Optimal State Choice for Rydberg-Atom Microwave Sensors

Rydberg electromagnetically induced transparency (EIT) enables the realization of atom-based Systeme-International-traceable microwave sensing, imaging, and communication devices by exploiting the strong microwave electric dipole coupling of highly excited Rydberg states. Essential to the development of robust devices is a careful characterization of the sensor performance and systematic uncertainties. In this work, we present a comparison of microwave-induced EIT splitting in a cesium atomic vapor for four possible Rydberg couplings, $65S_{1/2}\to 65P_{1/2}$, $66S_{1/2}\to 66P_{3/2}$, $79D_{5/2}\to 81P_{3/2}$, and $62D_{5/2}\to 60F_{7/2}$, at microwave transition frequencies around 13 GHz. Our work highlights the impact of multiphoton couplings on neighboring Rydberg states in breaking both the symmetry and linearity of the observed splitting, with excellent agreement between experimental observations and a theoretical model accounting for multiphoton couplings. We identify an optimal angular-state choice for robust microwave measurements, as well as demonstrating an alternative regime in which microwave polarization can be measured.

Figure 1

(a) The cesium energy levels involved in the microwave EIT scheme for coupling to $n{S}_{1/2}$ or $n{D}_{5/2}$ states. (b) The experimental setup, using a probe and a coupling laser, both circularly polarized and counterpropagating along the $\hat{z}$ axis: DM, dichroic mirror; FP, Fabry-Pérot cavity used as frequency reference; PD, photodiode. (c) Example spectra showing AT splitting of EIT resonance due to a resonant MW field.

Figure 2

(a) The measured AT splitting as a function of the MW power and corresponding linear fits for the four Rydberg transitions. The error bars are the standard error of the fit and are smaller than the symbol sizes. (b) The linear fit residuals. (c) The electric field obtained by dividing the AT splitting by the corresponding dipole moment $d$. The error bars are smaller than the symbol sizes.

Figure 3

(a)–(d) The probe-beam transmission as a function of the MW field when the coupling laser is scanned. The MW field is tuned on resonance. (e)–(h) The theoretical eigenenergies, with a color map proportional to fractional population of the laser-coupled Rydberg state. The dashed lines correspond to the expected linear AT splitting.

Figure 4

(a)–(d) The probe-beam absorption as a function of the MW frequency (coupling laser scanned) for a fixed MW power. In each case, the white arrow indicates the resonance of the target MW transition. (e)–(h) The corresponding energy levels obtained with our model for a MW field magnitude of 6 V/m. The red circles indicate Rydberg couplings that break the linearity of the AT splitting.

Figure 5

The polarization sensitivity. (a) $65S_{1/2}\to 65P_{1/2}$ and (b) $62D_{5/2}\to 60F_{7/2}$ spectra as a function of the MW field when the antenna is rotated by $5^{\circ }$ around the $\hat{y}$ axis. (c),(d) The corresponding energy lines obtained with our model. The dashed lines indicate the AT splitting expected in the fine structure basis. In (c), the data points represent the AT peak positions extracted using a four-Gaussian fit. The error bars are the standard error of the fit normalized by the reduced ${\chi }_{\nu }^2$.

Figure 6

The theoretical AT splitting calculated for ${}^{87}\mathrm{Rb}$ for the same transitions as measured in $\mathrm{Cs}$ (a)–(d) AT splitting as a function of the MW field strength and (e)–(h) eigenenergies as a function of the MW frequency for a MW field magnitude of 6 V/m. The color bar corresponds to the relative population of the laser-coupled Rydberg state.

Figure 7

The AT eigenenergies in units of ${\mathrm{\Omega }}_0=d{\tilde{E}}_{\mu }/\sqrt{6}$ for $n{S}_{1/2}\to n^{\prime }{P}_{1/2}$ Rydberg levels for microwaves with linear polarization rotated at an angle $\theta$ with respect to the $z$ axis, showing symmetric splitting with equivalent energies for $\theta$ and ${90}^{\circ }-\theta$ when $0\le \theta \le {45}^{\circ }$.