† Corresponding author. E-mail:
Project supported by the National Key R&D Program of China (Grant No. 2017YFA0304203), the National Natural Science Foundation of China (Grant Nos. 61475090, 61675123, 61775124, and 11804202), the State Key Program of National Natural Science of China (Grant Nos. 11434007 and 61835007), and Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRT 17R70).
We present a precise measurement of a weak radio frequency electric field with a frequency of ≲ 3 GHz employing a resonant atomic probe that is constituted with a Rydberg cascade three-level atom, including a cesium ground state |6S1/2⟩, an excited state |6P3/2⟩, and Rydberg state |nD5/2⟩. Two radio frequency (RF) electric fields, noted as local and signal fields, couple the nearby Rydberg transition. The two-photon resonant Rydberg electromagnetically induced transparency (Rydberg-EIT) is employed to directly read out the weak signal field having hundreds of kHz difference between the local and signal fields that is encoded in the resonant microwave-dressed Rydberg atoms. The minimum detectable signal fields of ESmin = 1.36 ± 0.04 mV/m for 2.18 GHz coupling |68D5/2⟩ → |69P3/2⟩ transition and 1.33 ± 0.02 mV/m for 1.32 GHz coupling |80D5/2⟩ → |81P3/2⟩ transition are obtained, respectively. The bandwidth dependence is also investigated by varying the signal field frequency and corresponding −3 dB bandwidth of 3 MHz is attained. This method can be employed to perform a rapid and precise measurement of the weak electric field, which is important for the atom-based microwave metrology.
Precise measurements of a weak radio frequency field with frequency less than 3 GHz play an important role in science, communication, and everyday life. Rydberg atom-based electric field sensor has achieved great progress in recent years due to its large electric polarizability (∝ n7) and big microwave-transition dipole moments (∝ n2).[1] It covers the frequency range over from megahertz to terahertz, and has a potential to outperform the traditional electrometry due to the self-calibration characteristics. An all-optical sensing method based-on Rydberg electromagnetically induced transparency (Rydberg-EIT)[2] and Autler–Townes (AT) splitting[3] has been employed to character the properties of electric fields, including the measurements of microwave fields magnitude,[4–6] polarization,[7,8] phase,[9] as well as millimeter waves,[10] static electric fields,[11,12] subwavelength imaging of microwave electric-field distributions,[13,14] field inhomogeneities,[15,16] and nonlinearity.[17] Rydberg atoms have been also used as a radio frequency receiver for retrieving amplitude modulated (AM) base band signals that result in the “Rydberg atom radio”[18–20] and can also be used to realize the extension of the feasibility of digital communication via a continuously tunable radio-frequency carrier.
A few techniques have been proposed for improving the sensitivity of weak field measurements, for example, (i) using high fineness optical cavities to narrow the EIT linewidth for improving the AT splitting resolution; (ii) using Mach–Zehnder interferometer detection[21] and a frequency modulation technique[22] to increase the signal-to-noise ratio; (iii) a Rydberg atom-based mixer has been used to realize the weak electric-field detection with sub-Hz resolution for the microwave field.[23,24] In this work, we present a precise measurement of weak electric field in a room-temperature cesium vapor cell, where an atomic probe is employed to directly readout the weak radio frequency field that is encoded in the local microwave field. The RF field frequency of ∼ 2.18 GHz (∼ 1.32 GHz) couples a nearby Rydberg transition |68D5/2⟩ → |69P3/2⟩ (|80D5/2 ⟩ → |81P3/2⟩). The frequency of the weak signal electric field is hundreds of kHz different from the local field. The Rydberg-EIT is employed to directly detect the weak signal field, the corresponding minimum detectable field is ∼ 1.36 ± 0.04 mV/m (1.33 ± 0.02 mV/m) with a −3 dB measurement bandwidth of 3 MHz.
Experiments are implemented in a room-temperature cesium cell of length 50 mm and diameter 20 mm, as shown in Fig.
A local radio frequency field, generated with a function generator (SRS SG384) and emitted from a horn antenna, is applied transversely to the laser beams propagating through the vapor cell, where it interacts with cesium Rydberg atoms. The local field has a frequency ∼ 2.18 GHz (1.32 GHz), resonantly driving the |68D5/2⟩ → |69P3/2⟩ (|80D5/2⟩ → |81 P3/2⟩) Rydberg transition with Rabi frequency ΩRF. A signal field with hundreds of kHz difference in frequency from the local field, is originated from another function generator (Keysight N5183B) and emitted by another antenna. The local field causes an AT splitting of the Rydberg-EIT illustrated in Fig.
Microwave field measurement based on Rydberg EIT-AT splitting is no longer applicable for the weak electric field when the field induced AT splitting is less than the EIT linewidth, fAT ≲ΓEIT. To detect the weak field, we encode this weak field, considered as a signal field
For the signal field with its polarization being parallel to the local field and the frequency difference satisfying the condition of
![](cpb_29_3_033201/cpb_29_3_033201_ieqn5.gif)
![](cpb_29_3_033201/cpb_29_3_033201_ieqn6.gif)
![](cpb_29_3_033201/cpb_29_3_033201_ieqn7.gif)
The probe-power transmission is P = P0exp(−α L), with the probe-laser absorption coefficient α = 2πIm(χ)/λp and L the vapor cell length. The χ is the susceptibility of the medium seen by the probe laser. The χ is written as
![](cpb_29_3_033201/cpb_29_3_033201_ieqn8.gif)
In a preliminary experimental test, we set local field frequency ωL = 2π × 2.185740 GHz that couples the nearby Rydberg transition |68D5/2 ⟩ → |69P3/2⟩. The local field results in the AT splitting, fAT = 2π × 15.89 MHz, that is close to the EIT linewidth, see Fig.
When the signal field decreases further, the detected probe transmission displays a deformed sine profile that can not be well fitted with a sine function. To read out the amplitude of weak field ES, we employ a lock-in amplifier triggered by the beat signal
![](cpb_29_3_033201/cpb_29_3_033201_ieqn11.gif)
Finally, we measure the bandwidth of the signal field. We change the frequency of the signal field while keep the local field fixed and do the similar measurements of Fig.
In summary, we have presented a weak electric field measurement for a frequency ωS ≲ 2π × 3 GHz employing a resonant atomic probe. When the signal field is much weaker than the local field, ES ≪ EL, the two-photon resonant Rydberg EIT displays a sine profile with frequency difference of the local and signal fields, Δω, and sine amplitude of
[1] | |
[2] | |
[3] | |
[4] | |
[5] | |
[6] | |
[7] | |
[8] | |
[9] | |
[10] | |
[11] | |
[12] | |
[13] | |
[14] | |
[15] | |
[16] | |
[17] | |
[18] | |
[19] | |
[20] | |
[21] | |
[22] | |
[23] | |
[24] | |
[25] |