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Bulletin of the American Physical Society

Ground state cooling of a radio-frequency LC circuit in an optoelectromechanical system

Nicola Malossi, Paolo Piergentili, Jie Li, Enrico Serra, Riccardo Natali, Giovanni Di Giuseppe, David Vitali

Published Sep 9, 2020• 1 citation
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Abstract

We present a complete theory for laser cooling of a macroscopic radio-frequency LC electrical circuit by means of an optoelectromechanical system, consisting of an optical cavity dispersively coupled to a nanomechanical oscillator, which is in turn capacitively coupled to the LC circuit of interest. We determine the optimal parameter regime where the LC resonator can be cooled down to its quantum ground state, which requires a large optomechanical cooperativity, and a larger electromechanical cooperativity. Moreover, comparable optomechanical and electromechanical coupling rates are preferable for reaching the quantum ground state.

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We present a complete theory for laser cooling of a macroscopic radio-frequency LC electrical circuit by means of an optoelectromechanical system, consisting of an optical cavity dispersively coupled to a nanomechanical oscillator, which is in turn capacitively coupled to the LC circuit of interest. We determine the optimal parameter regime where the LC resonator can be cooled down to its quantum ground state, which requires a large optomechanical cooperativity, and a larger electromechanical cooperativity. Moreover, comparable optomechanical and electromechanical coupling rates are preferable for reaching the quantum ground state.
We present a complete theory for laser cooling of a macroscopic radio-frequency LC\mathit{LC}LC electrical circuit by means of an optoelectromechanical system, consisting of an optical cavity dispersively coupled to a nanomechanical oscillator, which is in turn capacitively coupled to the LC\mathit{LC}LC circuit of interest. The driven optical cavity cools the mechanical resonator, which in turn sympathetically cools the LC\mathit{LC}LC circuit. We determine the optimal parameter regime where the LC\mathit{LC}LC resonator can be cooled down to its quantum ground state, which requires a large optomechanical cooperativity, and a larger electromechanical cooperativity. Moreover, comparable optomechanical and electromechanical coupling rates are preferable for reaching the quantum ground state.
Abstract We explore the ground state cooling and quantum synchronization of the mechanical and low-frequency inductor-capacitor (LC) resonators in a hybrid three-mode optoelectromechanical system, in which the mechanical resonator is optically and capacitively coupled to the optical cavity and the LC circuit, respectively. We find that when the bias voltage modulation switch is incorporated into the direct current (DC) bias voltage, ground state cooling and quantum synchronization can be simultaneously achieved regardless of whether the mechanical resonator and the low-frequency LC resonator have the identical frequency. Furthermore, we elucidate the relationship between quantum synchronization and ground state cooling of the two resonators, that is, the simultaneous ground state cooling of the resonators must be accompanied by quantum synchronization. Our work may open up an alternative approach to the simultaneous ground state cooling and quantum synchronization of multiple resonators, which has fewer parametric limitations.
We present a cooling mechanism for a nanomechanical resonator that linearly couples with a LC oscillator. The linear coupling, when periodically modulated at red detuning, up-converts the low-frequency nanomechanical quanta to the high-frequency LC oscillator quanta which then dissipates in the circuits via the damping of the LC oscillator. We show that realistic circuit can be designed in the superconducting system to implement this scheme in the resolved-sideband regime and reach the quantum ground state of the nanomechanical mode. A detailed study of the origin of the quantum back-action noise in this cooling process is also presented.
Quantum control over a physical system requires thermal fluctuations and thermal decoherence to be negligible, which becomes more challenging with decreasing natural frequencies of the target system. For microwave circuits, the quantum regime can be reached simply by cooling them to mK temperatures. Radio-frequency (RF) systems in the MHz regime, however, require further cooling or have to be coupled to an auxiliary quantum system with a coupling rate exceeding their thermal decoherence rate. A powerful tool to cool below the thermodynamic bath temperature is sideband-cooling, a technique that originated from the field of trapped ions and cold atoms and that has been applied in cavity optomechanics for groundstate cooling of mechanical motion. Here, we engineer a system of two superconducting LC circuits coupled by a current-mediated photon-pressure interaction and demonstrate sideband-cooling of a hot RF circuit using a microwave cavity and the regime of quantum-coherent coupling between the circuits. Due to a dramatically increased coupling strength, we obtain a large single-photon quantum cooperativity Cq0∼1\mathcal{C}_{\mathrm{q}0} \sim 1Cq0​∼1 and reduce the residual thermal RF occupancy by 75% through sideband-cooling with less than a single pump photon. For larger pump powers, the photon-pressure coupling rate exceeds the RF thermal decoherence rate by a factor of three and the RF circuit is cooled into the quantum groundstate. Our results demonstrate photon-pressure coupling with a hot radio-frequency circuit in the quantum regime and lay the foundation for radio-frequency quantum photonics.
Abstract We study electro-mechanical entanglement in a system where a massive membrane is capacitively coupled to a low frequency LC resonator. In opto- and electro-mechanics, the entanglement between a megahertz (MHz) mechanical resonator and a gigahertz (GHz) microwave LC resonator has been widely and well explored, and recently experimentally demonstrated. Typically, coupling is realized through a radiation pressure-like interaction, and entanglement is generated by adopting an appropriate microwave drive. Through this approach it is however not evident how to create entanglement in the case where both the mechanical and LC oscillators are of low frequency, e.g., around 1 MHz. Here we provide an effective approach to entangling two low-frequency resonators by further coupling the membrane to an optical cavity. The cavity is strongly driven by a red-detuned laser, sequentially cooling the mechanical and electrical modes, which results in stationary electro-mechanical entanglement at experimentally achievable temperatures. The entanglement directly originates from the electro-mechanical coupling itself and due to its quantum nature will allow testing quantum theories at a more macroscopic scale than currently possible.
We propose effective generation of entangled and squeezed states in an optoelectromechanical system comprising of a macroscopic LC electrical circuit and an optomechanical system. We obtain enhanced entanglement between optical and LC circuit modes that are coupled via a common mechanical mode in the microwave regime. We achieve this enhancement by a stepwise application of modulation in the laser drive, the voltage drive and the spring constant of the moveable end-mirror. The maximum amount of entanglement is observed to be primarily dependent on the voltage modulation and changes slightly with the parameters of the spring constant. Alongside the generated entanglement, we also study the variation of the maximum degree of squeezing in the mechanical mode for different parameter regimes.