Generating Squeezed States of Nanomechanical Resonator

TL;DR

This paper introduces a method to generate squeezed states in a nanomechanical resonator using a solid-state circuit with a Cooper-pair box and a transmission line resonator, leveraging nonlinear interactions for quantum state engineering.

Contribution

The paper presents a novel scheme for producing squeezed states in nanomechanical resonators via a solid-state setup with a Cooper-pair box acting as a nonlinear medium.

Findings

Derivation of the interaction Hamiltonian using Frohlich transformation.

Implementation of a parametric down-conversion Hamiltonian in solid-state circuits.

Feasibility of generating squeezed states through three-wave mixing in the proposed system.

Abstract

We propose a scheme for generating squeezed states in solid state circuits consisting of a nanomechanical resonator (NMR), a superconducting Cooper-pair box (CPB) and a superconducting transmission line resonator (STLR). The nonlinear interaction between the NMR and the STLR can be implemented by setting the external biased flux of the CPB at certain values. The interaction Hamiltonian between the NMR and the STLR is derived by performing Fr$\rm\ddot o$hlich transformation on the total Hamiltonian of the combined system. Just by adiabatically keeping the CPB at the ground state, we get the standard parametric down-conversion Hamiltonian. The CPB plays the role of ``nonlinear media", and the squeezed states of the NMR can be easily generated in a manner similar to the three-wave mixing in quantum optics. This is the three-wave mixing in a solid-state circuit.