors. These results establish a realistic quantum-circuit platform for experimentally probing the timelike Unruh effect and, more broadly, for testing fundamental nature of quantum fields using engineered quantum systems.
Abstract It is found that the Unruh effect can not only arise out of the entanglement between two sets of modes spanning the left and right Rindler wedges, but also between modes spanning the future and past light cones. Furthermore, an inertial Unruh–DeWitt detector along a spacetime trajectory in one of these cones may exhibit the same thermal response to the vacuum as that of an accelerated detector confined in the Rindler wedge. This feature thus could be an alternative candidate to verify the “Unruh effect”, termed as the timelike Unruh effect correspondingly. In this paper we propose to detect the timelike Unruh effect by using an impurity immersed in a Bose–Einstein condensate (BEC). The impurity acts as the detector which interacts with the density fluctuations in the condensate, working as an effective quantum field. Following the paradigm of the emerging field ofquantum thermometry, we combine quantum parameter estimation theory with the theory of open quantum systems to realize a nondemolition Unruh temperature measurement in the nanokelvin ( nK\textrm{nK}nK nK ) regime. Our results demonstrate that the timelike Unruh effect can be probed using a stationary two-level impurity with time-dependent energy gap immersed in a BEC within current technologies.