Tunable multiphonon blockade in coupled nanomechanical resonators

TL;DR

This paper predicts tunable multiphonon blockade in coupled nonlinear nanomechanical resonators, enabling control over phonon states and entanglement through external tuning, with potential applications in quantum information processing.

Contribution

It introduces a method to achieve tunable multiphonon blockade in coupled NAMRs using TLS-induced nonlinearity and classical driving fields, expanding control over phonon quantum states.

Findings

Demonstrates control over phonon blockade by tuning driving fields.

Shows generation of entangled phonon states such as qubits, qutrits, and qudits.

Analyzes nonclassicality and entanglement of phonon states during dynamics.

Abstract

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, 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.