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arXiv:1305.6840 · Physical Review A

Optomechanics assisted by a qubit: From dissipative state preparation to many-partite systems

Anika C. Pflanzer, Oriol Romero‐Isart, J. I. Cirac

Published Sep 4, 2013• 30 citations
arXivHTMLPDF

Abstract

We propose and analyze nonlinear optomechanical protocols that can be implemented by adding a single atom to an optomechanical cavity. In particular, we show how to engineer the environment in order to dissipatively prepare the mechanical oscillator in a superposition of Fock states with fidelity close to 1. Furthermore, we demonstrate that a single atom in a cavity with several mechanical oscillators can be exploited to realize nonlinear many-partite systems by stroboscopically driving the mechanical oscillators. This can be used to prepare nonlinear many-partite states by applying either coherent protocols or engineering dissipation. The analysis of the protocols is carried out using a perturbation theory for degenerate Liouvillians and numerical tools. Our results apply to other systems where a qubit is coupled to a mechanical oscillator via a bosonic mode, e.g., in cavity quantum electromechanics.

DOI
10.1103/physreva.88.033804

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We propose and analyze nonlinear optomechanical protocols that can be implemented by adding a single atom to an optomechanical cavity. In particular, we show how to engineer the environment in order to dissipatively prepare the mechanical oscillator in a superposition of Fock states with fidelity close to 1. Furthermore, we demonstrate that a single atom in a cavity with several mechanical oscillators can be exploited to realize nonlinear many-partite systems by stroboscopically driving the mechanical oscillators. This can be used to prepare nonlinear many-partite states by applying either coherent protocols or engineering dissipation. The analysis of the protocols is carried out using a perturbation theory for degenerate Liouvillians and numerical tools. Our results apply to other systems where a qubit is coupled to a mechanical oscillator via a bosonic mode, e.g., in cavity quantum electromechanics.
We propose a scheme that exploits the combined effects of nonlinear dynamics and dissipation to generate macroscopic quantum superpositions in massive optomechanical oscillators. The effective degenerate three-wave mixing interaction between the mechanical and optical cavity modes that results from quadratic optomechanical coupling, together with the cavity dissipation, can result in the existence of dark macroscopic superpositions. We show analytically and confirm numerically that various quantum superpositions can be achieved deterministically, depending on the initial state of the mechanics. The effects of mechanical damping are also studied in detail and quantified by the negativity of the Wigner function. The present scheme can be realized in various optomechanical systems with current technology.
In a nutshell, a cavity optomechanical system consists of a mechanical oscillator inside an optical cavity. Cavity optomechanics studies the interplay between the light-matter radiation-pressure interaction and the change in the cavity frequency induced by mechanical motion. By leveraging the tools of quantum optics and quantum measurement, cavity quantum optomechanics enables the engineering of nonclassical quantum states of bulk matter. In this thesis, I present protocols for engineering such nonclassical quantum states in Part II. First, I introduce a scheme to ‘grow’ a quantum kitten state of a mechanical oscillator into a macroscopic Schrödinger cat state using a series of nonlinear pulsed optomechanical interactions. Next, I detail our proposed schemes to generate and verify entanglement between two mechanical oscillators. Moving on from pulsed optomechanics, I describe the theory behind an experiment that achieved multi-phonon subtraction from a mechanical oscillator in a continuously driven Brillouin optomechanical system. In the final chapter of Part II, I provide a theoretical preview of an experiment that investigates the behaviour of the mechanical oscillator when no light is detected at the output. In Part III, I introduce a new framework for nonlinear cavity quantum optomechanics that incorporates the intrinsic nonlinearity of the radiation-pressure interaction, the nonlinearity from the cavity enhancement, and higher-order mechanical position terms in the expansion of the cavity frequency. I then propose a scheme for measuring mechanical position using general-dyne detection, applicable to pulsed and continuous measurements. This predicts a new regime of operation, the “stochastic Gaussian” regime. Finally, I discuss a protocol for deterministic mechanical squeezing that utilizes the cavity response.
We propose a scheme to prepare macroscopic quantum superpositions of motion in optomachanical nano- or micromechanical oscillators quadratically coupled to an intracavity field. The nonlinear optomechanical coupling leads to an effective degenerate three-wave mixing interaction between the mechanical and cavity modes. The quantum superpositions result from the combined effects of the interaction and cavity dissipation. We show analytically and confirm numerically that various deterministic quantum superpositions can be achieved, depending on initial mechanical state. The effect of mechanical damping is also studied in detail via the negativity of the Wigner function. The present scheme can be realized in various optomechanical systems with current technology.
Entanglement had played a crucial role in developing frontier technologies as a critical resource, for instance, in quantum teleportation and quantum sensing schemes. Notably, thanks to the ability to cool down the vibrational modes of mechanical oscillators to its quantum regime, entanglement between mechanical modes and the production of nonclassical mechanical states have emerged as central resources for quantum technological applications. Thus, proposing deterministic schemes to achieve those tasks is of paramount importance. While the dominant scheme for bipartite mechanical entanglement involves Gaussian optomechanical interactions (linearized regime) to generate two-mode squeezed vacuum states, entangling two-modes exploiting the bare non-Gaussian optomechanical interaction (nonlinear strong single-photon regime) remains less covered. This work proposes an on-demand scheme to engineer phononic non-Gaussian bipartite entanglement in the nonlinear regime by exploiting cavity dissipation. Interestingly, our protocol (operating in the resolved sideband and photon blockade regime) renders the possibility of achieving a high degree of steady-state entanglement. We further show that our deterministic scheme is robust in the presence of decoherence and temperature within state-of-the-art optomechanics, along with the required conditions to obtain non-Gaussianity of the achieved bipartite mechanical steady-state.
The ability to prepare a macroscopic mechanical resonator into a quantum superposition state is an outstanding goal of cavity optomechanics. Here, we propose a technique to generate cat states of motion using the intrinsic nonlinearity of a dispersive optomechanical interaction. By applying a bichromatic drive to an optomechanical cavity, our protocol enhances the inherent second-order processes of the system, inducing the requisite two-phonon dissipation. We show that this nonlinear sideband cooling technique can dissipatively engineer a mechanical resonator into a cat state, which we verify using the full Hamiltonian and an adiabatically reduced model. While the fidelity of the cat state is maximized in the single-photon, strong-coupling regime, we demonstrate that Wigner negativity persists even for weak coupling. Finally, we show that our cat state generation protocol is robust to significant thermal decoherence of the mechanical mode, indicating that such a procedure may be feasible for near-term experimental systems.
We put forward a deterministic dissipative protocol to prepare phonon Fock states in nonlinear quantum optomechanical devices. The system is composed of a mechanical mode interacting with an optical field via radiation pressure, whereas the light mode is laser driven in the resolved blue-sideband regime. To keep our results tractable, we switch to an interaction picture in a displaced basis, where the effective Hamiltonian exhibits the selective photon-phonon interaction explicitly. After proper parameter adjustment and similarly to cavity-cooling schemes, the quantum evolution allows steering of the mechanical degree of freedom to the desired Fock state by directing the optical excitations dynamically towards the target phonon state. The numerical results, including decoherence on both the mechanical and the optical degrees of freedom, prove to be quite robust in the good- and bad-cavity regimes, with fidelities exceeding 95%. Finally, characterization of the achieved nonclassicality, as well as the limitations and feasibility of our protocol under experimental parameters, is also discussed.