Collective Dynamics in Circuit Quantum Acoustodynamics with a Macroscopic Resonator

Abstract

Collective dynamics in engineered quantum systems offer a unique and versatile platform for exploring how many-body correlations bridge microscopic entanglement and macroscopic behavior. In this work, we report collective Dicke dynamics of acoustic modes in a macroscopic high-overtone bulk acoustic resonator (HBAR). To achieve this, we engineer a hybrid quantum acoustodynamic system comprising an HBAR strongly coupled to a superconducting transmon qubit. The HBAR device is distinctive in the sense that its narrow mode spacing, together with enhanced qubit-mode coupling strength, gives rise to efficient coupling between the transmon and clusters of near-resonant modes. By harnessing the system properties, we observe collective dynamics involving clusters composed by two or three mechanical modes, where their non-resonant spectrum allows for the observation of the transition between the Dicke static regime to dynamically induced timed-Dicke one. The coherent collective behavior of the system is supported by time-domain measurements of the qubit's purity, indicating the quantum nature of the collective dynamics. Overall, our work establishes HBAR-based hybrid quantum system as a promising platform for exploring many-body collective dynamics in macroscopic mechanical systems.

Figures (4)

• Figure 1: The hybrid quantum system. (a) Microscope image of the experimental device, featuring a superconducting transmon qubit coupled to a high-overtone bulk acoustic resonator (HBAR). (b) Schematic of the device, illustrating the hybrid quantum system fabricated by a flip-chip technique to align the bottom chip with the top chip. Top: the flux-tunable qubit with an antenna for coupling the HBAR; Bottom: The qubit control lines, The HBAR, readout resonators and a Purcell filter. (c) Representation of clustered modes obtained in our device, where the top figure shows two clustered modes separated in frequency by $\Delta_{c,c+1}$, much greater than the qubit-HBAR coupling strength. By analyzing the structure of each cluster, bottom figure, it shows that the intra-mode spacing $\delta^{n,m}_{c}$ is comparable to the coupling strength. (d) Spectroscopy of the qubit $Q_B$, experimentally showing nine different clusters with inter-mode FSR around $\Delta_{c,c+1} \approx 2\pi\times 30.2$ MHz. The red and green inset panels show the examples of two-mode clusters and three-mode clusters systems, where we highlight the spectral theoretical curves obtained from the model in Eq. \ref{['Eq:ThreeModeH']}, used to estimate the maximum intra-cluster frequency separation around $\delta_{c}^{n,m} \approx 2\pi\times1.4$ MHz, which is much smaller than the inter-cluster frequency gap $\Delta_{c,c+1}$. See SM for more details on the spectroscopy of the clusters systems considered in this work.
• Figure 2: Coherence energy swapping between the qubit and multi-mode HBAR. (a) and (b) show qubit spectroscopy near the HBAR modes, where the qubit frequency is tuned close to the HBAR modes, resulting in anti-crossings with three peaks (a) and four peaks (b), corresponding to the hybridization of the qubit with the two-mode HBAR in (a) and three modes HBAR in (b), respectively. (c) and (d) show the vacuum Rabi oscillations between the superconducting qubit and multimode HBAR. The experimental pulse sequence is shown in the top of (c) and (d), where the qubit is first excited and then tuned into resonance with the HBAR modes for a controlled interaction time $t$. The schematic illustrates coherent energy exchange between the qubit and two- or three-mode HBARs. The measured two-dimensional vacuum Rabi spectra in (c) and (d) reveal distinct features of the collective dynamics, consistent with the simulated circuit model shown in SM. $Q_{A}$ and $Q_{B}$ refers to different qubits chosen from two devices of the hybrid quantum system, see Ref. SM further details.
• Figure 3: Experimentally measured qubit population, normalized by the collective population of the static Dicke dynamics $P_{\mathrm{qu},N_c}^{\mathrm{col}}(t)$, as function of the time to systems (a) $S_{2,1}$ and (b) $S_{2,2}$ with two modes, and the three mode systems (c) $S_{3,1}$ and (d) $S_{3,2}$. Gray curves describe $P_{\mathrm{qu},N_c}^{\mathrm{col}}(t)/P_{\mathrm{qu},2}^{\mathrm{col}}(t)$ in (a) and (b), and $P_{\mathrm{qu},N_c}^{\mathrm{col}}(t)/P_{\mathrm{qu},3}^{\mathrm{col}}(t)$ for (c) and (d). Error bars are shown as filled regions in the graphs.
• Figure 4: Qubit purity as function of time for (a) system $S_{2,1}$ and (b) system $S_{3,1}$, with curves showing the expected behavior of static Dicke regime for different $N_{c}$. The red dashed vertical line is the minimum purity time predicted by the analytical $\tau_{\mathrm{min}\mathcal{P}}$. Error bars are shown as filled regions.