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arXiv:1803.10403 · Scientific Reports

Tunable phonon blockade in weakly nonlinear coupled mechanical resonators via Coulomb interaction

Bijita Sarma, Amarendra K. Sarma

Published Sep 25, 2018• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41598-018-32743-1

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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.
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.
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.
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.
A single phonon in a nonlinear nanomechanical resonator (NAMR) can block the excitation of a second phonon [Phys. Rev. A 82, 032101 (2010)]. This intrinsically quantum effect is called phonon blockade, and is an analog of Coulomb blockade and photon blockade. Here we predict tunable multiphonon blockade in coupled nonlinear NAMRs, where nonlinearity is induced by two-level systems (TLSs) assuming dispersive (far off-resonance) interactions. Specifically, we derive an effective Kerr-type interaction in a hybrid system consisting of two nonlinearly interacting NAMRs coupled to two TLSs and driven by classical fields. The interaction between a given NAMR and a TLS is described by a Jaynes-Cummings-like model. We show that by properly tuning the frequency of the driving fields one can induce various types of phonon blockade, corresponding to the entangled phonon states of either two qubits, a qutrit and quartit, or two qudits. Thus, a kkk-phonon Fock state (with k=1,2,3k=1,2,3k=1,2,3) can impede the excitation of more phonons in a given NAMR, which we interpret as a kkk-phonon blockade (or, equivalently, phonon tunneling). Our results can be explained in terms of resonant transitions in the Fock space and via phase-space interference using the sss-parametrized Cahill-Glauber quasiprobability distributions including the Wigner function. We study the nonclassicality, entanglement, and dimensionality of the blockaded phonon states during both dynamics and in the stationary limits.
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 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.