Abstract
We propose a scheme for controlling a radio-frequency mechanical resonator at the quantum level using a superconducting qubit. The mechanical part of the circuit consists of a suspended micrometer-long beam that is embedded in the loop of a superconducting quantum interference device (SQUID) and is connected in parallel to a transmon qubit. Using realistic parameters from recent experiments with similar devices, we show that this configuration can enable a tuneable optomechanical interaction in the single-photon ultrastrong-coupling regime, where the radiation-pressure coupling strength is larger than both the transmon decay rate and the mechanical frequency. We investigate the dynamics of the driven system for a range of coupling strengths and find an optimum regime for ground-state cooling, consistent with previous theoretical investigations considering linear cavities. Furthermore, we numerically demonstrate a protocol for generating hybrid discrete- and continuous-variable entanglement as well as mechanical Schr\"{o}dinger cat states, which can be realised within the current state of the art. Our results demonstrate the possibility of controlling the mechanical motion of massive objects using superconducting qubits at the single-photon level and could enable applications in hybrid quantum technologies as well as fundamental tests of quantum mechanics.
Highlights
The rapid progress in the field of cavity optomechanics and electromechanics over the last decade has enabled the study of massive micro- and nanomechanical objects in the quantum regime, paving the way for several technological applications as well as fundamental tests of quantum mechanics [1,2,3]
Using realistic experimental parameters obtained from recent experiments, we investigate the possibility of cooling the resonator via sideband driving of the qubit and find that ground-state cooling is possible with a fraction of a driving photon, circumventing the issues associated with strong driving and qubits
Upon application of an in-plane magnetic field (B) the loop picks up a flux due to the beam displacement (X ) which results in a fluxmediated optomechanical interaction between the superconducting quantum interference device (SQUID) cavity and the mechanical oscillator, as recently realized in Ref. [29]
Summary
The rapid progress in the field of cavity optomechanics and electromechanics over the last decade has enabled the study of massive micro- and nanomechanical objects in the quantum regime, paving the way for several technological applications as well as fundamental tests of quantum mechanics [1,2,3]. Note that the electromagnetic mode frequency is typically orders of magnitude larger than g0 and ωM, corresponding to an ultrastrong coupling regime of the radiation-pressure interaction in the strong dispersive limit This nonlinear regime of optomechanics offers rich opportunities for exploring photon blockade phenomena and generating nonclassical mechanical states [14,15,16,17,18]. A promising playground for enhancing the single-photon coupling is flux-mediated optomechanics, in which a vibrating mechanical element parametrically modulates the inductance of an LC microwave cavity This can be realized by integrating a mechanical beam into the arms of a superconducting quantum interference device (SQUID), which offers plenty of opportunities for reaching stronger couplings and observing coherent quantum phenomena in Josephson quantum circuits as well as achieving quantum-limited displacement detection [19,20,21,22,23,24]. Our results pave the way for the successful on-chip integration of mechanical elements with state-ofthe-art transmon-based processors and the manipulation of mechanical motion at single-photon levels, enabling technological applications and fundamental studies of quantum theory
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