Probing strong coupling between a microwave cavity and a spin ensemble with Raman heterodyne spectroscopy

Raman heterodyne spectroscopy is a powerful tool for characterizing the energy and dynamics of spins. The technique uses an optical pump to transfer coherence from a spin transition to an optical transition where the coherent emission is more easily detected. Here Raman heterodyne spectroscopy is used to probe an isotopically purified ensemble of erbium dopants in a yttrium orthosilicate $\left({\mathrm{Y}}_2{\mathrm{SiO}}_5\right)$ crystal coupled to a microwave cavity. Because the erbium electron spin transition is strongly coupled to the microwave cavity, we observed Raman heterodyne signals at the resonant frequencies of the hybrid spin-cavity modes (polaritons) rather than the bare erbium spin-transition frequency. Using the coupled system, we made saturation recovery measurements of the ground-state spin relaxation time $T_1=10\pm 3$ s and also observed Raman heterodyne signals using an excited state spin transition. We discuss the implications of these results for efforts toward converting microwave quantum states to optical quantum states.

Figure 1

(a) The loop loop-gap resonator, with the sample removed from the center of the cavity. B is the applied magnetic field; $b$, $D_1$, and $D_2$ are the axes of the ${}^{}\mathrm{Er}{}^{3+}$:YSO sample. The light propagates along $b$, which is also the direction of the RF magnetic field in the sample. The ends of the resonator have been removed for clarity. (b) A schematic of the apparatus. Cable (1) was connected to the NA input to measure the microwave transmission. Cable (2) was connected when measuring the Raman heterodyne signal. (c) A schematic of the relevant energy levels in the ${}^{}\mathrm{Er}{}^{3+}$ ion, as described in the text. The arrows show the four possible optical pump transitions, which we label 1–4. The dashed arrow indicates the transition resonant with the microwave resonator in each case. (d), (e) Different arrangements for generating Raman heterodyne measurements, which are discussed in the text.

Figure 2

(a) Microwave cavity transmission as a function of magnetic field strength. (b) Simulation of (a). Strong coupling between the erbium spins results in an avoided crossing as the spins are tuned through the microwave resonator. In this figure, $\delta f=0$ corresponds to 5020 MHz. The color scale shows the overall transmission efficiency from one NA port to the other.

Figure 3

Raman heterodyne signal measured in the ground state. (a) Raman heterodyne scan at a fixed magnetic field, with optical absorption spectrum (yellow). The horizontal dashed line indicates the optical frequency for parts (b) and (c) were collected. For part (b), the microwave power was $-15$ dBm at entry to the fridge, a power level chosen to limit the saturation of the spins. For part (c), the microwave power was 8 dB higher. (d) and (e) show simulations of (b) and (c), respectively. In all these, the bare cavity frequency is 5020 MHz. The pump laser frequency is denoted by $\nu$. The color scale is common to all these and shows the overall efficiency from one NA port to the next.

Figure 4

(a) Raman heterodyne signal in the excited state. An optical absorption spectrum is plotted against the right-hand axis. The four spots correspond to the four transitions as shown. The horizontal dashed line indicates the optical frequency where the data in (b) was collected. The color bar scale is in dB transmitted from one port of the NA to the other and is common to all these subfigures. (b) Changing the magnetic field, the microwave resonator frequency (vertical) doesn't change, while the frequency of the ions does. (c) Simulated version of (b). The empty cavity frequency is 4732 MHz in these figures.

Figure 5

Measurements of the $T_1$ time of the system by saturation recovery. The dots and lines relate to the fit as described in the text. Part 1 is empty because the resonator was driven at a different frequency, as explained in the text. The horizontal dashed line is the resonance frequency of the empty cavity. The vertical dot-dash lines separate the different powers and frequency ranges. The power shown is the output of the NA and $\delta f=0$ corresponds to 5020 MHz.