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Abstract
We demonstrate the measurement of super low-frequency electric field using Rydberg atoms in an atomic vapor cell with inside parallel electrodes, thus overcoming the low-frequency electric-field-screening effect at frequencies below a few kHz. Rydberg electromagnetically induced transparency (EIT) spectra involving 52D5/2 state is employed to measure the signal electric field. An auxiliary DC field is applied to improve the sensitivity. A DC Stark map is demonstrated, where the utilized 52D5/2 exhibits mj = 1/2, 3/2, 5/2 Stark shifts and splittings. The mj = 1/2 state is employed to detect the signal field because of its larger polarizability than that of mj = 3/2, 5/2. Also, we show that the strength of the spectrum is dependent on the angle between the laser polarizations and the electric field. With optimization of the applied DC field to shift the mj = 1/2 Rydberg energy level to a high sensitivity region and the laser polarizations to obtain the maximum mj = 1/2 signal, we achieve the detection of the signal electric field with a frequency of 100 Hz down to 214.8 µV/cm with a sensitivity of 67.9 µV cm−1Hz−1/2, and the linear dynamic range is over 37 dB. Our work extends the measurement frequency of Rydberg sensors to super low frequency with high sensitivity, which has the advantages of high sensitivity and miniaturization for receiving super low frequency.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
An atom-based measurement has made significant progress due to its unique advantages of high sensitivity, calibration-free, and intrinsic accuracy, including atomic clocks [1], magnetometers [2] and accelerometers [3]. Rydberg atoms with large DC polarizabilities and microwave-transition dipole moments [4] have widely been used for electric field measurements. Moreover, their ultra-broadband features, covering the electric field from DC to THz scale, make it easier to expand their operating bands without changing the sensing device. Rydberg electromagnetically induced transparency (Rydberg-EIT) spectroscopy is an all-optical method to probe the variation of Rydberg levels [5]. The Rydberg-EIT exhibits Autler–Townes (AT) splitting [6] or Stark shifts [7] in the presence of the electric field, which has been employed to measure the RF field over a wide frequency range from about 1 kHz [8] to over 1 THz [9], including the measurement of the RF field strength [10–14], polarization [15], phase [16], as well the near-field terahertz imaging [17] and sub-wavelength microwave imaging [18].
The electric field with frequency below kHz has significant applications in fields of satellite detection, underground mining, disaster relief, and particularly for submarine-to-air communication [19], because of the long wavelengths and long propagation distances of these fields. However, receiving such long waves with high sensitivity requires a huge antenna which could not be possible on the receiver end. In contrast, Rydberg atom-based sensor decouples from the electric field frequency, whose size is not limited by the Chu limit of conventional antennas [20]. The Rydberg sensor is generally a few cm of vapor cells. Therefore, it is meaningful to develop high sensitivity Rydberg atom-based sensor for the detection of the electric field with low frequency. However, the measurement of electric fields at frequency below a few kHz using an atomic vapor cell is quite challenging due to the low-frequency electric-field-screening effect that is caused by the alkali-metal atoms adsorbed on the inner surface of the cell [8,21], which makes Rydberg atoms inside the atomic vapor cell be incapable of sensing the electric field with frequency lower than the screening rate. The detection of low frequency and DC electric fields can be achieved by using the Stark shift of Rydberg levels with the electric field sources inside the vacuum environment [21,22]. However, it is difficult to measure the Stark shift of an EIT spectrum within a weak field as it causes very small perturbations to the Rydberg energy level. The low bound of the traceable measurement is larger than $10$ mV/cm owing to the limitation of Rydberg-EIT linewidth.
In this work, we demonstrate the measurement of a 100 Hz super low-frequency electric field using Rydberg atoms in a vapor cell containing two parallel electrode plates inside. Rydberg-EIT spectroscopy involving 52$D_{5/2}$ state is used to measure Rydberg level Stark shifts that are caused by the signal electric field. An auxiliary DC field is applied to improve the sensitivity of the Rydberg system. The Rydberg-EIT exhibits $m_j=1/2, 3/2, 5/2$ dependent Stark shifts and splitting in the presence of DC field, where the Stark shift of $m_j=1/2$ state is larger than that of $m_j=3/2, 5/2$, indicating that $m_j=1/2$ state is most sensitive to the electric field. Therefore, we lock the coupling laser frequency to a large slope point of the $m_j=1/2$ Stark level, where the Rydberg-EIT is most sensitive to the signal electric field. The incident 100 Hz electric field causes the oscillation of the probe laser that is proportional to the strength of the applied field. We also demonstrate the dependence of the strength of the spectrum on the polarization of the excitation lasers, showing that the spectrum of $m_j=1/2$ state is strongest when the polarization of the excitation lasers is parallel to the electric field. After optimization of the DC field strength and the polarization of the excitation lasers, we achieve the detectable field strength down to $214.8$ $\mu$V/cm with a sensitivity of $67.9$ $\mu$V cm$^{-1}$Hz$^{-1/2}$, and the linear dynamic range is over $37$ dB.
2. Experimental setup
We perform the experiment in a cylindrical cesium room-temperature vapor cell with $50$ mm long and $25$ mm diameter. The experimental setup and the relevant three-level Rydberg-EIT diagram are illustrated in Fig. 1 (a) and (b). An 852 nm laser is split into a probe beam ($\lambda _p$) with a beam waist of $500$ $\mu$m and an identical reference beam, which are both propagating in parallel through the cell. A Rydberg coupling laser ($\lambda _c$=$510$ nm) with a beam waist of $550$ $\mu$m counter-propagate and overlap with the probe laser, but not the reference beam. The probe laser drives the transition of $|6S_{1/2}, F = 4\rangle \to |6P_{3/2}, F^\prime = 5\rangle$ with Rabi frequency $\Omega _p = 2\pi \times 13.77$ MHz and the coupling laser with Rabi frequency $\Omega _c =2\pi \times 0.94$ MHz is scanned through the Rydberg transition of $|52D_{5/2}\rangle$ from $|6P_{3/2}, F^\prime = 5\rangle$, thus establishing Rydberg-EIT spectroscopy to enhance the probe transmission at two-photon resonant condition. The transmission EIT signal is detected with a differential photodetector as a transmission difference with the reference beam, eliminating the intensity noise of the probe laser. The probe and coupling lasers keep co-linear polarization. A pair of coppery electrode plates (size of 44 mm $\times$ 20 mm $\times$ 1 mm) is parallel integrated into the cesium cell with a spacing of $12$ mm. Two lead wires to electrodes are used to connect the DC field and signal field, which are generated by a signal generator (Suin TFG6803). The electric-field vector points along the y-axis. The angle $\theta$ between the laser polarizations and the electric fields is varied by rotating the polarization of the laser beams with half-wave plates. In the presence of an electric field, the $|52D_{5/2}\rangle$ Rydberg level exhibits $m_j=1/2, 3/2, 5/2$ dependent Stark shifts and splitting.
Fig. 1. (a) Schematic of the experimental setup. An 852 nm probe laser and an identical reference beam are both propagating in parallel through the vapor cell, where a pair of coppery electrode plates is parallel integrated into the cell with a spacing of $12$ mm, while a 510 nm Rydberg laser counter-propagate and overlap with the probe laser, but not the reference beam. The transmission of the probe and reference beam are incident into a differential photodetector as a transmission difference. DPD: Differential Photodetector; DM: Dichroic Mirror; HWP: Half-Wave Plate; HR: High Reflectivity. (b) Energy-level diagram for the three-level Rydberg-EIT. A probe laser is resonant with the transition of $|6S_{1/2}, F=4\rangle \to |6P_{3/2}, F^\prime =5\rangle$ with $\Omega _p$, and a coupling laser drives the transition of $|6P_{3/2}, F^\prime =5\rangle \to |52D_{5/2}\rangle$ with $\Omega _c$. In the presence of an electric field, the Rydberg level exhibits $m_j=1/2, 3/2, 5/2$ dependent Stark shifts and splitting.
3. Results and discussion
In Fig. 2(a), we utilize Rydberg-EIT to demonstrate the DC Stark spectra of $|52D_{5/2}\rangle$ state for $\theta$ = $0^\circ$. The top curve displays the field-free EIT spectrum by scanning the detuning of the coupling laser $\Delta _c$, used for a reference EIT. The detuning axis is calibrated using the $|52D_{J}\rangle$ fine structure components [23]. The middle and bottom curves are measured EIT spectra with DC fields $E_{DC}$ = 0.325 V/cm and 0.375 V/cm, respectively. The degeneracy of the $m_j$ magnetic substates becomes lifted in the presence of DC fields, resulting in $m_j=1/2, 3/2, 5/2$ dependent Stark shifts and splitting. We measure a series of EIT spectra by varying the DC field in a range of 0-0.5 V/cm with a step of 0.025 V/cm, and contour plots show in Fig. 2(b). Each data is normalized to its maximum. The Rydberg-EIT exhibits $m_j=1/2, 3/2, 5/2$ dependent Stark shifts and splitting with increasing the DC field strength, where the Stark shift of $m_j=1/2$ state is larger than that of $m_j=3/2, 5/2$, indicating that $m_j=1/2$ state has larger polarizability and is more sensitive to the electric field. Therefore, we select the $m_j=1/2$ state for the signal field measurements below. The red line is the calculated Stark shift of $|52D_{5/2}\rangle$ state using Alkali Rydberg Calculator (ARC) [24]. The experimental DC electric field (x-axis) is calibrated by the theoretical calculations.
Fig. 2. (a) Measured Rydberg-EIT spectra for the $|52D_{5/2}\rangle$ state with indicated DC field $E_{DC}$=$0$ (top curve), 0.325 V/cm (middle curve), and 0.375 V/cm (bottom curve) at $\theta$= $0^\circ$. (b) DC Stark spectra of the Rydberg state $|52D_{5/2}\rangle$ by varying the DC field in a range of 0-0.5 V/cm. The red line is the calculated Stark shift of $|52D_{5/2}\rangle$ state.
Fig. 3. (a) Measured DC-Stark EIT spectra for $\theta$= $0^\circ$ (top), $40^\circ$ (middle) and $90^\circ$ (bottom) at fixed DC field strength $E_{DC}$ = 0.375 V/cm. (b) The signal strength of $m_j = 1/2, 3/2, 5/2$ EIT spectra as a function of the $\theta$.
Since the D-state Rydberg-EIT has an inherent polarization selectivity feature as the response of state with different $m_j$ depends on the polarization of the incident field [23], we investigate the dependence of EIT spectra strength on the angle $\theta$ between the laser polarizations and the DC electric field by varying both laser polarizations using half-wave plates. Both lasers are kept co-linear polarizations in the measurements. As an example, we show the DC-Stark EIT spectra for $\theta$ = $0^\circ$ (top), $40^\circ$(middle) and $90^\circ$ (bottom) at a DC field strength $E_{DC}$ = 0.375 V/cm, as shown in Fig. 3(a). The results show that the relative strength of $m_j = 1/2, 3/2, 5/2$ EIT peaks are varied when we change the angle $\theta$. Next, we demonstrate the signal strength of $m_j = 1/2, 3/2, 5/2$ EIT spectra as a function of the $\theta$ for a range of $0^\circ$ - $90^\circ$, shown in Fig. 3(b). It is seen the $m_j = 1/2$ EIT signal reach maximum at $\theta$ = $0^\circ$, while the $m_j = 3/2, 5/2$ EIT signal reach maximum at $\theta$ = $45^\circ$ and $90^\circ$, respectively. As $m_j=1/2$ EIT signal is used for the signal field measurements, we set the $\theta$ = $0^\circ$ to get the maximum $m_j=1/2$ EIT signal.
Then, we add a 100 Hz signal field $E_{Sig}$ to the electrodes together with the DC field. The response of Rydberg atoms to the total field can be expressed as
where $E_{DC}$($E_{Sig}$) represents the amplitude of the DC field (signal field). $\omega _{Sig}$ and $\phi _{Sig}$ are the angular frequency and the phase of the signal field. The amplitude of squared total field isAfter selecting optimal DC field strength and lasers polarization, we lock the 510 nm coupling laser to the $m_j$=1/2 EIT peak to measure the 100 Hz signal field. The frequencies of both probe and coupling lasers are locked to a cavity with the finesse 150000, such reducing the frequency fluctuations of lasers. The inset of Fig. 4 shows the measured oscillation of the probe laser for three indicated signal fields $E_{Sig}$ = 4.28 mV/cm, 2.63 mV/cm and 1.62 mV/cm (corresponding to the electric field at red, black and blue dots), which demonstrate the transmitted EIT signal shows a 100 Hz oscillation and the amplitude of oscillation increases with the signal field strength. The signal field strength is $E_{Sig}$ = F$E_{Read}$, where $E_{Read}$ = $\frac {V}{\sqrt {2}d}$, V is the signal fields voltage (V) displayed on the signal generator, d is the spacing between two electrodes, and F is calibration transmission factor obtained by F = $E_{Exp}/E_{Read}$ in a strong field region. The $E_{Exp}$ is obtained by measuring the Stark shifts of $m_j=1/2$ EIT signal, shown as grey squares in Fig. 4. The Stark shift is $\Delta f_{stark}=-\frac {1}{2}\alpha E^{2}_{Exp}$, where $\alpha$ is the polarizability of the $|52D_{5/2},m_j= 1/2\rangle$ state in a field range of 0.33-0.55 V/cm about -1753 MHz cm$^{2}$ V$^{-2}$ calculated using ARC. We use six sets of data in different fields to obtain a mean value of F = 0.999545. After the above calibration, we can get the applied signal field strength in the weak regions. Then, we measure the power of oscillation signals as a function of the signal field strength in weak field region using a spectrum analyzer (ROHDE$\&$SCHWARZ FSVA3013) with a resolution bandwidth of $10$ Hz and a video bandwidth of $10$ Hz. The output of the spectrum analyzer linearly increases with the signal field strength, shown as green circles in Fig. 4. We demonstrate the detectable value of the signal field is down to $E_{det}=214.8$ $\mu$V/cm, which corresponds to a sensitivity of $67.9$ $\mu$V cm$^{-1}$Hz$^{-1/2}$ with the resolution bandwidth of $10$ Hz, and the linear response dynamic range is over $37$ dB. The sensitivity of our system could be limited by the noise of the system, such as optical shot noise, electronic noise, stray electric field, atomic transit noise and so on. A detailed noise analysis can pave its way to achieve its ultimate limit sensitivity, which will be our further work.
Fig. 4. Measurement of the signal field using the Stark effect with $f_{sig}=100$ Hz. The data are taken by measuring the power of oscillation signals in the weak field region using a spectrum analyzer with a resolution bandwidth of $10$ Hz and a video bandwidth of $10$ Hz (green circles) and the Stark shift in the strong regime (grey squares). The grey dashed line is a linear fitting of the grey squares. The detectable value of the signal field is down to $E_{det}=214.8$ $\mu$V/cm and the linear response dynamic range is over $37$ dB. Each data point is the average of ten independent measurements, and the error bar represents the standard error. Inset: the probe laser transmission at the time domain for three indicated signal fields $E_{Sig}$ with fixed DC field $E_{DC}$ = 0.3 V/cm.
4. Conclusions
In this paper, we achieve the measurement of super low frequency 100 Hz electric field by utilizing a room-temperature cesium vapor cell with inside parallel electrodes. Rydberg-EIT spectra involving 52$D_{5/2}$ state is employed to measure the signal electric field. An auxiliary DC field is applied to improve the sensitivity of the Rydberg system. The Rydberg-EIT exhibits $m_j$ dependent Stark shifts and splitting in the presence of the DC field, and the $m_j=1/2$ Stark state exhibits a high sensitivity due to its larger polarizability. We achieve a detectable signal field down to $214.8$ $\mu$V/cm with a sensitivity of $67.9$ $\mu$V cm$^{-1}$Hz$^{-1/2}$ and a linear dynamic range over $37$ dB. The sensitivity of our system can be greatly improved by selecting higher Rydberg states with larger polarizability. The work extends the measurement frequency of Rydberg sensors to super low frequency with high sensitivity, which has the advantages of high sensitivity and miniaturization for receiving super low frequency.
Funding
National Natural Science Foundation of China (12120101004, 12241408, 61835007, 62175136); the Scientific Cooperation Exchanges Project of Shanxi Province (202104041101015); Program for Changjiang Scholars and Innovative Research Team in University (IRT 17R70); 1331 project of Shanxi Province; Research Fund of Key Laboratory of Space Utilization, Chinese Academy of Science (LSU-KFJJ-2021-03).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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