Cavity electromechanics with parametric mechanical driving

Abstract

Microwave optomechanical circuits have been demonstrated in the past years to be extremely powerfool tools for both, exploring fundamental physics of macroscopic mechanical oscillators as well as being promising candidates for novel on-chip quantum limited microwave devices. In most experiments so far, the mechanical oscillator is either used as a passive device element and its displacement is detected using the superconducting cavity or manipulated by intracavity fields. Here, we explore the possibility to directly and parametrically manipulate the mechanical nanobeam resonator of a cavity electromechanical system, which provides additional functionality to the toolbox of microwave optomechanical devices. In addition to using the cavity as an interferometer to detect parametrically modulated mechanical displacement and squeezed thermomechanical motion, we demonstrate that parametric modulation of the nanobeam resonance frequency can realize a phase-sensitive parametric amplifier for intracavity microwave photons. In contrast to many other microwave amplification schemes using electromechanical circuits, the presented technique allows for simultaneous cooling of the mechanical element, which potentially enables this type of optomechanical microwave amplifier to be quantum-limited. INTRODUCTIONSuperconducting microwave circuits have been demonstrated to be extremely powerful tools for the fields of quantum information processing 1-3 , circuit quantum electrodynamics 4-8 , astrophysical detector technologies 9 and microwave optomechanics 10-12 . In the latter, microwave fields in superconducting cavities are parametrically coupled to mechanical elements such as suspended capacitor drumheads or metallized nanobeams, enabling high-precision detection and manipulation of mechanical motion. Milestones achieved in the field include sideband-cooling of mechanical oscillators to the quantum ground state 11 , strong coupling between photons and phonons 13 , the generation of non-Gaussian states of motion [14][15][16] or the entanglement between two mechanial oscillators 17 .Recently, there are increasing efforts taken towards building passive and active quantum limited microwave elements for quantum technologies based on microwave optomechanical circuits, connecting the fields of microwave optomechanics, circuit quantum electrodynamics and quantum information science 18-20 . Among the most important developments into this direction are the demonstration of microwave amplification by blue sideband driving in simple optomechanical circuits 21 , and the realization of directional microwave amplifiers 22 as well as microwave circulators 23,24 in more complex multimode systems 25 .Recent theoretical work 26-28 on optomechanical systems with a parametrically driven mechanical oscillator proposed the use of mechanical parametric driving to enable parametric amplification with enhanced bandwidth and reduced added noise, compared to the case of a optomechanical amplifier using a blue-sideband drive 26 . Furthermore, the authors pre...

Combining Floquet and Lyapunov techniques for time-dependent problems in optomechanics and electromechanics

“…The parametric squeezing is provided by the modulation of the trapping frequency according to the second term in Eq. (35). To see how the dissipative squeezing arises, we set the detuning to the red mechanical sideband, ∆ = ω m , and move to the rotating frame with respect to the free oscillations,Ĥ 0 = ω mĉ †ĉ + 1 2 ω m (q 2 2 +p 2 2 ); under the RWA, we then obtain the interaction-picture Hamiltonian…”

“…To describe the generated squeezing beyond the RWA, we write the interaction Hamiltonian (35) including the counterrotating terms,…”

“…A crucial obstacle for a more widespread application of these techniques is the explicit time dependence of the driving electromagnetic fields. Dissipative preparation of mechanical states [4,[9][10][11][12][13][18][19][20][21][22][23][24][25] and tomographic backactionevading measurements of mechanical motion [26][27][28][29][30][31][32][33][34] rely on driving the system with multiple fields at different frequencies while parametric squeezing requires modulation of the optical spring [5,[35][36][37]; both of these approaches result in time-dependent optomechanical Hamiltonians. The steady-state Lyapunov equation can then only be applied under the rotating wave approximation (RWA) which neglects fast oscillating terms in the interaction and only keeps those that are resonant.…”

Optomechanically induced transparency, amplification, and Fano resonance in a multimode optomechanical system with quadratic coupling

“…Zhai et al proposed that mechanical driving field can serve as a switch of photon blockade and photon-induced tunneling [77]. In experiments, mechanical driving field has been exploited to realize electro-optomechanically induced transparency [78], cascaded optical transparency [79], phase-sensitive parametric amplifier [80], injection locking [81], and virtual exceptional points [82]. Recently, optomechanically induced opacity and amplification of two-phonon higher-order sidebands have been studied in a quadratically coupled optomechanical system with mechanical driving [83,84].…”

Amplifying the Response of a Driven Resonator via Nonlinear Interaction with a Secondary Resonator

“…The importance of signal amplification stems from the need to operate above the noise-floor of the device with a large signal-to-noise ratio in order to use these tiny resonators for sensitive detection of displacement [1], mass [2], force [3], torque [4], and charge [5]. Due to its practical significance, signal amplification has received a considerable amount of attention [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Diverse methods have been devised for signal amplification including electrical means, such as lock-in amplifiers [21] and phase-locked loops [22], where the backaction from the inherently noisy electrical amplifier needs to be treated, and mechanical means, where the motion of the resonator is mechanically preamplified by a large factor before being transduced into an electrical signal.…”