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Photonics

Two-Phonon Blockade in Quadratically Coupled Optomechanical Systems

Zi-Yuan Li, Guangri Jin, Tai-Shuang Yin, Aixi Chen

Published Jan 27, 2022• 9 citations
Publisher

Abstract

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.

DOI
10.3390/photonics9020070

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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.
We study photon, phonon statistics, and the cross-correlation between photons and phonons in a quadratically coupled optomechanical system. Photon blockade, phonon blockade, and strong anticorrelation between photons and phonons can be observed in the same parameter regime with the effective nonlinear coupling between the optical and the 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 interference between different paths for two-photon excitation in the optical mode with a moderate effective nonlinear coupling strength. Furthermore, we show that phonon (photon) pairs or correlated photons and phonons can be generated in the strong nonlinear coupling regime with a proper detuning between the weak mechanical driving field and mechanical mode. Our results open up a way to generate anticorrelated and correlated photons and phonons, which may have important applications in quantum information processing.
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.
We propose a scheme to enhance phonon blockade effect in a quadratically coupled optomechanical system. By applying a degenerate parametric drive to the mechanical oscillator, we introduce a mechanical parametric amplifier (MPA) to the system. We show that the phonon blockade can be achieved in both the single-phonon resonant regime and multipath interference regime due to the optomechanical nonlinearity and MPA. By combining the two regimes together, we show that the phonon blockade effect is enhanced compared to the regime without MPA. What is more, the two-time second-order correlation function gradually tends to one without rapid oscillations in our scheme, which suggests that high time resolution is not necessary in the detection.
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 both the resonators can be beneficial in many aspects; such as, in terms of the temperature sensitivity of phonon blockade and also with regard to the tunability, by controlling the amplitude and the phase of the second drive externally. We also show that via a radiation pressure induced coupling in an optomechanical cavity, phonon correlations can be measured indirectly in terms of photon correlations of the cavity mode.
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.