Quantum-Limited Atomic Receiver in the Electrically Small Regime

We use a quantum sensor based on thermal Rydberg atoms to receive data encoded in electromagnetic fields in the extreme electrically small regime, with a sensing volume over $10^7$ times smaller than the cube of the electric field wavelength. We introduce the standard quantum limit for data capacity, and experimentally observe quantum-limited data reception for bandwidths from 10 kHz up to 30 MHz. In doing this, we provide a useful alternative to classical communication antennas, which become increasingly ineffective when the size of the antenna is significantly smaller than the wavelength of the electromagnetic field.

Figure 1

The quantum limit for data capacity. (a) Data can be sent, for example, by encoding information in the strength of the electric field. The quantum sensor detects symbols by measuring the evolved phase $\varphi$ at the end of each period, therefore inferring the transmitted symbol (right axis). (b) The Chu limit to data capacity for an efficient 7 cm classical antenna is shown in green (see text for details). The maximum standard quantum limit $C_{\max }$ for our experimental parameters is shown in pink. The corresponding maximum measured data capacity of our sensor is shown as black points.

Figure 2

(a) Experimental setup and (b) Level diagram. (c) When no $E$ field is applied, we observe a single EIT transmission window (red circles). Low-frequency electric fields cause scalar and tensor Stark shifts that split the resonance into three peaks (blue triangles). (d) At $t=0$, we apply a square pulse to the electric field. The probe transmission rapidly follows the applied field, but then slowly relaxes over 0.5 ms due to free charges in the glass cell that shield the electric field.

Figure 3

Quantum-limited operation. (a) We measure probe transmission through the cell in bandwidth $f_d=1/t_d$ by averaging for time $t_d$ (inset). Directly measured SNR (black points) and SNR with technical noise subtracted (open circles) are plotted versus $f_d$. At high frequencies, we observe the standard-quantum-limited SNR scaling (red dashed line). At lower frequencies, we observe a steady-state, square-root scaling of SNR (blue dots). The data are fit to the complete quantum noise model (pink line). The SNR data (open circles) lie within 2 standard deviations of the fit over the fitted range of $f_d=5\times {10}^4\mathrm{Hz}$ to $f_d={10}^7\mathrm{Hz}$. The larger deviations at low frequencies are due to the cell shielding effect. (b) The SNR data from (a) are used to plot data capacity versus $f_d$. The quantum limit, for our fitted effective atom number and signal size, is shown as a pink line. Inset: We plot the SNR for receiving symbols in a bandwidth $f_d=0.5\mathrm{MHz}$ as a function of the effective atom number. The data are fit to a square-root scaling.