Robust entanglement of a micromechanical resonator with output optical fields

Genes, Claudiu; Mari, Andrea; Tombesi, Paolo; Vitali, David

doi:10.1103/physreva.78.032316

Cited by 331 publications

(350 citation statements)

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“…It would thus be especially interesting to study resonators coupled to other systems such as cavity optomechanical systems. Such nanomechanical systems have attracted considerable interest recently [14][15][16][17][18][19][20][21]. In this letter, we demonstrate the possibility of EIT in the context of cavity optomechanics.…”

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confidence: 98%

Electromagnetically induced transparency in mechanical effects of light

2010

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We consider the dynamical behavior of a nanomechanical mirror in a high-quality cavity under the action of a coupling laser and a probe laser. We demonstrate the existence of the analog of electromagnetically induced transparency (EIT) in the output field at the probe frequency. Our calculations show explicitly the origin of EIT-like dips as well as the characteristic changes in dispersion from anomalous to normal in the range where EIT dips occur. Remarkably the pump-probe response for the optomechanical system shares all the features of the Λ system as discovered by Harris and collaborators.PACS numbers: 42.50. Gy,42.50.Wk Since its original discovery in the context of atomic vapors, electromagnetically induced transparency (EIT) [1][2][3] has been at the center of many important developments in optical physics [4] and has led to many different applications, most notably in the context of slow light [5][6][7] and the production of giant nonlinear effects. EIT is helping the progress towards studying nonlinear optics at the single-photon level. EIT has been reported in many other systems [8]. More recently, EIT has been discovered in meta materials [9][10][11][12] where resonant structures can be fabricated to correspond to dark and bright modes. Resonators provide certain advantages [13] because by design we can manipulate EIT to produce desired transmission properties of a structure. It would thus be especially interesting to study resonators coupled to other systems such as cavity optomechanical systems. Such nanomechanical systems have attracted considerable interest recently [14][15][16][17][18][19][20][21]. In this letter, we demonstrate the possibility of EIT in the context of cavity optomechanics. Before discussing our model and results, we set the stage for EIT in cavity optomechanics. As in typical EIT experiments [1][2][3][4], for example, in the context of atomic vapors, we need to examine the pump-probe response of a nanomechanical oscillator of frequency ω m coupled to a high-quality cavity via radiation pressure effects [22,23] as schematically shown in Fig. 1. Thus, the cavity oscillator of frequency ω 0 and the nano-oscillator interact nonlinearly with each other. The system is driven by a strong pump field of frequency ω c . This is the coupling field. The probe field has frequency ω p and is much weaker than the pump field. The mechanical oscillator's damping is much smaller than that of the cavity oscillator. This is very important for considerations of EIT. The decay rate of the mechanical oscillator plays the same role as the decay rate of the ground-state coherence in EIT experiments. The analog of the two-photon resonance condition where EIT occurs would be ω c + ω m = ω p . We show how the absorptive and dispersive responses of the probe change by the coupling field and how EIT emerges. We present a clear physical origin of EIT in such a system.Let us denote the cavity annihilation (creation) operator by c (c † ) with the commutation relation [c, c † ] = 1.The momentum and position o...

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confidence: 98%

Electromagnetically induced transparency in mechanical effects of light

2010

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“…Firstly, we drive the cavity on the blue sideband (∆ = −Ω M ) and assume to work in the resolvedsideband regime (κ Ω M ) to enhance the down-conversion dynamics. Note that in this regime a stable steady state only exists for very weak optomechanical coupling [78], which poses a fundamental limit to the amount of entanglement that can be created in a continuous-wave scheme [5]. In contrast, a pulsed scheme does not suffer from these instability issues.…”

Section: Entanglement With Pulsed Lightmentioning

confidence: 99%

“…Entanglement of a mechanical oscillator with light has been predicted in a number of theoretical studies [5,55,56,57,58,59,60,61,62,63] and would be an intriguing demonstration of optomechanics in the quantum regime. These studies, as well as similar ones investigating entanglement among several mechanical oscillators [64,65,66,67,68,69,70,71,72], explore entanglement in the steady-state regime.…”

Section: Light Mirror Entanglement In Steady Statementioning

confidence: 99%

“…However, proper detection around the Stokes sideband (which carries the photons entangled with the mirror) in the sense described in 2.2 can extract optimal light-mirror entanglement [5]. We show this by choosing a central frequency of the detected mode Ω and its bandwidth τ −1 and computing the bipartite system negativity.…”

Section: Light Mirror Entanglement In Steady Statementioning

confidence: 99%

“…By means of spectral filters, the continuous wave field emerging from the cavity can be split in many traveling modes thus offering the option of producing and manipulating a multipartite system [5]. In particular we focus on detecting the first two motional sidebands at frequencies ω opt ± Ω M and show that they posses quantum correlations of the Einstein-Podolsky-Rosen type [6].…”

Section: Epr Correlated Beams Of Lightmentioning

confidence: 99%

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This chapter reports on theoretical protocols for generating nonclassical states of light and mechanics. Nonclassical states are understood as squeezed states, entangled states or states with negative Wigner function, and the nonclassicality can refer either to light, to mechanics, or to both, light and mechanics. In all protocols nonclassicallity arises from a strong optomechanical coupling. Some protocols rely in addition on homodyne detection or photon counting of light.

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We propose a protocol able to prepare two remote and initially uncorrelated microwave modes in an entangled stationary state, which is certifiable using only local optical homodyne measurements. The protocol is an extension of continuous variable entanglement swapping, and exploits two hybrid quadripartite opto-electro-mechanical systems in which a nanomechanical resonator acts as a quantum interface able to entangle optical and microwave fields. The proposed protocol allows to circumvent the problems associated with the fragility of microwave photons with respect to thermal noise and may represent a fundamental tool for the realization of quantum networks connecting distant solid-state and superconducting qubits, which are typically manipulated with microwave fields. The certifying measurements on the optical modes guarantee the success of entanglement swapping without the need of performing explicit measurements on the distant microwave fields.

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Robust entanglement of a micromechanical resonator with output optical fields

Cited by 331 publications

References 97 publications

Electromagnetically induced transparency in mechanical effects of light

Electromagnetically induced transparency in mechanical effects of light

Nonclassical States of Light and Mechanics

Entangling two distant non‐interacting microwave modes

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