PaperlayerView exact revision on arXiv

Source-linked AI summary

An Optical Pathway to Movable Rydberg Atomic Quantum Receivers

Qihao Peng, Qu Luo, Lixia Xiao, De Mi, Neng Ye, Cunhua Pan, Pei Xiao, Cheng-Xiang Wang, Jiangzhou Wang

arXiv:2608.30718v1eess.AS

TL;DR

The paper addresses the limited spatial reconfigurability of existing RF and RAQR receivers by developing an optically movable RAQR. It derives and validates a differentiable baseband model, characterizes optical channel-shaping mechanisms, and optimizes optical positions with LO design. Simulations demonstrate interference suppression, user decorrelation, and sum-rate improvements enabled by optical movability.

  • Problem

    Existing RAQR architectures use fixed sensing regions and therefore lack spatial reconfigurability comparable to movable antennas and fluid antenna systems.

  • Method

    The paper steers probe–coupling overlap regions, derives a factorized closed-form baseband model validated against Lindblad solutions, and applies gradient-based alternating optimization over optical positions and LO design.

  • Results

    RF-to-optical transduction and optical displacement suppress interference by 14 dB and 87 dB, respectively, while simulations show user-decorrelation and sum-rate improvements.

  • Takeaways & Limitations

    Optical movability provides a programmable receiver architecture by combining intrinsic beam-pattern shaping with per-cell phase control.

Abstract

from arXiv · show

This paper develops an optically movable Rydberg atomic quantum receiver (RAQR), in which the probe and coupling beams are steered within each vapor cell to dynamically reconfigure the effective radio-frequency (RF) sensing position without mechanical actuation. A closed-form equivalent baseband model is derived by separating the atomic transduction coefficient, optical steering phase, and cell-center array response into distinct factors and the accuracy of the resulting model is validated against numerical solutions of the Lindblad master equation. Based on the derived model, we reveal two complementary channel-shaping mechanisms, including intrinsic beam-pattern shaping through RF-to-optical transduction and per-cell phase control enabled by optical displacement. To further exploit these capabilities, a non-convex sum-rate maximization problem is formulated over the optical positions and local oscillator design and solved via an alternating optimization framework with analytical gradients. Simulation results validate the derived model and demonstrate substantial performance gains enabled by optical movability, highlighting its potential as a programmable receiver architecture for future wireless networks.

I. INTRODUCTION

The paper proposes an optically movable RAQR that reconfigures RF sensing positions through beam steering, addressing fixed-array limitations. It derives and validates a differentiable channel model and uses optical positioning for channel shaping and sum-rate optimization.

  • Motivation: Conventional RF receivers face thermal-noise and electrically small-antenna limits, while fixed arrays restrict real-time channel programmability and spatial reconfiguration.
  • Motivation: Existing RAQRs use fixed probe–coupling overlap regions, limiting intra-cell spatial degrees of freedom despite prior evidence that optical scanning can reposition atomic sensing regions.
  • Architecture: The proposed RAQR continuously reconfigures optical sensing positions by steering probe and coupling beams within each vapor cell, without mechanical actuation.
  • Model: A closed-form equivalent baseband model separates atomic transduction, optical steering phase, and cell-array response, making the effective channel differentiable with respect to optical positions.
  • Channel shaping: RF-to-optical transduction provides intrinsic beam-pattern shaping, while optical displacement enables per-cell phase reconfiguration and can suppress inter-user interference beyond real-valued transduction control.
  • Optimization: A joint optical-position and LO-design problem is solved using alternating optimization with analytical gradients to maximize MRC-based sum rate.

C. Near-field LO Electric Field

The near-field LO is modeled using a planar array whose elements have controllable amplitudes and phases, producing a position-dependent field at each vapor cell. This LO is combined with far-field user signals under a strong-LO assumption and drives the four-level atomic response.

  • LO array geometry: The LO uses a P_xP_y-element uniform planar array parallel to the vapor-cell array’s x-y plane.The two-dimensional element index is mapped to a one-dimensional index for analysis.
  • LO excitation: Each LO element has controllable amplitude β_p and phase φ_p, represented by a_p = β_pe^jφ_p.The LO vector collects all element coefficients for field synthesis.
  • Near-field propagation: The LO field at each vapor cell depends on the element-to-sensing-point distances and the optical displacement q_m.The resulting field is formed by summing element contributions with propagation-dependent phases.
  • Superimposed RF field: The superimposed RF field is expressed relative to the LO, with the user–LO phase difference determined by propagation phase, user phase, and LO phase.The model introduces the RF field at the sensing position before atomic transduction.
  • Signal assumptions: The derivation assumes a strong LO, E_LO,m ≫ E_k, and sets the LO frequency equal to the carrier so that Δf_k = f_D,k.These assumptions simplify the relative-frequency and phase representation of the received RF signal.
  • Atomic response: The vapor cells follow a four-level ladder governed by a Lindblad master equation, with the measured probe susceptibility proportional to ρ_21.The RF Rabi frequency is proportional to the incident RF electric field through the dipole moment μ_34.

III. EQUIVALENT CHANNEL MODEL

The equivalent-channel derivation approximates the vapor-cell field using center amplitudes and retained first-order phase variation. This yields a tractable model based on cell-center quantities, LO geometry, and user-induced phase slopes along each sensing line.

  • Model objective: The section derives a closed-form output probe power and equivalent baseband channel model for the movable vapor-cell array RAQR.The derivation addresses the position-dependent field inside each cell.
  • Cell-center approximation: The cell-center approximation treats field amplitude as constant at the cell center while retaining phase variation through a first-order Taylor expansion.This approximation resolves the otherwise intractable integral produced by the position-dependent atomic response.
  • Center quantities: The vapor-cell center is used as the reference point for evaluating the local LO and user-field quantities.The center coordinate is defined from the cell center c_m and the optical displacement q_m.
  • LO amplitude: The LO field amplitude is approximated as constant along a vapor cell because the cell length is smaller than the LO-to-cell propagation distance.The approximation concerns field strength, not the longitudinal phase.
  • LO phase: The LO phase variation along the cell is retained because the cell length is comparable to the RF wavelength.A first-order expansion is applied around the midpoint l = L/2.
  • User phase: The far-field user phase varies linearly with sensing position and can therefore be expressed exactly along the sensing line.The derivation separates the center relative phase from the effective longitudinal phase slope.
  • RF envelope: Under the strong-LO condition, the RF envelope strength along the sensing line is approximated using the center-based field and phase representation.This produces the local RF quantity needed for the closed-form probe-output model.

B. Closed-Form Probe Output

The closed-form probe-output derivation converts the position-dependent RF and LO fields into an AC photocurrent and then a stacked equivalent baseband observation. The resulting channel factors optical and cell-center effects for array-level analysis.

  • B. Closed-Form Probe Output: The LO-biased operating point is defined from the RF Rabi frequency, and the user-induced perturbation is introduced around that operating point.These quantities parameterize the local atomic response to the received RF signal.
  • B. Closed-Form Probe Output: A first-order Taylor expansion linearizes the atomic response around the LO-biased operating point.The resulting approximation is substituted into the probe-output expression.
  • B. Closed-Form Probe Output: The derivation defines the LO-biased DC probe power and evaluates the remaining sensing-line integral using sinc(x) = sin(x)/x.The integrated expression is then used to approximate the total output probe power.
  • B. Closed-Form Probe Output: For weak user signals, e^x ≈ 1 + x yields an output probe beam with a separable AC component.The AC component is the part used to form the detected signal.
  • C. Equivalent Channel Model: The AC photocurrent is converted through the photodetector and amplifier into an equivalent baseband voltage with additive noise.The noise includes quantum projection, photon shot, and thermal noise.
  • C. Equivalent Channel Model: The received field for each user is modeled from transmit power, antenna gain, propagation distance, channel coefficient, and transmitted symbol.These terms provide the user-side input to the cell-level equivalent channel.
  • C. Equivalent Channel Model: At the cell level, the equivalent channel is the product of the optical factor, conversion factor, and cell-center response.The factorized form makes optical displacement and local transduction explicit.
  • C. Equivalent Channel Model: For the vapor-cell array, cell observations are stacked into a baseband vector and optical displacements are collected in Q.The resulting matrix model uses the factorized channel together with Doppler, transmitted-symbol, and noise vectors.

D. Analysis

The analysis interprets movable RAQR channels through RF-to-optical conversion, analog phase matching, and optical displacement. It also identifies conditions governing gain, channel decorrelation, and the physical equivalence to translated antennas.

  • RF-to-optical conversion: The RF-to-optical conversion coefficient is interpreted as a product of analog phase matching, RF-to-optical conversion gain, and LO-biased DC probe power.The conversion gain depends on the slope of the dispersive EIT response and is programmable through the LO bias.
  • RF-to-optical conversion: Full aperture gain occurs when the LO phase gradient matches the user’s transverse wavevector; otherwise, the user signal is attenuated.This identifies analog phase matching as a beam-pattern shaping mechanism.
  • Optical-based movable antenna: Optical displacement makes each vapor cell operate as a movable antenna without mechanical actuation.The probe–coupling overlap region changes while the vapor cell and optical and electrical interfaces remain stationary.
  • Optical-based movable antenna: The movable channel is equivalent to that of a conventional antenna translated to c_m + q_m.This gives the architecture the channel-conditioning capability associated with movable or fluid antennas.
  • Multiuser decorrelation: Perfect multiuser decorrelation requires the user-channel Gram matrix to be diagonal, meaning nonzero user channels are mutually orthogonal.The condition is stated through the off-diagonal correlation terms ϱ̂_ij(Q) = 0 for i ≠ j.

1) Larger vapor-cell radii enhance user decorrelation:

The design links optical positions and local-oscillator parameters to MRC sum-rate maximization through user-channel energy and correlation. Larger vapor-cell radii expand geometric phase tuning, while projected-gradient updates address the resulting coupled nonconvex problem.

  • Larger vapor-cell radii enhance user decorrelation:: Larger vapor-cell radii increase the available geometric phase range and enhance spatial reconfigurability through position-dependent conversion gain.The phase range is 2kcRVC|∆u⊥,i,j|2 under |qm|2 ≤ RVC.
  • Larger vapor-cell radii enhance user decorrelation:: MRC rewards optical and LO designs that enlarge per-user captured energy and reduce inter-user correlations.The effective energy and interference depend on the design variables through user correlation.
  • Larger vapor-cell radii enhance user decorrelation:: Optical positions and LO designs are constrained to keep sensing lines inside vapor cells and limit normalized LO excitation power.These constraints define feasibility for the joint design problem.
  • Larger vapor-cell radii enhance user decorrelation:: The joint sum-rate problem is solved by alternating optimization of optical positions and LO parameters using projected-gradient ascent.Analytical gradients are derived for optical coordinates and LO amplitudes and phases.

1) Optical Design:

The optical-design block updates sensing positions with projected-gradient ascent while preserving cell-boundary feasibility. Sequential position updates are embedded in an alternating procedure for MRC sum-rate maximization.

  • Optical Design:: Algorithm 1 initializes optical positions and iteratively updates them using projected ascent with adaptive step-size reduction.Backtracking recomputes tentative positions until the update satisfies the stopping rule.
  • Optical Design:: The optical gradients differentiate equivalent-channel factors with respect to each sensing-line coordinate.The channel derivative uses the product rule for the cell-response and optical-response terms.
  • Optical Design:: Sequential projected-gradient position updates are performed for the optical block.The resulting procedure is summarized in Algorithm 1.

2) LO Design:

The LO-design block optimizes LO amplitudes and phases using projected-gradient ascent, alternating with optical-position updates. Projection preserves feasibility, backtracking yields monotonic sum-rate improvement, and block costs are characterized explicitly.

  • LO Design:: Algorithm 2 updates LO amplitudes and phases by projected-gradient ascent with projection and backtracking.Tentative LO vectors are projected before evaluating the MRC sum rate.
  • LO Design:: The MRC combiner is recomputed from the updated LO excitation and equivalent channel, and the two design blocks alternate until sum-rate convergence.The combiner is WMRC(Q, a) = ΦcLO(Q, a)H(Q, a).
  • LO Design:: Projection keeps every optical and LO update feasible, while backtracking ensures sufficient increase and a monotonically non-decreasing objective sequence.The resulting alternating procedure has stable convergence behavior.
  • LO Design:: The optical and LO blocks require O(MP + MK2) and O(MPK + MK2) operations, respectively, per block evaluation.Overall complexity also depends on alternating, LO-block, and optical-block iteration counts.

V. SIMULATION RESULTS

The simulations validate the closed-form model and show that optical displacement and RF-to-optical transduction enable channel shaping, rapid optimization, and improved multiuser performance.

  • Model validation: Approximation errors remain below -20 dB, validating the center approximation against numerical results and confirming the derived analytical expressions.The error increases toward the vapor-cell boundary, while AC voltage outputs further confirm the expressions.
  • Movable RAQR capabilities: RF-to-optical conversion suppresses interference from -19.1 dB to -33.3 dB with fixed optical position.This demonstrates intrinsic beam-pattern shaping through the receiver’s RF-to-optical conversion.
  • Sum-rate evaluation: The proposed algorithm approaches genetic-algorithm sum-rate performance with fewer objective evaluations and lower computational complexity.The comparison averages the sum-rate CDF over 100 trials with users randomly distributed within 100 km2.
  • Sum-rate evaluation: Sum rate initially increases with user count and then decreases slightly as available spatial DoFs become insufficient for user separation.Across 100 random channel realizations, the proposed algorithm outperforms the benchmarks.
  • Conclusions: Optical displacement suppresses interference by 87 dB, complementing the 14 dB suppression provided by RF-to-optical transduction.The paper uses alternating optimization with analytical gradients to exploit these channel-shaping mechanisms for MRC-based sum-rate maximization.

APPENDIX A PROOF OF LEMMA 1

The appendix derives the analytical gradient of the MRC-based objective by applying the chain rule, collecting channel-derivative terms, and differentiating optical and LO variables.

  • Gradient derivation: The objective derivative is formed with respect to real optical-position and LO-design variables using the chain rule.The variables include ym, zm, βp, and φp.
  • Gradient derivation: Strict positivity of Sk(Q, a) follows from ϱ̂kk(Q, a) = ∥hk(Q, a)∥2, supporting the derivative manipulation.The appendix substitutes intermediate expressions for diagonal and off-diagonal terms in the objective derivative.
  • Gradient derivation: The two off-diagonal streams are merged using the Hermitian property ϱ̂ji(Q, a) = ϱ̂ij(Q, a), yielding a collector-vector form.Every derivative term is reduced to the standard form ℜ{(·)H∂hi(Q, a)/∂κ}.
  • Proof completion: The proof concludes after establishing the relationship between gi(Q, a) and the i-th column of Λ(Q, a).This completes the stated lemma proof.
  • Optical derivatives: The appendix provides derivatives of the LO contribution with respect to optical coordinates ym and zm.These derivatives account for the geometry relating cell positions, optical positions, and LO positions.

APPENDIX C CLOSED-FORM DERIVATIVES FOR THE LO DESIGN

This appendix supplies closed-form derivatives for the LO-design variables while evaluating all quantities at a fixed optical position.

  • LO derivatives: The appendix provides closed-form expressions for derivatives with respect to the LO variables βp and φp.These variables represent LO amplitudes and phases in the design optimization.
  • Evaluation condition: All quantities in the LO-derivative expressions are evaluated at the fixed optical position qm = q(r).The resulting formulas isolate the LO-design derivatives from the optical-position update.
Loading 2608.30718v1…