Parametric coupling between macroscopic quantum resonators

TL;DR

This paper explores parametric coupling schemes between macroscopic quantum resonators, enabling entanglement and squeezing generation, with practical measurement methods for the quantum states involved.

Contribution

It introduces specific coupling schemes between mechanical and electrical resonators using microwave voltages and SQUIDs, advancing quantum control techniques.

Findings

Quantitative analysis of entanglement at finite temperatures

Demonstration of state characterization via electrical resonator detection

Effective generation of squeezing and entanglement in coupled resonators

Abstract

Time-dependent linear coupling between macroscopic quantum resonator modes generates both a parametric amplification also known as a {}"squeezing operation" and a beam splitter operation, analogous to quantum optical systems. These operations, when applied properly, can robustly generate entanglement and squeezing for the quantum resonator modes. Here, we present such coupling schemes between a nanomechanical resonator and a superconducting electrical resonator using applied microwave voltages as well as between two superconducting lumped-element electrical resonators using a r.f. SQUID-mediated tunable coupler. By calculating the logarithmic negativity of the partially transposed density matrix, we quantitatively study the entanglement generated at finite temperatures. We also show that characterization of the nanomechanical resonator state after the quantum operations can be achieved by detecting the electrical resonator only. Thus, one of the electrical resonator modes can act as a probe to measure the entanglement of the coupled systems and the degree of squeezing for the other resonator mode.