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arXiv:2406.07360

A mechanical qubit

Yu Yang, Igor Kladarić, Maxwell Drimmer, Uwe von Lüpke, Daan Lenterman, Joost Bus, Stefano Marti, Matteo Fadel, Yiwen Chu

Published Jun 11, 2024• 0 citations
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Abstract

Strong nonlinear interactions between quantized excitations are an important resource for quantum technologies based on bosonic oscillator modes. However, most electromagnetic and mechanical nonlinearities arising from intrinsic material properties are far too weak compared to dissipation in the system to allow for nonlinear effects to be observed on the single-quantum level. To overcome this limitation, electromagnetic resonators in both the optical and microwave frequency regimes have been coupled to other strongly nonlinear quantum systems such as atoms and superconducting qubits, allowing for the demonstration of effects such as photon blockade and coherent quantum protocols using the Kerr effect. Here, we demonstrate the realization of the single-phonon nonlinear regime in a solid-state mechanical system. The single-phonon anharmonicity in our system exceeds the decoherence rate by a factor of 6.8, allowing us to use the lowest two energy levels of the resonator as a mechanical qubit, for which we show initialization, readout, and a complete set of direct single qubit gates. Our work adds another unique capability to a powerful quantum acoustics platform for quantum simulations, sensing, and information processing.

DOI
10.48550/arxiv.2406.07360

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Strong nonlinear interactions between quantized excitations are an important resource for quantum technologies based on bosonic oscillator modes. However, most electromagnetic and mechanical nonlinearities arising from intrinsic material properties are far too weak compared to dissipation in the system to allow for nonlinear effects to be observed on the single-quantum level. To overcome this limitation, electromagnetic resonators in both the optical and microwave frequency regimes have been coupled to other strongly nonlinear quantum systems such as atoms and superconducting qubits, allowing for the demonstration of effects such as photon blockade and coherent quantum protocols using the Kerr effect. Here, we demonstrate the realization of the single-phonon nonlinear regime in a solid-state mechanical system. The single-phonon anharmonicity in our system exceeds the decoherence rate by a factor of 6.8, allowing us to use the lowest two energy levels of the resonator as a mechanical qubit, for which we show initialization, readout, and a complete set of direct single qubit gates. Our work adds another unique capability to a powerful quantum acoustics platform for quantum simulations, sensing, and information processing.
Although strong nonlinear interactions between quantized excitations are an important resource for quantum technologies based on bosonic oscillator modes, most electromagnetic and mechanical nonlinearities are far too weak to allow for nonlinear effects to be observed at the single-quantum level. This limitation has been overcome in electromagnetic resonators by coupling them to other strongly nonlinear quantum systems such as atoms and superconducting qubits. We demonstrate the realization of the single-phonon nonlinear regime in a solid-state mechanical system. The single-phonon anharmonicity in our system exceeds the decoherence rate by a factor of 6.8, allowing us to use it as a mechanical qubit and demonstrate initialization, readout, and single-qubit gates. Our approach provides a powerful quantum acoustics platform for quantum simulations, sensing, and information processing.
Silicon nanomechanical resonators display ultra-long lifetimes at cryogenic temperatures and microwave frequencies. Achieving quantum control of single-phonons in these devices has so far relied on nonlinearities enabled by coupling to ancillary qubits. In this work, we propose using atomic forces to realize a silicon nanomechanical qubit without coupling to an ancillary qubit. The proposed qubit operates at 60 MHz with a single-phonon level anharmonicity of 5 MHz. We present a circuit quantum acoustodynamics architecture where electromechanical resonators enable dispersive state readout and multi-qubit operations. The combination of strong anharmonicity, ultrahigh mechanical quality factors, and small footprints achievable in this platform could enable quantum-nonlinear phononics for quantum information processing and transduction.
Mechanical qubits offer unique advantages over other qubit platforms, primarily in terms of coherence time and possibilities for enhanced sensing applications, but their potential is constrained by the inherently weak nonlinearities and small anharmonicity of nanomechanical resonators. We propose overcoming this shortcoming by using squeezed-Fock states of phonons in a parametrically driven nonlinear mechanical oscillator. We find that, under two-phonon driving, squeezed-Fock states become eigenstates of a Kerr-nonlinear mechanical oscillator, featuring an energy spectrum with exponentially enhanced and tunable anharmonicity, such that the transitions to higher energy states are exponentially suppressed. This enables us to encode the mechanical qubit within the ground and first excited squeezed-Fock states of the driven mechanical oscillator. This kind of mechanical qubit is termed mechanical squeezed-Fock qubit. We also show that our mechanical qubit can serve as a quantum sensor for weak forces, with its resulting sensitivity increased by at least one order of magnitude over that of traditional mechanical qubits. The proposed mechanical squeezed-Fock qubit provides a powerful quantum phonon platform for quantum sensing and information processing.
Mechanical resonators are emerging as a powerful platform for quantum information science, offering compactness, long coherence times, and scalability. In this thesis, we explore a circuit quantum acoustodynamics (cQAD) device based on integrating high-overtone bulk acoustic resonators (HBARs) with superconducting transmon qubits. This architecture harnesses the dense mode structure and high quality factors of HBARs alongside the fast control and high-fidelity readout of superconducting qubits. We demonstrate essential building blocks for phonon-based quantum operations, including direct measurements of phonon number and parity, as well as Wigner tomography of nonclassical states. We also realize Schrödinger cat states in a mechanical resonator with an effective mass of 16.2 micrograms and investigate their decoherence dynamics. Additionally, we demonstrate the creation and coherent control of a mechanical qubit enabled by strong single-phonon anharmonicity. Building on these capabilities, we introduce the concept of Acoustic Resonator-Based Quantum Circuits (ARQCs), where multiple phonon modes act as encoded qubits and a single transmon mediates interactions between them. This architecture supports compact, reconfigurable, and highly scalable quantum circuits capable of controlling hundreds of modes within a single device. Our experimental and simulation results position the cQAD platform as a compelling and versatile candidate for future quantum information processing technologies.
Hybrid mechanical-superconducting systems for quantum information processing have attracted significant attention due to their potential applications. In such systems, the weak coupling regime, dominated by dissipation, has been extensively studied. The strong coupling regime, where coherent energy exchange exceeds losses, has also been widely explored. However, the transition-coupling regime, which lies between the above two and exhibits rich, unique physics, remains underexplored. In this study, we fabricate a tunable coupling device to investigate the coupling of a superconducting transmon qubit to a seven-mode surface acoustic-wave resonator (SAWR), with a particular focus on the transition-coupling regime. Through a series of phonon oscillation experiments and studies in the dispersive regime, we systematically characterize the performance of the SAWR. We then explore the complex dynamics of energy exchange between the qubit and the mechanical modes, highlighting the interplay between dissipation and coherence. Finally, we propose a protocol for qubit readout and fast reset with a multimode mechanical cavity using one mode for readout and another mode for reset. We have demonstrated in simulation that the qubit achieves both fast reset and high coherence performance when the qubit is coupled to the reset mode in the transition-coupling regime.
Phonon blockade is a purely quantum phenomenon, analogous to Coulomb and photon blockades, in which a single phonon in an anharmonic mechanical resonator can impede the excitation of a second phonon. We propose an experimental method to realize phonon blockade in a driven harmonic nanomechanical resonator coupled to a qubit, where the coupling is proportional to the second-order nonlinear susceptibility ${\ensuremath{\chi}}^{(2)}$. This is in contrast to the standard realizations of phonon and photon blockade effects in Kerr-type ${\ensuremath{\chi}}^{(3)}$ nonlinear systems. The nonlinear coupling strength can be adjusted conveniently by changing the coherent drive field. As an example, we apply this model to predict and describe phonon blockade in a nanomechanical resonator coupled to a Cooper-pair box (i.e., a charge qubit) with a linear longitudinal coupling. By obtaining the solutions of the steady state for this composite system, we give the conditions for observing strong antibunching and sub-Poissonian phonon-number statistics in this induced second-order nonlinear system. Besides using the qubit to produce phonon blockade states, the qubit itself can also be employed to detect blockade effects by measuring its states. Numerical simulations indicate that the robustness of the phonon blockade, and the sensitivity of detecting it, will benefit from this strong induced nonlinear coupling.