Quantum nonlinear optics near optomechanical instabilities

Abstract

Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation pressure interaction. Here we show that it is not necessary to reach the single-photon strong-coupling regime in order to realize significant optomechanical nonlinearities. Instead, nonlinearities at the few quanta level can be achieved, even with weak-coupling, in a two-mode optomechanical system driven near instability. In this limit, we establish a new figure of merit for realizing strong nonlinearity which scales with the single-photon optomechanical coupling and the sideband resolution of the mechanical mode with respect to the cavity linewidth. We find that current devices based on optomechanical crystals, thought to be in the weak-coupling regime, can still achieve strong quantum nonlinearity; enabling deterministic interactions between single photons.PACS numbers: 42.50. Wk, 07.10.Cm, 42.50.Lc, 42.50.Dv Recent years have seen dramatic progress in realizing deterministic interactions between single photons, which has profound implications for future optical technologies [1][2][3][4]. The most striking success has been achieved with cavity quantum electrodynamics (cQED) [5][6][7][8][9][10][11][12], where photons inherent the saturation of a single two-level atom due to strong interactions between the atom and the cavity field. Alternative approaches have been explored based on slow-light-enhanced Kerr nonlinearites [13][14][15], single dye-molecules [16], strong photon interactions mediated by Rydberg atoms [17][18][19][20], enhanced nonlinearities in plasmonic systems [21,22] and atoms coupled to wave guides [23][24][25][26].Optomechanical systems, where light and mechanical motion are coupled by radiation pressure [27][28][29][30][31][32][33], are a promising approach to realizing strong photon interactions. Unfortunately no experiment has yet managed to reach the single-photon strong coupling regime. Recently it was noted that, in the weak coupling regime, there are still signatures of optomechanical nonlinearity [34][35][36]; however, strong coupling is required to achieve significant nonlinear quantum effects and deterministic photon interactions with optomechanics [37][38][39][40].In this Letter, we show it is not necessary to reach the quantum strong coupling regime in order to obtain large single-photon nonlinearities. Instead, in two-mode optomechanical systems with strong side-band resolution, the nonlinearity can be enhanced to the single-photon level by driving the system near an instability. In particular, as the strength of the driving field increases, the frequency of one of the optomechanical normal modes approaches zero and the associated harmonic oscillator length becomes large [41]. The increased quantum fluctuations associated with this mode result in an enhanced nonlinear interaction. We show that when the mechanical mode is sideband resolved with...

Antibunching in an optomechanical oscillator

“…To this end, several recent proposals have studied possible nonlinearities in optomechanical setups exploiting, for example, an enhanced optomechanical nonlinearity based on an optomechanical system employing a few optical modes * hseok@kongju.ac.kr [25][26][27][28], an intrinsic mechanical nonlinearity [29,30], and the coupling of mechanical systems to a qubit [31,32].…”

Theory of parametrically amplified electron-phonon superconductivity

“…(34). To keep the notation uncluttered, we will work out the results for a general Wigner-transformed propagators as a first step.…”

“…For example, the same framework can be employed to study the recently observed enhancement of electron-phonon coupling in periodically distorted graphene [33] and driven opto-mechanical cavities [34][35][36][37].…”

Sub-Poissonian phonon lasing in three-mode optomechanics

“…The enhanced nonlinearity has been discussed in the context of detectors for phonons or photons [26], quantum memory [28], and to improve [27] the parameters of mechanically induced photon antibunching [29,30]. In the context of the phonon laser transition the enhanced optomechanical instability with two optical modes has been anticipated as a possible complication for gravitational wave detectors [31], and has been studied experimentally [11][12][13][14][15]32] and theoretically [33][34][35][36][37][38] in the classical regime.…”

“…However, the requirements to see phonon antibunching scale unfavorably with the system parameters, so that sub-Poissonian phonon statistics has eluded experimental observation. In this Rapid Communication we propose to make use of the enhanced optomechanical nonlinearity [25][26][27] of a setup with two optical modes to overcome this difficulty and prepare phonon laser states featuring antibunching in steady state with state of the art optomechanical crystals.…”