Quantum-enabled complete RF-polarimetry with an optically-wired atomic sensor

Abstract: Rydberg atomic electrometry leverages the extreme sensitivity of highly excited atoms for calibration-free electric field measurements. The technique uses a non-metallic vapor cell to link properties of an RF field to a spectroscopic readout in the optical domain. Most demonstrations have so far focused on detecting linearly-polarized fields, for which the induced splitting of dressed atomic levels is rotationally invariant. Here we report on Rydberg atomic measurements of RF fields in a general state of polarization (SOP) which we map onto the Poincaré sphere through spectroscopic fingerprints. For a Stokes vector circumnavigating a Poincaré sphere meridian, we witness a continuous transformation of the atomic eigenenergy spectrum. Because the relative positions of eigenenergies are locked in place by quantization of angular momentum, the framework is universal and calibration free. We provide a specific demonstration in rubidium, which generalizes to all systems with a single valence electron.

• The paper demonstrates complete RF polarimetry using a single rubidium vapor cell and two optical beams, mapping RF polarization onto quantized Rydberg spectral fingerprints without auxiliary RF fields.
• The method retrieves the RF Stokes vector from power-independent peak positions and resolves helicity by optically changing the probe geometry, while achieving agreement across several Rydberg transitions.
• The results show that nearby fine-structure levels can distort the ideal spectrum, highlighting the need for careful transition selection or multilevel modeling in practical sensors.

Overview

This paper demonstrates a complete Rydberg-atomic RF polarimeter that determines the full state of polarization (SOP) of an incoming radio-frequency field without any auxiliary RF fields. The sensor consists solely of a rubidium vapor cell interrogated by two optical beams in a ladder-type electromagnetically-induced transparency (EIT) configuration. The SOP of the device-under-test (DUT) field is encoded in the eigenenergy spectrum of RF-dressed Rydberg manifolds, and the relative positions of spectral peaks—locked by quantized angular momentum—map the field's Stokes vector onto the Poincaré sphere. Because the framework rests only on angular momentum algebra, it is calibration-free, independent of DUT field power, and independent of atomic species details such as radial transition matrix elements (2605.14529).

Transition hierarchy and spectroscopic fingerprints

The core theoretical construct is an analytic coupling matrix $\mathbf{M}^{(Jp)}$ of dimension $(2J+2J'+2)\times(2J+2J'+2)$ describing dipole-allowed transitions between Rydberg levels with total angular momenta $J$ and $J'$ ($J'-J=0,1$), for an alkali atom with $S=1/2$. The index $p=0,\pm1$ labels the three allowed transition families. Diagonalizing $\mathbf{M}^{(Jp)}$ yields closed-form eigenvalues as functions of the phase angle $\phi$ controlling the field's ellipticity. For the simplest member, $\updownarrow^{1/2}_{1/2}$, the four eigenvalues are $(2J+2J'+2)\times(2J+2J'+2)$0.

The number of unique eigenvalues grows linearly with $(2J+2J'+2)\times(2J+2J'+2)$1: for linearly polarized fields the counts are $(2J+2J'+2)\times(2J+2J'+2)$2 across the hierarchy $(2J+2J'+2)\times(2J+2J'+2)$3, rising to maxima of $(2J+2J'+2)\times(2J+2J'+2)$4 when degeneracies are lifted by field chirality off the Poincaré equator. This establishes that the spectrogram is a universal, analytically known fingerprint of the SOP.

Experimental realization

Experiments use $(2J+2J'+2)\times(2J+2J'+2)$5Rb atoms in a vapor cell with a $(2J+2J'+2)\times(2J+2J'+2)$618 GHz DUT field dressing Rydberg states near principal quantum number 50. A 780 nm probe and counter-propagating 480 nm coupling beam, both linearly polarized along $(2J+2J'+2)\times(2J+2J'+2)$7, scan the coupling detuning over $(2J+2J'+2)\times(2J+2J'+2)$8200 MHz to record EIT spectra while $(2J+2J'+2)\times(2J+2J'+2)$9 sweeps $J$0, tracing a meridian of the Poincaré sphere through LVP–LCP–LHP–RCP–LVP. Density-matrix simulations incorporating the optical fields reproduce both peak positions and their $J$1-dependent prominence.

Key experimental findings include:

• $J$2: excellent agreement with theory; exactly two peaks for linear and three for circular polarization, four for elliptical.
• $J$3: one fewer spectral peak than eigenenergies because the central dressed state has purely $J$4 character and is EIT-inaccessible by Laporte's rule—a selection-rule effect captured by simulation.
• $J$5: poor agreement with the isolated two-level model due to interference from the nearby $J$6 level (~100 MHz detuning); agreement is restored only by extending the density matrix to three levels. This is a candid limitation: real atoms do not always present clean two-level systems at the required transitions.
• $J$7: well described by the two-level framework with excellent correspondence among analytics, experiment, and simulation.

Inversion procedure and ambiguity resolution

The inversion from spectrum to phase angle uses the ratio $J$8 of inner to outer eigenvalue envelopes, extracted from relative peak positions only—hence power-independent. For $J$9, mirror symmetries yield a fourfold ambiguity; for $J'$0, combining $J'$1 with the $J'$2-dependent prominence of the central EIT peak reduces this to a twofold ambiguity, since $J'$3 and $J'$4 produce identical spectra. Notably, opposite-helicity circular fields ($J'$5 vs. $J'$6) give indistinguishable spectra in the standard probing geometry.

The authors break this symmetry by rotating the probe/coupling beams to propagate along $J'$7 with circular polarization. Peak positions are unchanged (they are fixed by the RF SOP), but the central peak is enhanced for LCP and suppressed for RCP, experimentally revealing helicity and removing the remaining ambiguity. This demonstrates a genuinely complete polarimeter using only optical reconfiguration—no additional RF references.

Limitations and open questions

The method requires judicious choice of transition: the $J'$8 case shows that nearby fine-structure levels can corrupt the idealized fingerprint, so applicability depends on isolatable transitions or extended multi-level modeling. The demonstrated unambiguous SOP retrieval covers a meridian trajectory under controlled conditions; robustness against background magnetic fields and other symmetry-breaking perturbations is addressed only prospectively via a proposed tomographic scanning of optical beam directions and polarizations. Whether such a scheme can simultaneously recover an unknown direction of arrival (DoA) of the RF field from a single vapor cell remains an open question the authors raise but do not demonstrate.

Conclusion

The paper establishes that a single vapor cell, "wired" only with two laser beams, performs complete RF polarimetry by exploiting angular-momentum-quantized spectroscopic fingerprints, generalizing prior work limited to linearly polarized fields and eliminating the multiple auxiliary local oscillators required in earlier elliptical-polarization demonstrations. Its universality across alkali species and its calibration-free, power-independent inversion make it a compact alternative to dual-polarized metallic antennas, which necessarily distort the fields they measure.