Abstract
Massive mechanical resonators operating at the quantum scale can enable a large variety of applications in quantum technologies as well as fundamental tests of quantum theory. Of crucial importance in that direction is both their integrability into state-of-the-art quantum platforms as well as the ability to prepare them in generic quantum states using well-controlled high-fidelity operations. Here, we propose a scheme for controlling a radio-frequency mechanical resonator at the quantum scale using two superconducting transmon qubits that can be integrated on the same chip. Specifically, we consider two qubits coupled via a capacitor in parallel to a superconducting quantum interference device (SQUID), which has a suspended mechanical beam embedded in one of its arms. Following a theoretical analysis of the quantum system, we find that this configuration, in combination with an in-plane magnetic field, can give rise to a tuneable three-body interaction in the single-photon strong-coupling regime, while enabling suppression of the stray qubit-qubit coupling. Using state-of-the-art parameters and qubit operations at single-excitation levels, we numerically demonstrate the possibility of ground-state cooling as well as high-fidelity preparation of mechanical quantum states and qubit-phonon entanglement, i.e. states having negative Wigner functions and obeying non-classical correlations. Our work significantly extends the quantum control toolbox of radio-frequency mechanical resonators and may serve as a promising architecture for integrating such mechanical elements with transmon-based quantum processors.
Highlights
The ability to control massive mechanical objects at the quantum level constitutes a very interesting task for many technological applications, ranging from microwave-to-optical conversion to quantum memories, as well as fundamental studies regarding the quantum-classical divide.[1,2,3,4,5,6,7,8,9,10] The rapid development of cavity optomechanics over the last decade has enabled the exploration of mechanical resonators in regimes where quantum effects become prominent
A promising route towards high-fidelity mechanical quantum control is the ability to operate in the single-photon strongcoupling regime, where interaction times are faster than dissipation processes, which still remains an experimental challenge for far-detuned parametrically coupled mechanical resonators.[19,21]
By connecting two superconducting transmon qubits[32] directly via this mechanical superconducting quantum interference device (SQUID), a tuneable three-body interaction arises as the qubit-qubit flux-mediated coupling is modulated by the mechanical displacement
Summary
The ability to control massive mechanical objects at the quantum level constitutes a very interesting task for many technological applications, ranging from microwave-to-optical conversion to quantum memories, as well as fundamental studies regarding the quantum-classical divide.[1,2,3,4,5,6,7,8,9,10] The rapid development of cavity optomechanics over the last decade has enabled the exploration of mechanical resonators in regimes where quantum effects become prominent. Following the pioneering work on acoustic resonators,[11] recently, quantum superpositions of the ground and first excited state were for the first time generated in a parametrically coupled mechanical resonator.[18] In this approach, a superconducting qubit is used to create the excitation, which decays into a microwave resonator on a different chip and subsequently transferred to the mechanical element via an effective linearised interaction It is recognised, that this method has severe limitations as it relies on strong driving, which is challenging with qubits, and suffers from unavoidable losses during the state transfer between different chips, limiting the fidelity of the prepared state.[19] A different scheme, implemented in the optical domain, uses entanglement and post-selective measurements to generate single-photon states,[20] the non-deterministic nature of the protocol in combination with low count rates limits the types of states that can be prepared. We devise a protocol consisting of qubit flux-pulsing and post-selective measurements for synthesizing multi-phonon superposition states, extending the quantum control toolbox and the plurality of engineerable quantum states in radio-frequency mechanical resonators
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