Signal-Dependent Shot Noise Modeling of Rydberg Atomic Quantum Receivers: A Design Perspective

Abstract: In this paper, we develop a communication-oriented complex baseband equivalent model for superheterodyne Rydberg atomic quantum receivers (RAQRs). The model explicitly captures photodetection-induced signal-dependent shot noise and its coupling with the optical operating point. By leveraging an atomic superheterodyne architecture and a strong local oscillator, we construct a complex baseband representation for both the received signal and the signal-dependent shot noise under both direct incoherent optical detection and balanced coherent optical detection. The derived model reveals that the optical operating point jointly determines the normalized effective receive gain and the equivalent noise background, thereby establishing a traceable gain-noise tradeoff governed by system design. More importantly, the proposed model shows that neglecting signal-dependent shot noise may lead to inaccurate operating-point design. Finally, by extending to the multiple-input-multiple-output (MIMO) case, we derive a lower bound on the achievable rate while considering the signal-dependent shot noise. Our analysis \textcolor{black}{reveals} that the non-zero asymptotic rate of RAQ-MIMO and its superiority over conventional RF-MIMO hinge on the normalized noise floor of the RAQ receive chain falling below that of RF MIMO. Simulation results validate our analysis and yield practical, closed-form design guidelines for RAQR front ends, revealing parameter regimes in which RAQ-MIMO outperforms conventional MIMO systems.

• The paper develops a complex baseband model for signal-dependent photodetection shot noise in direct and balanced optical Rydberg receivers, showing that noise variance changes with the instantaneous signal and optical operating point.
• The paper derives practical LO, coupling-beam, probe-beam, and local-optical-power design rules, with simulations showing optimized settings match exhaustive searches within 0.1 dB while revealing different DIOD and BCOD noise tradeoffs.
• The paper extends the model to RAQ-MIMO and shows that its rate advantage over conventional RF-MIMO is conditional on the user-signal-independent noise floor remaining below the RF thermal-noise floor, while classical 1/M power scaling still preserves a nonzero asymptotic rate.

Motivation and contribution

Rydberg atomic quantum receivers (RAQRs) transduce incident RF fields into optical responses via electromagnetically induced transparency (EIT) in a four-level atomic system, and have attracted attention as an alternative to conventional RF front ends. Prior communication-theoretic treatments of RAQRs—equivalent baseband models, RAQ-MIMO formulations, achievable-rate analyses (Gong et al., 2 Jun 2025), dynamic signal models—have largely treated photodetection noise as additive and signal-independent. This paper addresses that gap by developing a complex baseband equivalent model for superheterodyne RAQRs in which the shot noise induced at the photodetector is explicitly signal-dependent, i.e., its variance scales with the instantaneous photocurrent, and by tracing how the resulting gain–noise tradeoff governs receiver design.

The paper builds directly on the steady-state complex baseband framework of Gong et al. [gong2026rydbergatomicquantumreceivers] and makes three principal contributions: (i) a tractable complex baseband representation of signal-dependent shot noise under both direct incoherent optical detection (DIOD) and balanced coherent optical detection (BCOD); (ii) closed-form design criteria for the local oscillator (LO), coupling beam, and probe beam that maximize effective received SNR; and (iii) a multiuser RAQ-MIMO extension with UatF-type lower bounds on achievable rates under MRC and ZF detection, together with an explicit crossover condition against conventional RF-MIMO.

Quantum response and RF-to-optical conversion

The receiver uses a ladder configuration ($$|1\rangle \to |2\rangle \to |3\rangle \to |4\rangle$$) driven by probe, coupling, and RF/LO fields, governed by the standard Lindblad master equation. Under the approximation $\gamma_c = 0$, $\gamma_3 = \gamma_4 = 0$—justified on the grounds that upper-state decay and collisional dephasing are negligible relative to intermediate-state decay and EIT linewidth—the steady-state coherence $\rho_{21}(\Omega_{\mathrm{RF}})$ admits a rational closed form whose coefficients are inherited from prior work. The superheterodyne operation relies on a strong LO satisfying $U_{\mathrm{LO}} \gg U_x$, so that the Rabi frequency seen by the atoms is approximately $$\Omega_{\mathrm{RF}} \approx \Omega_{\mathrm{LO}} + \Omega_x\cos(2\pi f_\delta t + \theta_\delta)$$. The authors verify numerically that this linearization error is negligible for field ratios above roughly 10 dB, which bounds the validity of all downstream results to the strong-LO regime.

Signal-dependent shot noise model

For DIOD, the Poissonian photon-counting process yields an output voltage of the form $\sqrt{G}\alpha P_1 + \xi(t)\sqrt{G\alpha P_1}$, where the noise standard deviation scales as $\sqrt{P_1}$; a first-order Taylor expansion around the LO operating point separates the output into a desired term proportional to $U_x$, a user-signal-dependent noise term, and a direct-current-dependent noise term. For BCOD, a strong local optical beam interferes with the probe on two photodetectors; differential combining produces analogous structure but with different dependence of the noise prefactors on $P_l$ and $\gamma_c = 0$0.

After bandpass filtering around the intermediate frequency $\gamma_c = 0$1 and quadrature downconversion, the raw real-valued Poisson process is mapped to a circularly symmetric complex Gaussian baseband process via the central limit theorem plus narrowband decomposition—an argument the authors state carefully, noting that the CSCG property is representational rather than intrinsic. The resulting SISO model takes the form

$\gamma_c = 0$2

where $\gamma_c = 0$3 and $\gamma_c = 0$4 are explicit functions of the optical operating point ($\gamma_c = 0$5, $\gamma_c = 0$6, $\gamma_c = 0$7, $\gamma_c = 0$8), and $\gamma_c = 0$9 aggregates direct-current-dependent shot noise, thermal noise, and quantum projection noise (QPN). The key structural insight is that the operating point jointly determines the normalized receive gain $\gamma_3 = \gamma_4 = 0$0 and each normalized noise component, producing a traceable gain–noise tradeoff rather than a fixed additive-noise floor.

Operating-point design

Under ideal resonance ($\gamma_3 = \gamma_4 = 0$1), the paper derives stationary-point conditions for the normalized noise $\gamma_3 = \gamma_4 = 0$2 with respect to each optical parameter. Three regimes emerge:

• User-signal-dependent-noise regime: minimizing this noise reduces to maximizing $\gamma_3 = \gamma_4 = 0$3, which decreases monotonically with LO power but increases with coupling/probe power; the optimum lies at the feasible boundary.
• Direct-current shot / thermal-noise regime: closed-form optima exist for coupling and LO powers (exact for DIOD, approximate for BCOD under $\gamma_3 = \gamma_4 = 0$4), while the probe-beam optimum couples polynomial and exponential dependencies and must be solved numerically via Newton's method—a limitation the authors acknowledge explicitly.
• Mixed regime: the LO should be set between the minimum feasible value and the thermal-noise stationary point, with the probe balancing the noise composition.

A notable asymmetry: DIOD is more sensitive to thermal noise, whereas BCOD is dominated by signal-dependent shot noise tied to the local optical power $\gamma_3 = \gamma_4 = 0$5. Lemma 1 shows the optimal local optical beam power is simply $\gamma_3 = \gamma_4 = 0$6, since $\gamma_3 = \gamma_4 = 0$7 is strictly decreasing in $\gamma_3 = \gamma_4 = 0$8. Simulations confirm the derived optima agree with exhaustive search to within 0.1 dB, and that detuning degrades the resonance-based design more severely for DIOD than BCOD.

RAQ-MIMO analysis

Extending to an $\gamma_3 = \gamma_4 = 0$9-sensor, $\rho_{21}(\Omega_{\mathrm{RF}})$0-user uplink with Rayleigh fading, the received vector becomes

$\rho_{21}(\Omega_{\mathrm{RF}})$1

where $\rho_{21}(\Omega_{\mathrm{RF}})$2 captures per-sensor signal-dependent noise. Using the use-and-then-forget bounding technique, the paper derives lower bounds on ergodic rates under MRC and ZF. The MRC SINR contains an additional term scaling with $\rho_{21}(\Omega_{\mathrm{RF}})$3 that cannot be absorbed into constant noise; the ZF bound requires $\rho_{21}(\Omega_{\mathrm{RF}})$4 and diverges at $\rho_{21}(\Omega_{\mathrm{RF}})$5, a restriction stated plainly in the appendix.

Two remarks carry the main system-level conclusions. First, the classical power-scaling law survives: when transmit power scales as $\rho_{21}(\Omega_{\mathrm{RF}})$6, a non-zero asymptotic rate remains,

$\rho_{21}(\Omega_{\mathrm{RF}})$7

because channel hardening suppresses interference while the signal-dependent shot noise vanishes as $\rho_{21}(\Omega_{\mathrm{RF}})$8. Second—and this is the paper's most consequential claim—RAQ-MIMO outperforms conventional RF-MIMO only if the normalized user-signal-independent noise floor falls below the RF-MIMO thermal floor:

$\rho_{21}(\Omega_{\mathrm{RF}})$9

This condition defines critical thresholds $U_{\mathrm{LO}} \gg U_x$0 and $U_{\mathrm{LO}} \gg U_x$1: beyond them, the RAQ-MIMO advantage diminishes or reverses. Monte Carlo simulations with $U_{\mathrm{LO}} \gg U_x$2, $U_{\mathrm{LO}} \gg U_x$3 confirm both the tightness of the lower bounds and the sharpness of these crossover points, showing that RAQ-MIMO superiority is conditional rather than universal and is dictated primarily by front-end design.

Limitations and open questions

Several assumptions constrain the generality of the results. The strong-LO condition $U_{\mathrm{LO}} \gg U_x$4 dB underpins the entire linearization chain, and the authors note that amplitude modulation increases the approximation error, mitigated only by higher LO voltage. The neglect of collisional dephasing and upper-Rydberg decay is an approximation valid for dilute, buffer-gas-free vapor cells with narrow-linewidth lasers, not a physical absence of those processes. Closed-form optima for the coupling and LO beams are exact only for DIOD; BCOD solutions rely on the weak-probe condition $U_{\mathrm{LO}} \gg U_x$5, and the probe-beam optimum has no closed form. The MIMO analysis assumes perfect CSI, independent identically distributed signal-dependent noise across sensors, and Rayleigh fading; the ZF bound fails at $U_{\mathrm{LO}} \gg U_x$6. Finally, the crossover condition is derived under matched array size and fading statistics between RAQ-MIMO and RF-MIMO baselines, leaving open how robust the threshold is to correlated fading, imperfect LO phase alignment across the array, and non-resonant operation.

Conclusion

This paper supplies the missing noise-side counterpart to existing RAQR signal models: a complex baseband treatment in which photodetection shot noise is signal-dependent and coupled to the optical operating point. Its central findings—that the operating point jointly sets gain and noise floor, that ignoring signal-dependent shot noise yields suboptimal front-end designs, and that RAQ-MIMO's advantage over RF-MIMO holds only below explicit LO/probe-power thresholds—are validated against master-equation simulations and provide concrete, closed-form guidance for atomic receiver design.