Entanglement dynamics of photon pairs and quantum memories in the gravitational field of the earth

Roy Barzel1, Mustafa Gündoğan2,3, Markus Krutzik2,3,4, Dennis Rätzel1,2, and Claus Lämmerzahl1,5

1ZARM, University of Bremen, Am Fallturm 2, 28359 Bremen, Germany
2Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
3IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 2, 12489 Berlin, Germany
4Ferdinand-Braun-Institut (FBH), Gustav-Kirchoff-Str.4, 12489 Berlin, Germany
5Institute of Physics, Carl von Ossietzky University Oldenburg, Ammerländer Heerstr. 114-118, 26129 Oldenburg, Germany

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Abstract

We investigate the effect of entanglement dynamics due to gravity – the basis of a mechanism of universal decoherence – for photonic states and quantum memories in Mach-Zehnder and Hong-Ou-Mandel interferometry setups in the gravitational field of the earth. We show that chances are good to witness the effect with near-future technology in Hong-Ou-Mandel interferometry. This would represent an experimental test of theoretical modeling combining a multi-particle effect predicted by the quantum theory of light and an effect predicted by general relativity. Our article represents the first analysis of relativistic gravitational effects on space-based quantum memories which are expected to be an important ingredient for global quantum communication networks.

It has become one of the major problems of theoretical physics to understand the interplay between our most successful theories, quantum mechanics (QM) and general relativity (GR). A resolution of this problem can only be driven by experiments or observations at the interface of the two theories. In addition, the race in the development of space-based quantum technologies, where quantum resources are generated and probed locally or are exchanged over thousands of kilometers through the inhomogeneous gravitational field of Earth, fuels the need to understand the influence of general relativistic effects on quantum resources also from a practical point of view.

A particular example of an interesting fundamental effect at the interface of quantum mechanics and general relativity is the generation of entanglement between the internal energy structure of a quantum system and its external (motional) degrees of freedom (DOFs) due to gravitational time dilation or redshift. These entanglement dynamics (EDs) due gravity have been proposed to be witnessed in atom interferometry, with single photons in Mach-Zehnder (MZ) interference, photon pairs in Hong-Ou-Mandel (HOM) interference and phonons in Bose-Einstein condensates. For the case of massive quantum systems that are in superposition states of their center of mass degree of freedom, EDs due to gravity were found to induce decoherence, underlining their fundamental significance.

In this article, the case of EDs of photons and Quantum Memories (QMems) due to gravity in MZ and HOM interferometry setups is investigated. Furthermore, the article provides an experimental proposal and a feasibility study to witness the effect in HOM experiments whose necessary spatial extensions are dramatically smaller than those of proposed experiments that only employ photons. Such an experiment would represent an experimental test of theoretical modeling combining a multi-particle effect predicted by the quantum theory of light and an effect predicted by general relativity. On the applied side, the article represents the first analysis of relativistic gravitational effects on space-based quantum memories which are expected to be an important ingredient for global quantum communication networks.

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