Abstract
The effect of the Earth’s gravitational potential on a quantum wave function has only been observed for massive particles. In this paper we present a scheme to measure a gravitationally induced phase shift on a single photon traveling in a coherent superposition along different paths of an optical fiber interferometer. To create a measurable signal for the interaction between the static gravitational potential and the wave function of the photon, we propose a variant of a conventional Mach–Zehnder interferometer. We show that the predicted relative phase difference of 10−5 rad is measurable even in the presence of fiber noise, provided additional stabilization techniques are implemented for each arm of a large-scale fiber interferometer. Effects arising from the rotation of the Earth and the material properties of the fibers are analysed. We conclude that optical fiber interferometry is a feasible way to measure the gravitationally induced phase shift on a single-photon wave function, and thus provides a means to corroborate the equivalence of the energy of the photon and its effective gravitational mass.
Highlights
Interferometry has proven to be an effective tool for high-sensitivity measurements in physics
Optical fiber interferometry is a promising technique for table-top experiments aimed at measuring gravitationally induced phase shifts on a single photon wave function
We have presented a scheme for overcoming the static nature of the gravitational interaction by exploiting a modified Mach–Zehnder interferometer (MZI)
Summary
Interferometry has proven to be an effective tool for high-sensitivity measurements in physics. The recent groundbreaking detection of gravitational waves [1] relied on Michelson interferometers to measure ripples in the curvature of space–time predicted 100 years ago by the theory of General Relativity (GR). This achievement indicates that state-of-the-art technology enables the realization of interferometers capable of detecting gravitational effects even on quantum particles. We expect the visibility to start decreasing once the relative GR proper time difference between the arms approaches the photon coherence time (the precision of the clock) The observation of such a drop in visibility would constitute a genuine test of the interplay between GR and quantum mechanics. Commercially available fiber spools containing 100 km of fiber do not exceed 2 × 10−2 m3 of volume and 10 kg of weight which makes them suitable for implementations in the laboratory despite the long path lengths required
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