Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators

Abstract

The observation of quantized nanomechanical oscillations by detecting femtometer-scale displacements is a significant challenge for experimentalists. We propose that phonon blockade can serve as a signature of quantum behavior in nanomechanical resonators. In analogy to photon blockade and Coulomb blockade for electrons, the main idea for phonon blockade is that the second phonon cannot be excited when there is one phonon in the nonlinear oscillator. To realize phonon blockade, a superconducting quantum two-level system is coupled to the nanomechanical resonator and is used to induce the phonon self-interaction. Using Monte Carlo simulations, the dynamics of the induced nonlinear oscillator is studied via the Cahill-Glauber s-parametrized quasiprobability distributions. We show how the oscillation of the resonator can occur in the quantum regime and demonstrate how the phonon blockade can be observed with currently accessible experimental parameters.

Phase-dependent optical response properties in an optomechanical system by coherently driving the mechanical resonator

“…Meanwhile, a weak coherent driving field with frequency ω a and amplitude ε a is applied to excite the mechanical resonator. Experimentally, a micro/nano scale mechanical resonator can be driven by microwave electrical signals [39][40][41]. For example, in a recent experiment [39], the mechanical element is a thin film of piezoelectric materials AlN, which is sandwiched between two aluminium metal electrodes, enabling strong electromechanical coupling through the piezoelectric effect.…”

Generating the Schrödinger cat state in a nanomechanical resonator coupled to a charge qubit

“…Using the realistic parameter values from Refs. [15,28,30,[33][34][35][36], we show in Figure 3 the numerical results for the fidelities of the generated state and the corresponding average phonon number T r(ρ(t)a † a) versus the decays of the charge qubit and the NAMR with respect to different Rabi frequencies, where we consider ±10% change of the Rabi frequency by parameter fluctuations.…”

“…The charge qubit is not only controlled by a DC voltage V 0 , but also driven by two AC voltages V g (t) = V cos ω l t and V ′ g (t) = V ′ cos ω ′ l t via the gate capacitor C g . If the charge qubit works in a near optimal point, which means [C g V 0 + C(x)| x=0 V x ]/2e ≈ 0.5, and the charge energy E c is much less than the effective Josephson energy E J [24,30], the charge noise can be effectively suppressed, and the transition frequency between the first excited and ground states is ω 0 ≈ √ 8E J E c /h [28]. By neglecting the higher-order terms regarding the multi-photon excitations, the Hamiltonian describing our model in the rotating-wave approximation is given by (in units of h = 1) [28,29] where σ z = |e e| − |g g|, σ + = |e g|, and σ − = |g e| with the excited and ground states |e and |g in the charge qubit, respectively.…”

“…Moreover, the last condition ensures that the terms proportional to |g| 2 are negligible. Therefore, we obtain the following effective Hamiltonian Figure 2, the effective Hamiltonian (5) presents the main feature of the interaction Hamiltonian (4), particularly within the decoherence times of the transmon-type charge qubit and the NAMR (i.e., t < 50 µs [15,25,28,33]). …”

“…(17) collapse into the cat states (|α + | − α )/ √ 2 and (|α − | − α )/ √ 2 of the NAMR, respectively, which can be detected by applying a static magnetic field and an alternating current [28].…”