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Nano Letters

Thermally Induced Parametric Instability in a Back-Action Evading Measurement of a Micromechanical Quadrature near the Zero-Point Level

Junho Suh, Matthew D. Shaw, Henry George LeDuc, Alan J Weinstein, Keith Schwab

Published Nov 7, 2012• 29 citations
Publisher

Abstract

We report the results of back-action evading experiments utilizing a tightly coupled electro-mechanical system formed by a radio frequency micromechanical resonator parametrically coupled to a NbTiN superconducting microwave resonator. Due to excess dissipation in the microwave resonator, we observe a parametric instability induced by a thermal shift of the mechanical resonance frequency. In light of these measurements, we discuss the constraints on microwave dissipation needed to perform BAE measurements far below the zero-point level.

DOI
10.1021/nl303353r

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We report the results of back-action evading experiments utilizing a tightly coupled electro-mechanical system formed by a radio frequency micromechanical resonator parametrically coupled to a NbTiN superconducting microwave resonator. Due to excess dissipation in the microwave resonator, we observe a parametric instability induced by a thermal shift of the mechanical resonance frequency. In light of these measurements, we discuss the constraints on microwave dissipation needed to perform BAE measurements far below the zero-point level.
We show that the two-level systems (TLS) in lithographic superconducting circuits act as a power-dependent dielectric leading to non-linear responses in a parametrically coupled electromechanical system. Driven TLS shift the microwave resonance frequency and modulate the mechanical resonance through the optical spring effect. By pumping with two tones in a back-action evading measurement, these effects produce a mechanical parametric instability which limits single quadrature imprecision to 1.4 xzp. The microwave resonator noise is also consistent to a TLS-noise model. These observations suggest design strategies for minimizing TLS effects to improve ground-state cooling and quantum non-demolition measurements of motion.
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.
We review a scheme for performing a backaction-evading measurement of one mechanical quadrature in an optomechanical setup. The experimental application of this scheme has been limited by parametric instabilities caused in general by a slight dependence of the mechanical frequency on the electromagnetic energy in the cavity. We find that a simple modification to the optical drive can effectively eliminate the parametric instability even at high intracavity power, allowing realistic devices to achieve sub-zero-point uncertainties in the measured quadrature.
The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for force detection and quantum physics of macroscopic objects. In the first experiment, the dispersive mechanical resonance shift from the interaction with a Cooper-pair box qubit is studied. The measured coupling strength is large enough to satisfy one of the conditions required to perform many of the proposed quantum nanomechanical measurements. The resonance shift also probes the microwave-driven response of the qubit, showing Rabi oscillation and Landau-Zener tunneling, proving the coherent dynamics of the qubit. Second, the parametric excitation of nanomechanical motion is studied via experiments with a driven qubit. Degenerate parametric amplification and oscillation are demonstrated, with a new observation of nonlinear dissipation. The squeezing of the back-action noise from the detection amplifier is also observed, up to 4dB. It is the first demonstration using a qubit as an auxiliary system to modify the nanomechanical dynamics, showing a possible route for generation of nanomechanical quantum states. Finally, back-action cooling of nanomechanical motion has been investigated, which is implemented by capacitively coupling a high-Q coplanar waveguide microwave resonator to a nanomechanical resonator. The thermal state with 7.5 mechanical quanta on average is reached, a result that is ultimately limited due to increased bath heating with microwave power. The heating is consistent with a model based on two-level systems resonantly coupled to the nanomechanical mode. This additional heating suggests future efforts to improve coupling and for reducing two-level system density in materials employed to reach the motional ground state via back-action cooling.
We present a new optomechanical device where the motion of a micromechanical membrane couples to a microwave resonance of a three-dimensional superconducting cavity. With this architecture, we realize ultrastrong parametric coupling, where the coupling not only exceeds the dissipation in the system but also rivals the mechanical frequency itself. In this regime, the optomechanical interaction induces a frequency splitting between the hybridized normal modes that reaches 88% of the bare mechanical frequency, limited by the fundamental parametric instability. The coupling also exceeds the mechanical thermal decoherence rate, enabling new applications in ultrafast quantum state transfer and entanglement generation.