Coupling of a Nuclear Transition to a Surface Acoustic Wave

Abstract

Mechanical modulation of recoilless nuclear transitions allows the dynamic control of $γ$-ray emission and absorption. Accessing modulation frequencies well above the nuclear linewidth enables coherent manipulation of the nuclear response. Here we demonstrate high frequency control via efficient coupling a film of enriched $^{57}$Fe to a $97.9~\mathrm{MHz}$ surface acoustic wave, nearly two orders of magnitude higher than the nuclear linewidth. The mechanical drive produces a comb of absorption sidebands in the Mössbauer spectrum, reflecting the periodic time modulation of the nuclear transitions. This constitutes the highest frequency mechanically driven Mössbauer resonance to date. Our solid-state, monolithic platform establishes a new interface between nuclear transitions and high-frequency acoustics, with applications in $γ$-ray quantum optics and precision nuclear spectroscopy.

Figures (12)

• Figure 1: a) Schematic view of the experiment. A $(0.9 \times 4.0)~\mathrm{mm}^2$ film of $^{57}$Fe is deposited between two SAW couplers on a quartz substrate and characterized in a Mössbauer spectrometer. The inset shows the setup to scale, with the SAW device and $^{57}$Fe absorbing film (gray) placed at a distance of $10~\mathrm{cm}$ from the $^{57}$Co source (purple). A tungsten collimator (green) blocks all non-interacting photons from reaching the detector (black). b) Nuclear level scheme, showing the the unmodulated hyperfine transitions (purple) and the first (magenta) and second (yellow) order vibrational sidebands driven by the SAW. c) Cartoon of the expected spectrum without (purple) and with (all colors) the SAW drive on.
• Figure 2: Main panel: Microphotograph of part of the absorber device on the quartz substrate, including sections of the $^{57}$Fe film and of one of the SAW couplers. Inset: higher magnification detail of one of the SAW couplers.
• Figure 3: a) Mössbauer absorption spectra of the device with no SAW excitation and two cases of increasing SAW drive power. As the modulation strength grows, higher-order sidebands emerge while amplitudes decrease to maintain a constant overall integral over the absorption spectrum. Continuous lines, overlaying the data points, represent fits to the data appendix. b) Reconstructed amplitudes of the first three sidebands accessible within the available velocity range, as a function of the applied SAW drive power. The solid lines are a global fit to all three datasets using a model based on the squared Bessel functions integrated over the SAW amplitude distribution. The two fit parameters are the modulation scaling factor $C_\perp$ and the reflection coefficient $\alpha$, which encodes the degree of standing-wave formation due to SAW reflections.
• Figure A1: Definition of the coordinate system: the $\gamma$-rays travel along $z$, encountering an ${}^{57}$ Fe film parellel to the $x-y$ plane and driven by a SAW travelling along $x$.
• Figure A2: Numerical calculation of the decay constants (a) and the speed of the SAW (b) versus the cut angle of the Y-cut quartz. These figures reproduce figures 3 and 4 in ref. coquin_analysis_1967. The gray lines indicate the angle of ST-cut quartz ($+42.75^{\circ}$).