Quantum gravity witness via entanglement of masses: Casimir screening

Thomas W. van de Kamp, Ryan J. Marshman, Sougato Bose, and Anupam Mazumdar

Phys. Rev. A 102, 062807 – Published 4 December 2020

Abstract

A recently proposed experimental protocol for quantum gravity induced entanglement of masses (QGEM) requires in principle realizable, but still very ambitious, set of parameters in matter-wave interferometry. Motivated by easing the experimental realization, in this paper, we consider the parameter space allowed by a slightly modified experimental design, which mitigates the Casimir potential between two spherical neutral test masses by separating the two macroscopic interferometers by a thin conducting plate. Although this setup will reintroduce a Casimir potential between the conducting plate and the masses, there are several advantages of this design. First, the quantum gravity induced entanglement between the two superposed masses will have no Casimir background. Secondly, the matter-wave interferometry itself will be greatly facilitated by allowing both the mass $10^{- 16} - 10^{- 15} kg$ and the superposition size $Δ x \sim 20 μ m$ to be a one-two order of magnitude smaller than those proposed earlier, and thereby also two orders of magnitude smaller magnetic field gradient of $10^{4} {Tm}^{- 1}$ to create that superposition through the Stern-Gerlach effect. In this context, we will further investigate the collisional decoherences and decoherence due to vibrational modes of the conducting plate.

Received 25 June 2020
Accepted 27 October 2020

DOI:https://doi.org/10.1103/PhysRevA.102.062807

Physics Subject Headings (PhySH)

Atom interferometry Casimir effect & related phenomena Entanglement detection Gravitation Laboratory studies of gravity Quantum gravity Quantum sensing

Atomic, Molecular & OpticalGravitation, Cosmology & AstrophysicsQuantum Information, Science & TechnologyInterdisciplinary Physics

Authors & Affiliations

Thomas W. van de Kamp ¹, Ryan J. Marshman ², Sougato Bose², and Anupam Mazumdar³

¹University of Groningen P.O. Box 72, 9700 Groningen, The Netherlands
²Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, United Kingdom
³Van Swinderen Institute, University of Groningen, 9747 AG Groningen, The Netherlands

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Vol. 102, Iss. 6 — December 2020

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Images

Figure 1
The QGEM setup comprises two interferometers, systems 1 and 2 with the two spatially superposed particles and their trajectories. Their respective spin states have been shown. Note the three paths, Step 1, where the superposition is created by inhomogeneous magnetic field. Step 2, where the test masses and their superpositions are freely-falling after being released from the exact same height, and Step 3, where the trajectories are brought back for the measurement of spin correlations. The center of mass distance is $d$ and the superposition is denoted as $Δ x$ . The figure has been adopted from Ref. [1], where the details of the pulse sequence that enables the Stern-Gerlach interferometry is also described.
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Figure 2
Alternative setup for step 2 of the QGEM protocol, where we have a perfect conducting plate in between both test masses. The Casimir force not present between the test masses, allowing for smaller initial separations between the test masses, generating a higher entanglement phase for a given mass. However, we have to deal with the dynamic distance $s$ caused by the acceleration of the states toward the conducting plate. This displacement $s$ will be controlled principally by the free, dimensionless variable $N$ which sets the initial separation with $d - Δ x = N R$ .
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Figure 3
The plot shows the maximum entanglement phase generated during step 2 using the alternative setup of the QGEM protocol as a function of mass for different initial separations, characterized by the parameter $N$ . The lowest mass indicates the minimum mass for which the acceleration requirement Eq. (14) is barely met. The values of $\partial_{x} B, ρ, τ_{acc}, ε, W$ are labeled above.
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Figure 4
The plot shows the maximum entanglement phase generated during step 2 using the alternative setup of the QGEM protocol as a function of mass for different initial separations, characterized by the parameter $N$ . The lowest mass indicates the minimum mass for which the acceleration requirement given in Eq.(14) is barely met. The values of $\partial_{x} B, ρ, τ_{acc}, ε, W$ are labeled above.
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Figure 5
Decoherence of a single superposition as a function of the number density of the environmental gas for different external temperatures computed with Eq. (19) together with the maximum allowed decoherence factor (horizontal dashed line) for measuring entanglement for the parameters giving next to the graph. Note that the actual decoherence rate is $\exp [- \sum γ_{k} Δ t]$ .
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Figure 6
Deflection of the conducting plate, which is assumed to be made out of copper, for an range of displacement errors of the test masses to the right of Fig. 2 in terms of the radius of the test mass for the parameters given next to the graph.
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