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arXiv:1408.3423 · New Journal of Physics

Entangling the motion of two optically trapped objects via time-modulated driving fields

Mehdi Abdi, Michael J. Hartmann

Published Jan 27, 2015• 39 citations
arXivHTMLPDF

Abstract

We study entanglement of the motional degrees of freedom of two tethered and optically trapped microdisks inside a single cavity. By properly choosing the position of the trapped objects in the optical cavity and driving proper modes of the cavity, it is possible to equip the system with linear and quadratic optomechanical couplings. We show that a parametric coupling between the fundamental vibrational modes of two tethered microdisks can be generated via a time-modulated input laser. For a proper choice of the modulation frequency, this mechanism can drive the motion of the microdisks into an inseparable state in the long time limit via a two-mode squeezing process. We numerically confirm the performance of our scheme for current technology and briefly discuss an experimental setup that can be used for detecting this entanglement by employing the quadratic coupling. We also comment on the perspectives for generating such entanglement between the oscillations of optically levitated nanospheres.

DOI
10.1088/1367-2630/17/1/013056

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We study entanglement of the motional degrees of freedom of two tethered and optically trapped microdisks inside a single cavity. By properly choosing the position of the trapped objects in the optical cavity and driving proper modes of the cavity, it is possible to equip the system with linear and quadratic optomechanical couplings. We show that a parametric coupling between the fundamental vibrational modes of two tethered microdisks can be generated via a time-modulated input laser. For a proper choice of the modulation frequency, this mechanism can drive the motion of the microdisks into an inseparable state in the long time limit via a two-mode squeezing process. We numerically confirm the performance of our scheme for current technology and briefly discuss an experimental setup that can be used for detecting this entanglement by employing the quadratic coupling. We also comment on the perspectives for generating such entanglement between the oscillations of optically levitated nanospheres.
Stationary entanglement between the motion of macroscopic objects and light is a long-standing goal of quantum optomechanics, with implications for both fundamental tests of quantum physics and emerging quantum technologies. We report the generation of quantum entanglement between the center-of-mass motion of a nanosphere levitated in an optical tweezer inside an optical cavity and the electromagnetic field. By heterodyne detection, we reconstruct the full set of optomechanical correlations and observe a violation of separability bounds between the mechanical motion and the quadratures of a propagating optical mode. This demonstrates the distribution of nonclassical correlations beyond the interaction region. The entanglement is generated at room temperature and remains robust over a broad range of parameters. Our results establish levitated optomechanical systems as a promising platform for continuous-variable quantum communication and for tests of macroscopic quantum physics.
An optomechanical cavity driven by a periodically amplitude-modulated laser can generate steady light-mechanical entanglement with time periodicity. Similar results can be alternatively obtained by pumping an especially tuned optical degenerate parametric amplifier (DPA) inside the cavity. While the two laser beams are simultaneously applied, the optomechanical entanglement can exhibit constructive and destructive interference patterns, depending on their cooperative phase, which further gives rise to beating in entanglement dynamics if the two modulation frequencies are slightly different, followed by a beating frequency-dependent dynamical behavior in the energy exchange between light and a mechanical oscillator. The optimal dynamical entanglement goes beyond what is attainable by the scenario with two superimposed cavity drivings, as a result of the specially DPA-modulated quantum dynamics. Moreover, we calculate correlation spectra between the cavity and mechanical modes, and we find correspondence between the light-oscillator entanglement and the correlation spectra under the cooperative effect. The cooperation-enhanced optomechanical entanglement is robust against the thermal temperature, and is potentially useful for continuous variable quantum information processing.
We discuss the generation of strong stationary mechanical squeezing and entanglement in the modulated two-and three-mode optomechanics. Following the reservoir engineering scheme, the beam-splitter and parametric optomechanical interactions can be simultaneously achieved through appropriately choosing the modulation frequency on mechanical motion, which is essential to strong squeezing and entanglement. In the two-mode modulated optomechanics, squeezing is tunable by the relative ratio of parametric and beam-splitter couplings, and also robust to thermal noise due to the simultaneously optically induced cooling process. In the three-mode modulated optomechanics, strong EPR-type entanglement is also attainable, which can surpass the 3dB limit of nondegenerate parametric interaction. However, the ideal entanglement is impossible since only one of mechanical Bogoliubov modes is cooled by the cavity mode, which also makes the entanglement fragile to the mechanical noise.
The dynamical behavior of the entanglement and the squeezing in the system of two ions trapped in a lossy optical cavity is discussed, in which the vibrational mode of the first ion is coupled to the cavity field via a linear-mixing interaction and the vibrational mode of the second ion is coupled to the cavity field via an effective parametric interaction, respectively. It is found that when the effective strength r1{r}_{1}r1​ of the coupling between the first ion and the cavity field is stronger than the strength r2{r}_{2}r2​ of the coupling between the second ion and the cavity field, the motional state of the two ions develops into a robust two-mode mixed Gaussian entangled state and the two-mode squeezing of phonons appears. But the entanglement between the cavity mode and the vibrational mode of the second ion can only happen periodically in a small time range. When r1<r2{r}_{1}<{r}_{2}r1​<r2​, only the entanglement between the two vibrational modes appears but the two-mode squeezing does not exist. And the entanglement between the cavity mode and the motional mode of the second ion can also take place in a small time range.
Quantum entanglement in macroscopic systems is not only essential for practical quantum information processing, but also valuable for the study of the boundary between quantum and the classical world. However, it is very challenging to achieve the steady remote entanglement between distant macroscopic systems. We consider two distant nanoparticles, both of which are optically trapped in two cavities. Based on the coherent scattering mechanism, we find that the ultrastrong optomechanical coupling between the cavity modes and the motion of the levitated nanoparticles could be achieved. The large and steady entanglement between the filtered output cavity modes and the motion of nanoparticles can be generated if the trapping laser is under the red sideband. Then through entanglement swapping, the steady motional entanglement between the distant nanoparticles can be realized. We numerically simulate and find that the two nanoparticles with 10 km distance can be entangled for the experimentally feasible parameters, even in room temperature environments. The generated continuous variable multipartite entanglement is the key to realizing the quantum enhanced sensor network and the sensitivity beyond the standard quantum limit.
We theoretically investigate the generation of steady-state entanglement in a levitated optomechanical system with a cascade three-level atomic medium and a dielectric nanosphere. There are two cavity modes, driven by two external laser beams with different frequencies, which are responsible for trapping and cooling the nanosphere. Atoms prepared in coherent superposition are injected into the cavity to manipulate the optical fields and the effective optomechanical coupling. We show that the entanglement between the nanosphere and the cavity modes can be enhanced by selecting properly the initial population of the lower atomic level. In particular, when the atoms are prepared at that level, the corresponding optomechanical entanglement increases with the increase of the atom-field coupling strength. We also investigate in detail the influence of the effective cavity field detunings, the atomic detunings, the driving power, and the nanosphere's radius and found that there exist optimal values of the effective cavity field detuning and the driving power that maximize the optomechanical entanglement. By selecting the system's parameters properly, we further demonstrate the generation of genuine tripartite entanglement between three degrees of freedom in the system. The findings here may help flexible control of the steady-state entanglement in hybrid optomechanical systems.