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Advanced Quantum Technologies

Atom Mediated Single‐Photon Nonlinearity in a Quadratically Coupled Optomechanical System

Q. H. Liu, Gangcheng Wang, T. Z. Luan, H. Z. Shen

Published Feb 29, 2024• 6 citations
Publisher

Abstract

Abstract In this paper, conventional phonon blockade (CPNB) and conventional photon blockade (CPTB) effects, as well as unconventional phonon blockade (UPB) effects, are studied in an optomechanical system with nonlinear interaction between the cavity frequency and the square of the mechanical displacement driven by an external field, where a two‐level atom couples with the mechanical mode and a microwave driving field pumps cavity mode. The second‐order correlation function is analytically calculated, which is in good agreement with the numerical simulation given by the master equation. With energy‐level diagram, the atom‐mechanical mode coupling is found to induces the degeneracy splitting of the states and give the optimal conditions for CPNB and CPTB in this system. With the origin of UPB, the optimal conditions are derived and it is found that the realization of UPB is determined by the two couplings of the cavity and atom with respect to the mechanical mode. Moreover, some discussions on the experimental implementation in this quadratically coupled optomechanical system are presented. This study provides a possible way for realizing single‐photon nonlinearity and can extend the applications of optomechanical systems in the field of quantum optics.

DOI
10.1002/qute.202300422

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Abstract In this paper, conventional phonon blockade (CPNB) and conventional photon blockade (CPTB) effects, as well as unconventional phonon blockade (UPB) effects, are studied in an optomechanical system with nonlinear interaction between the cavity frequency and the square of the mechanical displacement driven by an external field, where a two‐level atom couples with the mechanical mode and a microwave driving field pumps cavity mode. The second‐order correlation function is analytically calculated, which is in good agreement with the numerical simulation given by the master equation. With energy‐level diagram, the atom‐mechanical mode coupling is found to induces the degeneracy splitting of the states and give the optimal conditions for CPNB and CPTB in this system. With the origin of UPB, the optimal conditions are derived and it is found that the realization of UPB is determined by the two couplings of the cavity and atom with respect to the mechanical mode. Moreover, some discussions on the experimental implementation in this quadratically coupled optomechanical system are presented. This study provides a possible way for realizing single‐photon nonlinearity and can extend the applications of optomechanical systems in the field of quantum optics.
We theoretically study the photon blockade (PB) effect in a double-cavity optomechanical system with the two-photon driving. By analytical calculations and numerical simulations, the physical mechanisms of conventional photon blockade (CPB) and unconventional photon blockade (UPB) are discussed in detail. And then we obtain the optimal parameter conditions for PB. In our work, there exist both the CPB induced by strong nonlinear interaction and the UPB caused by quantum interference. In particular, we find that CPB and UPB can occur simultaneously under the same parameters. In addition, we also prove that the appropriate values of nonreciprocal coupling and two-photon driving are favorable to the improvement of PB. Our proposal provides an idea for simultaneously realizing CPB and UPB in the optomechanical system and offers a route for constructing high-quality single-photon sources.
We propose a scheme to realize the two-phonon blockade effect in a quadratically coupled optomechanical system. We consider the case that the optical cavity is simultaneously driven by a strong pumping field and a weak driving field. By strongly driving the optical cavity, the nonlinear interaction between the optical mode and the mechanical resonator can be significantly enhanced and an effective second-order nonlinearity between photons and phonons is induced. Based on this effectively strong nonlinearity, the two-phonon blockade effect can be achieved when a weak driving field is applied into the optical cavity. By contrast, we study the case of weakly driving the mechanical resonator. In this case, the single-phonon blockade is generated, while the two-phonon blockade cannot be observed. By numerically calculating the second-order and third-order correlation function, we investigate the statistical characteristics of phonons. In addition, we also study the influence of the thermal noise on the achieved two-phonon blockade effect. Our work provides an alternative approach for implementing multiphonon blockade and has potential applications in quantum information processing.
Quantum control of phonons has become a focus of attention for developing quantum technologies. Here, we present 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 the realization of phonon blockade, where the nonlinearity is achieved by coupling the mechanical system to superconducting qubits. We both analytically and numerically study the phonon statistical properties via the steady-state solution of the second-order correlation function and find phonon blockade can be efficiently realized for a large cooperativity of the system, which is achievable based on the optically enhanced nonlinear coupling and high quality mechanical system.
Abstract A phonon blockade is achieved in a hybrid optomechanical system including an ensemble of two‐level quantum emitters. The introduction of the ensemble of quantum emitters sets up a mechanism of quantum destructive interference within the system, by which the phonon statistical characteristic exhibits strong antibunching under the condition of weak driving and weak coupling. By analyzing the analytic solution of the second‐order correlation function, the optimal parametric condition for ideal phonon blockade effect is obtained. The numerical simulation of the second‐order correlation function perfectly accord with the analytical solution. The validity of the effective Hamiltonian is proved by the numerical simulations with quantum master equation. The proposed scheme provides a possible way to realize the single‐phonon source experimentally.
Abstract Phonon statistics in a hybrid optomechanical system, where a mechanical resonator is quadratically coupled to a cavity and couples with another resonator via Coulomb interaction is studied. It is found that the conventional and unconventional phonon blockade can be both achieved at the same parameter regime, which is confirmed by analytical and numerical results. By analyzing the energy level structure, it is found that the anharmonicity of the system is the joint action of both the Coulomb interaction and the optomechanical coupling, where the nonlinearity introduced by the latter has a more significant effect on one branch of the conventional phonon blockade. In addition, the phonon blockade can be enhanced by introducing the mechanical parametric amplifier with optimal parameters, where the physical mechanism underlying comes from the multi‐pathway destructive interference. It is found that the phonon blockade is fragile toward thermal noise due to the weak quantum interference, which can be overcome by increasing the driving strength and applying the mechanical parametric amplifier with suitable parameters. This work may provide a way to manipulate the phonon blockade and can be helpful to the application of quantum information processing.
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, 133603 (2017)10.1103/PhysRevLett.118.133603], is fundamentally different from standard ones. In the enhanced atom-phonon coupling, the strong phonon nonlinearity at a single-excitation level is obtained in the originally weak-coupling regime, which leads to the appearance of phonon blockade. Moreover, the optimal parameter regimes are presented both for the cases of one and two cavities. We compared phonon-number correlation functions of different orders for mechanical steady states generated in the one-cavity hybrid system, revealing the occurrence of phonon-induced tunneling and different types of phonon blockade. Our approach offers an alternative method to generate and control a single phonon in the quantum regime and could have potential applications in single-phonon quantum technologies.