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arXiv:1107.0750 · Physical Review A

Probing mechanical quantum coherence with an ultracold-atom meter

Nicola Lo Gullo, Thomas Busch, G. Massimo Palma, Mauro Paternostro

Published Dec 6, 2011• 4 citations
arXivHTMLPDF

Abstract

We propose a scheme to probe quantum coherence in the state of a nanocantilever based on its magnetic coupling (mediated by a magnetic tip) with a spinor Bose Einstein condensate (BEC). By mapping the BEC into a rotor, its coupling with the cantilever results in a gyroscopic motion whose properties depend on the state of the cantilever: the dynamics of one of the components of the rotor angular momentum turns out to be strictly related to the presence of quantum coherence in the state of the cantilever. We also suggest a detection scheme relying on Faraday rotation, which produces only a very small back-action on the BEC and is thus suitable for a continuous detection of the cantilever's dynamics.

DOI
10.1103/physreva.84.063815

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We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.
We propose a scheme to entangle two mechanical nanocantilevers through indirect interactions mediated by a gas of ultracold atoms. We envisage a system of nanocantilevers magnetically coupled to a Bose-Einstein condensate of atoms and focus on studying the dark states of the system. These dark states are entangled states of the two nanocantilevers, with no coupling to the atomic condensate. In the absence of dissipation, the degree of entanglement is found to oscillate with time, while if dissipation is included, the system is found to relax to a statistical mixture of dark states which remains time independent until the inevitable thermal dephasing destroys the nanocantilever coherence. This opens up the possibility of achieving long-lived entangled nanocantilever states.
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Abstract A concept of hybrid atom-optical quantum gyroscope based on ring-shaped Bose–Einstein condensate (BEC) of atoms is developed. Optical probe field grants the systems sensitivity to rotation and detects the condensate response to rotation via optical interferometry. Measurement of rotation angular velocity may ideally be fulfilled without loss of atoms, but inevitably leads to degradation of BEC spatial coherence. We construct a mathematical model of this crucial phenomenon. A quantum master equation for BEC state is derived and solved analytically in the slow decoherence limit.
We propose the possibility of a phonon laser by coupling a Bose–Einstein condensate to a nanomechanical cantilever with a magnetic tip. Due to the magnetic coupling, atomic spin flips induce cantilever motion, which can be used to produce a phonon laser. The system is described by the equivalent of the Jaynes–Cummings Hamiltonian. By controlling the number of atoms and the population inversion, one can obtain either a continuous wave or transient lasing. The two-body atom–atom interaction is also shown to coherently manipulate the lasing process. We also show that in the strong coupling limit, the same system can undergo a Dicke–Hepp–Lieb superradiant phase transition. Exotic phase diagrams can be obtained by tuning the two body atom–atom interaction.