Theoretical and Numerical Study of Models of Entanglement for Neutrons
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Part III project submitted as part of the Experimental and Theoretical
Physics course of the Natural Sciences Tripos at the University of
Cambridge.

Abstract
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We propose and investigate a scheme for detecting gravitational waves
using the entanglement generated by the dynamics of a pair of neutrons
trapped in a harmonic well. We develop a model that combines the
effects due to plane gravitational wave solutions of the linearised
field equations in the weak-field limit of general relativity with the
time-dependent Schrödinger equation. Numerical simulations show that
entanglement amplifies the effect of high frequency gravitational
waves on the quantum state. In the proposed experiment, for realistic
wave amplitudes and frequencies, the final state is practically
indistinguishable from one unaffected by gravitational
radiation. However, the results also show that quantum entanglement
could be used in the future for high frequency gravitational wave
detection.

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