Compressive Spectrum Sensing via Spectral Multiplexing in Rydberg Atomic Receiver

Abstract: Rydberg-atomic receivers exhibit exceptional sensitivity yet are fundamentally constrained by the narrow instantaneous bandwidth, limiting their practical deployment in broadband scenarios. Prior approaches typically expand the bandwidth by physically broadening the atomic response, which usually requires auxiliary electromagnetic fields or stringent parameter tuning, thereby increasing overall system complexity. Here, we propose a compressive spectral multiplexing framework implemented in a waveguide-coupled Rydberg atomic receiver using a frequency-modulated local oscillator (FMLO). The FMLO creates multiple parallel sensing channels that collectively constitute a physical compressive sensing matrix, generating multiple narrowband intermediate-frequency replicas of the input signal. Thus, a broadband microwave spectrum is projected onto a set of narrowband atomic responses. It is demonstrated that spectral information spanning a bandwidth of over 640 MHz can be effectively compressed into the intrinsic atomic bandwidth of 126 kHz, achieving a spectrum compression ratio exceeding 1000. Furthermore, these output replicas offer intrinsic measurement redundancy and facilitate signal-to-noise ratio enhancement. An approximate 10 dB gain is achieved in the required bit-energy-to-noise-power-density ratio for multi-channel communication via maximal-ratio combining. This approach requires no auxiliary fields or broadband electronics, providing a simple and scalable pathway for chip-scale quantum receivers, latency-critical sensing, and next-generation wireless communications.

• The paper introduces a compressive sensing framework using an FMLO to multiplex the narrowband atomic receiver, achieving a spectral compression ratio greater than 1000.
• The method replaces the conventional single-tone LO with an FMLO that projects broadband microwaves into multiple narrow channels, providing intrinsic measurement redundancy and a diversity gain of about 10 dB.
• Experimental results validate robust multi-channel demodulation for BPSK signals over a 640 MHz span, paving the way for scalable, quantum-enabled broadband receivers.

Compressive Spectrum Sensing via Spectral Multiplexing in Rydberg Atomic Receivers

Introduction and Context

Rydberg atomic receivers have emerged as platforms offering high sensitivity and quantum-level traceability for microwave spectrum measurements, underpinned by phenomena such as electromagnetically induced transparency (EIT) and Autler-Townes splitting. Despite their sensitivity, these receivers are fundamentally restricted by ultranarrow instantaneous bandwidths—frequently limited to hundreds of kHz—constraining their efficacy for broadband spectrum monitoring. Prior bandwidth extension strategies, such as optical field engineering, multi-wave mixing, or frequency combs, invariably amplify system complexity and hardware demands, while preserving inherent single-channel limitations and lacking intrinsic measurement redundancy.

This work proposes and demonstrates a compressive spectrum sensing framework, leveraging a frequency-modulated local oscillator (FMLO) to introduce spectral multiplexing within a waveguide-coupled Rydberg atomic receiver. By harnessing intrinsically parallel mixing channels generated by the FMLO, the system realizes a deterministic, physical compressive sensing matrix that redistributes broadband microwave signals as multiple narrowband proxies within the atomic bandwidth. This approach yields a broadband access solution that substantially relaxes the conventional requirements for auxiliary fields or broadband electronics.

Compressive Spectral Multiplexing Architecture

The central architectural advance lies in replacing the conventional single-tone LO with an FMLO. The FMLO produces a comb of $N$ phase-locked, equally spaced spectral tones spanning a bandwidth set by its frequency deviation ($f_{\mathrm{dev}}$) and modulation rate ($f_{\mathrm{mod}}$). Each tone acts as an independent, concurrent heterodyne mixing channel with signal fields, resulting in physical compressive multiplexing: a high-dimensional (broadband) input spectrum is projected into a lower-dimensional (narrowband) measurement domain.

Mathematically, the measurement can be described by $y = Ax + n$, where $x$ is the high-dimensional, sparse input spectrum, $A$ is the deterministic sensing matrix defined by the FMLO spectrum, $y$ is the collection of intermediate frequency (IF) outputs, and $n$ captures additive noise. The multi-heterodyne process thus physically realizes a dimensionality reduction analogous to classical compressive sensing, but without requiring synthetic random matrices or iterative numerical recovery.

The experiment utilizes $^{85}\mathrm{Rb}$ vapor cells, two-photon EIT excitation (780 nm and 480 nm lasers), and a resistive power divider for combining the FMLO and input signal, subsequently coupled into a waveguide. The atomic system’s instantaneous bandwidth is fixed (e.g., $126$ kHz), while the FMLO parameters set the span and granularity of the compressive measurement space.

Experimental Results and Numerical Performance

Single-Frequency and Multi-Tone Sensing

Empirical characterization confirms the multi-heterodyne framework. A single-frequency input outside the atomic bandwidth but within the FMLO span produces multiple IF replicas, each corresponding to a distinct compressive projection determined by a different FMLO tone. The response amplitude across replicas follows the Bessel function envelope imposed by the FMLO's modulation index. Signal frequencies detuned complementary to the FMLO spacing produce mirror-symmetric frequency distributions, differing only in projection intensities.

For multi-tone (sparse) signals, the IF response adheres to superposition: the measured spectra are linear sums of the individual projections, directly verifying the physical compressive measurement model. This property holds as long as intermodulation products remain negligible—a regime valid for weak signal fields.

Recoverable Bandwidth and Compression Ratio

A key result is the demonstration of spectral compression exceeding three orders of magnitude. Using an FMLO span of up to $f_{\mathrm{dev}}$0 MHz, the system projects a broadband spectrum into an atomic bandwidth of $f_{\mathrm{dev}}$1 kHz, yielding a spectrum compression ratio greater than $f_{\mathrm{dev}}$2. The recoverable bandwidth is fundamentally delimited by the FMLO’s spectral coverage and by the practical SNR constraints imposed by distributing finite LO power among an increased number of tones.

Multi-Branch Redundancy and Diversity Gain

Owing to the structured multiplexing, each sparse input frequency is mapped to multiple uncorrelated IF projections (i.e., multiple measurement vectors, MMV). Experimentally, maximal-ratio combining (MRC) of these independent IF replicas yields an observed diversity gain of approximately $f_{\mathrm{dev}}$3 dB in bit-energy-to-noise-power-density ratio ($f_{\mathrm{dev}}$4) for multi-channel BPSK communication, as compared to single-branch demodulation. This gain is realized without hardware replication: the physical compressive framework itself generates the necessary redundancy, and each added replica is statistically independent, permitting additive SNR improvements.

Multi-Channel Broadband Communication

The architecture supports simultaneous demodulation of multiple concurrent BPSK channels mapped onto distinct IF bands by virtue of the FMLO’s frequency comb. Seven-channel transmission experiments confirm robust demodulation, with MRC across compressive projections causing monotonic BER improvements as a function of the number of branches combined. Such resilience, realized with a single atomic receiver, highlights scalability toward future multi-band and cognitive radio scenarios.

Theoretical Implications and Trade-offs

The FMLO-based architecture exemplifies a deterministic, physically realized compressive measurement matrix, departing from conventional CS paradigms based on randomness and iterative, algorithmic recovery. The matrix structure is fully dictated by FMLO parameters, primarily the modulation index and tone spacing, with projection nonuniformity directly encoded in the Bessel envelope (and correctable during signal recovery).

A core practical trade-off emerges between spectral span and per-channel sensitivity: expanding FMLO bandwidth subdivides the finite power across more spectral teeth, diminishing the SNR of each branch. This imposes an upper bound on effective bandwidth expansion, mitigable by atomic physics advances that broaden the intrinsic instantaneous bandwidth (allowing increased channel spacing with constant channel SNR).

The architecture demonstrates the capacity for frequency estimation analogous to comb-based schemes, leveraging Chinese Remainder Theorem principles to resolve sign and aliasing ambiguities arising from the modular nature of projections. Higher-order nonlinear mixing, observable at elevated signal powers, yields additional mixing products and can be theoretically exploited for enhanced frequency resolution.

Practical and Future Implications

The proposed framework provides a markedly simplified, scalable pathway toward chip-scale, quantum-enabled broadband receivers for spectrum sensing and next-generation wireless communications. Its hardware simplicity—eschewing broadband electronics or auxiliary local oscillators—positions it as a viable platform for both quantum-enabled radio and latency-critical applications. The intrinsic measurement redundancy offers both SNR enhancement and resilience to channel impairments without multi-antenna architectures.

The compressive multiplexing paradigm could be generalized to sparse recovery scenarios in diverse spectral environments. Integration with architectures that further increase atomic bandwidth (via field engineering or quantum control) could extend both coverage and SNR, likely benefiting quantum radar, remote sensing, and secure communication.

Conclusion

This study introduces and experimentally validates a compressive spectral multiplexing framework exploiting FMLO-driven multi-heterodyne mixing in Rydberg atomic receivers. The approach enables physical spectrum compression by three orders of magnitude beyond the atomic instantaneous bandwidth, a recovery span exceeding $f_{\mathrm{dev}}$5 MHz, and achieves approximately $f_{\mathrm{dev}}$6 dB diversity gain in SNR for multi-channel communications. The deterministic, all-physical compressive measurement establishes new directions for quantum receiver design, with compelling practical and theoretical implications for broadband sensing, quantum information processing, and wireless communication technologies (2607.02001).