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Quantum states of mechanical motion can be important resources for quantum information, metrology, and studies of fundamental physics. Recent demonstrations of superconducting qubits coupled to acoustic resonators have opened up the possibility of performing quantum operations on macroscopic motional modes, which can act as long-lived quantum memories or transducers. In addition, they can potentially be used to test for novel decoherence mechanisms in macroscopic objects and other modifications to standard quantum theory. Many of these applications call for the ability to create and characterize complex quantum states, putting demanding requirements on the speed of quantum operations and the coherence of the mechanical mode. In this work, we demonstrate the controlled generation of multi-phonon Fock states in a macroscopic bulk-acoustic wave resonator. We also perform Wigner tomography and state reconstruction to highlight the quantum nature of the prepared states. These demonstrations are made possible by the long coherence times of our acoustic resonator and our ability to selectively couple to individual phonon modes. Our work shows that circuit quantum acousto-dynamics (circuit QAD) enables sophisticated quantum control of macroscopic mechanical objects and opens the door to using acoustic modes as novel quantum resources.
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Phonon modes at microwave frequencies can be cooled to their quantum ground state using conventional cryogenic refrigeration, providing a convenient way to study and manipulate quantum states at the single phonon level. Phonons are of particular interest because mechanical deformations can mediate interactions with a wide range of different quantum systems, including solid-state defects, superconducting qubits, as well as optical photons when using optomechanically-active constructs. Phonons thus hold promise for quantum-focused applications as diverse as sensing, information processing, and communication. Here, we describe a piezoelectric quantum bulk acoustic resonator (QBAR) with a 4.88 GHz resonant frequency that at cryogenic temperatures displays large electromechanical coupling strength combined with a high intrinsic mechanical quality factor $Q_i approx 4.3 times 10^4$. Using a recently-developed flip-chip technique, we couple this QBAR resonator to a superconducting qubit on a separate die and demonstrate quantum control of the mechanics in the coupled system. This approach promises a facile and flexible experimental approach to quantum acoustics and hybrid quantum systems.
Solid-state quantum acoustodynamic (QAD) systems provide a compact platform for quantum information storage and processing by coupling acoustic phonon sources with superconducting or spin qubits. The multi-mode composite high-overtone bulk acoustic wave resonator (HBAR) is a popular phonon source well suited for QAD. However, scattering from defects, grain boundaries, and interfacial/surface roughness in the composite transducer severely limits the phonon relaxation time in sputter-deposited devices. Here, we grow an epitaxial-HBAR, consisting of a metallic NbN bottom electrode and a piezoelectric GaN film on a SiC substrate. The acoustic impedance-matched epi-HBAR has a power injection efficiency > 99% from transducer to phonon cavity. The smooth interfaces and low defect density reduce phonon losses, yielding fxQ products and phonon lifetimes up to 1.36 x 10^17 Hz and 500 microseconds respectively. The GaN/NbN/SiC epi-HBAR is an electrically actuated, multi-mode phonon source that can be directly interfaced with NbN-based superconducting qubits or SiC-based spin qubits.
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 qubit-phonon interaction engineered by coupling the qubit to surface acoustic waves in two locations separated by $sim40$ acoustic wavelengths. In analogy to double-slit diffraction, the resulting self-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.
Optomechanical systems typically use light to control the quantum state of a mechanical resonator. In this paper, we propose a scheme for controlling the quantum state of light using the mechanical degree of freedom as a controlled beam splitter. Preparing the mechanical resonator in non-classical states enables an optomechanical Stern-Gerlach interferometer. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, we recover single photon and two-photon interference via a classically controlled beam splitter. The visibility of the two-photon interference is particularly sensitive to coherent excitations in the mechanical resonator and this could form the basis of an optically transduced weak-force sensor.
The superposition of quantum states is one of the hallmarks of quantum physics, and clear demonstrations of superposition have been achieved in a number of quantum systems. However, mechanical systems have remained a challenge, with only indirect demonstrations of mechanical state superpositions, in spite of the intellectual appeal and technical utility such a capability would bring. This is due in part to the highly linear response of most mechanical systems, making quantum operation difficult, as well as their characteristically low frequencies, making it difficult to reach the quantum ground state. In this work, we demonstrate full quantum control of the mechanical state of a macroscopic mechanical resonator. We strongly couple a surface acoustic wave resonator to a superconducting qubit, using the qubit to control and measure quantum states in the mechanical resonator. Most notably, we generate a quantum superposition of the zero and one phonon states and map this and other states using Wigner tomography. This precise, programmable quantum control is essential to a range of applications of surface acoustic waves in the quantum limit, including using surface acoustic waves to couple disparate quantum systems.
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