By exploiting recent developments associated with coupled microcavities, we introduce the concept of PT -symmetric phonon laser with balanced gain and loss. This is accomplished by introducing gain to one of the microcavities such that it balances the passive loss of the other. In the vicinity of the gain-loss balance, a strong nonlinear relation emerges between the intracavity photon intensity and the input power. This then leads to a giant enhancement of both optical pressure and mechanical gain, resulting in a highly efficient phonon-lasing action. These results provide a promising approach for manipulating optomechanical systems through PT -symmetric concepts. Potential applications range from enhancing mechanical cooling to designing phonon-laser amplifiers.PACS numbers: 03.75.Pp, 03.70.+k Recent advances in materials science and nanofabrication have led to spectacular achievements in cooling classical mechanical objects into the subtle quantum regime (e.g., [1][2][3][4]). These results are having a profound impact on a wide range of research topics, from probing basic rules of classical-to-quantum transitions [4][5][6][7] to creating novel devices operating in the quantum regime, e.g. ultra-weak force sensors [8] or electric-to-optical wave transducers [9,10]. The emerging field of cavity optomechanics (COM) [1] is also experiencing rapid evolution that is driven by studies aimed at understanding the underlying physics and by the fabrication of novel structures and devices enabled by recent developments in nanotechnology.The basic COM system includes a single resonator, where a highly-efficient energy transfer between the mechanical mode and intracavity photons is enabled by detuning an input laser from the cavity resonance [1]. A new extension, closely related to the present study, is the photonic molecule or compound microresonators [11][12][13], where a tunable optical tunneling can be exploited to bypass the frequency detuning requirement [12]. More strikingly, in this architecture, an analogue of two-level optical laser is provided by phonon-mediated transitions between two optical supermodes [13]. This phonon laser [13,14] provides the core technology to integrate coherent phonon sources, detectors, and waveguides -allowing the study of nonlinear phononics [15] and the operation of functional phononic devices [16].In parallel to these works, intense interest has also emerged recently in PT -symmetric optics [17][18][19]. A variety of optical structures, whose behaviors can be described by parity-time (PT ) symmetric Hamiltonians, have been fabricated [17]. These exotic structures provide unconventional and previously-unattainable control of light [1,18,19,21]. In very recent work, by manipulating the gain (in one active or externally-pumped resonator) to loss (in the other, passive, one) ratio, Ref.[1] realized an optical compound structure with remarkable PT -symmetric features, e.g. field localization in the active resonator and accompanied enhancement of optical nonlinearity leading to nonreci...

We investigate the nonlinear interaction between a squeezed cavity mode and a mechanical mode in an optomechanical system (OMS) that allows us to selectively obtain either a radiation-pressure coupling or a parametric-amplification process. The squeezing of the cavity mode can enhance the interaction strength into the single-photon strong-coupling regime, even when the OMS is originally in the weak-coupling regime. Moreover, the noise of the squeezed mode can be suppressed completely by introducing a broadband-squeezed vacuum environment that is phase-matched with the parametric amplification that squeezes the cavity mode. This proposal offers an alternative approach to control OMS using a squeezed cavity mode, which should allow single-photon quantum processes to be implemented with currently available optomechanical technology. Potential applications range from engineering single-photon sources to nonclassical phonon states. Cavity optomechanics has progressed enormously in recent years [1], with achievements including cooling of mechanical modes to their quantum ground states [2,3], demonstration of optomechanically-induced transparency [4,5], coherent state transfer between cavity and mechanical modes [6][7][8][9], and the realization of squeezed light [10][11][12]. In these experiments, a strong linearized optomechanical coupling is obtained under the condition of strong optical driving. However, the intrinsic nonlinearity of the radiation-pressure coupling in these OMSs is negligible [13][14][15][16][17][18][19].To explore the intrinsic nonlinearity of the optomechanical interaction, much theoretical research has recently focused on the single-photon strong-coupling regime, where the single-photon optomechanicalcoupling strength g 0 exceeds the cavity decay rate κ. In this regime, several interesting single-photon quantum processes are predicted, for both the optical and the mechanical modes. For example: photon blockade, the preparation of the nonclassical states of the optical and mechanical modes, multi-phonon sidebands, and quantum state reconstruction of the mechanical oscillator [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. However, these effects have not yet been realized experimentally due to the intrinsically weak radiation-pressure coupling in current OMSs, i.e., g 0 κ. To achieve g 0 ∼ κ, it has been proposed to use the collective mechanical modes in transmissive scatter arrays [35,36]. The ratio g 0 /κ may also be increased in superconducting circuits using the Josephson effect, but such devices are limited to electromechanical systems [37][38][39]. Moreover, postselected weak measurements [40] and optical coalescence [41] could also be used to increase the effective linear and quadratic optomechanical interactions, respectively.Here we present a method to reach the single-photon strong-coupling regime in an OMS, which is originally in the weak-coupling regime. In contrast to normal optomechanics, we focus on the nonlinear interaction between a parametric-amplification-squeezed ...

Optomechanically-induced transparency (OMIT) and the associated slowing of light provide the basis for storing photons in nanoscale devices. Here we study OMIT in parity-time (PT)-symmetric microresonators with a tunable gain-to-loss ratio. This system features a sideband-reversed, non-amplifying transparency , i.e., an inverted-OMIT. When the gain-to-loss ratio is varied, the system exhibits a transition from a PT-symmetric phase to a broken-PT-symmetric phase. This PT-phase transition results in the reversal of the pump and gain dependence of the transmission rates. Moreover, we show that by tuning the pump power at a fixed gain-to-loss ratio, or the gain-to-loss ratio at a fixed pump power, one can switch from slow to fast light and vice versa. These findings provide new tools for controlling light propagation using nanofabricated phononic devices.