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Inducing Strong Nonlinearities in a Phonon Trapping Quartz Bulk Acoustic Wave Resonator Coupled to a Superconducting Quantum Interference Device

Maxim Goryachev, Eugene N. Ivanov, Serge Galliou, Michael Edmund Tobar

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10¹⁸ Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID) amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structure of the spectrum in both incident power and frequency. The result gives an insight into the open loop behaviour of a future Cryogenic Quartz Oscillator in the strong signal regime.

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A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10¹⁸ Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID) amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structure of the spectrum in both incident power and frequency. The result gives an insight into the open loop behaviour of a future Cryogenic Quartz Oscillator in the strong signal regime.
Low-loss, high frequency acoustic resonators cooled to millikelvin temperatures are a topic of great interest for application to hybrid quantum systems. When cooled to 20 mK, we show that resonant acoustic phonon modes in a bulk acoustic wave quartz resonator demonstrate exceptionally low loss (with Q-factors of order billions) at frequencies of 15.6 and 65.4 MHz, with a maximum f · Q product of 7.8 × 1016 Hz. Given this result, we show that the Q-factor in such devices near the quantum ground state can be four orders of magnitude better than previously attained. Such resonators possess the low losses crucial for electromagnetic cooling to the phonon ground state, and the possibility of long coherence and interaction times of a few seconds, allowing multiple quantum gate operations.
Thermal Nyquist noise fluctuations of high-Q bulk acoustic wave cavities have been observed at cryogenic temperatures with a DC superconducting quantum interference device amplifier. High Q modes with bandwidths of few tens of milliHz produce thermal fluctuations with a signal-to-noise ratio of up to 23 dB. The estimated effective temperature from the Nyquist noise is in good agreement with the physical temperature of the device, confirming the validity of the equivalent circuit model and the non-existence of any excess resonator self-noise. The measurements also confirm that the quality factor remains extremely high (Q > 108 at low order overtones) for very weak (thermal) system motion at low temperatures, when compared to values measured with relatively strong external excitation. This result represents an enabling step towards operating such a high-Q acoustic device at the standard quantum limit.
We demonstrate that Bulk Acoustic Wave (BAW) quartz resonator cooled down to millikelvin temperatures are excellent building blocks for hybrid quantum systems with extremely long coherence times. Two overtones of the longitudinal mode at frequencies of 15.6 and 65.4 MHz demonstrate a maximum f.Q product of 7.8×1016 Hz. With this result, the Q-factor in such devices near the quantum ground state can be four orders of magnitude better than previously attained in other mechanical systems. Tested quartz resonators possess the ultra low acoustic losses crucial for electromagnetic cooling to the phonon ground state.
High-frequency mechanical resonators subjected to low thermal phonon occupancy are easier to be prepared to the ground state by direct cryogenic cooling. Their extreme stiffness, however, poses a significant challenge for external interrogations. Here we demonstrate a superconducting cavity piezoelectromechanical system in which multiple modes of a bulk acoustic resonator oscillating at 10 GHz are coupled to a planar microwave superconducting resonator with a cooperativity exceeding 2×10^{3}, deep in the strong coupling regime. By implementation of the noncontact coupling scheme to reduce mechanical dissipation, the system exhibits excellent coherence characterized by a frequency-quality-factor product of 7.5×10^{15} Hz. Interesting dynamics of classical temporal oscillations of the microwave energy is observed, implying the coherent conversion between phonons and photons. The demonstrated high-frequency cavity piezoelectromechanics is compatible with superconducting qubits, representing an important step towards hybrid quantum systems.
Hybrid systems that couple superconducting qubits to mechanical oscillators facilitate quantum control of individual phonons and have the potential to enable compact, highly coherent quantum memories and processors. To date, however, the utility of hybrid quantum acoustic devices has been limited by poor qubit and mechanical coherence times that are far shorter than those exhibited by their unhybridized counterparts. A primary challenge lies in the intrinsic nature of elastic waves in solids: the slow speed of sound results in a dense spectrum of acoustic modes, making it difficult to prevent spontaneous emission of the qubit into phononic degrees of freedom. In this thesis, I will present a systematic effort to suppress loss mechanisms in superconducting qubits and mechanical resonators in the context of circuit quantum acoustics. I begin by demonstrating the use of crystallographic orientation optimization to passively suppress diffraction losses in narrow-aperture quartz surface acoustic wave (SAW) resonators. We then study the coupling of SAW resonators to a quasi-continuum of bulk acoustic modes; this motivates us to abandon bulk piezoelectric media in favor of bandgap-protected thin-film devices. By fabricating suspended phononic crystal resonators from thin-film quartz, we demonstrate an order-of-magnitude improvement in the coherence of this class of devices. I conclude by presenting preliminary measurements of a new flip-chip architecture for circuit quantum acoustics -- the `acoustic trampoline' -- that is designed to maximize qubit-mechanical coupling while simultaneously suppressing spontaneous acoustic emission.
Mechanical objects have important practical applications in the fields of quantum information and metrology as quantum memories or transducers for measuring and connecting different types of quantum systems. The field of electromechanics is in pursuit of a robust and highly coherent device that couples motion to nonlinear quantum objects such as superconducting qubits. Here, we experimentally demonstrate a high-frequency bulk acoustic wave resonator that is strongly coupled to a superconducting qubit using piezoelectric transduction with a cooperativity of 260. We measure qubit and mechanical coherence times on the order of 10 microseconds. Our device requires only simple fabrication methods and provides controllable access to a multitude of phonon modes. We demonstrate quantum control and measurement on gigahertz phonons at the single-quantum level.