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Register a new userOperator approach to quantum optomechanics
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Added by
Blas Manuel Rodr\\'iguez-Lara
Publication date
2014
fields
Physics
and research's language is
English
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We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment and when a two-level atom is introduced in the cavity. By using operator techniques we show how these problems may be either solved or how the Hamiltonians involved, via sets of unitary transformations, may be taken to known Hamiltonians for which there exist approximate solutions.
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Studying mechanical resonators via radiation pressure offers a rich avenue for the exploration of quantum mechanical behavior in a macroscopic regime. However, quantum state preparation and especially quantum state reconstruction of mechanical oscillators remains a significant challenge. Here we propose a scheme to realize quantum state tomography, squeezing and state purification of a mechanical resonator using short optical pulses. The scheme presented allows observation of mechanical quantum features despite preparation from a thermal state and is shown to be experimentally feasible using optical microcavities. Our framework thus provides a promising means to explore the quantum nature of massive mechanical oscillators and can be applied to other systems such as trapped ions.
Wave mixing is an archetypical phenomenon in bosonic systems. In optomechanics, the bi-directional conversion between electromagnetic waves or photons at optical frequencies and elastic waves or phonons at radio frequencies is building on precisely this fundamental principle. Surface acoustic waves provide a versatile interconnect on a chip and, thus, enable the optomechanical control of remote systems. Here, we report on the coherent nonlinear three-wave mixing between the coherent fields of two radio frequency surface acoustic waves and optical laser photons via the dipole transition of a single quantum dot exciton. In the resolved sideband regime, we demonstrate fundamental acoustic analogues of sum and difference frequency generation between the two SAWs and employ phase matching to deterministically enhance or suppress individual sidebands. This bi-directional transfer between the acoustic and optical domains is described by theory which fully takes into account direct and virtual multi-phonon processes. Finally, we show that the precision of the wave mixing is limited by the frequency accuracy of modern radio frequency electronics.
The recently increasing explorations for cavity optomechanical coupling assisted by a single atom or an atomic ensemble have opened an experimentally accessible fashion to interface quantum optics and nano (micro) -mechanical systems. In this paper, we study in details such composite quantum dynamics of photon, phonon and atoms, specified by the triple coupling, which only exists in this triple hybrid system: The cavity QED system with a movable end mirror. We exactly diagonalize the Hamiltonian of the triple hybrid system under the parametric resonance condition. We find that, with the rotating-wave approximation, the hybrid system is modeled by a generalized spin-orbit coupling where the orbital angular momentum operator is defined through a Jordan-Schwinger realization with two bosonic modes, corresponding to the mirror oscillation and the single mode photon of the cavity. In the quasi-classical limit of very large angular momentum, this system will behave like a standard cavity-QED system described by the Jaynes-Cummings model as the angular momentum operators are transformed to bosonic operators of a single mode. We test this observation with an experimentally accessible system with the atom in the cavity with a moving mirror.
We study the simplest optomechanical system with a focus on the bistable regime. The covariance matrix formalism allows us to study both cooling and entanglement in a unified framework. We identify two key factors governing entanglement, namely the bistability parameter, i.e. the distance from the end of a stable branch in the bistable regime, and the effective detuning, and we describe the optimum regime where entanglement is greatest. We also show that in general entanglement is a non-monotonic function of optomechanical coupling. This is especially important in understanding the optomechanical entanglement of the second stable branch.
Interaction with a thermal environment decoheres the quantum state of a mechanical oscillator. When the interaction is sufficiently strong, such that more than one thermal phonon is introduced within a period of oscillation, quantum coherent oscillations are prevented. This is generally thought to preclude a wide range of quantum protocols. Here, we introduce a pulsed optomechanical protocol that allows ground state cooling, general linear quantum non-demolition measurements, optomechanical state swaps, and quantum state preparation and tomography without requiring quantum coherent oscillations. Finally we show how the protocol can break the usual thermal limit for sensing of impulse forces.
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