47 lines
2.6 KiB
TeX
47 lines
2.6 KiB
TeX
\section{Conclusions}\label{sec:conclusions}
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We have proposed and investigated the feasibility of an experiment to
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detect gravitational waves using the entanglement of two neutrons
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trapped in a harmonic well. The quantum dynamics of the two particles
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lead to entanglement which is affected by the presence of
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gravitational radiation. We have shown that entanglement amplifies the
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effect of high frequency gravitational waves on the
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wavefunction. However, for realistic values of the wave amplitudes the
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effect is too small to be measured in a device with the dimensions of
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a typical multilayer.
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The effects of gravitational waves were combined with the quantum
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dynamics of the two neutrons in the weak-field limit, where the
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linearised field equation could be used. The effects of the
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oscillating metric were combined with the Schr\"{o}dinger equation by
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modifying the kinetic energy term. The potential due to the harmonic
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well and the inter-nucleon interaction remained unchanged.
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Numerical solutions to the modified time-dependent Schr\"{o}dinger
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equation were obtained with the explicit staggered method. It was
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shown that there are two different behaviour regimes. For low
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frequency waves there are no additional quantum effects and the
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difference in the final quantum state is due to the different
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classical particle trajectories. These waves were not investigated as
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there are better ways of detecting them. However, the high frequency
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regime couples with the particle interaction and the effect is
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strongly dependent on its strength and is maximised close to the value
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for which the particles maximally entangle. This is an interesting
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result as it is a possible mechanism for detecting high frequency
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gravitational waves. However, for any experimentally accessible values
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we would not observe anything as the neutron-neutron interaction is
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too strong for any entanglement to be generated via the system's
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dynamics alone.
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This experiment is not solely limited by the size of the signal. One
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other issue that would be difficult to resolve when building such an
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experiment is the isolation of the system from all environmental
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effects except for the gravitational waves. We have shown that the
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effect of radiation on the quantum state is extremely small and that
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entanglement is a key element, but with current technologies it is
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difficult to even maintain entangled resources for times longer than a
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few nanoseconds \cite{decoherence} unless we are working with trapped
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particles in ultra-high vacuum. Limiting undesirable decoherence is
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difficult with current technology and so any effects due to
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gravitational waves would be unobservable.
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