In-equilibrium thermodynamics and ground-state fluctuations of a mesoscopic mechanical object

Abstract:

In the early 80’s, Braginsky and Caves proposed that a quantum mechanical oscillator could implement the ultimate detector for a tiny classical field: namely a gravitational wave. But it is also a unique sensing capability for quantum fields. The subject of study is then the baths to which the mechanical mode is coupled to, tackling topical questions linked e.g. to Material Science or Quantum Gravity [1].  Studying in-equilibrium properties of a quantum mesoscopic mechanical mode is obviously extremely challenging: for objects of reasonable sizes, the fundamental mode resonance frequency lies in the MHz range, which requires sub-milliKelvin brute-force cooling to achieve a thermal population n_th < 1. We created a microwave optomechanical platform implemented on a nuclear demagnetisation cryostat for this purpose [2]. Recently, through a collaboration with Aalto we indeed demonstrated that a drumhead aluminum device of about 15 μm diameter can be cooled to its quantum ground state, meaning that all its mechanical modes shall satisfy n_th < 1 [3]. Quantum signatures such as sideband asymmetry are reported. But this result is based on the measurement of mean quantities; much more can be learned from fluctuations. We developed a new approach to optomechanics, based on a Traveling Wave Parametric Amplifier (TWPA) that enables us to resolve in real-time the energy fluctuations of a mechanical mode. At high temperature (in the classical limit), we obtained both the Power Spectral Density (PSD) and the Probability Distribution Function (PDF) for the first flexure of a beam device. The former is characteristic of an Ornstein-Uhlenbeck process, while the latter is nothing but the Boltzmann exponential law [4]. Pushing this technique to the quantum regime would open up unique new capabilities.

References

[1] E. Collin. “Mesoscopic quantum thermo-mechanics: a new frontier of experimental physics”. AVS Quantum Sci., 4:020501, 2022.

[2] X. Zhou, D. Cattiaux, R. Gazizulin, A. Luck, O. Maillet, T. Crozes, J.-F. Motte, O. Bourgeois, A. Fefferman, and E. Collin. “On-chip thermometry for microwave optomechanics implemented in a nuclear demagnetization cryostat”. Phys. Rev. Applied, 12:044066, 2019.

[3] D. Cattiaux, I. Golokolenov, S. Kumar, M. Sillanpää, L. Mercier de Lépinay, R. Gazizulin, X. Zhou, A. Armour, O. Bourgeois, A. Fefferman, and E. Collin. “A macroscopic object passively cooled into its quantum ground state of motion beyond single-mode cooling”. Nature Comm., 12:6182, 2021.

[4] I. Golokolenov, A. Ranadive, L. Planat, M. Esposito, N. Roch, X. Zhou, A. Fefferman, and E. Collin. “Single mesoscopic phononic mode thermodynamics”. Phys. Rev. Research, 5:013046, 2023.