Quantum Nondemolition Measurement of a Quantum Squeezed State Beyond the 3 dB Limit

Abstract

We use a reservoir engineering technique based on two-tone driving to generate and stabilize a quantum squeezed state of a micron-scale mechanical oscillator in a microwave optomechanical system. Using an independent backaction-evading measurement to directly quantify the squeezing, we observe 4.7 AE 0.9 dB of squeezing below the zero-point level surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of squeezing obtained in the experiment. DOI: 10.1103/PhysRevLett.117.100801 Generating nonclassical states of a massive object has been a subject of considerable interest. It offers a route toward fundamental tests of quantum mechanics in an unexplored regime [1]. One of the most important and elementary quantum states of an oscillator is a squeezed state [2], which is a minimum uncertainty state that has a quadrature which is smaller than the zero-point level. Such states have long been discussed in the context of gravitational wave detection to improve the measurement sensitivity [3][4][5]. It is well known that a coherent parametric drive can be used to squeeze mechanical fluctuations [6,7], which is essentially equivalent to the technique first used to squeeze ground-state optical fields [8]. However, the maximum steady-state squeezing achieved by this method is limited to 3 dB due to the onset of parametric instability. Therefore, it is, in principle, impossible to have a steady state where the mechanical motion is squeezed below one half of the zero-point level using only parametric driving. These limitations may be overcome by combining continuous quantum measurement and feedback [9][10][11][12], but it would substantially increase the experimental complexity.Another method to generate a robust quantum state is quantum reservoir engineering [13], which has been used to generate quantum squeezed states and entanglement with trapped ions [14,15] and superconducting qubits [16]. It can also be applied to an optomechanical system to generate strong steady-state squeezing without quantumlimited measurement and feedback [17]. By modulating the optomechanical coupling with two imbalanced classical drive tones, the driven cavity acts effectively as a squeezed reservoir. When the engineered dissipation from the cavity dominates the dissipation from the environment, the mechanical resonator relaxes to a steady squeezed state. This technique has been applied recently to generate quantum squeezed states of macroscopic mechanical resonators [18][19][20].In addition to being a tool for state preparation, optomechanics also provides a means to probe the quantum behavior of macroscopic objects [21][22][23]. In particular, a backaction-evading (BAE) measurement [10,20,[24][25][26][27]] of a single motional quadrature can be implemented in an optomechanical system. If the drive tones that modulate the coupling are balanced, a continuou...

‘Mechano-optics’: an optomechanical quantum simulator

“…Following the first observations of the cooling of a mechanical oscillator using radiation pressure [3] came that of strongcoupling [4], and a host of architectures have appeared that incorporated mechanical elements in optical or microwave cavities. Cooling of a mechanical oscillator to its ground state first by cryogenic cooling [5] and then by means of radiation pressure [6] opened the door to experimenting with solid-state mechanical systems in the quantum regime, culminating in the observation of squeezed states of motion [7,8] and mechanical entanglement [9,10].…”

Generation of mechanical interference fringes by multi-photon counting

“…While our continuous-wave readout technique is suitable for the regime experimentally tested here, this technique cannot resolve displacements below the size of the ground state, which is required for mechanical quantum state reconstruction. Different techniques, such as quantum non-demolition pulsed quadrature measurements [32,43], or two-toned driving schemes [44], can allow this limit to be surpassed [45]. A detailed discussion of position measurements and mechanical state reconstruction is beyond the scope of the present work and the reader is encouraged to refer to these references for further details.…”

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

“…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.…”