We demonstrate an acoustical analog of a circuit quantum electrodynamics system that leverages acoustic properties to enable strong multimode coupling in the dispersive regime while suppressing spontaneous emission to unconfined modes. Specifically, we fabricate and characterize a device that comprises a flux tunable transmon coupled to a 300  μm long surface acoustic wave resonator. For some modes, the qubit-cavity coupling reaches 6.5 MHz, exceeding the cavity loss rate (200 kHz), qubit linewidth (1.1 MHz), and the cavity free spectral range (4.8 MHz), placing the device in both the strong coupling and strong multimode regimes. With the qubit detuned from the confined modes of the cavity, we observe that the qubit linewidth strongly depends on its frequency, as expected for spontaneous emission of phonons, and we identify operating frequencies where this emission rate is suppressed.

We resolve phonon number states in the spectrum of a superconducting qubit coupled to a multimode acoustic cavity. Crucial to this resolution is the sharp frequency dependence in the qubitphonon interaction engineered by coupling the qubit to surface acoustic waves in two locations separated by ∼ 40 acoustic wavelengths. In analogy to double-slit diffraction, the resulting interference generates high-contrast frequency structure in the qubit-phonon interaction. We observe this frequency structure both in the coupling rate to multiple cavity modes and in the qubit spontaneous emission rate into unconfined modes. We use this sharp frequency structure to resolve single phonons by tuning the qubit to a frequency of destructive interference where all acoustic interactions are dispersive. By exciting several detuned yet strongly coupled phononic modes and measuring the resulting qubit spectrum, we observe that, for two modes, the device enters the strong dispersive regime where single phonons are spectrally resolved.Quantum control over mechanical degrees of freedom promises insight into fundamental physics as well as the development of innovative quantum technologies. As mechanical resonators are massive and macroscopic, they can probe quantum theories at large scales [1][2][3], while the ability of mechanical motion to couple to a variety of quantum systems has inspired numerous mechanicsbased transduction schemes [4][5][6][7][8][9][10]. Additionally, mechanical elements are compact compared to their electromagnetic counterparts, enabling the on-chip fabrication of many wavelength microwave structures such as high-performance filters and multimode resonators [11][12][13]. High-fidelity control over the large number of modes achievable in acoustic platforms would be a powerful resource for quantum information processing [14].The field of circuit quantum electrodynamics (cQED) has provided both guidance and tools for achieving quantum control over mechanical excitations. In cQED, the state of a photonic mode is measured and manipulated using superconducting qubits. These qubits can also interact with mechanical systems using piezoelectric materials. Two seminal works leveraged this fact to couple a qubit to a dilatational resonator [15] and to propagating surface acoustic waves (SAWs) [16]. Both surface and bulk acoustic waves can be confined to form highovertone resonators [17,18], leading to demonstrations of qubit-phonon coupling in multimode cavities [19][20][21][22][23]. Most recently, a pair of experiments used resonant interactions to create number and superposition states of an acoustic cavity mode, thereby demonstrating basic quantum control of acoustic phonons [3,24]. Following the example of cQED, achieving strong dispersive interactions in acoustic systems would lead to improved quantum control through quantum nondemolition phonon measurement [25,26] and qubit mediated phonon-phonon interactions [27,28]. Realizing these techniques in acoustic * lucas.sletten@colorado.edu systems would enable the exploration...

We report on the design and performance of an on-chip microwave circulator with a widely (GHz) tunable operation frequency. Nonreciprocity is created with a combination of frequency conversion and delay, and requires neither permanent magnets nor microwave bias tones, allowing on-chip integration with other superconducting circuits without the need for high-bandwidth control lines. Isolation in the device exceeds 20 dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at select operation frequencies. Furthermore, the device is linear with respect to input power for signal powers up to hundreds of fW (≈10 3 circulating photons), and the direction of circulation can be dynamically reconfigured. We demonstrate its operation at a selection of frequencies between 4 and 6 GHz.