Capacitive coupling of two transmission line resonators mediated by the phonon number of a nanoelectromechanical oscillator

Abstract

Detection of quantum features in mechanical systems at the nanoscale constitutes a challenging task, given the weak interaction with other elements and the available technics. Here we describe how the interaction between two monomodal transmission-line resonators (TLRs) mediated by vibrations of a nano-electromechanical oscillator can be described. This scheme is then employed for quantum non-demolition detection of the number of phonons in the nano-electromechanical oscillator through a direct current measurement in the output of one of the TLRs. For that to be possible an undepleted field inside one of the TLR works as a amplifier for the interaction between the mechanical resonator and the remaining TLR. We also show how how the non-classical nature of this system can be used for generation of tripartite entanglement and conditioned mechanical coherent superposition states, which may be further explored for detection processes.

Temperature measurement and phonon number statistics of a nanoelectromechanical resonator

“…We consider the coupling of two transmission line resonators (TLRs) mediated by a mechanical resonator as considered in [18] and represented in figure 2. By assuming the regime of rapid mechanical oscillations at the GHz scale, and that the TLR-1, being in a undepleted regime, is treated classically, the interaction Hamiltonian between the NEMS and the field in the TLR-2 is given by H tbb a a , 1…”

“…where t ( ) a is proportional to the microwave amplitude in the TLR-1 [18] and a (a † ) is the annihilation (creation) operator of the normal mode in the TLR-2. b (b † ) is the mechanical resonator annihilation (creation) operator.…”

“…The Josephson junction acts as a source of coherent pulses, with time interval t 1 , on the TLR-2 In sequence, a coherent pulse is applied to TLR-1, with amplitude 1 a and time interval t 2 . The radiation field there is treated classically, as a result of the undepleted regime [18]. After these pulses, the density operator is given by…”

Generating Squeezed States of Nanomechanical Resonator via a Flux Qubit in a Hybrid System

“…Presently, the hybrid system consisting of superconducting circuits and the NAMRs has been intensively investigated. [3,8,18,19] Fast quantum operation and information storage have been realized, based on quantum interface between the superconducting qubit and the atom via the NAMR. [20] In addition, Ref.…”