Nonlinear Optomechanical Interaction Research Articles

Photon Blockade in Cavity Optomechanics Via Parametric Amplification

AbstractPhoton blockade is a quantum phenomenon in driven nonlinear systems. It can be observed in cavity optomechanical systems when nonlinear optomechanical interaction occurs at the single‐photon level. However, achieving photon blockade in experiments is challenging due to the small single‐photon optomechanical coupling strength. Here, photon blockade in an optomechanical system is investigated, where the cavity mode is either strongly or weakly squeezed. When the cavity mode is strongly squeezed, the coupling between squeezed mode and mechanical mode will be exponentially enhanced, leading to strong optical nonlinearity that is required for the realization of photon blockade. In contrast, when the cavity mode is weakly squeezed, the nonlinear optomechanical interaction is weak. It is shown that photon blockade can also be realized through the destructive interference of two paths for two‐photon excitation. Interestingly, it is found that a larger mechanical decay rate facilitates the implementation of the interference‐based photon blockade, and thermal noise effects can be significantly suppressed by the destructive interference.

Selective enhancement of difference sideband generation in a quadratically coupled optomechanical system with mechanical driving

We explore theoretically the generation and selective enhancement of difference sidebands in a quadratically coupled optomechanical system in which the membrane is driven resonantly by an additional coherent mechanical driving field. We show that the generation of frequency components at the difference sideband is directly related to the nonlinear optomechanical interactions under two-phonon resonance condition, while an additional weak coherent mechanical driving field acting on the membrane can considerably establish a selective enhancement of difference sideband generation (DSG). Our analytical solution with experimentally achievable parameters demonstrates that even if the input power of the control field is relatively low DSG can be induced and greatly enhanced when the matching conditions are satisfied. It also indicates that the efficiencies of upper difference sideband generation (UDSG) and lower difference sideband generation (LDSG) can be selectively increased about three orders by properly adjusting the frequency and amplitude of the weakly coherent mechanical driving field. Furthermore, we also show that the matching conditions of UDSG and LDSG are modified by the weakly coherent mechanical driving field. The present investigation may help to achieve the practical application of DSG relevant to nonlinear optics, chip-scale optical communications, and precision measurement.

High-precision realization for sensing charged particles based on optomechanically induced two-color second-order sidebands

We propose an effective scheme to sense charged particles by employing two-color second-order sidebands (TSSs) in a hybrid optomechanical system. This is realized in an optomechanical cavity with a double-oscillator structure, where the Coulomb force acting on two charged oscillators participates in nonlinear optomechanical interaction. With the aid of mechanical mode splitting induced by the Coulomb force, we report that the TSS spectrum can be generated and enhanced when the strong absorption in the transmission spectrum allows the TSS generated pathways to be readily accessed. More importantly, after seeking two correlations between the TSS spectra and the charged particles deposited on the oscillator, we design a dual-parameter sensor to measure the mass and the charge of the external particles simultaneously. Through evaluating the influence of the thermomechanical noise on the optomechanical sensing device, the resolution for detecting the mass and the charge of the measured particles can be identified as δm≈1.7×10−18g and δQ≈1.6×10−18C, respectively.

Simultaneous measurement for amplitude and frequency of time-harmonic force based on optomechanically induced nonlinearity

An accurate readout of the mechanical motion using optomechanical coupling is highly desired for on-chip sensing applications but it remains challenging due to the uncertainty caused by time-dependent parameters and noisy fluctuations. Here, we propose an efficient scheme to realize simultaneous measurement for both amplitude and frequency of the time-harmonic force (THF) in a hybrid optomechanical system via a nonlinear sum sideband effect. In this optomechanical system assisted by a degenerate parametric amplifier (DPA), the nonlinear optomechanical interaction between the external THF, optical, and mechanical modes is used to construct the frequency component of optical sum sidebands. Using experimentally achievable parameters, we find that the conversion efficiency of the sum sidebands has a significant enhancement when the nonlinear gain coefficient of DPA increases. In the scheme of the dual-parameter measurement, we also report that the amplitude of THF could be independently detected by observing the intensity variation of the lower sum sideband, while the frequency of THF could be separately read by monitoring the frequency of the prominent peak in this nonlinear spectrum. Benefitting from the optical cooling of a mechanical element, the theoretical results show that the minimum resolutions for detecting the amplitude and the frequency of THF are approximately 8.8×10−12N and 16Hz, respectively.

Enhancement of charge sensitivity by nonlinear optomechanics

Quantum estimation of electrical charge is investigated by using nonlinear optomechanical interaction. Due to the light-matter decoupling at one mechanical period, we need to consider only the cavity state, meaning that no direct access to the oscillator state is required. It is shown that the charge sensitivity can be greatly improved by enhancing optomechanical coupling. Further, we find that our theoretical result can surpass the sensitivity obtained from electrical measurements.

General formula for the natural width of optical parametric oscillator spectral lines

A new approach to the quantum analysis of the spectral linewidths of optical parametric oscillators (OPOs) is proposed. The approach is based on introducing a Hermitian frequency deviation operator. The spectral linewidths in the triply resonant OPO above-threshold regime have been calculated. It has been found that the width of the generated spectral line depends on the loss at all interacting frequencies, the photon number of frequency under study, and the threshold photon number of pump. The formula obtained for the spectral width is general; in particular cases, it yields the well-known results. The developed simple approach can be applied to the quantum analysis of the spectra of various oscillatory systems, for example, the multifrequency parametric and non-linear optomechanical interactions and lasers.

Critical quantum fluctuations and photon antibunching in optomechanical systems with large single-photon cooperativity

A pertinent question in cavity optomechanics is whether reaching the regime of large single-photon cooperativity, where the single-photon coupling rate exceeds the geometric mean of the cavity and mechanical decay rates, can enable any new phenomena. We show that in some multimode optomechanical systems, the single-photon cooperativity can indeed be a figure of merit. We first study a system with one cavity mode and two mechanical oscillators which combines the concepts of levitated optomechanics and coherent scattering with standard dispersive optomechanics. Later, we study a more complicated setup comprising three cavity modes which does not rely on levitated optomechanics and only features dispersive optomechanical interactions with direct cavity driving. These systems can effectively realize the degenerate or the nondegenerate parametric oscillator models known from quantum optics, but in the unusual finite-size regime for the fundamental mode(s) when the single-photon cooperativity is large. We show that the response of these systems to a coherent optical probe can be highly nonlinear in probe power even for average photon occupation numbers below unity. The nonlinear optomechanical interaction has the peculiar consequence that the probe drive will effectively amplitude-squeeze itself. For large single-photon cooperativity, this occurs for small occupation numbers, which enables observation of nonclassical antibunching of the transmitted probe photons due to a destructive interference effect. Finally, we show that as the probe power is increased even further, the system enters a critical regime characterized by intrinsically nonlinear dynamics and non-Gaussian states.

Exceptional points enhancing second-order sideband generation in a whispering-gallery-mode microresonator optomechanical system coupled with nanoparticles

We theoretically investigate the second-order sideband generation (SSG) in a whispering-gallery-mode (WGM) microresonator optomechanical system, in which the WGM microresonator couples with two nanoparticles. The nanoparticles can induce the optical coupling of the clockwise (CW) and the counterclockwise (CCW) WGM fields. And by continuously adjusting the relative phase angle between two nanoparticles, two eigenmodes of the optomechanical system coalesce and the so-called exceptional points (EPs) emerge periodically. It is shown that in the WGM microresonator optomechanical system coupled with nanoparticles in the second-order sideband can be generated due to the nonlinear optomechanical interactions, modulated periodically by the relative phase angle between two nanoparticles, and enhanced significantly at the EPs. Particularly, considering the frequency shift caused by the nanoparticles at the EPs, the generation and absorption of the second-order sideband can be flexibly realized. These results may have potential applications for high precision measurements and the manipulation of light propagation in optical cavities.

Generation and enhancement of sum sideband in a quadratically coupled optomechanical system with parametric interactions.

We investigate theoretically the generation and enhancement of sum sideband in a quadratically coupled optomechanical system with parametric interactions. It is shown that the generation of frequency components at the sum sideband stems from the nonlinear optomechanical interactions via two-phonon processes in the quadratically coupled optomechanical system, while an optical parametric amplifier (OPA) inside the system can considerably improve the sum sideband generation (SSG). The dependence of SSG on the system parameters, including the power of the control field, the frequency detuning of the probe fields and the nonlinear gain of OPA are analyzed in detail. Our analytic calculation indicates that the SSG can be obtained even under weak driven fields and greatly enhanced via meeting the matching conditions. The effect of SSG may have potential applications for achieving measurement of electric charge (or other weak forces) with higher precision and on-chip manipulation of light propagation.

Highly sensitive mass detection based on nonlinear sum-sideband in a dispersive optomechanical system.

We present a theoretical scheme to realize high-sensitive mass detection in a dispersive optomechanical system (DOMS) via nonlinear sum-sideband. In this scheme, DOMS assisted by a degenerate parametric amplifier (DPA) provides a well-established optomechanical circumstance, where nonlinear optomechanical interaction between cavity mode and mechanical mode of dielectric membrane is expected for creating the frequency components at optical sum-sideband. Such a scheme for mass detection mainly relies on monitoring the conversion efficiency of generated sum-sideband after the added mass is absorbed on the dielectric membrane. Using experimentally achievable parameters, we find that the conversion efficiency of sum-sideband and the sensitivity of mass detection can be simultaneously improved when the nonlinear gain of DPA increases. Furthermore, our results also demonstrate that this mass detection of DOMS can reach femtogram (fg) level resolution, when the method of mass detection relies on a direct relationship between maximum efficiency of sum-sideband and mass-change of membrane.

Polarization-selective control of nonlinear optomechanical interactions in subwavelength elliptical waveguides.

Photonic devices that exhibit all-optically reconfigurable polarization dependence with a large dynamic range would be highly attractive for active polarization control. Here, we report that strongly polarization-selective nonlinear optomechanical interactions emerge in subwavelength waveguides. By using full-vectorial finite element analysis, we find, at certain core ellipticities (or aspect ratios), that the forward simulated light scattering mediated by a specific acoustic resonance mode is eliminated for one polarization mode. Whereas, that for the other polarization mode is rather enhanced. This intriguing phenomenon can be explained by the interplay between the electrostrictive force and radiation pressure and turns out to be tailorable by the choice of waveguide materials.

Enhanced generation of charge-dependent second-order sideband and high-sensitivity charge sensors in a gain-cavity-assisted optomechanical system

We theoretically investigate the enhanced charge-dependent generation of the optical second-order sidebands (OSS) in a gain-cavity-assisted optomechanical (GCAOM) system coupled to a charged object. The hybrid optomechanical system is coherently driven by an external two-tone laser field which consists of a continuous-wave pump field and a pulsed probe field. Beyond the conventional linearized description of optomechanical interactions, the nonlinear optomechanical interactions are included in the Heisenberg-Langevin equations and are treated analytically by means of the perturbation method. It is shown that an assisted gain cavity can significantly enhance the OSS generation and can also lead to higher charge dependence of the output OSS spectrum than that achieved from a lossy cavity optomechanical system. Subsequently we discuss the application of such a GCAOM system as a family of high-sensitivity sensor for measuring the charges. Using experimentally achievable parameters, we identify the conditions under which the assisted gain cavity allows us to enhance the OSS generation and improve sensitivity of the sensor beyond what is achievable in a lossy cavity optomechanical system. The present investigation may provide a route toward modulating the nonlinear optical properties of the electro-optic hybrid system, as well as to guide the design of sensitive devices.

Enhanced nonlinear interaction effects in a four-mode optomechanical ring

With a perturbative treatment based on the Keldysh Green's function technique, we study the resonant enhancement of nonlinear interaction effects in a four-mode optomechanical ring. In such a system, we identify five distinct types of resonant scattering between unperturbed polariton modes, induced by the nonlinear optomechanical interaction. By computing the cavity density of states and optomechanical induced transparency signal, we find that the largest nonlinear effects are induced by a decay process involving the two phonon-like polaritons. In contrast to the conventional two-mode optomechanical system, our proposed system can exhibit prominent nonlinear features even in the regime when the single-photon coupling is much smaller than the cavity damping.

High-order sideband generation in a two-cavity optomechanical system with modulated photon-hopping interaction

The high-order sideband generation in a two-cavity optomechanical system is discussed, where photon hopping between the two cavity modes is modulated sinusoidally. We show that the high-order sideband generation can be induced originating from two processes: the parametric frequency conversion between the photon–photon interactions and the nonlinear optomechanical interactions between the photon–phonon interactions. Both the modulation amplitude and frequency of photon hopping between the two cavities have flexible manipulation on the high-order sideband generation at the low pump power level. With the modulation amplitude varying, we are able to obtain a robust comb-type spectral structure and a weak spectral structure, which can be amplified by tuning the modulation frequency. Selective generation of particular sidebands may also been achieved via transforming the modulation frequency when the parametric conversion process is dominant. Moreover, the dependence of the high-order sideband generation on other important parameters is also discussed in detail, including the cavities linewidthes, the frequency detuning of the two input laser fields and the intensity of control field. These results may provide further insights into the understanding of the high-order sideband generation, and find applications in optical frequency converters and optical frequency combs.

Enhanced photon-phonon cross-Kerr nonlinearity with two-photon driving.

We propose a scheme to significantly enhance the cross-Kerr (CK) nonlinearity between photons and phonons in a quadratically coupled optomechanical system (OMS) with two-photon driving. This CK nonlinear enhancement originates from the parametric-driving-induced squeezing and the underlying nonlinear optomechanical interaction. Moreover, the noise of the squeezed mode can be suppressed completely by introducing a squeezed vacuum reservoir. As a result of this dramatic nonlinear enhancement and the suppressed noise, we demonstrate the feasibility of the quantum nondemolition measurement of the phonon number in an originally weak coupled OMS. In addition, the photon-phonon blockade phenomenon is also investigated in this regime, which allows for performing manipulations between photons and phonons. This Letter offers a promising route towards the potential application for the OMS in quantum information processing and quantum networks.

Highly sensitive optical sensor for precision measurement of electrical charges based on optomechanically induced difference-sideband generation.

Difference-sideband generation in an optomechanical system coupled to a charged object is investigated beyond the conventional linearized description of optomechanical interactions. An exponential decay law for difference-sideband generation in the presence of electric interaction is identified which exhibits more sensitivity to electrical charges than the conventional linearized effects. Using the exact same parameters with previous work based on the linearized dynamics of the optomechanical interactions, we show that optomechanically induced difference-sideband generation may enable an all-optical sensor for precision measurement of electrical charges with higher precision and lower power. The proposed mechanism is especially suited for on-chip optomechanical devices, where nonlinear optomechanical interaction in the weak coupling regime is within current experimental reach.

Shelving-style QND phonon-number detection in quantum optomechanics

We propose a new method for optomechanical quantum non-demolition detection of phonon number, based on a ‘shelving’ style measurement. The scheme uses a two-mode optomechanical system where the frequency splitting of the two photonic modes is near-resonant with the mechanical frequency. The combination of a strong optical drive and the underlying nonlinear optomechanical interaction gives rise to spin-like dynamics which facilitate the measurement. This approach allows phonon number measurement to be accomplished parametrically faster than in other schemes which are restricted to weak driving.

Perfect photon absorption in hybrid atom-optomechanical system

We propose a scheme to investigate the perfect photon absorption in a hybrid atom-optomechanical system under and beyond the low-excitation limit. The perfect photon absorption is present in both cases and always accompanied by the optical bistability or multistability. We find that the coupling with the atomic ensemble provides the sufficient and necessary condition for the perfect photon absorption in such a system, but the optomechanical coupling is only a necessary condition for the bistability (in the low-excitation regime)/multistability (beyond the low-excitation limit). It is especially interesting that the optical nonlinearities induced by the nonlinear optomechanical interaction and nonlinear atomic excitation can be overlap-added, which results in the optical multistability and further causes an additional perfect photon absorption point.

Radiation pressure induced difference-sideband generation beyond linearized description

We investigate radiation-pressure induced generation of the frequency components at the difference-sideband in an optomechanical system, which beyond the conventional linearized description of optomechanical interactions between cavity fields and the mechanical oscillation. We analytically calculate amplitudes of these signals, and identify a simple square-root law for both the upper and lower difference-sideband generation which can describe the dependence of the intensities of these signals on the pump power. Further calculation shows that difference-sideband generation can be greatly enhanced via achieving the matching conditions. The effect of difference-sideband generation, which may have potential application for manipulation of light, is especially suited for on-chip optomechanical devices, where nonlinear optomechanical interaction in the weak coupling regime is within current experimental reach.

Cancelation of thermally induced frequency shifts in bimaterial cantilevers by nonlinear optomechanical interactions

Bimaterial cantilevers have recently been used in, for example, the calorimetric analysis with picowatt resolution in microscopic space based on state-of-the-art atomic force microscopes. However, thermally induced effects usually change physical properties of the cantilevers, such as the resonance frequency, which reduce the accuracy of the measurements. Here, we propose an approach to circumvent this problem that uses an optical microcavity formed between a metallic layer coated on the back of the cantilever and one coated at the end of an optical fiber irradiating the cantilever. In addition to increasing the sensitivity, the optical rigidity of this system diminishes the thermally induced frequency shift. For a coating thickness of several tens of nanometers, the input power is 5–10 μW. These values can be evaluated from parameters derived by directly irradiating the cantilever in the absence of the microcavity. The system has the potential of using the cantilever both as a thermometer without frequency shifting and as a sensor with nanometer-controlled accuracy.