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Optical and Quantum Sensing and Precision Metrology II

Toward resonant coupling between a nm-scale electromechanical membrane and a MHz qubit

P.-F. Cohadon, Kyrylo Gerashchenko, Léo Balembois, Luis Najera, Himanshu Patange, Rémi Rousseau, Paul Manset, A. Heidmann, Tristan Briant, T. Jacqmin, S. Deléglise

Published Mar 19, 2025• 0 citations
Publisher

Abstract

We present experiments aimed at the creation and study of non-Gaussian states of a mesoscopic mechanical oscillator. On the mechanical front, we have developped, fabricated and operated phononic-crystal SiN membranes, with mechanical quality factors in the 10^8 to 10^9 range. To allow resonant coupling of the membrane (typically in the MHz band) to a two-level system, we have developped a heavy fluxonium superconducting qubit architecture, with a transition frequeny as low as 1.8 MHz.. Design, fabrication and operation of the qubit in a 10 mK environment are discussed, together with a charge sensing experiment The long-term goal of these experiments is to create and explore non-Gaussian states of an electromechanical membrane.

DOI
10.1117/12.3053457

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We use the strong intrinsic nonlinearity of a microwave superconducting qubit with a 4 GHz transition frequency to directly detect and control the energy of a micromechanical oscillator vibrating at 25 MHz. The qubit and the oscillator are coupled electrostatically at a rate of approximately 2π×22 MHz. In this far off-resonant regime, the qubit frequency is shifted by 0.52 MHz per oscillator phonon, or about 14% of the 3.7 MHz qubit linewidth. The qubit behaves as a vibrational energy detector and from its line shape we extract the phonon number distribution of the oscillator. We manipulate this distribution by driving number state sensitive sideband transitions and creating profoundly nonthermal states. Finally, by driving the lower frequency sideband transition, we cool the oscillator and increase its ground state population up to 0.48±0.13, close to a factor of 8 above its value at thermal equilibrium. These results demonstrate a new class of electromechanics experiments that are a promising strategy for quantum nondemolition measurements and nonclassical state preparation.

arXiv:1808.02673•Physical Review Letters•Oct 29, 2018•67 citations
We present experiments aimed at the creation and study of non-Gaussian states of a mesoscopic mechanical oscillator. On the mechanical front, we have developped, fabricated and operated phononic-crystal SiN membranes, with mechanical quality factors in the 10^8 to 10^9 range. To allow resonant coupling of the membrane (typically in the MHz band) to a two-level system, we have developped a heavy fluxonium superconducting qubit architecture, with a transition frequeny as low as 1.8 MHz.. Design, fabrication and operation of the qubit in a 10 mK environment are discussed, together with a charge sensing experiment The long-term goal of these experiments is to create and explore non-Gaussian states of an electromechanical membrane.
Long-lived mechanical resonators like drums oscillating at MHz frequencies and operating in the quantum regime are a powerful platform for quantum technologies and tests of fundamental physics. Yet, quantum control of such systems remains challenging, owing to their low energy scale and the difficulty of achieving efficient coupling to other well-controlled quantum devices. Here, we demonstrate repeated coherent interactions between a 4 MHz suspended silicon nitride membrane and a resonant superconducting heavy-fluxonium qubit. The qubit is initialized at an effective temperature of 21 μK21~\mathrm{μK}21 μK and read out with 77% single-shot fidelity. During the 6 ms6~\mathrm{ms}6 ms lifetime of the membrane the two systems swap excitations more than 300 times. After each interaction, a state-selective qubit detection is performed, implementing a stroboscopic series of weak measurements that provide information about the mechanical state. The accumulated records reconstruct the position noise spectrum of the membrane, revealing both its thermal occupation nth≈47n_\mathrm{th}\approx47nth​≈47 at 10 mK10~\mathrm{mK}10 mK and the qubit-induced back-action. By preparing the qubit either in its ground or excited state before each interaction, we observe an imbalance between the emission and absorption spectra, proportional to nthn_\mathrm{th}nth​ and nth+1n_\mathrm{th}+1nth​+1, respectively-a hallmark of the non-commutation of phonon creation and annihilation operators. Since the predicted Diósi-Penrose gravitational collapse time is comparable to the measured mechanical decoherence time, our architecture enters a regime where gravity-induced decoherence could be tested directly.
We demonstrate strong dispersive coupling between a fluxonium superconducting qubit and a 690 megahertz mechanical oscillator, extending the reach of circuit quantum acousto-dynamics (cQAD) experiments into a new range of frequencies.We have engineered a qubit-phonon coupling rate of g ≈ 2π × 14 MHz, and achieved a dispersive interaction that exceeds the decoherence rates of both systems while the qubit and mechanics are highly nonresonant ( /g 10).Leveraging this strong coupling, we perform phonon-number-resolved measurements of the mechanical resonator and investigate its dissipation and dephasing properties.Our results demonstrate the potential for fluxonium-based hybrid quantum systems, and a path for developing new quantum sensing and information processing schemes with phonons at frequencies below 700 MHz to significantly expand the toolbox of cQAD.
The ability to access a broad range of quantum states with mechanical oscillators has many applications and is an enduring ambition in the fields of opto- and electromechanics. However, as mechanical oscillators are linear at the quantum scale, arbitrary quantum control over them requires an extrinsic nonlinearity. In this thesis, I aim to provide this extrinsic nonlinearity and establish quantum control over the motion of a suspended aluminum disk by coupling it strongly to a superconducting qubit. To this end, I design and fabricate a device, when operated at its maximum coupling strength, could enable phonon-number-resolved measurements and arbitrary quantum control over the mechanical motion. However, limited by unclear reasons that break the qubit readout, I operate at approximately a quarter of the maximum coupling strength. Nevertheless, at this smaller coupling strength, I demonstrate the preparation of a non-Gaussian nonclassical state of motion.Because of the large coupling achieved in this work, the sideband transitions are phonon-number-sensitive, selectively altering the phonon populations in only a few Fock states. Using these phonon-number-sensitive sideband transitions, I dissipatively stabilize the mechanical oscillator into a highly-energized sub-Poissonian state, where its energy fluctuations are below the classical limit. This result represents a major step toward the long-time ambition of accessing a broad range of nonclassical states with macroscopic mechanical oscillators. Moreover, requiring neither number-resolution nor coherent control of the qubit, the dissipative stabilization technique demonstrated in this work also provides an accessible path toward preparing nonclassical states in other harmonic oscillators coupled to qubits.
Superconducting fluxonium qubits show a highly tunable energy-level structure, with transition frequencies spanning from a few MHz to few GHz. This range is well-aligned to the operational frequencies of highly coherent micro- and nano-mechanical resonators, making fluxonium an attractive candidate for hybrid electromechanical systems. In this work, we theoretically investigate a flux-tunable electromechanical system consisting of a fluxonium qubit coupled to a suspended mechanical resonator. The coupling arises from the motion-induced modulation of magnetic flux through the fluxonium loop, enabling both transverse and longitudinal electromechanical interactions that are tunable via external magnetic fields. By optimizing the design parameters of the fluxonium qubit, we demonstrate the feasibility of achieving strong resonant single-photon coupling near the flux-frustration point. We analyze the system dynamics across different coupling regimes, identifying signatures of electromagnetically induced transparency (EIT) in the longitudinal regime and mode splitting in the transverse regime. Additionally, we show that ground-state preparation of both subsystems is possible through sideband cooling of the mechanical resonator. These results suggest that a fluxonium-based hybrid electromechanical device could be a promising platform for studying macroscopic quantum phenomena and for applications in quantum technology.
Mechanical oscillators can be implemented to store and transfer information or to build hybrid systems. In order to couple a mechanical oscillator to a superconducting qubit, we fabricate a superconducting capacitor, in which diluted photoresist or electron beam photoresist is used as sacrificial layers. The upper plate of the capacitor, a suspended membrane, acts as a mechanical oscillator. We obtain its mechanical resonant frequency and response to the input microwave. Such mechanical oscillators can be used as the capacitor of a superconducting qubit to form a coupled system. In order to control the resonant frequency of the mechanical oscillator and the microwave resonator, we introduce a dc voltage bias between the upper and lower plates of the capacitor. We analyze the electromechanical coupling such as pull-in effect and experimentally demonstrate the dependence of the resonant frequency on the applied dc voltage. These results will contribute to the design and fabrication of hybrid systems comprising voltage-controlled mechanical oscillators and other systems.
We use the strong intrinsic nonlinearity of a microwave superconducting qubit with a 4 GHz transition frequency to directly detect and control the energy of a micromechanical oscillator vibrating at 25 MHz. The qubit and the oscillator are coupled electrostatically at a rate of approximately 2π×22 MHz. In this far off-resonant regime, the qubit frequency is shifted by 0.52 MHz per oscillator phonon, or about 14% of the 3.7 MHz qubit linewidth. The qubit behaves as a vibrational energy detector and from its line shape we extract the phonon number distribution of the oscillator. We manipulate this distribution by driving number state sensitive sideband transitions and creating profoundly nonthermal states. Finally, by driving the lower frequency sideband transition, we cool the oscillator and increase its ground state population up to 0.48±0.13, close to a factor of 8 above its value at thermal equilibrium. These results demonstrate a new class of electromechanics experiments that are a promising strategy for quantum nondemolition measurements and nonclassical state preparation.