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Nature Physics

Quantum squeezing in a nonlinear mechanical oscillator

Stefano Marti, Uwe von Lüpke, Om Joshi, Yu Yang, Marius Bild, Andraz Omahen, Yiwen Chu, Matteo Fadel

Published Jun 21, 2024• 58 citations
Publisher

Abstract

Abstract Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic quantum simulations. However, these applications require the engineering of squeezing and nonlinearities in the quantum regime. Here we demonstrate squeezing below the zero-point fluctuations of a gigahertz-frequency mechanical resonator coupled to a superconducting qubit. This is achieved by parametrically driving the qubit, which results in an effective two-phonon drive. In addition, we show that the resonator mode inherits a nonlinearity from the off-resonant coupling with the qubit, which can be tuned by controlling the detuning. We, thus, realize a mechanical squeezed Kerr oscillator, in which we demonstrate the preparation of non-Gaussian quantum states of motion with Wigner function negativities and high quantum Fisher information. This shows that our results can also have applications in quantum metrology and sensing.

DOI
10.1038/s41567-024-02545-6

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Abstract Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic quantum simulations. However, these applications require the engineering of squeezing and nonlinearities in the quantum regime. Here we demonstrate squeezing below the zero-point fluctuations of a gigahertz-frequency mechanical resonator coupled to a superconducting qubit. This is achieved by parametrically driving the qubit, which results in an effective two-phonon drive. In addition, we show that the resonator mode inherits a nonlinearity from the off-resonant coupling with the qubit, which can be tuned by controlling the detuning. We, thus, realize a mechanical squeezed Kerr oscillator, in which we demonstrate the preparation of non-Gaussian quantum states of motion with Wigner function negativities and high quantum Fisher information. This shows that our results can also have applications in quantum metrology and sensing.
Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic quantum simulations. These applications, however, require the engineering of squeezing and nonlinearities in the quantum regime. Here we demonstrate ground state squeezing of a gigahertz-frequency mechanical resonator coupled to a superconducting qubit. This is achieved by parametrically driving the qubit, which results in an effective two-phonon drive. In addition, we show that the resonator mode inherits a nonlinearity from the off-resonant coupling with the qubit, which can be tuned by controlling the detuning. We thus realize a mechanical squeezed Kerr oscillator, where we demonstrate the preparation of non-Gaussian quantum states of motion with Wigner function negativities and high quantum Fisher information. This shows that our results also have applications in quantum metrology and sensing.
Quantum squeezed states, with biased quantum noise, have been widely utilized in quantum sensing and quantum error correction applications. However, generating and manipulating these nonclassical states with a large squeezing degree typically requires strong nonlinearity, which inevitably induces additional decoherence that diminishes the overall performance. Here, we demonstrate the generation and amplification of squeezed states in a superconducting microwave cavity with weak Kerr nonlinearity. By subtly engineering an off-resonant microwave drive, we observe cyclic dynamics of the quantum squeezing evolution in a displaced frame of the cavity. Furthermore, we deterministically realize quantum squeezing amplification by alternately displacing the Kerr oscillator using the Trotterization technique, achieving a maximum squeezing degree of 14.6 dB and a squeezing rate of 0.28 MHz. Our demonstrated displacement-enhanced squeezing operation offers a hardware-efficient approach for generating large squeezed states, promising potential applications in quantum-enhanced sensing and quantum information processing.
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.
We propose the realization of a mechanically squeezed Kerr oscillator with a single ion in a tapered trap. We show that the motion coupling between the axial and radial modes caused by the trap geometry leads to Kerr nonlinearity of the radial mode with magnitude controlled by the trap frequencies. This allows the realization of non-Gaussian quantum gates, which play a significant role in the universal set of continuous variable quantum gates. Furthermore, we show that, because of the nonlinearity of the ion trap, applying an off-resonant time-varying electric field along the trap axis causes a motion squeezing of the radial mode. Finally, we discuss the motion mode frequency spectrum of an ion crystal in a tapered trap. We show that the frequency gap between the motion modes increases with trap nonlinearity, which benefits the realization of faster quantum gates.
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.
Two-mode squeezed states, which are entangled states with bipartite quantum correlations in continuous-variable systems, are crucial in quantum information processing and metrology. Recently, continuous-variable quantum computing with the vibrational modes of trapped atoms has emerged with significant progress, featuring a high degree of control in hybridizing with spin qubits. Creating two-mode squeezed states in such a platform could enable applications that are only viable with photons. Here, we experimentally demonstrate two-mode squeezed states by employing atoms in a two-dimensional optical lattice as quantum registers. The states are generated by a controlled projection conditioned on the relative phase of two independent squeezed states. The individual squeezing is created by sudden jumps of the oscillators' frequencies, allowing generating of the two-mode squeezed states at a rate within a fraction of the oscillation frequency. We validate the states by entanglement steering criteria and Fock state analysis. Our results can be applied in other mechanical oscillators for quantum sensing and continuous-variable quantum information.