Revealing and concealing entanglement with noninertial motion

Marko Toroš, Sara Restuccia, Graham M. Gibson, Marion Cromb, Hendrik Ulbricht, Miles Padgett, and Daniele Faccio

Phys. Rev. A 101, 043837 – Published 27 April 2020

Abstract

Photon interference and bunching are widely studied quantum effects that have also been proposed for high-precision measurements. Here, we construct a theoretical description of photon interferometry on rotating platforms, specifically exploring the relation between noninertial motion, relativity, and quantum mechanics. On the basis of this, we then propose an experiment where photon entanglement can be revealed or concealed solely by controlling the rotational motion of an interferometer, thus providing a route towards studies at the boundary between quantum mechanics and relativity.

Received 14 November 2019
Revised 24 March 2020
Accepted 30 March 2020

DOI:https://doi.org/10.1103/PhysRevA.101.043837

Physics Subject Headings (PhySH)

Entanglement detection Entanglement manipulation Quantum entanglement Quantum foundations Quantum measurements Special relativity

Optical materials & elements

Group theory Optical techniques

Atomic, Molecular & OpticalQuantum Information, Science & TechnologyGravitation, Cosmology & AstrophysicsGeneral Physics

Authors & Affiliations

Marko Toroš ^1,*, Sara Restuccia², Graham M. Gibson², Marion Cromb ², Hendrik Ulbricht³, Miles Padgett², and Daniele Faccio^2,†

¹Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
²School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
³Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom

^*m.toros@ucl.ac.uk
^†daniele.faccio@glasgow.ac.uk

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Vol. 101, Iss. 4 — April 2020

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Images

Figure 1
Conceptual setup. (a) Description from the viewpoint of the corotating observer. The counter-rotating (corotating) quantities are shown on the left (right). The counter-rotating (corotating) Hamiltonians are different, while the light speed in the two directions is equal ( $c / n$ ). D1 (D2) indicate the detectors for the counter-rotating (corotating) direction, respectively. (b) Description from the inertial laboratory frame represented in a straight line. Here, both the Hamiltonian and the speed of light differ in the two directions, i.e., $v^{(-)} \neq v^{(+)}$ and $v^{(\pm)} \neq \frac{c}{n}$ . (b1) Only the light-drag effect is taken into account; $t_{i}^{(+)}, t_{i}^{(-)}$ denote how long it would take to reach the detectors assuming they would not have moved; the subscript $i$ stands for “initial.” (b2) Both the light-drag effect and the motion of detectors is taken into account. $t_{a}^{(+)}, t_{a}^{(-)}$ denote how long it takes to reach the detectors; the subscript $a$ stands for “actual.” $v = r Ω$ is the speed of the detectors as seen from the inertial laboratory reference frame.
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Figure 2
(a) Quantum Sagnac experiment [16]. The element $C$ denotes the circulator which allows only the paths 1 to 2 and 2 to 3. A photon enters through the path 1, is directed into path 2, and then interferes for the first time with the beam splitter. After evolving in counterprogating directions, the photon then interferes again at the beam splitter, after which it is detected. (b) Hong-Ou-Mandel experiment on a rotating platform [17]. Two identical photons counterpropagate before interfering at a beam splitter. One detects the arrival of the photons and extracts the coincidence probability $P^{(2)}$ . In both cases, the setups are placed on a rotating platform.
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Figure 3
Layout of proposed quantum Sagnac/Hong-Ou-Mandel interferometer on a rotating platform. Two entangled photons are emitted from the BBO crystal: Photon a (purple arrow) enters a Sagnac interferometer using the lower 50/50 beam splitter (BS) and exits towards the upper 50/50 BS where two-photon HOM interference occurs with photon b (green arrow) that circles around the setup (in order to maintain the same overall path length as photon a). Coincidence counts are measured between detectors PD1 and PD2 as a function of the rotation frequency $Ω$ .
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Figure 4
Coincidence plot as a function of the angular frequency $Ω = 2 π f$ . We have set the interferometer area $A = 22.7 m^{2}$ , $μ = 2.36 \times 10^{15} Hz$ , corresponding to a typical photon carrier wavelength of 800 nm. Two curves are shown for two different bandwidths, $σ = 1.47 \times 10^{13} Hz$ (blue solid curve) and $σ = 1.18 \times 10^{14} Hz$ (dashed red curve), corresponding to 5- and 40-nm bandwidths, respectively. The shaded region corresponding to $P^{(2)} > 0.5$ indicates the region where measurements imply photon entanglement.
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