The observation of phonon blockade in a nanomechanical oscillator is clear evidence of its quantum nature. However, it is still a severe challenge to measure the strong phonon blockade in an optomechanical system with effective nonlinear coupling. In this paper, we propose a theoretical proposal for detecting the phonon blockade effect in a quadratically coupled optomechanical system by exploiting supervised machine learning. The detected optical signals are injected into the neural network as the input, while the output is the mechanical equal-time second-order correlation. Our results show our scheme performs superior performance on detecting phonon blockade. Specifically, it is efficient for nonlinear coupling systems; it performs a high precision for strong photon blockade; it is robust against the small disturbance of system parameters. Our work opens a promising way to build a phonon blockade detector.
The photon blockade effect is commonly exploited in the development of single-photon sources. While the photon blockade effect could be used to prepare high-fidelity single-photon states in idealized regimes, practical implementations in optomechanical systems suffer from an interplay of competing processes. Here we derive a control scheme that exploits destructive interference of Fock state amplitudes of more than one photon. The resulting preparation time for photon-blockaded quantum states is limited only by the optomechanical interaction strength and can thus be orders of magnitude shorter…
Photon blockade is an effective way to generate single photon, which is of great significance in quantum state preparation and quantum information processing. Here we investigate the statistical properties of photons in a double-cavity optomechanical system with nonreciprocal coupling, and explore the photon blockade in the weak and strong coupling regions respectively. To achieve the strong photon blockade, we give the optimal parameter relations under different blockade mechanisms. Moreover, we find that the photon blockades under their respective mechanisms exhibit completely different beha…
We propose to mechanically control photon blockades (PB) in an optomechanical system with driving oscillators. We show that by tuning the mechanical driving parameters we achieve selective single-photon blockade (1PB) or two-photon blockade (2PB) as well as simultaneous 1PB and 2PB at the same frequency. This mechanical engineering of 1PB and 2PB can be understood from the anharmonic energy levels due to the modulation of the mechanical driving. In contrast to the optomechanical systems without any mechanical driving featuring PB only for specific optical detuning, our results can be useful fo…
Quantum optomechanical system serves as an interface for coupling between photons and phonons due to mechanical oscillations. We used the Heisenberg-Langevin approach under Markovian white noise approximation to study a quadratically coupled optomechanical system which contains a thin dielectric membrane quadratically coupled to the cavity field. A decorrelation method is employed to solve for a larger number of coupled equations. Transient mean numbers of cavity photons and phonons that provide dynamical behaviour are computed for different coupling regime. We have also obtained the two-boson…
We propose a scheme to implement quantum controlled NOT gate and quantum phase gate in an optomechanical system based on phonon blockade. For appropriate choices of system parameters, fidelities of both the quantum gate operations are very close to unity in the absence of dissipation. Using recently achieved experimental values in a mechanical resonator coupled to a microwave cavity, we show that the quantum gate can be realized experimentally with very high fidelity.
It is well-known that some nonlinear phenomena such as strong photon blockade are hard to be observed in optomechanical system with current experimental technology. Here, we present a coherent feedback control strategy in which a linear cavity is coherently controlled by an optomechanical controller in a feedback manner. The coherent feedback loop transfers and enhances quantum nonlinearity from the controller to the controlled cavity, which makes it possible to observe strong nonlinear effects in either linear cavity or optomechanical cavity. More interestingly, we find that the strong photon…
We study photon blockade and anti-bunching in the cavity of an optomechanical system in which the mechanical resonator is coupled to a two-level system (TLS). In particular, we analyze the effects of the coupling strength (to the mechanical mode), transition frequency, and decay rate of TLS on the photon blockade. The statistical properties of the cavity field are affected by the TLS, because the TLS changes the energy-level structure of the optomechanical system via dressed states formed by the TLS and the mechanical resonator. We find that the photon blockade and tunneling can be significant…
We study the effects of parity-time(PT)-symmetry on the photon blockade and distinguish the different blockade mechanisms in a double-cavity optomechanical system. By studying the light statistics of the system, we find the completely different photon blockade behaviors when the PT-symmetry is broken or unbroken, which is related to the PT phase transition. Furthermore, an interesting phenomenon that the two cavities are blocked at the same time is found with the appropriate system parameters. Those statistical phenomenons are all analyzed in detail and demonstrated by analytically solving the…
We study the steady-state photon statistics of a quadratically coupled optomechanical cavity, which is weakly driven by a monochromatic laser field. We examine the photon blockade by evaluating the second-order correlation function of the cavity photons. By restricting the system within the zero-, one-, and two-photon subspace, we obtain an approximate analytical expression for the correlation function. We also numerically investigate the correlation function by solving the quantum master equation including both optical and mechanical dissipations. The results show that, in the deep-resolved-s…
We propose a scheme to enhance the single- and two-photon blockade effect significantly in a standard optomechanical system (OMS) via optical parametric amplification (OPA). The scheme does not rely on the strong single-photon optomechanical coupling and can eliminate the disadvantages of suppressing multi-photon excitation incompletely. Through analyzing the single-photon blockade (1PB) mechanism and optimizing the system parameters, we obtain a perfect 1PB with a high occupancy probability of single-photon excitation, which means that a high quality and efficient single-photon source can be …
We describe how electromagnetically induced transparency can arise in quadratically coupled optomechanical systems. Due to quadratic coupling the underlying optical process involves a two phonon process in optomechanical system and this two phonon process makes the mean amplitude, which plays the role of atomic coherence in traditional EIT, zero. We show how the fluctuation in displacement can play a role similar to atomic coherence and can lead to EIT-like effects in quadratically coupled optomechanical systems. We show how such effects can be studied using the existing optomechanical systems…
Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical displacement has been realized, presenting new possibilities for non-demolition measurements and mechanical squeezing. In this article we present a quantum mechanical study of a generic quadratic-coupling optomechanical Hamiltonian. First, neglecting dissipation, we provide analytical results for the dressed states, spectrum, phonon statistics and entanglement. …
Quantum control of phonons has being become a focus of attention for developing quantum technologies. Here, we propose a proposal to realize phonon blockade in a quadratically coupled optomechanical system, where a strong nonlinear interaction between photons and phonons can be induced by an external field coherently driving the cavity, and the effective coupling strength is tunable by adjusting the amplitude of the driving field. This optically induced nonlinearity is different from standard methods for realization of phonon blockade, where the nonlinearity is achieved by coupling the mechani…
We propose how to achieve quantum nonreciprocity via unconventional photon blockade (UPB) in a compound device consisting of an optical harmonic resonator and a spinning optomechanical resonator. We show that, even with an extremely weak single-photon nonlinearity, nonreciprocal UPB can emerge in this system, i.e., strong photon antibunching can emerge only by driving the device from one side, but not from the other side. This nonreciprocity results from the Fizeau drag, leading to different splitting of the resonance frequencies for the counter-circulating modes. Such nonreciprocal quantum UP…
We propose a quantum heat engine based on a quadratically coupled optomechanical system. The optical component of the system is driven periodically with an incoherent thermal drive, which induces periodic oscillations in the mechanical component. Under the action of the quadratic optomechanical interaction, the mechanical mode evolves from an initial thermal state to a thermal-squeezed steady state, as verified by calculating the Wigner functions. The dynamics of the system is identified as an effective four-stroke Otto cycle. We investigated the performance of the engine by evaluating the dis…
The hybrid microwave optomechanical-magnetic system has recently emerged as a promising candidate for coherent information processing because of the ultrastrong microwave photon-magnon coupling and the longlife of the magnon and phonon. As a quantum information processing device, the realization of a single excitation holds special meaning for the hybrid system. In this paper, we introduce a single two-level atom into the optomechanical-magnetic system and show that an unconventional blockade due to destructive interference cannot offer a blockade of both the photon and magnon. Meanwhile, unde…
Phonon nonlinearities play an important role in hybrid quantum networks and on-chip quantum devices. We investigate the phonon statistics of a mechanical oscillator in hybrid systems composed of an atom and one or two standard optomechanical cavities. An efficiently enhanced atom-phonon interaction can be derived via a tripartite atom-photon-phonon interaction, where the atom-photon coupling depends on the mechanical displacement without practically changing a cavity frequency. This novel mechanism of optomechanical interactions, as predicted recently by Cotrufo et al. [Phys. Rev. Lett. 118, 1…
We analyze the photon statistics of a weakly driven optomechanical system and discuss the effect of photon blockade under single photon strong coupling conditions. We present an intuitive interpretation of this effect in terms of displaced oscillator states and derive analytic expressions for the cavity excitation spectrum and the two photon correlation function $g^{(2)}(0)$. Our results predict the appearance of non-classical photon correlations in the combined strong coupling and sideband resolved regime, and provide a first detailed understanding of photon-photon interactions in strong coup…
We propose to manipulate the statistic properties of the photons transport nonreciprocally via quadratic optomechanical coupling. We present a scheme to generate quadratic optomechanical interactions in the normal optical modes of a whispering-gallery-mode (WGM) optomechanical system by eliminating the linear optomechanical couplings via anticrossing of different modes. By optically pumping the WGM optomechanical system in one direction, the effective quadratic optomechanical coupling in that direction will be enhanced significantly, and nonreciprocal photon blockade will be observed consequen…
Photon statistics in a weakly driven optomechanical photonic crystal cavity, with Kerr-type nonlinearity, is analyzed both analytically and numerically. Single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function $g^{(2)}(0)$. The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. The experimental feasibility with state-of-the-art device parameters is discussed. It is observed that photon blockade could be gener…
In contrast to recent studies [Rabl, Phys. Rev. Lett. 107, 063601 (2011); Nunnenkamp et al., Phys. Rev. Lett. 107, 063602 (2011)] on photon blockade that prevents subsequent photons from resonantly entering the cavity in optomechanical systems, we study the photon-induced tunneling that increases the probability of admitting subsequent photons in those systems. In particular, we analytically and numerically show how twoor three-photon tunneling can occur by avoiding single-photon blockade. Our study provides another way on photon control using a single mechanical resonator in optomechanical sy…
We show that in laser-driven coupled optomechanical systems, photon antibunching can occur under weak optomechanical coupling, contrarily to common expectation. This unconventional photon blockade originates from destructive quantum interference between different excitation pathways bringing from the ground to two-photon states. Using a quantum open-system approach, we study the antibunching as a function of driving field amplitude, temperature, and pure dephasing rate, and derive optimal values of the system parameters for its occurrence. These values are remarkably close to those characteriz…
In a hybrid optomechanical setup consisting of a two-level atom in a cavity with a pendular end-mirror, the interplay between the light field's radiation pressure on the mirror and the dipole interaction with the atom can lead to a blockade effect, which manifests itself in a suppression of Rabi oscillations in the atomic population. This effect is present when the system is in the single photon strong coupling regime and has an analogy in the photon blockade of optomechanics.
We propose a novel scheme for realizing single-photon blockade in a weakly driven hybrid cavity optomechanical system consisting of a nonlinear photonic crystal. Sub-Poissonian statistics is realized even when the single-photon optomechanical coupling strength is smaller than the decay rate of the optical mode. The scheme relaxes the requirement of strong coupling for photon blockade in optomechanical systems. It is shown that photon blockade could be generated at the telecommunication wavelength.
We study the photon-blockade effect in a loop-coupled optomechanical system consisting of two cavity modes and one mechanical mode. Here, the mechanical mode is optomechanically coupled to the two cavity modes, which are coupled with each other via a photon-hopping interaction. By treating the photon-hopping interaction as a perturbation, we obtain the analytical results of the eigenvalues and eigenstates of the system in the subspaces associated with zero, one, and two photons. We find a phenomenon of optical normal-mode-induced phonon-sideband splitting in the photon-blockade effect by analy…
The properties of open quantum system in quantum information science is now extensively investigated more generally by the research community as a fundamental issue for a variety of applications. Usually, the states of the open quantum system might be disturbed by the decoherence which will reduce the fidelity in the quantum information processing. So it is better to eliminate the influence of the environment. However, as part of the composite system, rational use of the environment system could be beneficial to quantum information processing. Here we theoretically studied the environment indu…
We study photon, phonon statistics and the cross-correlation between photons and phonons in a quadratically coupled optomechanical system. Photon blockade, phonon blockade and strongly anticorrelated photons and phonons can be observed in the same parameter regime with the effective nonlinear coupling between the optical and mechanical modes, enhanced by a strong optical driving field. Interestingly, an optimal value of the effective nonlinear coupling strength for the photon blockade is not within the strong nonlinear coupling regime. This abnormal phenomenon results from the destructive inte…
A scheme of single-photon multi-port router is put forward by coupling two optomechanical cavities with waveguides. It is shown that the coupled two optomechanical cavities can exhibit photon blockade effect, which is generated from interference of three mode interaction. A single-photon travel along the system is calculated. The results show that the single photon can be controlled in the multi-port system because of the radiation pressure, which should be useful for constructing quantum network.
We study a hybrid semiconductor-optomechanical system, which consists of a cavity with an oscillating mirror made by semiconducting materials or with a semiconducting membrane inside. The cavity photons and the excitons in the oscillating mirror or semiconducting membrane form into polaritons. And correspondingly, the optomechanical interaction between the cavity photons and the mirror or membrane is changed into the polariton-mechanical interaction. We theoretically study the eigenenergies and eigenfunctions of this tripartite hybrid system with the generalized rotating-wave approximation. We…
A major goal within the field of optomechanics is to achieve the single-photon strong coupling regime, wherein even a mechanical displacement as small as the zero-point uncertainty is enough to shift an optical cavity resonance by more than its linewidth. This goal is difficult, however, due to the small zero-point motion of conventional mechanical systems. Here, we show that an atom trapped in and coupled to a cavity constitutes an attractive platform for realizing this regime. In particular, while many experiments focus on achieving strong coupling between a photon and the atomic internal de…
We propose to synthesize arbitrary nonclassical motional states in optomechanical systems by using sideband excitations and photon blockade. We first demonstrate that the Hamiltonian of the optomechanical systems can be reduced, in the strong single-photon optomechanical coupling regime when the photon blockade occurs, to one describing the interaction between a driven two-level trapped ion and the vibrating modes, and then show a method to generate target states by using a series of classical pulses with desired frequencies, phases, and durations. We further analyze the effect of the photon l…
We propose a scheme to prepare macroscopic quantum superpositions of motion in optomachanical nano- or micromechanical oscillators quadratically coupled to an intracavity field. The nonlinear optomechanical coupling leads to an effective degenerate three-wave mixing interaction between the mechanical and cavity modes. The quantum superpositions result from the combined effects of the interaction and cavity dissipation. We show analytically and confirm numerically that various deterministic quantum superpositions can be achieved, depending on initial mechanical state. The effect of mechanical d…
We consider a quantum optomechanical scheme wherein an ordered two-dimensional array of laser-trapped atoms is used as a movable membrane. The extremely light mass of the atoms yields very strong optomechanical coupling, while their spatial order largely eliminates scattering losses. We show that this combination opens the way for quantum optomechanical nonlinearities, well within the ultimate single-photon strong-coupling regime. As an example, we analyze the possibility to observe optomechanically induced quantum effects such as photon blockade and time-delayed non-classical correlations. We…
We describe a novel type of blockade in a hybrid mode generated by linear coupling of photonic and phononic modes. We refer to this effect as hybrid photon-phonon blockade and show how it can be generated and detected in a driven nonlinear optomechanical superconducting system. Thus, we study boson-number correlations in the photon, phonon, and hybrid modes in linearly coupled microwave and mechanical resonators with a superconducting qubit inserted in one of them. We find such system parameters for which we observe eight types of different combinations of either blockade or tunnelling effects…
Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Herewe investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows t…
We investigate a dual membrane active-passive cavity where each mechanical membrane individually quadratically coupled to passive and active cavities via two-phonon process. Due to the fact that in the quadratically coupled optomechanical system mean-field approximation fails, hence to analyze the system completely, we switch to a more generalized out of equilibrium approach, namely Keldysh Green's functional approach. We calculate transmission rate using predetermined full retarded Green's function, and then numerically examine the effect of the various parameters on the transmission coeffici…
Based on photon-phonon nonlinear interaction, a scheme is proposed to realize a controllable multi-path photon-phonon converter at single-quantum level in a composed quadratically coupled optomechanical system. Considering the realization of the scheme, an associated mechanical oscillator is introduced to enhance the effective nonlinear effect. Thus, the single-photon state can be converted to the phonon state with high fidelity even under the current experimental condition that the single-photon coupling rate is much smaller than mechanical frequency ($g\llω_m$). The state transfer protocols …
In a hybrid micromaser system consisting of an optical cavity with a moving mirror connected to a low temperature thermal bath, we demonstrate, both analytically and numerically, that for certain interaction times between a random atomic flux and the optomechanical cavity, vacuum phonon trapping states are generated. Furthermore, under the approach of the master equation with independent phonon and photon thermal baths, we show that the trapping of the phonons and photons is achieved for the same interaction times. The results also indicate that by increasing the cavity-oscillator coupling one…
Optically coupled optomechanical oscillators has turned out to be a versatile experimental resource for exploring optomechanical synchronizations and correlations. In this work, we investigate the phenomena of quantum synchronization and quantum correlations in two optically coupled optomechanical oscillators with two different topologies. In one case the oscillators are coupled with optical photons in a reversible manner, termed as bidirectional coupling, while in the other photons are allowed to enter to the other oscillator but not allowed to exchanged back in the opposite direction, termed…
We investigate theoretically a hybrid system consisting of a Bose-Einstein condensate (BEC) trapped inside a laser driven membrane-in-the-middle optomechanical cavity assisted with squeezed vacuum injection whose moving membrane interacts both linearly and quadratically with the radiation pressure of the cavity. It is shown that such a hybrid system is very suitable for generating strong quadrature squeezing in the mechanical mode of the membrane and the Bogoliubov mode of the BEC in the unresolved sideband regime. More interestingly, by choosing a suitable sign for the quadratic optomechanica…
We investigate a hybrid electro-optomechanical system that allows us to obtain controllable strong Kerr nonlinearities 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 predicted in the weak-coupling regime, which is feasible for most curre…
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 h…
Nonlinear interactions in optomechanical systems play a crucial role in many emerging number of interesting studies and phenomena such as existence of optomechanical chaos introduced by F. Monifi et al. [Nature Photonics 10, 399405 (2016)] and optomechanical symmetry breaking proposed by Zhong-Peng Liu et al. [Phys. Rev. Lett.117, 110802 (2016)]. In this article we have theoretically examined quadratically coupled optomechanical system containing two atomic levels. We have first studied the solution of various modes of the system at steady state and later we have observed the variation of Tran…
We theoretically analyze antibunching of the phonon field in an optomechanical oscillator employ- ing the membrane-in-the-middle geometry. More specifically, a single-mode mechanical oscillator is quadratically coupled to a single-mode cavity field in the regime in which the cavity dissipation is a dominant source of damping, and adiabatic elimination of the cavity field leads to an effective cubic nonlinearity for the mechanics. We show analytically in the weak coupling regime that the mechan- ics displays a chaotic phonon field for small optomechanical cooperativity, whereas an antibunched s…
We analyze the photon correlations in an optomechanical system containing two nonlinear optical modes and one mechanical mode which are coupled via a three-mode mixing. Under a weak driving condition, we determine the optimal conditions for photon antibunching in the weak Kerr-nonlinear regime and we find that the analytical calculations are consistent with the numerical results. The photon blockade effect is attributed to destructive quantum interference in the two-photon excitation pathways created as a result of the three-mode interaction.
We propose a reliable scheme to realize a generalized ultrastrong optomechanical coupling in a two-mode cross-Kerr-type coupled system, where one of the bosonic modes is strongly driven. The effective optomechanical interaction takes the form of a product of the photon number operator of one mode and the quadrature operator of the other mode. The coupling strength and quadrature phase are both tunable via the driving field. The coupling strength can be strongly enhanced to reach the ultrastrong-coupling regime, where the few-photon optomechanical effects such as photon blockade and macroscopic…
Effects of Quadratic Optomechanical Coupling on Bipartite Entanglements, Mechanical Ground-State Cooling and Squeezing in an Electro-Optomechanical System
We propose a scheme for the generation of a robust stationary squeezed state of a mechanical resonator in a quadratically coupled optomechanical system, driven by a pulsed laser. The intracavity photon number presents periodic intense peaks suddenly stiffening the effective harmonic potential felt by the mechanical resonator. These "optical spring kicks" tend to squeeze the resonator position, and due to the interplay with fluctuation-dissipation processes one can generate a stationary state with more than 13 dB of squeezing even starting from moderately "pre-cooled" initial thermal states.
We implement nonlinear anharmonic interaction in the coupled van der Pol oscillators to investigate the quantum synchronization behaviour of the systems. We study the quantum synchronization in two oscillator models, coupled quantum van der Pol oscillators and anharmonic self-oscillators. We demonstrate that the considered systems exhibit a high-order synchronization through coupling in both classical and quantum domains. We show that due to the anharmonicity of the nonlinear interaction between the oscillators the system exhibits phonon blockade in the phase locking regime which is a pure non…
Realizing quantum mechanical behavior in micro- and nanomechanical resonators has attracted continuous research effort. One of the ways for observing quantum nature of mechanical objects is via the mechanism of phonon blockade. Here, we show that phonon blockade could be achieved in a system of two weakly nonlinear mechanical resonators coupled by a Coulomb interaction. The optimal blockade arises as a result of the destructive quantum interference between paths leading to two-phonon excitation. It is observed that, in comparison to a single drive applied on one mechanical resonator, driving b…
The nonlinear quantum regime is crucial for implementing interesting quantum effects, which have wide applications in modern quantum science. Here we propose an effective method to reach the nonlinear quantum regime in a modulated optomechanical system (OMS), which is originally in the weak-coupling regime. The mechanical spring constant and optomechanical interaction are modulated periodically. This leads to the result that the resonant optomechanical interaction can be effectively enhanced into the single-photon strong-coupling regime by the modulation-induced mechanical parametric amplifica…
