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Scientific Reports

Gravitational Field effects on the Decoherence Process and the Quantum Speed Limit

Sh. Dehdashti, Zakieh Avazzadeh, Z. Xu, Jian Qi Shen, Behrouz Mirza, H. Wang

Published Nov 2, 2017• 7 citations

Abstract

In this paper we use spinor transformations under local Lorentz transformations to investigate the curvature effect on the quantum-to-classical transition, described in terms of the decoherence process and of the quantum speed limit. We find that gravitational fields (introduced adopting the Schwarzschild and anti-de Sitter geometries) affect both the decoherence process and the quantum speed limit of a quantum particle with spin-1/2. In addition, as a tangible example, we study the effect of the Earth's gravitational field, characterized by the Rindler space-time, on the same particle. We find that the effect of the Earth's gravitational field on the decoherence process and quantum speed limit is very small, except when the mean speed of the quantum particle is comparable to the speed of light.

DOI: 10.1038/s41598-017-15114-0

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In this paper we use spinor transformations under local Lorentz transformations to investigate the curvature effect on the quantum-to-classical transition, described in terms of the decoherence process and of the quantum speed limit. We find that gravitational fields (introduced adopting the Schwarzschild and anti-de Sitter geometries) affect both the decoherence process and the quantum speed limit of a quantum particle with spin-1/2. In addition, as a tangible example, we study the effect of the Earth's gravitational field, characterized by the Rindler space-time, on the same particle. We find that the effect of the Earth's gravitational field on the decoherence process and quantum speed limit is very small, except when the mean speed of the quantum particle is comparable to the speed of light.

The phase shift due to gravitation and rotation in the quantum interference of two coherent beams is obtained relativistically and compared with the recent experiment of Colella, Overhauser, and Werner. A general expression relating the quantum phase shift to the transverse acceleration of a classical particle in the plane of interference for an arbitrary interaction with any external field is given. This can serve as a correspondence principle between quantum physics and classical physics. The phase shift due to the coupling of spin to curvature of space-time is deduced and written explicitly for the special case of a Schwarzschild field. The last result implies that a massless spinning particle can have at most two helicity states and its world line in a gravitational field is a null geodesic. Finally, new experiments are proposed to test the effect of rotation on quantum interference and to obtain direct evidence of the equivalence principle in quantum mechanics.

Using a model quantum clock, I evaluate an expression for the time of a non-relativistic quantum particle to transit a piecewise geodesic path in a background gravitational field with small spacetime curvature (gravity gradient), in the case that the apparatus is in free fall. This calculation complements and extends an earlier one (Davies 2004) in which the apparatus is fixed to the surface of the Earth. The result confirms that, for particle velocities not too low, the quantum and classical transit times coincide, in conformity with the principle of equivalence. I also calculate the quantum corrections to the transit time when the de Broglie wavelengths are long enough to probe the spacetime curvature. The results are compared with the calculation of Chaio and Speliotopoulos (2003), who propose an experiment to measure the foregoing effects.

Using a model quantum clock, I evaluate an expression for the time of a non-relativistic quantum particle to transit a piecewise geodesic path in a background gravitational field with small spacetime curvature (gravity gradient), in the case in which the apparatus is in free fall. This calculation complements and extends an earlier one (Davies 2004) in which the apparatus is fixed to the surface of the Earth. The result confirms that, for particle velocities not too low, the quantum and classical transit times coincide, in conformity with the principle of equivalence. I also calculate the quantum corrections to the transit time when the de Broglie wavelengths are long enough to probe the spacetime curvature. The results are compared with the calculation of Chiao and Speliotopoulos (2003), who propose an experiment to measure the foregoing effects.