Generation of large amplitude phonon states in quantum acoustics

Abstract

The development of quantum acoustics has enabled the cooling of mechanical objects to their quantum ground state, generation of mechanical Fock-states, and Schrödinger cat states. Such demonstrations have made mechanical resonators attractive candidates for quantum information processing, metrology, and macroscopic tests of quantum mechanics. However, generating large-amplitude phonon states in quantum acoustic systems has been elusive. In this work, a single superconducting qubit coupled to a high-overtone bulk acoustic resonator is used to generate a large phonon population in an acoustic mode of a high-overtone resonator. We observe extended ringdowns of the qubit, confirming the generation of a large amplitude phonon state, and also observe an upper threshold behavior, a consequence of phonon quenching predicted by our model. This work provides a key tool for generating arbitrary phonon states in circuit quantum acoustodynamics, which is important for fundamental and quantum information applications.

Fig. 1. Schematic of the on-chip ℏBAR device.

Rendering of the ℏBAR device. The ℏBAR device comprises two chips bonded in a flip-chip orientation. The top chip is 650 μm of sapphire, hosts the high-overtone bulk acoustic wave resonances (HBAR) modes (red), and is coupled to the superconducting antenna using an aluminum nitride pad (red). The pocket-style transmon qubit (silver) is fabricated from niobium titanium nitride on the bottom silicon chip and coupled to the feedline via an on-chip readout resonator (blue). Art produced by Enrique Sahagun.

Fig. 2. Qubit-induced acoustic linewidth narrowing.

a Definition of modes and the coupling rates between the modes. The readout resonator $\widehat{a}$ has input-output modes labelled 1 and 2, and is dispersively coupled to the qubit ${\widehat{\sigma }}_{\mathrm{z}}$ with a rate χ. The mechanical mode is labeled $\widehat{b}$ and has a qubit-phonon coupling rate g_qb. b Measured two-tone spectroscopy for drive power of −12.0 dBm set at room temperature. c Measured phonon-induced transparency window as a function of qubit drive power. Starting from the lowest curve, drive powers are −12.0, −6.0, and −2.0 dBm set at room temperature, respectively. With increasing power, two features can be noticed. The transparency window reduces in depth, and the full-width half-maximum linewidth narrows. d Extracted experimental full-width half-maximum of the transparency window as a function of qubit drive power. Colored points match the corresponding curves in c.

Fig. 3. Large amplitude phonon states observed through qubit ringdown dynamics.

a Schematic of the energy levels for the weakly hybridized phonon-qubit system. The qubit acts as an artificial two-level atom, with ground state $∣g⟩$ and excited state $∣e⟩$. A coherent drive of strength Ω_q drives the qubit between its ground and excited state. The qubit-mechanical couple at a rate g_qb and a qubit and mechanics decay at a rate γ_q and γ_b, respectively. The rate at which excitation transfer processes $∣e,N-1⟩\to ∣g,N⟩$ occur scales as $\sqrt{N}$, where N is the total number of excitations, while the phonon relaxation scales linearly with N. The qubit is rapidly re-excited for strong pump powers, resulting in a build-up of phonon excitations. b Measured qubit ringdown for a qubit drive of −3.0 dBm. Blue line: the qubit drive is detuned from the HBAR by 250 kHz with the phonon mode in the non-lasing state, decaying on a time scale of the  ~200 ns decay of the qubit. Red line: The qubit drive is tuned directly on resonance with the HBAR mode, exciting it into the lasing state, exhibiting a dramatically longer, non-exponential decay due to re-excitation from the coherently excited phonon mode. The master equation simulation (dashed black line) is plotted over the data.

Fig. 4. Unique signatures of predicted upper threshold.

a Measured gated qubit ringdown for a qubit drive of −12.0, −8.0, −6.0, and −2.0 dBm. With increasing drive power, the gated qubit ringdowns increase in amplitude and duration as the phonon mode population increases. b Measured gated qubit ringdown for a qubit drive of −2.0, 2.0, 4.0, and 8.0 dBm. The qubit drive is tuned directly on resonance with the HBAR mode for all measurements. With increasing drive power, the gated qubit ringdowns decrease in amplitude and duration as the phonon mode population decreases above the self-quenching threshold. For all measurements in (a) and (b), the qubit drive is tuned directly on resonance with the HBAR mode. c Simulated phonon state population $⟨{\widehat{b}}^{†}\widehat{b}⟩$ as a function of qubit drive power. The phonon population is at its maximum at a drive power of approximately −2.0 dBm and decreases for drive powers above the upper threshold. The colored data points indicate the corresponding trace colors in (a) and (b).