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Acta Physica Sinica

Phonon blockade induced by a non-Hermitian Hamiltonian in a nanomechanical resonator coupled with a qubit

Qinghong Liao, Weican Deng, Jian Wen, Nanrun Zhou, Nian-Hua Liu

Published Jan 1, 2019• 2 citations
Publisher

Abstract

Nanomechanical resonator has important applications in the field of high-precision detection because it has a high-Q factor, high vibration frequency, small size, and other excellent characteristics. Superconducting qubit has very large magnetic dipole moments, so it can be easily combined with nanomechanical resonator. Furthermore, the system parameters including frequency and coupling strength can be designed according to requirements beforehand, which makes a superconducting qubit an ideal artificial atom. Compared with natural atom, superconducting qubit has abundant energy levels. For these reasons, nanomechanical system has aroused wide interest in the engineering, electron, physical and other fields of science and technology. According to the recent research, a new approach to the zero eigenvalues of non-Hermitian Hamiltonian is applied to the optomechanical system. It was found that the scheme is superior to conventional photon blockade (CPB) and unconventional photon blockade (UPB) in the cavity quantum electrodynamics (QED) system. So we propose a scheme to induce phonon blockade in order to explore a new avenue to the research about phonon blockades in the quantum open system. We study the phonon blockade in an optomechanical system that a qubit is coupled with nanomechanical resonator (NAMR) driven by two external weakly driving fields respectively in this way. In this paper, the Hamiltonian of such a system can be treated by the non-Hermitian Hamiltonian and it can be described in the form of matrix. Then the phenomenon of phonon blockade occurs when all the eigenvalues in the form of matrix are equal to zero. It is found that strong phonon antibunching can be triggered in both strong and weak nonlinearity when we use the method which has been already used in a gain optical cavity system. The distinct result reflects the advantage of our approach which possesses some outstanding characters between the ordinary methods (conventional phonon blockade and unconventional phonon blockade). In addition, the effect of our avenue on phonon blockade is analyzed and also the distinction between the conventional phonon blockade (CPNB) and unconventional phonon blockade (UPNB) is compared with each other in detail. By analytical calculation, the optimal conditions are given and the underlying physical mechanism is explained. In the comparison between CPNB and UPNB, we show the superiority of our scheme through some graphs. Finally, we describe briefly the measurements of phonon blockade in the NAMR-qubit system via a superconducting cavity. The proposal may provide a theoretical way to guide the manufacture of phonon devices in the future. The results obtained here may have a great significance and application in the field of quantum information processing and precision measurement.

DOI
10.7498/aps.68.20182263

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Nanomechanical resonator has important applications in the field of high-precision detection because it has a high-Q factor, high vibration frequency, small size, and other excellent characteristics. Superconducting qubit has very large magnetic dipole moments, so it can be easily combined with nanomechanical resonator. Furthermore, the system parameters including frequency and coupling strength can be designed according to requirements beforehand, which makes a superconducting qubit an ideal artificial atom. Compared with natural atom, superconducting qubit has abundant energy levels. For these reasons, nanomechanical system has aroused wide interest in the engineering, electron, physical and other fields of science and technology. According to the recent research, a new approach to the zero eigenvalues of non-Hermitian Hamiltonian is applied to the optomechanical system. It was found that the scheme is superior to conventional photon blockade (CPB) and unconventional photon blockade (UPB) in the cavity quantum electrodynamics (QED) system. So we propose a scheme to induce phonon blockade in order to explore a new avenue to the research about phonon blockades in the quantum open system. We study the phonon blockade in an optomechanical system that a qubit is coupled with nanomechanical resonator (NAMR) driven by two external weakly driving fields respectively in this way. In this paper, the Hamiltonian of such a system can be treated by the non-Hermitian Hamiltonian and it can be described in the form of matrix. Then the phenomenon of phonon blockade occurs when all the eigenvalues in the form of matrix are equal to zero. It is found that strong phonon antibunching can be triggered in both strong and weak nonlinearity when we use the method which has been already used in a gain optical cavity system. The distinct result reflects the advantage of our approach which possesses some outstanding characters between the ordinary methods (conventional phonon blockade and unconventional phonon blockade). In addition, the effect of our avenue on phonon blockade is analyzed and also the distinction between the conventional phonon blockade (CPNB) and unconventional phonon blockade (UPNB) is compared with each other in detail. By analytical calculation, the optimal conditions are given and the underlying physical mechanism is explained. In the comparison between CPNB and UPNB, we show the superiority of our scheme through some graphs. Finally, we describe briefly the measurements of phonon blockade in the NAMR-qubit system via a superconducting cavity. The proposal may provide a theoretical way to guide the manufacture of phonon devices in the future. The results obtained here may have a great significance and application in the field of quantum information processing and precision measurement.
We study phonon statistics in a nanomechanical resonator (NAMR) which is resonantly coupled to a qubit. We find that there are two different mechanisms for phonon blockade in such a resonantly coupled NAMR-qubit system. One is due to the strong anharmonicity of the NAMR-qubit system with large coupling strength; the other one is due to the destructive interference between different paths for two-phonon excitation in the NAMR-qubit system with a moderate coupling strength. We find that the phonon blockade is fragile towards thermal mode occupations and can only be observed for NAMR being at ultracold effective temperature. In order to enlarge the mean phonon number for strong phonon antibunching with a moderate NAMR-qubit coupling strength, we assume that two external driving fields are applied to the NAMR and qubit, respectively. In this case, we find that the phonon blockades under two mechanisms can appear at the same frequency regime by optimizing the strength ratio and phase difference of the two external driving fields.
We investigate phonon statistics in a nanomechanical resonator (NAMR), which is quadratically coupled to a two-level system, by driving the NAMR and two-level system simultaneously. We find that unconventional phonon blockade (UCPNB), i.e., strong phonon antibunching effect based on quantum interference, can be observed when driven fields are weak. By increasing the strengths of the driving fields, we show the crossover from the UCPNB to the conventional phonon blockade (CPNB), which is induced by the strong nonlinear interaction of the system. Moreover, under the strong coupling condition for CPNB, quantum interference effect can also be used to enhanced the phonon blockade by optimizing the phase difference of the two external driving fields.
Phonon blockade is a purely quantum phenomenon, analogous to Coulomb and photon blockades, in which a single phonon in an anharmonic mechanical resonator can impede the excitation of a second phonon. We propose an experimental method to realize phonon blockade in a driven harmonic nanomechanical resonator coupled to a qubit, where the coupling is proportional to the second-order nonlinear susceptibility ${\ensuremath{\chi}}^{(2)}$. This is in contrast to the standard realizations of phonon and photon blockade effects in Kerr-type ${\ensuremath{\chi}}^{(3)}$ nonlinear systems. The nonlinear coupling strength can be adjusted conveniently by changing the coherent drive field. As an example, we apply this model to predict and describe phonon blockade in a nanomechanical resonator coupled to a Cooper-pair box (i.e., a charge qubit) with a linear longitudinal coupling. By obtaining the solutions of the steady state for this composite system, we give the conditions for observing strong antibunching and sub-Poissonian phonon-number statistics in this induced second-order nonlinear system. Besides using the qubit to produce phonon blockade states, the qubit itself can also be employed to detect blockade effects by measuring its states. Numerical simulations indicate that the robustness of the phonon blockade, and the sensitivity of detecting it, will benefit from this strong induced nonlinear coupling.
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 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.
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.