Quadratic Optomechanical Coupling Research Articles

The manipulation of photon blockade via Newtonian gravity

We theoretically investigate the model of a quadratically coupled optomechanical system with a Newtonian gravitational potential in the weak-driving regime, where the optical cavity is driven by an external laser. The steady state of the whole system is treated in the framework of a few-photon subspace. We find that the conventional single-photon blockade, nonstandard types of single-photon blockade, two-photon blockade, and photon-induced tunneling can be induced by gravity when the quadratic optomechanical coupling strength remains constant. Moreover, we find that gravitational potential energy can compensate for the lack of quadratic optomechanical coupling for observation photon blockade. In particular, the photon stream with super-Poissonian distribution can be converted into a sub-Poissonian, antibunching photon stream by changing the driving detuning when the gravitational potential energy is included. These results show that the gravity has potential for realizing the manipulation of photon blockade in a quadratically coupled optomechanical system.

Intracavity-squeezed Cooling in the via Quadratic Optomechanical Coupling with the Hybrid Optomechanical System

Intracavity-squeezed Cooling in the via Quadratic Optomechanical Coupling with the Hybrid Optomechanical System

Ultrasensitive displacement measurement with nonlinear optomechanical coupling and squeezed light injection

We propose an ultrasensitive displacement measurement scheme to overcome the standard quantum limit (SQL) in the unresolved sideband cavity optomechanical system with nonlinear optomechanical coupling and squeezed light injection. By introducing the optimized quantum correlation, which is enabled by suitable choices of the squeezing angle, squeezing level, power of the probe light, and measurement angle of homodyne detection, the off-resonant displacement sensitivity reaches 6 dB below the SQL in linear optomechanical coupling. In contrast, displacement sensitivities with a coherent probe plus variational readout and squeezed probe plus fixed measurement angle (phase quadrature) are 2.6 dB and 4.6 dB below the SQL, respectively. By combining linear and quadratic optomechanical coupling, we show that the displacement sensitivity can be further improved to 9.6 dB below the SQL. Our results have potential applications in gravitational-wave detectors, quantum metrology, and the search for dark matter.

Tunable optical response and fast (slow) light in optomechanical system with phonon pump

We theoretically investigate the tunable optical response of a weak probe field in a single phonon mechanical driven cavity optomechanical system where an oscillating membrane acts as a mechanical mode. This membrane is also coupled to the optical cavity mode through both the linear optomechanical coupling (LOC) and the quadratic optomechanical coupling (QOC) simultaneously. An external single phonon mechanical driving field present in our scheme gives an additional coherence effect as well as its relative phase and intensity can control significantly the absorption (amplification) profile of the output probe field. We have also shown that the phase dispersion and group delay of the probe field can be controlled flexibly through both types of optomechanical coupling strengths as well as the mean number of thermal phonons. Our results provide a flexible and generalised route to control the light propagation in such kinds of complex cavity optomechanical systems with coherent mechanical excitation.

Effects of quadratic coupling on optical response of a hybrid optomechanical cavity assisted by Kerr non-linear medium

We theoretically investigate the effect of non-linearity on the optical response of a hybrid optomechanical system. The optical cavity consists of a Kerr non-linear medium. We study how the presence of quadratic optomechanical coupling and Kerr nonlinearity in the conventional optomechanical system affects the system’s stability. It is shown that the presence of all the non-linearities in the system leads to seven real roots in the optical bistability. However, if any of the two non-linearities (quadratic optomechanical coupling or Kerr non-linearity) decreases, the roots in the optical bistability also decrease. Hence, quadratic optomechanical coupling and Kerr nonlinearity can be used as handles to control the optical bistability of the system. Therefore, we propose this system to be used as an all-optical switch in quantum information devices.

Optomechanical isolation with tunable center frequency

Optomechanical (OM) isolators have the ability to stop the optical field for one direction and to pass the field in the opposite direction. Thus they work as bandstop filter in one direction and bandpass filter in the opposite direction. The maximum isolation happens when the frequency of the field becomes equal to that of the mechanical membrane inside the isolator. This frequency, called the isolation (or center) frequency, however is restricted by the fact that the fundamental frequency of the membrane depends upon its physical parameters (such as mass and length), which are fixed during fabrication of the membrane. We propose a dynamical way of tuning this center frequency, by using a mechanical drive attached to a membrane with quadratic OM coupling in a membrane-in-the-middle setup. This provides a way for future applications where tunable filtering is required.

Quantum simulation of tunable and ultrastrong mixed-optomechanics.

We propose a reliable scheme to simulate tunable and ultrastrong mixed (first-order and quadratic optomechanical couplings coexisting) optomechanical interactions in a coupled two-mode bosonic system, in which the two modes are coupled by a cross-Kerr interaction and one of the two modes is driven through both the single- and two-excitation processes. We show that the mixed-optomechanical interactions can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. The strengths of both the first-order and quadratic optomechanical couplings can be controlled on demand, and hence first-order, quadratic, and mixed optomechanical models can be realized. In particular, the thermal noise of the driven mode can be suppressed totally by introducing a proper squeezed vacuum bath. We also study how to generate the superposition of coherent squeezed state and vacuum state based on the simulated interactions. The quantum coherence effect in the generated states is characterized by calculating the Wigner function in both the closed- and open-system cases. This work will pave the way to the observation and application of ultrastrong optomechanical effects in quantum simulators.

Force sensing in a dual-mode optomechanical system with linear-quadratic coupling and modulated photon hopping.

A weak force sensor scheme is presented in an optomechanical system, in which the two cavity modes couple to a mechanical mode with linear and quadratic coupling. Due to introducing time-dependent hopping, the linear and quadratic coupling terms coexist under the rotating-wave approximation in the interaction picture. Compared with the quantum non-demolition measurement (ignoring the quadratic optomechanical coupling), the current scheme can decrease the additional noise to a lower level. Our proposal provides a promising platform for improving the detection of a weak force.

Displacement sensing beyond the standard quantum limit with intensity-dependent optomechanical coupling

We study an optomechanical (OM) system with optical and mechanical modes interacting through a dispersive linear and quadratic optomechanical coupling (QOC) in an unresolved sideband limit. The presence of a QOC plays a crucial role in altering the effective OM interaction and the spring constant of the mechanical resonator. The choice of a positive QOC in the system increases the spring constant, inducing a `stiffer mode.' The existence of this stiffer mode leads to unconventional behavior in the total displacement noise consisting of imprecision, backaction, and thermal noises. We further show that unlike the conventional OM system wherein the optimal total displacement noise is limited by the imprecision and backaction noises, it is due to the competing imprecision and thermal noise, making it feasible to observe displacement sensing below the conventional standard quantum limit.

Nonreciprocal Mechanical Squeezing in a Spinning Optomechanical System

AbstractA scheme for nonreciprocal mechanical squeezing (NMS) based on the three‐mode optomechanical interaction is proposed. In this scheme, a mechanical mode couples to a spinning whispering‐gallery‐cavity (WGC) mode and to an optical mode. An external laser is coupled into and thus drives the WGC via a waveguide. Mechanical squeezing results from the joint effect of the mechanical intrinsic nonlinearity and the quadratic optomechanical coupling, which, in the presence of strong thermal noise, is still considerable, while the nonreciprocity originates from the optical Sagnac effect. There are two NMS areas in the parametric space, one works for the laser driving from the left of the waveguide and another, from the right. For a given spinning speed of the WGC, the squeezing values in these two areas are equal if the corresponding detunings of the WGC differ from each other by two‐times of the Sagnac–Fizeau shift. At the red‐detuning resonance, the analytical results for the mechanical squeezing and cooling are obtained. The NMS scheme is robust to the thermal noise of the mechanical environment.

Quadratic optomechanical coupling in an active-passive-cavity system

We investigate an active-passive-cavity system where a membrane is quadratically coupled to the passive cavity. When the passive cavity is strong coherently driven to enhance the optomechanical coupling, the optical field interacts with the mechanical oscillator through the two-phonon process. By calculating the eigenfrequencies of system in Keldysh framework, we show the significant splitting of exceptional point in the presence of the optomechanical coupling. We also calculate the transmission rate to show how this system responds to an additional weak probe field. We find the gain effect will induce the two-phonon process amplification window. However, the gain effect becomes weak when the photon-tunneling strength increases. Then the transmission rate of the probe field changes from amplification to absorption. These results have potential applications in quantum metrology, quantum information processing, and quantum optical devices.

Prospects of reinforcement learning for the simultaneous damping of many mechanical modes

We apply adaptive feedback for the partial refrigeration of a mechanical resonator, i.e. with the aim to simultaneously cool the classical thermal motion of more than one vibrational degree of freedom. The feedback is obtained from a neural network parametrized policy trained via a reinforcement learning strategy to choose the correct sequence of actions from a finite set in order to simultaneously reduce the energy of many modes of vibration. The actions are realized either as optical modulations of the spring constants in the so-called quadratic optomechanical coupling regime or as radiation pressure induced momentum kicks in the linear coupling regime. As a proof of principle we numerically illustrate efficient simultaneous cooling of four independent modes with an overall strong reduction of the total system temperature.

Photon-assisted entanglement and squeezing generation and decoherence suppression via a quadratic optomechanical coupling.

Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to an ancillary cavity field via a quadratic optomechanical coupling. We find that their performances can be significantly modulated via the photon of the ancillary cavity, which comes from photon-dependent spin-oscillator coupling and detuning. Specifically, a fully switchable spin-oscillator entanglement can be achieved, meanwhile a strong mechanical squeezing is also realized. Moreover, we study the environment-induced decoherence and dissipation, and find that they can be mitigated by increasing the number of photons. This work provides an effective way to manipulate entanglement and quantum squeezing and to suppress decoherence in the cavity quantum electrodynamics with a quadratic optomechanics.

Normal-mode splitting in a linear and quadratic optomechanical system with an ensemble of two-level atoms

We theoretically calculate normal-mode splitting (NMS) in a linear and quadratic optomechanical system (OMS) with an ensemble of two-level atoms, where the interaction between the mechanical membrane and the optical cavity includes linear optomechanical coupling and quadratic optomechanical coupling (QOC). In the presence of atomic ensemble, a negative QOC strength is instrumental for generating NMS, while the positive QOC restricts NMS, and eventually it disappears. Further, for the hybrid OMS assisted with the atomic ensemble, the displacement spectrum of the mechanical resonator displays three peaks, where the middle peak results from the effective coupling strength between the cavity field and the atomic ensemble. Here the negative QOC strength and the effective ensemble-field coupling can provide an efficient control of the amplitude and position of the three peaks.

Tunable transparency and amplification in a hybrid optomechanical system with quadratic coupling

We theoretically study the optical response of a hybrid optomechanical system with quadratic coupling, where an optomechanical cavity with a movable membrane in the middle is coupled to an auxiliary cavity with a tunable gain rate. We show that the optical transmission of the system can be controlled by a variety of parameters, including power of the control field, coupling strength between the two cavities, the gain rate of the auxiliary cavity, reflectivity of the membrane, and the temperature of the environment. In particular, tunable transparency and amplification can be realized by modifying the gain rate of the auxiliary cavity. Under the condition of two-phonon resonance, we find that (i) for the no-loss-gain cavity, a broad transparency window appears in the probe transmission due to the coupling between the two cavities; (ii) for the passive cavity, an extremely narrow transparency window occurs within a broad transmission window due to quadratic optomechanical coupling; (iii) for the active cavity, the probe field can be amplified in a wide frequency regime. Our proposal provides a new platform to control the propagation of light.

Exceptional Point Enhances Sensitivity of Optomechanical Mass Sensors

We propose an efficient optomechanical mass sensor operating at exceptional points (EPs), non-hermitian degeneracies where eigenvalues of a system and their corresponding eigenvectors simultaneously coalesce. The benchmark system consists of two optomechanical cavities (OMCs) that are mechanically coupled, where we engineer mechanical gain (loss) by driving the cavity with a blue (red) detuned laser. The system features EP at the gain and loss balance, where any perturbation induces a frequency splitting that scales as the square-root of the perturbation strength, resulting in a giant sensitivity factor enhancement compared to the conventional optomechanical sensors. For non-degenerated mechanical resonators, quadratic optomechanical coupling is used to tune the mismatch frequency in order to get closer to the EP, extending the efficiency of our sensing scheme to mismatched resonators. This work paves the way towards new levels of sensitivity for optomechanical sensors, which could find applications in many other fields including nanoparticles detection, precision measurement, and quantum metrology.

Ground-state cooling of mechanical oscillator via quadratic optomechanical coupling with two coupled optical cavities.

We present a scheme for the electromagnetically induced transparency (EIT)-like nonlinear ground-state cooling in a double-cavity optomechanical system in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator, an additional auxiliary cavity is coupled to the optomechanical cavity. The optimum cooling conditions is derived, based on which the heating process can be well suppressed and the mechanical resonator can be cooled with an optimal effect to near its ground state through EIT-like cooling mechanism even in unresolved sideband regime. It is demonstrated by numerical simulations that not only the average phonon number of steady state is lower than that of single-cavity optomechanical system, but also the cooling rate is greatly faster than that of the linear optomechanical coupling due to the two-phonon cooling process in the quadratic coupling. Also, the ground-state cooling is achievable even with a relatively weak quadratic coupling strengthby tunning the coupling between two cavities to reach the optimum cooling conditions, thus provides an solution for overcoming the limitations of weak quadratic coupling rate in experiments. The proposed approach provides a platform for quantum manipulation of macroscopic mechanical devices beyond the resolved sideband limit and linear coupling regime.

Generation of Optical and Mechanical Squeezing in the Linear‐and‐Quadratic Optomechanics

AbstractGeneration of strong stationary optical and mechanical squeezing is proposed for the linear‐and‐quadratic optomechanical system, where two cavity modes induce linear and quadratic optomechanical couplings, respectively. Through the linearization treatment, linearized coupling between cavity mode and mechanical mode and the mechanical parametric amplification process are achievable and controllable by independent driving lasers. Optical and mechanical squeezing are generated following different mechanisms. Optical squeezing works in the strong coupling regime, and mechanical amplification would push the system close to instability threshold, which could deeply improve ponderomotive squeezing even significantly beyond the 3 dB squeezing limit. Mechanical squeezing is generated based on the reservoir engineering method, where parametric amplification induces the squeezing transformation of mechanical mode; and linearized coupling, which operates in the red‐sideband and weak coupling limits, induces the ground‐state cooling of transformed mechanical mode. Finally, the original mechanical mode would be squeezed, which could also exceed 3 dB limit.

Enhancing quadratic optomechanical coupling via a nonlinear medium and lasers

We propose a scheme to significantly increase quadratic optomechanical couplings of optomechanical systems with the help of a nonlinear medium and two driving lasers. The nonlinear medium is driven by one laser and the optical cavity mode is driven by a strong laser. We derive an effective Hamiltonian using squeezing transformation and rotating wave approximation. The effective quadratic optomechanical coupling strength can be larger than the decay rate of the cavity mode by adjusting the two optical driving fields. The thermal noise of squeezed cavity mode can be suppressed totally with the help of a squeezed vacuum field. Then, a driving field is applied to the mechanical mode. We investigate the equal-time second order correlations and find there are photon, phonon, and photon-phonon blockades even the original single-photon quadratic coupling is much smaller than the decay rate of the optical mode. In addition, the sub-Poissonian window of the two-time second order correlations can be controlled by the mechanical driving field. Finally, we show the squeezing and entanglement of the model could be tuned by the driving fields of the nonlinear medium and mechanical mode.

Single-photon-induced phonon blockade in a hybrid spin-optomechanical system

We explore the photon-controlled phonon statistics in a hybrid spin-optomechanical system. Here the proposed phonon blockade is based on the nonlinearity of system induced by the strong spin-mechanical coupling. Our approach involves introducing an ancillary quadratic optomechanical coupling (i.e., the cavity field quadratically coupled to mechanical motion) and simultaneously considering the cavity field with a single photon. By injecting the auxiliary photons, one can not only enhance the spin-resonator interaction, but also realize fully switchable phonon blockade. This work offers an approach to manipulate phonon statistics with photons, which should inspire the engineering of new single-phonon quantum devices and have potential applications in the future hybrid photon-phonon quantum networks.