Very-high- and ultrahigh-frequency electric-field detection using high angular momentum Rydberg states

We demonstrate resonant detection of rf electric fields from 240 to 900 MHz (very high frequency to ultrahigh frequency) using electromagnetically induced transparency to measure orbital angular momentum $L=3\to L^{\prime }=4$ Rydberg transitions. These Rydberg states are accessible with three-photon infrared optical excitation. By resonantly detecting rf in the electrically small regime, these states enable a new class of atomic receivers. We find good agreement between measured spectra and predictions of quantum defect theory for principal quantum numbers $n=45$ to 70. Using a superhetrodyne detection setup, we measure the noise floor at $n=50$ to be $13\mu \mathrm{V}/\left(\mathrm{m}\sqrt{\mathrm{Hz}}\right)$. Additionally, we utilize data and a numerical model incorporating a five-level master equation solution to estimate the fundamental sensitivity limits of our system.

Figure 1

(a) Level diagram for $F$-state Rydberg excitation and rf-induced Autler-Townes splitting in ${}^{87}\mathrm{Rb}$. Three electric dipole-allowed infrared transitions connect the ground state to the Rydberg $n{F}_{7/2}$ (or $n{P}_{3/2}$) states. Dashed virtual levels show the single-photon detunings of each step from atomic resonance. UHF to VHF fields, depicted with a green bidirectional arrow, can be detected via Autler-Townes splitting on the $nF\to nG$ Rydberg transitions, while 1 to 500 GHz can be detected on $nS\to nP, nP\to (n-1)D$, and $nF\to (n+1)D$ transitions. (b) Experimental schematic: the 780-nm probe beam counterpropagates in a Rb vapor cell with 776- and 1260-nm beams which form the effective EIT coupling beam. PD: photodiode; DBS: dichroic beam splitter; BD: beam displacer; Pset: polarization optics consisting of a $\lambda /2$ wave plate and a polarizing beam-splitter cube for power control followed by $\lambda /2$ and $\lambda /4$ wave plates for polarization control.

Figure 2

(a) AT-EIT spectrum of the $50F\to 50G$ transition with an applied rf field of 655 MHz (red). A five-level simulated spectrum is underlaid by the data (blue). (b) Autler-Townes splitting of the $50F\to 50G$ EIT signal as a function of an applied UHF electric field. Point markers (red) are the measured uncertainties, with a linear fit to guide the eye (blue). This plot confirms the expected linear scaling between the rf electric field and Autler-Townes splitting.

Figure 3

The top three (blue dashed, red, and black) curves show calculated rf carrier frequencies [34] of commonly used lower angular momentum Rydberg states accessible by two-photon optical excitation. The middle (green) curve, located primarily in the UHF band, is the calculated rf carrier frequency associated with $n{F}_{7/2}\to n{G}_{9/2}$ transitions; the overlaid green point markers with uncertainty show corresponding measured carrier frequencies in the $n=45$ to $n=70$ range. The bottom (yellow) trace shows the calculated rf carrier frequency associated with $n{G}_{9/2}\to n{H}_{11/2}$ transitions.

Figure 4

Dephasing rates versus principal quantum number. Due to competing Rydberg state lifetime and collisional broadening effects, the atom-limited dephasing rate is minimized at intermediate principal quantum numbers $40<n<80$. This illustrates the advantage of decreasing rf carrier frequency by increasing $L$ rather than increasing $n$. The traces in the legend have the same vertical ordering as the $n=20$ data.

Figure 5

Amplitude spectral density noise measurements at $n=50, f_{\mathrm{rf}}=655$ MHz utilizing a superheterodyne technique and the parameters described in the text. The traces in the legend have the same vertical ordering as the data. The top red trace shows the noise with a 9.3 mV/m calibration field on, with a $13\mu \mathrm{V}/\left(\mathrm{m}\sqrt{\mathrm{Hz}}\right)$ white-noise floor near the calibration frequency offset of 50 kHz from the LO field. The calibrated noise with only probe light (black solid trace) and without any light (light gray trace) and the photon shot noise (psn; black dashed trace) are shown for reference. The estimated quantum projection noise is $34\mathrm{nV}/\left(\mathrm{m}\sqrt{\mathrm{Hz}}\right)$, well below the range displayed.