Optically-biased Rydberg microwave receiver enabled by hybrid nonlinear interferometry

TL;DR

This paper addresses achieving high-sensitivity, all-optical microwave detection with Rydberg atoms. It introduces optical-bias detection that replaces the microwave LO with optical fields to realize all-optical mixing and reads out the MW signal via the probe field. A central innovation is laser-phase-noise cancellation through a DFG-based reference path, enabling compensation $z_C = z_S z_R^*$ for high-fidelity baseband signals. The results show sensitivity of $176\ \mathrm{nV/cm/\sqrt{Hz}}$ and reliable operation up to $3.5\ \mathrm{mV/cm}$ at $13.9\ \mathrm{GHz}$, plus a quadrature-amplitude modulation (QAM4) data transmission demonstration, illustrating competitive performance with state-of-the-art superhet while preserving all-optical operation.

Abstract

The coupling of Rydberg vapour medium to both microwave and optical fields allows harnessing the merits of all-optical detection, e.g. weak disruption of the measured field and invulnerability to extremely strong fields, owing to the lack of a conventional antenna in the detector. However, the highest sensitivity in this approach is typically achieved by introducing an additional microwave field acting as a local oscillator, thereby compromising the all-optical nature of the measurement. Here we propose an alternative method, optical-bias detection, that allows truly all-optical operation, while retaining exceptional sensitivity. We tackle the issue of laser phase noise, emerging in this type of detection, via a simultaneous measurement of the laser phase noise in a nonlinear process and real-time data processing, which overall yields an improvement of $35\ \mathrm{dB}$ in terms of signal-to-noise ratio compared with the basic approach. We report the sensitivity of $176\ \mathrm{nV/cm/\sqrt{Hz}}$ and reliable operation up to $3.5\ \mathrm{mV/cm}$ of $13.9\ \mathrm{GHz}$ electric field. We also demonstrate a quadrature-amplitude modulated data transmission, underlining the capability of the system to detect quadratures of the microwave field. This approach is thus directly comparable to the state-of-the-art superheterodyne, while retaining the merits of all-optical detection.

Figures (12)

• Figure 1: Comparison between superhet and optical-bias ideas.a, Operating principle of a MW superhet receiver. The atoms act as a microwave mixer, with optical fields, $E_p$ and $E_{C}$, having a role only in the detection. The signal $\mathcal{E}$ is thus mixed with the LO field $E_{LO}$, transduced to the RF domain $\mathcal{I}_S$, detected with a photodiode, converted to digital data with analogue-digital converter (ADC), and then demodulated to a complex baseband signal $z_S$ via FPGA digital signal processing (DSP). b, In the spectral picture the atoms act as a mixer between the MW signal $\mathcal{E}$ (represented as a modulated three peaks feature) and the LO $E_{LO}$, yielding a signal in the RF range $\mathcal{I}_S$, centred at the detuning $\Delta = \omega_S - \omega_{LO}$. c At the end, a digital IQ mixer recovers the original modulation as a complex signal $z_S$. d, Operating principle of a MW optical-bias receiver. The optical fields, $E_{C1}$, $E_{C2}$ and $E_{D}$, now have a primary role in the mixing process. An additional measurement of the combined optical phase noise $\mathcal{I}_R$ (realised via difference frequency generation (DFG) of the optical fields in MgO:PPLN nonlinear crystal) allows the phase compensation. e, The atoms now act as a mixer between the MW signal and optical fields. Because of the optical phase noise, the resulting photodiode (PD) signal in the RF range $\mathcal{I}_S$, centred at $\Delta = \omega_{C1} + \omega_S - \omega_D - \omega_{C2}$, is noisy and degraded. f, To solve the problem with the noise, a reference path mixes the optical fields with a MW $\mathrm{LO'}$, using a DFG process, a fast PD, and a mixer, in a three-step process. The reference signal $\mathcal{I}_R'$ contains all required information about the optical phase noise. g, At the end, both the signal $z_S$ and the reference $z_R$ are IQ-mixed to a baseband complex signal, and correction is applied as a digitally-implemented complex multiplication. This results in the original modulation being fully recovered in the $z_C$ complex signal.
• Figure 2: Optically-biased MW receiver.a, Energy level structure utilised in the optical-bias detection. Two-photon (probe--coupling) and three-photon (probe--dressing--coupling) Rydberg excitation paths are used to access both energy levels connected by the MW transition. The $\sigma^{+}$ transitions ensure the largest transition dipole moments. All of the optical fields are atomic resonant, apart from the indicated detuning $\Delta_{5\mathrm{D}} = - 1.8\ \mathrm{MHz}$. The beat modulation in probe transmission, i.e., the transduced signal, is also observed at $\Delta = 1.8\ \mathrm{MHz}$ due to the detuning of the MW field. b, Experimental setup of the optical-bias receiver. Three optical ($480\ \mathrm{nm}$, $776\ \mathrm{nm}$ and $1258\ \mathrm{nm}$) fields are divided into two paths. In the first path, they counter-propagate with respect to the $780\ \mathrm{nm}$ probe field, enabling partial Doppler effect cancellation. The laser fields are propagated as Gaussian beams focused to waists of around $w_0 = 250\ \mathrm{\mu m}$. They have matched circular polarisations and are combined inside ${}^{85}\mathrm{Rb}$ vapour cell using dichroic mirrors and spectral filters, while the signal is detected in the signal photodiode (PD). The second path leads to a difference-frequency generation (DFG) setup for laser phase spectrum detection. The $480\ \mathrm{nm}$ and $776\ \mathrm{nm}$ fields induce DFG at $1258\ \mathrm{nm}$ shifted by the frequency of the detected MW field, as dictated by the conservation of energy. Combined with the non-shifted $1258\ \mathrm{nm}$ field used in the detection setup, they generate a beat-note at $13.9\ \mathrm{GHz}$ on a reference PD. Then, downmixing with the $\mathrm{LO'}$ signal enables the retrieval of laser-noise spectrum shifted to lower frequencies. For measurements, the cell is placed inside a MW absorbing shield with a helical MW antenna acting as a signal source. In the case of superhet detection measured for comparison, the $776\ \mathrm{nm}$ and $1258\ \mathrm{nm}$ are switched off and MW LO is combined with the signal at the antenna.
• Figure 3: Phase referencing the signal enables Fourier-limited spectral detection.a, Spectrum of the probe field modulation $\mathsf{S}_{\mathcal{I}_S}(\omega)$ obtained in optical-bias detection of $720\ \mathrm{\mu V / cm}$ MW field. The maximum of the signal is $25\ \mathrm{dB}$ above the noise level, and the spectral width is $62\ \mathrm{kHz}$ FWHM. The $\mathcal{I}_S$ signal frequency is centred around $\Delta=1.8\ \mathrm{MHz}$. The visible peak at $\sim2.8\ \mathrm{MHz}$ is a small superhet-type signal resulting from cross-talk. It is outside the set detection bandwidth. b Respective spectrum $\mathsf{S}_{\mathcal{I'}_R}(\omega)$ of the reference signal obtained via DFG and subsequent beating with the 1258 nm laser. The $\mathcal{I'}_R$ signal frequency is centred around $\Delta'=4.6\ \mathrm{MHz}$. The maximum of the signal is $41\ \mathrm{dB}$ above the noise level. c, Respective spectrum of the phase-compensated signal $\mathsf{S}_{z_C}(\omega)$. The maximum of the signal is $60\ \mathrm{dB}$ above the noise level. The spectral width of the signal is Fourier-limited at $10\ \mathrm{Hz}$. The artefact spurs are at $-38\ \mathrm{dB}$ below the signal. The spectra are estimated from experimental data using Welch's method.
• Figure 4: Dynamic range of optical-bias parallels the superhet method.a Comparison between results obtained in superhet measurement (blue dots) and optical-bias (red dots). Both results are presented in relation to their respective detection noise levels (black dashed line), which in both cases is mainly the shot noise of the detected probe field transmission. This is denoted by the use of shot noise units (s.n.u.). The optical-bias measurement method results in comparable, though slightly worse, sensitivity and overall efficiency. Notably, however, it becomes saturated for larger MW fields than the superhet method, thus retaining a very similar dynamic range. The results presented here are averaged over $n = 8$ shots for each point to facilitate better comparison. The yellow solid line represents a theoretical prediction. Noteworthy, the saturation point is predicted accurately, and the experimental results differ from the theoretical predictions only in the stronger MW field regime, where the atomic response can no longer be considered instantaneous. The horizontal dashed lines represent the shot noise (s.n., black) and electronic noise (e.n., grey) levels. b Relative standard error (SE) of the data points from the Subfig. a.
• Figure 5: Phase-sensitivity of the detection allows the study of signal transduction. Comparison of EIT effects (upper row, a--c) and signal transduction (lower row, d--f) for superhet (left column, a and d) and optical-bias (middle column, b and e), and the theoretical prediction for optical-bias (right column, c and f) in the domain of probe field detuning $\delta_p$. For signal transduction both amplitude $|z_{(S/C)}(\delta_p)|$ (red lines) and phase $\arg(z_{(S/C)}(\delta_p))$ (blue lines) are shown. The MW field in all cases is $720\ \mathrm{\mu V / cm}$. Notably, despite similarities in the shape of signal transduction amplitude, the optical-bias method exhibits a different direction of the transition of phase in the demodulated signal than the superhet method. The presented data is averaged over $n=9$ separate measurements. The shaded blue regions represent the uncertainty (standard error) of the phase. The uncertainty of the measured transmission and amplitude in all cases is smaller than the thickness of the plot lines.