In a paper recently published in the journal Nature Communications, researchers investigated phonon coherence using a quantum sensor.
a False-color scanning electron micrograph of the mechanical resonators. Lithium niobate (LN) phononic crystal cavities (red) are patterned with aluminum electrodes (orange) and undercut from the silicon substrate (blue). Inset shows an optical micrograph of the coupling capacitor pad, which is galvanically connected to the mechanical electrodes. The resonators are too small to be seen in this image, but their location is indicated in red. b Optical micrograph of the bottom chip, showing the superconducting qubit, control lines, and readout resonator. Inset shows the qubit’s SQUID and flux line. c Mechanical device fabrication. Cross-sectional illustration of the patterning, cleaning, metallization, and release etching steps. Bandages create electrical contact between the active mechanics electrode and the coupling capacitor pad, as well as between the ground electrode and the chip’s ground plane. d Photograph of the composite flip-chip assembly. Control lines on the qubit (bottom) chip are visible, as well as the polymer adhesive which fixes the top chip in place. e Approximate location of the cross-chip coupling capacitor. The illustration shows the two halves of the coupling capacitor (orange) aligned vertically and separated by approximately 1 μm. Image Credit: https://www.nature.com/articles/s41467-024-48306-0
Mechanical Decoherence in Nanomechanical Systems
Nanomechanical oscillators offer several benefits for quantum technologies owing to their ability to detect motion and force, long lifetimes, and compact size. The integration of nanomechanical oscillators with superconducting qubits has shown potential for hardware-efficient quantum error-correction protocols, which involve the superpositions of mechanical coherent states.
However, understanding the decoherence processes impacting mechanical oscillators within the quantum limit is crucial to fully realize this hybrid platform's potential. Two-level system (TLS) defects are an important loss channel impacting nanomechanical systems. TLS can create a dissipation channel for nearby modes by coupling to elastic and electromagnetic fields.
The TLS-induced decoherence and decay dynamics at microwave frequencies have been studied extensively in both nanomechanical and electromagnetic systems. Their impact on microwave loss depends on temperature and power, allowing the extraction of the TLS-induced loss tangent from measurements of the resonator's quality factor and frequency.
Specifically, the TLS's impact on dielectric loss is suppressed when the intra-cavity energy exceeds a critical threshold. In this condition, the TLS spontaneous emission and excitation rates equilibrate as the TLS attains a steady state where no energy is absorbed from the resonator mode.
Although previous TLS saturation studies have involved monitoring a resonator's scattered response at various drive powers, superconducting qubits with their set of control and readout techniques offer a more sensitive investigation of TLS behavior.
The Proposed Approach
In this study, researchers performed phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity using a superconducting qubit to achieve high-resolution analysis of mechanical dephasing and dissipation in variable-size coherent states. They extended the flexibility of circuit QED measurement techniques into the domain of mechanical devices to better understand TLS behavior.
The mechanical oscillators employed were one-dimensional (1D) phononic crystal cavities constructed from thin-film lithium niobate. Although the device contained two resonators, the experiments focused on one cavity that supported the higher frequency mode.
The cavity was formed from periodic structures acting as acoustic mirrors, which suspended a defect site from both ends. These cavities, with their small mode volume, were ideal for TLS studies as a mechanical loss channel due to their robust coupling to fewer TLS. The device was assembled using a hybrid flip-chip architecture.
The qubit's nonlinearity enabled quantum nondemolition measurement of the mechanical state. A Ramsey protocol with a superconducting qubit was employed to perform phonon number- and time-resolved measurements on the mechanical resonator.
Specifically, a dispersive phonon number measurement was applied to study coherent states in a phononic crystal resonator. Researchers examined how the initial phonon state size influenced the energy decay and dephasing of these states and reproduced several of these signatures using a simple numerical model that included an ensemble of saturable TLS.
This approach allowed the observation of TLS-induced dissipation signatures in the time domain. The method can also be extended to other bosonic systems, providing a highly detailed picture of the evolution of an oscillator's larger mechanical states over time. This offers fresh insights into quantum nonlinear dissipation processes.
Significance of the Study
A nonexponential relaxation and state size-dependent reduction of the dephasing rate were observed, attributed to TLS. The observed mechanical dissipation dynamics were consistent with emission into a bath of rapidly dephasing TLS.
Results of the ringdown measurements of variable-size mechanical coherent states showed an initial period of fast decay, which eventually led to substantially slower dissipation. The mechanical dissipation rate varied with the evolving phonon state size, indicating that the process could not be described by the simple linear relation expected for a harmonic oscillator.
This behavior was reproduced using a simple numerical model incorporating a small ensemble (N = 5) of TLS. The initial fast decay was due to the mechanical mode decaying into the TLS, while the slower decay emerged after the saturation of TLS. Researchers also performed mechanical dephasing measurements involving the mechanical state's coherent displacements and studied them numerically.
To summarize, this study conducted a detailed investigation of TLS-induced phonon decoherence in the quantum regime. The results are directly relevant for bosonic error-correction schemes involving phonons' coherent states and emphasize the need for enhanced fabrication and materials processing techniques to mitigate the presence of TLS. A more complex computational model and additional measurements, such as spectral hole burning, could benefit future studies investigating the saturation dynamics.
Journal Reference
Cleland, A. Y., Wollack, E. A., Safavi-Naeini, H. A. (2024). Studying phonon coherence with a quantum sensor. Nature Communications, 15(1), 1-7. https://doi.org/10.1038/s41467-024-48306-0, https://www.nature.com/articles/s41467-024-48306-0
Disclaimer: The views expressed here are those of the author expressed in their private capacity and do not necessarily represent the views of AZoM.com Limited T/A AZoNetwork the owner and operator of this website. This disclaimer forms part of the Terms and conditions of use of this website.