Cryogenic Magnomechanics for Thermometry Applications

Abstract

Cavity magnomechanics combines strong coupling between magnons in a dielectric material and microwave cavity photons with long-lived mechanical resonances. Forming a triple resonance condition, this hybrid quantum system promises many advantages in quantum technologies, yet has never been studied at the cryogenic temperatures required to reveal such quantum properties. We report the observation of magnomechanics at cryogenic temperatures down to \qty9K. The experiment was conducted using a YIG sphere inside a microwave cavity, where we measured both the thermomechanical motion and the temperature-dependence of the magnon linewidth.

Figures (5)

• Figure 1: The experimental setup. a) A schematic drawing illustrating the interactions between subsystems: cavity photons ($\hat{a}$) are coupled to magnons ($\hat{m}$) with coupling constant $g_\textrm{am}$, and the magnons are coupled to phonons ($\hat{b}$) with coupling constant $g_\textrm{mb}$. The dashed arrows for $g_\textrm{mb}$ denotes the fact that it is much weaker than $g_\textrm{am}$. b) The microwave cavity used for the measurements. The circular insert provides a magnified view of the YIG sphere mounted on a copper post. c) Normalized reflection spectra $|S_{11}|$ of the cavity with YIG sphere as a function of the bias magnetic field $B$. Note the avoided level crossing as a result of the strong coupling and hybridization between photons and magnons. d) Slice of data taken from c) at the dashed line ($B=\qty{253.7}{mT}$), illustrating the triple resonance regime. The bottom is the $S_{11}$ reflection spectrum of the microwave cavity with the YIG sphere, given by Eq. \ref{['eq:spectrum']}, where hybridized peaks at frequencies $\omega_-$ and $\omega_+$ are tuned to satisfy $\omega_+ - \omega_- = \Omega_\textrm{b}$ (see text, Eq. \ref{['eq:peak_separation']}); the top portion shows a probe tone $\omega_\textrm{d}$ that coincides with $\omega_-$, whose blue sideband $\omega_\textrm{d} + \Omega_\textrm{b}$ is then at $\omega_+$, satisfying the triple resonance condition. There is also a red sideband at $\omega_\textrm{d} - \Omega_\textrm{b}$, but it is not cavity enhanced and therefore its amplitude is negligible compared to the blue sideband.
• Figure 2: Schematic of the experimental setup. The microwave signals from the RF source ($\omega_\textrm{d}$) and the VNA were sent to the cavity, and the reflected signals were amplified by a high-electron-mobility transistor (HEMT) amplifier before being transmitted up to the room temperature stage. When tuning the polariton spectrum or locating the mechanical modes using magnomechanically induced transparency (MMIT), the VNA was turned on to sweep and measure the targeted frequency range. When taking homodyne measurements, the VNA was switched off to avoid undesirable beat frequencies. The reflected RF frequency and its sidebands were sent to an IQ-mixer whose local oscillator (LO) also runs at frequency $\omega_\textrm{d}$, effectively down-mixing the spectrum so the center frequency is now at DC. The output of the mixer was then fed to the lock-in, demodulated by a frequency close to the mechanical frequency, the resulting time-domain data digitized by its analog/digital converter (ADC), and fast-Fourier transformed (FFT) to eventually produce a frequency spectrum centered around the mechanical frequency.
• Figure 3: A subset of measured magnon linewidth $\gamma_\textrm{m}$ at various temperature $T$ and photon-magnon detuning $\Delta$. The markers represent the measured data points, while the solid lines show fifth-order polynomial fitting for those points in the same color.
• Figure 4: Temperature obtained by fitting of magnon linewidth compared to temperature read by the NRC thermometer. Blue dots are temperature obtained by fitting $\gamma_\textrm{m}$ and $\Delta$, while dashed line is a guide for the eye showing where the actually temperature should be. The inset shows the difference between the fit temperature and the thermometer temperature, exhibiting a discrepancy of less than $\qty{0.5}K$. There is a noticeable discontinuity of slope at $\sim\qty{8.5}K$; the bias current had to be reduced significantly at that point during the cooldown so as to not impede the superconductive transition of the bias magnet wire. This greatly changed the magnon frequency and therefore the detuning $\Delta$, which consequently showed up as a slope change of the $T_\textrm{fit}$ due to fitting artifact.
• Figure 5: Measured magnomechanical signals. The top panels are the normalized $S_{11}$ scattering coefficient measured through MMIT/A on the VNA, showing the mechanical peaks with their polariton background removed, while the bottom two panels are the thermomechanical power spectral densities (PSD) measured using the homodyne setup. The dots in the PSD plots are the raw data taken, while the shaded areas are fittings of the data against a Loretzian function with Fano-like distortions. The dotted vertical lines are guides to the eye, showing the locations of the peaks. The temperatures in the legend correspond to the temperature of the cryostat. The plot for each temperature has been vertically shifted by a different amount to avoid clutter. The MMIT spectra have excellent signal-to-noise because they are driven through microwave interference Zhang2014Potts2021, but the homodyne measures the undriven, thermomechanical signals that are difficult to resolve. As the probe power is raised these become easier to resolve, but with the consequence of heating the YIG sphere. Note that for the $P=-\qty{9}{dBm}$ case, the mechanical signals are almost identical at $\qty{4.5}K$ and $\qty{7}K$; this is because the YIG sphere was heated by the RF drive, and its temperature was higher than it surrounding as read by the thermometer due to insufficient thermalization (see Table \ref{['tab:compare_temperature']}).