showed patience and understanding. He gave me the opportunity to work on a variety of interesting projects, from graphene, to superconducting amplifiers, to the results discussed here. Most of all, Keith taught me to be more decisive, to take more risks, and to do whatever it takes. Our theory collaborators on the squeezing project, Aashish Clerk, Florian Marquardt, and especially Andreas Kronwald, gave essential support before, during, and after measurement-taking.Although they sometimes seemed puzzled at the number of ways that things can go wrong in experimental work, they showed great patience as we tried to make their proposal a reality.I couldn't have made it through grad school without the support of my friends: Paul, Branimir, Helge, Alice, Tristan, Chris, Kris, Doron, Mo, and Carly. They gave me something to look forward to throughout the week, and something to talk about other than grad school. where an optical or microwave cavity is coupled to the mechanics in order to control and read out the mechanical state. In the proposal, two pump tones are applied to the cavity, each detuned from the cavity resonance by the mechanical frequency. The pump tones establish and couple the mechanics to a squeezed reservoir, producing arbitrarily-large, steady-state squeezing of the mechanical motion.In this dissertation, I describe two experiments related to the implementation of this proposal in an electromechanical system. I also expand on the theory presented in [30] to include the effects of squeezing in the presence of classical microwave noise, and without assumptions of perfect alignment of the pump frequencies.In the first experiment, we produce a squeezed thermal state using the method of Kronwald et. al..We perform back-action evading measurements of the mechanical squeezed state in order to probe the noise in both quadratures of the mechanics. Using this method, we detect single-quadrature fluctuations at the level of 1.09 ± 0.06 times the quantum zero-point motion.In the second experiment, we measure the spectral noise of the microwave cavity in the presence of the squeezing tones and fit a full model to the spectrum in order to deduce a quadrature variance of 0.80 ± 0.03 times the zero-point level. These measurements provide the first evidence of quantum squeezing of motion in a mechanical resonator.

The substrate is composed of a 100nm thick low-stress SiN layer on top of a Si wafer.The Cooper-Pair Box (CPB) is patterned using electron-beam lithography and double-angle evaporation of aluminum. 31 The thickness of the island and the ground leads are ~ 60 nm and ~ 20 nm respectively. The island is coupled to the ground leads via two small (~ 100 x 100 nm 2 ) Al/AlO x /Al Josephson tunnel junctions, and is arranged in a DC-SQUID configuration.The aluminum layer used to define the nanoresonator, and which ultimately serves as the electrode on top of the nanoresonator, is patterned in the same step as the CPB. This layer acts as an etch mask for undercutting the nanoresonator. To protect the CPB during etching, a layer of PMMA is spun on the sample, and a small window defining the nanoresonator is opened using a second e-beam lithography step. The nanoresonator is then undercut in an ECR etcher with Ar/NF3 plasma: The first step is an anisotropic SiN etch that defines the resonator beam; and the second is an isotropic etch of the underlying Si to undercut the beam.

Quantum electromechanical systems offer a unique opportunity to probe quantum noise properties in macroscopic devices, properties that ultimately stem from Heisenberg's uncertainty relations. A simple example of this behavior is expected to occur in a microwave parametric transducer, where mechanical motion generates motional sidebands corresponding to the up-and-down frequency conversion of microwave photons. Because of quantum vacuum noise, the rates of these processes are expected to be unequal. We measure this fundamental imbalance in a microwave transducer coupled to a radiofrequency mechanical mode, cooled near the ground state of motion. We also discuss the subtle origin of this imbalance: depending on the measurement scheme, the imbalance is most naturally attributed to the quantum fluctuations of either the mechanical mode or of the electromagnetic field.

During the theoretical investigation of the ultimate sensitivity of gravitational wave detectors through the 1970's and '80's, it was debated whether quantum fluctuations of the light field used for detection, also known as photon shot noise, would ultimately produce a force noise which would disturb the detector and limit the sensitivity. Carlton Caves famously answered this question with "They do." [1] With this understanding came ideas how to avoid this limitation by giving up complete knowledge of the detector's motion [2][3][4]. In these back-action evading (BAE) or quantum non-demolition (QND) schemes, one manipulates the required quantum measurement back-action by placing it into a component of the motion which is unobserved and dynamically isolated. Using a superconducting, electro-mechanical device, we realize a sensitive measurement of a single motional quadrature with imprecision below the zero-point fluctuations of motion, detect both the classical and quantum measurement back-action, and demonstrate BAE avoiding the quantum back-action from the microwave photons by 9 dB. Further improvements of these techniques are expected to provide a practical route to manipulate and prepare a squeezed state of motion with mechanical fluctuations below the quantum zero-point level, which is of interest both fundamentally [5] and for the detection of very weak forces [6].Since the discovery of Shor's Algorithm [7] almost 20 years ago, a major theme in physics has been about the untapped power and benefits of quantum phenomena, largely stemming from the resource of quantum entanglement. However much earlier, it was understood how quantum physics places limits on our knowledge [8,9]. This limitation can be useful, as in the case of quantum cryptography schemes where the required quantum measurement back-action of an eavesdropper leaves its trace on the transmitted information, providing proof of their snooping. For measurements of position, this limitation, called the Standard Quantum Limit (SQL) [9] is not beneficial: back-action due to the quantum nature of the measurement field, ultimately obscures our vision for a sufficiently sensitive measurement.Quantum limitations on the detection of position are no longer academic issues; in recent years, the detection of motion has now advanced to the point that quantum back-action engineering is now required to improve the sensitivity. Detections of motion have been realized with imprecision below that at SQL [10,11]. Back-action forces from the quantum noise of the detection field have been demonstrated to drive the motion of mechanical oscillators, first with electrons in an electro-mechanical structure [12] and then with photons in opto-mechanical systems [13,14]. In this work, we demonstrate the backaction forces due to the shot noise of microwave photons, which are 10 4 times lower in energy than optical photons.Strategies to manipulate the quantum measurement back-action have included modifying the quantum fluctuations of the measurement field [15,16], and modulati...

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...