On-chip Thermometry for Microwave Optomechanics Implemented in a Nuclear Demagnetization Cryostat

Abstract

We report on microwave optomechanics measurements performed on a nuclear adiabatic demagnetization cryostat, whose temperature is determined by accurate thermometry from below 500 µK to about 1 Kelvin. We describe a method for accessing the on-chip temperature, building on the blue-detuned parametric instability and a standard microwave setup. The capabilities and sensitivity of both the experimental arrangement and the developed technique are demonstrated with a very weakly coupled silicon-nitride doubly-clamped beam mode of about 4 MHz and a niobium on-chip cavity resonating around 6 GHz. We report on an unstable intrinsic driving force in the coupled microwave-mechanical system acting on the mechanics that appears below typically 100 mK. The origin of this phenomenon remains unknown, and deserves theoretical input. It prevents us from performing reliable experiments below typically 10-30 mK; however no evidence of thermal decoupling is observed, and we propose that the same features should be present in all devices sharing the microwave technology, at different levels of strengths. We further demonstrate empirically how most of the unstable feature can be annihilated, and speculate how the mechanism could be linked to atomic-scale two level systems. The described microwave/microkelvin facility is part of the EMP platform, and shall be used for further experiments within and below the millikelvin range.

Beyond linear coupling in microwave optomechanics

“…Finally, we note that our microwave-coupled mechanical devices are fully compatible with ultralow-temperature cryostats capable of operating below 1 mK [23]. Assuming equilibration of devices like the one used here can be achieved under such conditions, then they will naturally operate within the quantum regime.…”

“…The motion amplitude being very small, no extra nonlinearity has to be considered and the optical damping (when cooling) and antidamping (when amplifying) observed are linear in applied power P in [18]. This is used to calibrate the linear optomechanical interaction of our setup [23]. We obtain a single photon-phonon coupling strength |g 0 |/2π ≈ 10 Hz.…”

“…The capabilities offered by quantum NEMS devices are thus extremely rich, but are essentially all building on the linear parametric coupling between light and motion [18]. For instance, using a pump properly detuned from the resonance cavity (i.e., anti-Stokes sideband pumping), one can actively cool down a mechanical mode to its quantum ground state, or reversely (i.e., Stokes pumping) amplify the mechanical motion [11,[19][20][21][22][23]. From two-tone schemes, one can devise backaction evading measurements [24,25] that enable us to beat the standard quantum limit by measuring one quadrature while feeding the backaction noise of the detector to the other one.…”

A macroscopic object passively cooled into its quantum ground state of motion beyond single-mode cooling

“…1) which forms a drum-head 19 , and the cryogenic setup consists of a home-made laminar copper nuclear stage mounted on a wet dilution cryostat (see ref. 30 for details). The single-phonon optomechanical coupling g 0 for these modes is measured to be ~2π × 230 Hz.…”

Gravitational Forces Between Nonclassical Mechanical Oscillators

“…An overwhelming benefit of the microwave-frequency realization is its compatibility with standard cryogenic instrumentation. The mechanical resonators in this setup have usually been either nanowires [22,[51][52][53] or aluminum drumheads [37,46,[54][55][56]. A very promising recent advance has been achieved with high-stress silicon nitride membranes of several hundred microns in diameter that were implemented inside threedimensional (3D) microwave cavities [57,58], which is the setup we are interested in.…”