Rydberg atomic polarimetry of radio-frequency fields

TL;DR

Rydberg-atom RF sensing uses EIT in Rydberg ladders to transduce RF-field amplitudes into optical signals. The authors develop a dressed-state polarization-resolved framework that identifies Type-I and Type-II ladders, each with distinct EIT signatures, and validate it with experiments on ${}^{87}$Rb and density-matrix simulations. They show that the presence or absence of a central EIT peak at $ riangle_c=0$ depends on the ladder type and RF polarization, challenging simplified four-level interpretations. This work lays groundwork for SI-traceable, polarization-resolving quantum metrology and motivates machine-learning approaches to reconstruct arbitrary RF polarization from spectrograms.

Abstract

Rydberg atoms efficiently link photons between the radio-frequency (RF) and optical domains. They furnish a medium in which the presence of an RF field imprints on the transmission of a probe laser beam by altering the coherent coupling between atomic quantum states. The immutable atomic energy structure underpins quantum-metrological RF field measurements and has driven intensive efforts to realize inherently self-calibrated sensing devices. Here we investigate spectroscopic signatures owing to the angular momentum quantization of the atomic states utilized in an electromagnetically-induced transparency (EIT) sensing scheme for linearly polarized RF fields. Specific combinations of atomic terms are shown to give rise to universal, distinctive fingerprints in the detected optical fields upon rotating the RF field polarization. Using a dressed state picture, we identify two types of atomic angular momentum ladders that display strikingly disparate spectroscopic signatures, including the complementary absence or presence of a central spectral EIT peak. Our study adds important insights into the prospects of Rydberg atomic gases for quantum metrological electric field characterization. In particular, it calls into question prevailing interpretations of SI-traceable Rydberg atom electrometers.

Figures (10)

• Figure 1: (a) Level diagram of a four-level model atom with three-fold degeneracy of its ground ($g$) and second excited level ($r_1$). A linearly-polarised probe field is resonant with the transition from $g$ to the first excited level $i$. A coupling field has a frequency close to the transition from $i$ to $r_1$, giving rise to an EIT peak for the transmitted probe field when its detuning $\Delta_\text{c}$ is scanned (b). (c) The model atom dressed in an RF-field that is parallelly ($\theta=0^\circ$) or perpendicularly ($\theta=90^\circ$) polarized with respect to the optical probe and coupling fields. The resulting AT splitting is shown indicated with dashed lines. (d) Simulated probe transmission spectra for $\theta=0^\circ,45^\circ,90^\circ$. $\Omega_\text{RF}$ denotes the Rabi frequency characterizing the RF coupling.
• Figure 2: Hyperfine level diagrams for the $S_{1/2}^{F=2}\!\!\leftrightarrow\!\! P_{3/2}^{F=3}\!\!\leftrightarrow\!\! D_{5/2}\!\!\leftrightarrow\!\! P_{3/2}$ excitation ladder with the ultimate and penultimate levels (Rydberg levels) resonantly coupled by an RF field, which is linearly polarized along the atomic quantization axis and drives $\pi$-transitions (orange arrows). Red and blue arrows shows the allowed transitions for optical probe and coupling fields linear polarized (a) perpendicularly to the RF field (optical $\sigma$-transitions) and (b) parallel to the RF field (optical $\pi$-transitions). The $F$-levels for the Rydberg states are energetically degenerate, and have been offset vertically to illustrate the dipole-allowed transitions in play.
• Figure 3: Hyperfine level diagrams for the $S_{1/2}^{F=2}\!\!\leftrightarrow\!\! P_{3/2}^{F=3}\!\!\leftrightarrow\!\! D_{3/2}\!\!\leftrightarrow\!\! P_{1/2}$ excitation ladder with the ultimate and penultimate levels (Rydberg levels) resonantly coupled (orange arrows) by an RF field, which is linearly polarized along the atomic quantization axis. Optical coupling (blue arrows) and probe (red arrows) fields are also linearly polarized along the quantization axis and $\pi$-transitions are driven throughout the system.
• Figure 4: RF-dressed Rydberg levels---procedure for finding the energy structure probed by EIT. (a) A linearly-polarized RF field couples states of lower ($J=5/2$, black) and upper ($J=3/2$, grey) Rydberg levels via $\pi$-transitions with dipole matrix elements as indicated. (b) Field-dressed Rydberg levels with $m_J$-dependent AT-splitting. Each grey-black state in the diagram represents an equal two-component superposition of $J=5/2$ and $J=3/2$ states with the adjacent $\pm$ indicating its symmetry. (c) Labelling the lower dressed manifold of (b) to include all possible values for the nuclear spin projection $m_I$ so that each state inside the hexagon is designated by $|m_J,m_I\rangle$ (and hence $m_F=m_J+m_I$) as well as a symmetry parameter $s$. Each $|m_J,m_I;s\rangle$ can be expanded using (\ref{['eq:expansion']}) which facilitates the evaluation of the transition strength for the optical coupling from a state $|J'=3/2,F'=3,m_F'=m_F\rangle$ through (\ref{['eq:3j']}).
• Figure 5: Diagram for evaluating the optical coupling from a state $|J'=3/2,F'=3,m_F'=m_F\rangle$ to a state in a field-dressed $D_{3/2}\!\!\leftrightarrow\!\! P_{1/2}$ Rydberg manifold. The procedure for obtaining this diagram follows that of Fig. \ref{['fig:r1r2']} and each of the states $|m_J,m_I;s\rangle$ can be expanded using (\ref{['eq:expansion']}).