We theoretically propose a hybrid nanomechanical resonator (NR) system, where a doubly clamped suspended NR with an embedded quantum dot driven by two-tone fields is coupled to another NR via the Coulomb interaction, and we investigate the absorption spectra of the probe field under different exciton-pump field detuning. In the condition of pump on-resonance, the absorption spectrum gives a method to determine the coupling strength of the two NRs. In the pump off resonance, the absorption spectra exhibit double-Fano resonance, which is determined by the interaction of the two NRs, the frequencies of the two NRs, as well as the pump detuning. Furthermore, the double-Fano resonances are accompanied by the rapid normal phase dispersion, which indicates the slow- and fast-light effect. The results show that the group velocity index is tunable by the interaction of the two NRs, the detuning, and the different resonator frequencies, which can achieve the conversion from fast light to slow light.
We propose a scheme for generation of the stationary continuous-variable entanglement and Einstein-Podolsky-Rosen (EPR) steering between an optical cavity mode and a nanomechanical resonator (NMR) mode. The cavity and the NMR are commonly coupled with two separated quantum dots (QDs), where the two QDs are driven simultaneously by a strong laser field. By adjusting the frequency of the strong laser field, the two QDs are nearly trapped on different dressed states, which is helpful to generate the entanglement between the cavity mode and the NMR mode. Due to the combined resonant interaction of the two QDs with the NMR-cavity subsystem, the photon and the phonon created and (or) annihilated are correlated. In this regime, the optimal entanglement of the two modes is obtained and the purity of the state of the NMR-cavity subsystem is near to 1. Furthermore, the coupling strength between the cavity and two QDs is different from the dot-NMR coupling strength, which leads to the different mean occupation numbers of the cavity and the NMR. In this case, one-way EPR steering is observed. In addition, through analyzing the purity, we find the conditions of the existence for the different types of EPR steering.
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
k-phonon Fock state (with
k=1,2,3) can impede the excitation of more phonons in a given NAMR, which we interpret as a
k-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
s-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.