Calibration of electric fields in low-frequency off-resonant Rydberg receivers

Abstract

We present results on Rydberg atom-based electric field sensing in the range of 1 kHz - 300 MHz, using a three-photon Rydberg excitation scheme and a transverse electromagnetic (TEM) line waveguide to apply low-frequency rf fields to the cell. Measurements of low-frequency screening in quartz and sapphire vapor cells show excellent agreement with a phenomenological model of the effective vapor cell material properties based on an electrical 2-port measurement of the TEM line. We achieve a best noise-equivalent field of 106(4) $\mathrm{\frac{μV}{m \sqrt{Hz}}}$ at 300 MHz and characterize noise-equivalent fields in the ultra-low to very-low frequency (ULF-VLF) band.

Figures (9)

• Figure 1: Depiction of the vapor cell shielding effect, where the frequency-dependent bulk dielectric constant $\epsilon(\omega)$ and the sheet conductivity of the inner surface $\sigma_{surface}$ induced by adsorption of the alkali atoms conductively shields electric field $E_{sig}$ applied by a pair of external electrodes to yield a reduced field amplitude $E_{cell}~=~\eta(\omega)E_{sig}$ for $\eta(\omega)~\leq~1$. In the frequency range covered in this paper, vapor cell length $\ell \ll \lambda$ for signal field wavelength $\lambda$
• Figure 2: (Top) Level diagram for optical excitation in the off-resonant detection scheme, where three optical transitions connect the Rb ground state to the Rydberg state $55F_{7/2}$. An off-resonance signal field with frequency $\omega_{sig}$ and an off-resonance local oscillator with frequency $\omega_{LO}$ incident on the Rydberg atoms induce a heterodyne beatnote $\abs{\omega_{sig} - \omega_{LO}}$ modulating the transmitted probe intensity. The nearest resonant microwave transition is at approximately $\omega_{res} \approx 2\pi \times 495$ MHz. Also displayed are EOM sidebands induced on the 1257 nm coupler laser for scanning across resonance. (Bottom) Diagram of laser beam paths through vapor cell, showing region where co-propagating 780 and 776 nm lasers overlap with the 1257 nm coupler.
• Figure 3: Simplified experimental schematic. PD: photodiode; DBS: dichroic beam splitter; AOM: acousto-optical modulator; EOM: electro-optical modulator. In the middle is an image of the TEM waveguide with a sapphire vapor cell mounted under the central conductor, with wavevectors of probe and rf fields and the coordinate system used in HFSS simulation
• Figure 4: Simulated $E(x)/E(0)$ for $E(x)$ averaged across the cross-sectional beam overlap area against x-position for both vapor cells, derived from HFSS simulations of empty waveguide for a signal field at 300 MHz. Also included (inset text) are the matching RMS variances in electric field for both quartz and sapphire vapor cells.
• Figure 5: (Top) Plot showing lock-in amplifier (time constant $\tau$ = 1 ms) output and corresponding zero-crossing for $\omega = 2\pi \times 300$ MHz, yielding a 5.58 MHz shift for $V_{rf} = 0.12$ V ($E_1 = 1.67$ V/m) (Bottom) Frequency shift of zero-crossing versus $V_{rf}$ for $\omega = 2\pi \times 300$ MHz and overlaid fit according to Equation (\ref{['eq:5']}), in addition to signal field slope parameter $\xi$.