The construction and operation of a high-quality factor microwave sapphire resonator transducer coupled to a 1 kHz niobium membrane acoustic oscillator are presented in this paper. A four-stage passive vibration isolation system was included in the design to permit the measurement of the transducer’s parametric properties. The isolation system was shown to sufficiently suppress mechanical noise above 100 Hz and an upper limit to the displacement sensitivity of the transducer was measured to be 3.0±0.6×10−16 m/√Hz. The parametric behavior of the transducer with a single pump readout was measured for several transducer configurations, and the results were found to be in good agreement with theory. The measurements presented here display for the first time the complete parametric behavior in a high electrical Q system, where the transducer’s bandwidth is less than the mechanical oscillator’s frequency. The high stability and low losses of our system may allow the transducer to be configured as a back-action evasion or quantum nondemolition device.
The construction and operation of a high-quality factor microwave sapphire resonator transducer coupled to a 1 kHz niobium membrane acoustic oscillator are presented in this paper. A four-stage passive vibration isolation system was included in the design to permit the measurement of the transducer’s parametric properties. The isolation system was shown to sufficiently suppress mechanical noise above 100 Hz and an upper limit to the displacement sensitivity of the transducer was measured to be 3.0±0.6×10−16 m/√Hz. The parametric behavior of the transducer with a single pump readout was measured for several transducer configurations, and the results were found to be in good agreement with theory. The measurements presented here display for the first time the complete parametric behavior in a high electrical Q system, where the transducer’s bandwidth is less than the mechanical oscillator’s frequency. The high stability and low losses of our system may allow the transducer to be configured as a back-action evasion or quantum nondemolition device.
To measure the standard quantum limit (SQL) a high quality transducer must be coupled to a high quality mechanical system. Due to its monolithic nature, the monolithic sapphire transducer (MST) has high quality factors for both types of resonances. Single loop suspension is shown to yield a mechanical quality factor of 6.10^8 at 4 K. From standard analysis we show the MST has the potential to measure noise fluctuations of the mechanical oscillator at the SQL. also, we point out a new way to determine if the transducer back action is quantum limited. We show that if the fluctuations are at the quantum limit, then the amplitude of the oscillation will be amplified by the ratio of the ringdown time to the measurement time, which is an inherently easier measurement.
The high-sensitivity quantum detection of a resonant classical force acting on a quantum harmonic oscillator can be significantly improved by employing a resonant optical parametric transducer. This technique leverages the unique properties of parametric interactions to enhance the response of the measurement system while maintaining quantum-limited performance. We demonstrate that such a configuration not only enables quantum back-action evading (BAE) measurements, surpassing the Standard Quantum Limit (SQL) of sensitivity, it also provides a mechanism for noiseless amplification of the classical signal. The key to this enhancement lies in the ability of the parametric transducer to generate and separately measure the upper and lower modulation sidebands induced by the external force. By decoupling and analyzing these sidebands independently, the system becomes capable of amplifying the signal without introducing additional noise, effectively circumventing quantum measurement constraints.
In the measurements on an oscillator to detect short bursts of gravitational radiation, one important demand is the ability to use short integration times in order to decrease the contribution of thermal noise. This requires a strong coupling of the antenna to the measuring apparatus, i.e., a high value of the so-called electromechanical coupling parameter ${\mathrm{\ensuremath{\beta}}}_{0}$. A well-known solution is in the use of a resonant transducer, which entails the observation of a system of two harmonic oscillators. We extend to this system the back-action evasion technique by showing that one can perform a quantum nondemolition measurement on a double harmonic oscillator with essentially the same configuration as for the single one.
The application of quantum mechanics to macroscopic motion suggests many counterintuitive phenomena. While the quantum nature of the motion of individual atoms and molecules has long been successfully studied, an equivalent demonstration of the motion of a near-macroscopic structure remains a challenge in experimental physics. A nanomechanical resonator is an excellent system for such a study. It typically contains > 10 10 atoms, and it may be modeled in terms of macroscopic parameters such as bulk density and elasticity. Yet it behaves like a simple harmonic oscillator, with mass low enough and resonant frequency high enough for its quantum zero-point motion and single energy quanta to be experimentally accessible. In pursuit of quantum phenomena in a mechanical oscillator, two important goals are to prepare the oscillator in its quantum ground state, and to measure its position with a precision limited by the Heisenberg uncertainty principle. In this work we have demonstrated techniques that advance towards both of these goals. Our system comprises a 30 micron × 170 nm, 2.2 pg, 5.57 MHz nanomechanical resonator capacitively coupled to a 5 GHz superconducting microwave resonator. The microwave resonator and nanomechanical resonator are fabricated together onto a single silicon chip and measured in a dilution refrigerator at temperatures below 150 mK. At these temperatures the coupling of the motion to the thermal environment is very small, resulting in a very high mechanical Q, approaching ∼ 10 6 . By driving with a microwave pump signal, we observed sidebands generated by the mechanical motion and used these to measure the thermal motion of the resonator. Applying a pump tone red-detuned from the microwave resonance, we used the microwave field to damp the mechanical resonator, extracting energy and "cooling" the motion in a manner similar to optical cooling of trapped atoms. Starting from a mode temperature of ∼ 150 mK, we reached ∼ 40 mK by this "backaction cooling" technique, corresponding to an occupation factor only ∼ 150 times above the ground state of motion. We also determined the precision of our device in measurement of position. Quantum mechanics dictates that, in a continuous position measurement, the precision may be no better than the zero-point motion of the resonator. Increasing the coupling of the resonator to detector will eventually result in back-action driving of the motion, adding imprecision and enforcing this limit. We demonstrated that our system is capable of precisions approaching this limit, and identified the primary experimental factors preventing us from reaching it: noise added to the measurement by our amplifier, and excess dissipation appearing in our microwave resonator at high pump powers. Furthermore, by applying both red- and blue-detuned phase-coherent microwave pump signals, we demonstrated back-action evading (BAE) measurement sensitive to only a single quadrature of the motion. By avoiding the back-action driving in the measured quadrature, such a technique has the potential for precisions surpassing the limit of the zero-point motion. With this method, we achieved a measurement precision of ∼ 100 fm, or 4 times the quantum zero-point motion of the mechanical resonator. We found that the measured quadrature is insensitive to back-action driving by at least a factor of 82 relative to the unmeasured quadrature. We also identified a mechanical parametric amplification effect which arises during the BAE measurement. This effect sets limits on the BAE performance but also mechanically preamplifies the motion, resulting in a position resolution 1.3 times the zero-point motion. We discuss how to overcome the experimental limits set by amplifier noise, pump power and parametric amplification. These results serve to define the path forward for demonstrating truly quantum-limited measurement and non-classical states of motion in a nearly-macroscopic object.
Acoustic modes—in the form of collective vibrations trapped between the parallel and polished surfaces of a crystalline cavity—provide an intriguing opportunity for probing the quantum-mechanical regime of macroscopical mechanical resonators. Moreover, the exceptional quality factors in a compact size from mm to μm motivate the integration of acoustic resonators into quantum circuits to explore the applications of a quantum hybrid system.While the acoustic modes of a crystal are commonly isolated from electrical dynamics, piezoelectricityis employed to transduce energy between the two domains. In the first part of this thesis, we investigate the means to improve the quality factor of a low frequency plano-convex monolithic quartz resonator. The resonator is 7mm indiameter and 250 μm in thickness, made only of only piezoelectric crystalline material. By the removal of clamping losses and incorporating a distant non-contact measurement setup,we demonstrate quality factors as high as 108 at cryogenic temperatures close to the quantumground state. Additionally, we model the electromechanical clamping losses of a particular grounding setup using temperature-dependent data and the acoustic transmission line based Mason’s model. In the latter part of this thesis, we couple a bulk acoustic high-overtone resonator (HBAR) with a transmon qubit. The electrical actuation of GHz-frequency sound in a HBAR is based on a μm-thin piezo film grown on a low-loss crystalline non-piezo bulk substrate. With an analogy to an acoustic musical instrument, the driven oscillations are amplified at the resonant frequencies of the acoustic cavity, with the addition that a small subset of such modes are selectively listened by the qubit. By the introduction of the acoustic overtones, high quality factors are accessible at the high frequencies of a transmon qubit,while the coupling between the two systems is distributed over the multitude of modes. I model this coupling in detail with respect to the system parameters for guiding the design of related quantum acoustic devices. I cover several different parameter regimes and explore the rich physics taking place in the multimodal hybrid system: Landau-Zener Stuckelberg interference, photon assisted sideband transitions and parametrically modulated coupling that involve the resonant periodical exchange of energy quanta known as vacuum Rabi oscillations, and drive-dependent multiphonon transitions. Despite the otherwise common difficulty to observe quantum mechanics in a harmonic oscillator, we observe purely quantum mechanical effects in the macroscopic resonator, such as a specific square root dependence of the transition energies on the quantum number.