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arXiv:1204.2036

Entanglement of the Two Movable Mirrors in a Single Mode Cavity Field

Yong-Yi Huang

Published Apr 10, 2012• 0 citations
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Abstract

The entanglement of the two movable mirrors in a single mode cavity field is studied in an ideal situation without thermal noise. When gn/w <<1 where g is the coupling coefficient between the mirror and the field, w is the mirror' vibration frequency and n is photon number of the cavity field, we work out Wootters concurrence of the system initially with the field in Fock number state and the two mirrors in vacuum states, and find that the states of the mirrors are entangled into space spanned by |0>,|1> via radiation pressure, though the concurrence is very small.

DOI
10.48550/arxiv.1204.2036

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The entanglement of the two movable mirrors in a single mode cavity field is studied in an ideal situation without thermal noise. When gn/w <<1 where g is the coupling coefficient between the mirror and the field, w is the mirror' vibration frequency and n is photon number of the cavity field, we work out Wootters concurrence of the system initially with the field in Fock number state and the two mirrors in vacuum states, and find that the states of the mirrors are entangled into space spanned by |0>,|1> via radiation pressure, though the concurrence is very small.
We show that when an intense and quasi-monochromatic laser field is incident on a single vibrating and perfectly reflecting mirror in free space, radiation pressure realizes an effective coupling between a mirror vibrational mode and the first two optical sidebands of the incident field. The two reflected sidebands are in fact entangled by the optomechanical interaction and the resulting continuous variable entanglement proves to be robust against the thermal noise acting on the vibrational mode. If the duration of the incident laser pulse is appropriately chosen, the resulting state of the two sideband modes becomes an exact two-mode squeezed state.
The radiation pressure of two laser beams detuned from resonance in an optical cavity can create a stable optical trap for a mechanical oscillation mode of a movable cavity mirror. Here it is shown that such a configuration entangles the output light fields via interaction with a mirror that is suspended as a pendulum. The degree of entanglement is quantified spectrally using the logarithmic negativity, and related to the available optical restoring force. Entanglement survives in the experimentally accessible regime of gram-scale masses subject to thermal noise at room temperature.