Optimization of modulation transfer protocol for Rydberg RF receivers

TL;DR

This work theoretically and experimentally optimizes the modulation transfer protocol (MTP) for Rydberg-based RF receivers, showing that phase modulation of the coupling beam at $\omega_{\mathrm{mod}}$ with depth $\beta$ can convert into probe-intensity modulation via four-wave mixing, thereby broadening the detectable RF bandwidth compared to the conventional protocol (CP). By modeling both CP and MTP in a four-level $^{85}$Rb ladder and applying Floquet analysis to the MTP, the authors identify optimal parameters $\omega_{\mathrm{mod}}/2\pi \approx 3$ MHz and $\beta \approx 0.25$, with robust performance across a wide parameter range. Experimentally, the MTP shows markedly improved sensitivity for detuned RF fields (e.g., $\Delta_{\mathrm{RF}}/2\pi$ up to tens of MHz) and increases the $-10$ dB RF bandwidth by about 11.5 MHz, while CP remains superior only near resonance. The results indicate a complementary relationship between CP and MTP, enabling flexible all-optical RF sensing in hot Rydberg vapors and offering a pathway to wider-bandwidth quantum RF receivers without external RF antennas.

Abstract

We explore theoretically and experimentally the recently demonstrated modulation transfer protocol [D.-A. Trinh, K. V. Adwaith, M. Branco, A. Rouxel, S. Welinski, P. Berger, F. Goldfarb, and F. Bretenaker, Applied Physics Letters 125, 154001 (2024)] aiming at extending the bandwidth of quantum RF receivers based on hot Rydberg atoms. This protocol is based on a phase modulation of the coupling beam, which is transformed by the nonlinear response of the atoms into an amplitude modulation of the probe beam. We develop a theoretical model to optimize both the modulation frequency and the modulation amplitude of the coupling beam, thereby maximizing the atomic response. Once optimized, the sensitivity to detuned RF fields of this modulation transfer protocol is compared with that of the conventional protocol. This comparison shows that the new protocol outperforms the usual one as soon as the RF signal to be measured is detuned by more than a few MHz and offers a complementary approach to increase the detection bandwidth. In all cases, the experimental results are in good agreement with the simulations.

Figures (9)

• Figure 1: (a) Excitation scheme used for the conventional Rydberg RF receiver. (b) Excitation scheme used for the MTP Rydberg RF receiver, where the coupling field is phase modulated. (c) CP featuring single-frequency coupling and output probe fields. (d) MTP, including sidebands for both the coupling and output probe fields.
• Figure 2: Simulated evolution of the Relative Modulation Amplitude (R.M.A.) of the probe intensity versus probe detuning for (a) $E_{\mathrm{RF}}=0$ and (b) $E_{\mathrm{RF}}=0.65\,\mathrm{V/m}$. The insets show the corresponding evolutions of the probe transparency in the Conventional Protocol. The transparency is defined as the variation in probe transmission induced by the presence of the coupling beam. The values of the simulation parameters are given in Table \ref{['tab01']}. For the Modulation Transfer Protocol, $\omega_\mathrm{mod}/2\pi=3$ MHz and $\beta = 0.25$.
• Figure 3: Simplified experimental setup. BS: beam splitter, $\frac{\lambda}{4}$: quarter-wave plate, $\frac{\lambda}{2}$: half-wave plate, PD: amplified photodetector, APD: avalanche photodiode, DM: dichroic mirror, AOM: acousto-optic modulator, AWG: arbitrary waveform generator. The amplified photodetector (PD) and the avalanche photodiode (APD) are used to monitor the probe laser power both before and after it passes through the vapor cell. In the conventional protocol, the coupling laser is modulated in amplitude using a square wave signal. In contrast, the modulation transfer protocol employs phase modulation of the coupling laser by a sinusoidal signal.
• Figure 4: Experimental spectra corresponding to the simulations of Fig. \ref{['fig:Figure2']}.
• Figure 5: Simulated R.M.A signal (a) amplitude and (b) slope at $\Delta_{\mathrm{p}}=100\,\mathrm{kHz}$ versus $\beta$ and $\omega_\mathrm{mod}$. Black lines: iso-amplitudes (0.027 and 0.023). White lines: contours of constant signal slope (0.029 and 0.023 $\mathrm{MHz}^{-1}$). The colored crosses denote the parameters used to plot figures (c) and (d), which display experimental spectra of the MTP. (d) is a zoomed-in version of (c).