Mechanical resonators are a promising way for interfacing qubits in order to realize hybrid quantum systems that offer great possibilities for applications. Mechanical systems can have very long energy lifetimes, and they can be further interfaced to other systems. Moreover, integration of mechanical oscillator with qubits creates a potential platform for exploration of quantum physics in macroscopic mechanical degrees of freedom. Utilization of high overtone bulk acoustic resonators coupled to superconducting qubits is an intriguing platform towards these goals. These resonators exhibit a combination of high frequency and high quality factors. They can reach their quantum ground state at dilution refrigeration temperatures and they can be strongly coupled to superconducting qubits via their piezoelectric effect. In this report, we demonstrate our system where bulk acoustic phonons of a high overtone resonator are coupled to a transmon qubit in a planar circuit architecture. We show that the bulk acoustic phonons are interacting with the qubit in the simple design architecture at the quantum level, representing further progress towards quantum control of mechanical motion.

The studies of mechanical resonators in the quantum regime not only provide insight into the fundamental nature of quantum mechanics of massive objects, but also introduce promising platforms for novel hybrid quantum technologies. Here we demonstrate a configurable interaction between a superconducting qubit and many acoustic modes in the quantum regime. Specifically, we show how consecutive Landau-Zener-Stückelberg (LZS) tunneling type of transitions, which take place when a system is tuned through an avoided crossing of the coupled energy levels, interfere in a multimode system. The work progresses experimental LZS interference to cover situations where the coupled levels are those of a qubit interacting with a multitude of mechanical oscillators in the quantum limit. The work opens up applications in controlling multiple acoustic modes via parametric modulation.Advances in the control over mechanical degrees of freedom have taken great leaps forward allowing to engineer experiments that go deep into the quantum regime, consequently showing the underlying nature of the quantized vibration energy [1][2][3][4][5][6][7]. These works predominantly utilized superconducting quantum bits combined with a variety of different types of mechanical resonators that can be accessed resonantly through the qubit in the high gigahertz frequency range. The resonators can be made with surface acoustic waves (SAW) [5, 7-12], phononic crystals [6], or high overtone bulk acoustic wave resonators (HBAR) [2,13,14], with piezoelectric materials allowing for strong coupling between electric and mechanical quantities. Mechanical modes are better isolated from the electromagnetic environment and can have longer coherence times than superconducting qubits. They are also much more compact than microwave cavities [15,16]. Therefore, incorporating mechanical resonators is highly appealing in quantum computing that can utilize harmonic oscillators [17,18].In an HBAR system, the modes mostly reside in the substrate chip and hence feature diluted strain and low acoustic losses. The system exhibits a dense spectrum of acoustic modes that interact near resonance with the qubit, suggesting a possibility to manipulate the manymode system through the qubit. One way to do the latter is to combine slow adiabatic changes and abrupt rotations of the adiabatic basis. This type of control of qubits resembles a coherent version of Landau-Zener tunneling transitions, which have been studied extensively in various two-level systems either in quantum or classical limit. These include superconducting qubits [19][20][21][22][23][24][25][26][27][28][29][30][31][32], nanomechanical systems [33][34][35][36][37][38], Bose-Einstein condensates [34,39,40], optical lattices [41], and other systems [42][43][44][45][46].In Landau-Zener-Stückelberg (LZS) interference, the system energy levels are modulated back and forth through an avoided crossing at a frequency ω rf faster than the decay rates. Earlier work on LZS physics in |e |g |g, 1 (2)Photon-assisted Landau-Zener-S...

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Multimode bulk acoustic systems show promise for use in superconducting quantum computation. They can serve as a medium-term memory storage, with exceptional coherence times being demonstrated, and they exhibit a mode density that is physically highly compact. Here, we experimentally demonstrate accessing individual acoustic modes without being hindered by the uniform frequency spacing of the modes. We use sideband control where a low-frequency modulation is applied to the transmon qubit energy. The amplitude of the modulation defines the qubit-acoustic mode coupling and its frequency detunes the acoustic sidebands, therefore selectively enabling the switching on or off of the interaction, and it allows for full control of the individual modes.