Thermalization of neighboring nanomechanical resonators below 1 mK

Abstract

The position noise spectra of six drums on a single chip were measured on a single cooldown below 1.3 kelvin. Cryostat temperatures as low as 0.7 mK were achieved. The temperature dependence of the resonance frequency and linewidth of the drum modes was analyzed in the framework of the tunneling two level system (TLS) model. Departures of the resonance frequency and the position noise power from the expected logarithmic and linear temperature dependences, respectively, were interpreted as indications of thermal decoupling from the cryostat. This previously unexplored measurement configuration revealed that similar neighboring drums on a single chip may be at different temperatures. At the lowest temperatures, some drums exhibited excess damping that decreased with temperature. The magnitude of the excess damping of the drums was correlated with the thermal coupling of their TLS to the cryostat. In the case of one drum, a temporary increase in its damping coincided with a decrease in its mode temperature. The thermalization of the TLS to the cold finger was independent of pump power, pulse tube state and temperature of the pre-cooling stages of the cryostat. These results reveal an interplay between TLS damping and thermalization of nanomechanics that motivates further theoretical work and may impact efforts to extend the coherence of mechanical resonators.

Figures (9)

• Figure 1: A Keysight N5173B generator was used to pump the optomechanical device. One channel of an Anapico APMS12G generator was used as a microwave probe and the other channel was used to mix the signal reflected by the sample down to the low MHz range. A Zurich UHF lockin amplifier was then used to measure the noise power spectrum centered on the upper mechanical sideband of the reflected signal. Inside the cryostat, the indicated attenuators along with the 10 dB loss of the directional coupler yielded 50 dB of attenuation distributed between the 4 kelvin plate and the 100 mK cold plate. This attenuation and the isolation provided by the circulators protected the sample from noise. Initial amplification of the output signal was provided by a cryogenic Low Noise Factory LNC4_8C. Further amplification at room temperature was provided by a Low Noise Factory LNR4_8C.
• Figure 2: The sample holder clamped to the cold finger of the nuclear stage (image rotated 90 degrees counter-clockwise). The NbTi coaxial line transmits microwave signals to and from one port of the sample holder. An SMA connector attached to the other port (not visible) terminates the microwave circuit with a short to ground.
• Figure 3: Noise power spectral density due to vibrational modes of two different drums at 1.87 MHz (upper trace and upper axis, blue) and 1.68 MHz (lower trace and lower axis, red). The cryostat temperatures were 0.8 and 0.7 mK, respectively. The background level is much lower in the lower trace because a filter was inserted at room temperature on the output port of the cryostat. Dashed black curves are Lorentzian fits.
• Figure 4: Resonance frequency shift of 1.87 MHz (blue) and 1.68 MHz (red) drums obtained from spectra like those shown in Fig. \ref{['fig:spectra']}. Black dashed lines correspond to Eq. \ref{['eq:df']}. Dashed red and blue lines indicate the method for determining the saturation temperature $T_{\mathrm{eff}}$. Inset: No systematic dependence of $T_{\mathrm{eff}}$ on $C$.
• Figure 5: Mechanical linewidth of 1.87 MHz (blue) and 1.68 MHz (red) drums obtained from spectra like those shown in Fig. \ref{['fig:spectra']}. The magenta points were obtained from the red ones by accounting for thermal decoupling of the sample from the thermometer (Sec. \ref{['sec:ThermTLS']}). Dashed curves correspond to the resonant contribution to the damping (Eq. \ref{['eq:damp']}) based on $C$ obtained from the resonance frequency shift plus a constant offset. The dash-dot curve is a linear fit with slope 4.04 Hz/K and offset 0.10 Hz. Inset: Dependence of $T_{\mathrm{eff}}$ on mechanical linewidth at base temperature for six different drums.