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 propose and analyze a new approach based on parity-time (PT ) symmetric microcavities with balanced gain and loss to enhance the performance of cavity-assisted metrology. We identify the conditions under which PT -symmetric microcavities allow to improve sensitivity beyond what is achievable in loss-only systems. We discuss its application to the detection of mechanical motion, and show that the sensitivity is significantly enhanced in the vicinity of the transition point from unbroken-to broken-PT regimes. We believe that our results open a new direction for PT -symmetric physical systems and it may find use in ultra-high precision metrology and sensing.PACS numbers: 42.65. Yj, 06.30.Ft, 42.50.Wk Introduction.-The measurement of physical quantities with high precision is the subject of metrology. This has attracted much attention due to the increasing interest in, e.g., gravitational wave detection [1], sensing of nanostructures [2,3], as well as global positioning and navigation [4,5]. Developments in metrology over the past two decades have provided the necessary tools to determine the fundamental limits of measuring physical quantities and the resources required to achieve them [6,7].Among many different approaches, cavity-assisted metrology (CAM), where a high-quality (Q) factor cavity or resonator is coupled to a device under test (DUT), has emerged as a versatile and efficient experimental approach to achieve high-precision measurements. In CAM, the coupling between the resonator and the DUT manifests itself as a back-action-induced resonance frequency shift, resonance mode splitting, or a sideband in the output transmission spectrum [8]. Cavity-assisted metrology has been successfully applied for reading out the state of a qubit [9], measuring tiny mechanical motions [10,[12][13][14][15][16][17]42], and detecting nanoparticles with single-particle resolution [18,19].The readout signal (i.e., the transmission spectrum) of CAM is determined by the sum between the background spectrum of the cavity and the back-action spectrum of the DUT. The background spectrum is determined by the Q of the cavity whereas the back-action spectrum is determined by the strength of the cavity- * Electronic address: jing-zhang@mail.tsinghua.edu.cn † Electronic address: ozdemir@ese.wustl.edu DUT coupling (also dependent on Q) and the quantity to be measured. A broad background spectrum masks the back-action spectrum and decreases signal-to-noise ratio (SNR) [ Fig. 1(a)]. A higher coupling-strength between the cavity and the DUT and a higher Q of the cavity will be helpful to detect very weak signals and enable to resolve fine structures in the output spectra [ Fig. 1(b)]. A higher Q is also necessary to enhance the coupling strength between the cavity and the DUT. For example, for optomechanical resonators, the detection of tiny motions requires a strong optomechanical coupling, which is only possible with an high Q-factor. Therefore, CAM will benefit significantly from a narrower background spectrum which is fundamentally...
We investigate a hybrid electro-optomechanical system that allows us to realize controllable strong Kerr nonlinearities even in the weak-coupling regime. We show that when the controllable electromechanical subsystem is close to its quantum critical point, strong photon-photon interactions can be generated by adjusting the intensity (or frequency) of the microwave driving field. Nonlinear optical phenomena, such as the appearance of the photon blockade and the generation of nonclassical states (e.g., Schrödinger cat states), are demonstrated in the weak-coupling regime, making the observation of strong Kerr nonlinearities feasible with currently available optomechanical technology.
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