Electrometry of extremely-low frequencies from kHz to sub-Hz with a Rydberg-atom sensor

Abstract

Rydberg-atom electric field sensing has shown great potential from near-DC to THz with state-of-the-art measurement metrics realized in sensitivity, phase extraction, multi-band receptivity, etc. While Rydberg-atom sensors have shown exceptional performance in the GHz regime, low-frequency operation has remained challenging because of electric-field-screening in conventional vapor cells, which suppresses externally applied fields. We overcome this limitation by combining auxiliary modulation and lock-in detection with a paraffin-coated vapor cell, and demonstrate an electrode-free, wideband method for sensing frequencies, ranging from 0.5 Hz to 10 kHz. Our work extends Rydberg-atom sensor range to VLF, ULF, SLF, ELF and sub-ELF frequency bands. In our method, high state-of-the-art sensitivities have been achieved - 819 $μ$V/cm/$\sqrt{\text{Hz}}$ for 1 Hz, 33 $μ$V/cm/$\sqrt{\text{Hz}}$ for 10 Hz, 10 $μ$V/cm/$\sqrt{\text{Hz}}$ for 100 Hz and 2 $μ$V/cm/$\sqrt{\text{Hz}}$ for 1 kHz.

Figures (11)

• Figure 1: a) Experimental setup. Probe (852 nm) and coupling (510 nm) beams with effective Rabi frequencies $\Omega_{\text{p}}$ and $\Omega_{\text{c}}$ overlap in a paraffin-coated vapor cell to create two-photon Rydberg excitations to $60D_{5/2}$. A balanced photodetector measures the transmission difference between the probe and an identical reference beam. Auxiliary modulation and signal fields are applied via copper plate pairs, and the lock-in amplifier provides a filtered, demodulated high-SNR output. b) Energy-level diagram for excitation to $60D_{5/2}$. In an electric field, the state splits into $m_j$ sub-levels.
• Figure 2: Transient response induced by electric-field-screening in vapor cells. At $t=0$, when DC bias field of amplitude $\text{V}_p$ is switched on, the on-resonant transmission signal rapidly drops to zero as the resonant condition changes causing the Rydberg-EIT transmission peak to be frequency-shifted. Now, due to screening effect the field inside the vapor cell is slowly reduced to zero over some characteristic time (time constant, $\tau$), shifting the Rydberg-EIT peak back to its original resonant frequency. For standard (uncoated) cell, $\tau=10\text{ }\mu$s is independent of the magnitude of $\text{V}_p$. For paraffin-coated cell, $\tau =$ 0.1 (0.6) ms for $\text{V}_p=$ 2.55 (6) V, which in terms of field amplitude = 354 (833) mV/cm.
• Figure 3: (a) Calculated Stark spectrum of the 60D$_{5/2}$ state for fields from 0 to 380 mV/cm, showing the $m_j$-dependent Stark shift. (b) At $t=0$, a DC bias field of amplitude 354 mV/cm ($\text{V}_p=2.55$ V) is switched on and the transient response is recorded at different probe detunings in a paraffin-coated cell. The resulting 2D color map shows the three split branches corresponding to $m_j=\pm 5/2,\pm 3/2,\pm 1/2$, with most atoms in $\pm 3/2,\pm 1/2$. The red dashed line '$P$' marks $\delta_p=243$ MHz, used for sensor operation. Right: Rydberg-EIT spectrum in the absence of electric field.
• Figure 4: Output signal versus input field amplitude in the linear regime for different low frequencies. Each dashed line is a linear fit to the data for the sensed frequency. Inset: slope $m(f)$ from the linear fit, plotted versus signal frequency, giving the sensor responsivity.
• Figure 5: Sensitivity of the Rydberg-atom sensor with vapor-cell diameter $\phi=3$ cm (red), compared with the theoretically estimated field sensitivity of a classical receiver, a 3 cm dipole antenna (gray), at different frequencies. The Rydberg sensor shows about one to two orders of magnitude better sensitivity at extremely low frequencies. For frequencies $\gtrsim 1$ kHz, the two sensitivities begin to approach each other.