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Frequency modulation of Rydberg states by radio frequency electromagnetic fields

Nabendu S. Mishra

Published Sep 14, 2023• 1 citation
Publisher

Abstract

In this work, we demonstrate the generation of sidebands in electromagnetically induced transparency (EIT) signal due to frequency modulation of Rydberg states in $^{87}\text{Rb}$ thermal vapor. An oscillating radio-frequency (RF) electric field generated through a pair of parallel-placed copper plates leads to modulation of the Rydberg state by virtue of Stark effect where the frequency and strength of the sidebands quantify the RF electric field present. The variation of the strength of the EIT peak and the sidebands with RF voltage is observed to vary as a function of the Bessel function of modulation index. It provides an estimate of the atomic polarizability in the medium, which for $54S_{1/2}$ state, is found to be $(h)\cdot1.01\times10^8$ $\text{Hz/(V/cm)}^2$.

DOI
10.1364/opticaopen.24135294

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Frequency modulation of Rydberg states by radio frequency electromagnetic fields

Nabendu S. Mishra

In this work, we demonstrate the generation of sidebands in electromagnetically induced transparency (EIT) signal due to frequency modulation of Rydberg states in $^{87}\text{Rb}$ thermal vapor. An oscillating radio-frequency (RF) electric field generated through a pair of parallel-placed copper plates leads to modulation of the Rydberg state by virtue of Stark effect where the frequency and strength of the sidebands quantify the RF electric field present. The variation of the strength of the EIT peak and the sidebands with RF voltage is observed to vary as a function of the Bessel function of modulation index. It provides an estimate of the atomic polarizability in the medium, which for $54S_{1/2}$ state, is found to be $(h)\cdot1.01\times10^8$ $\text{Hz/(V/cm)}^2$.

arXiv:2309.07007•Sep 13, 2023•0 citations

Frequency modulation of Rydberg states by radio frequency electromagnetic fields

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In this work, we demonstrate the generation of sidebands in electromagnetically induced transparency (EIT) signal due to frequency modulation of Rydberg states in $^{87}\text{Rb}$ thermal vapor. An oscillating radio-frequency (RF) electric field generated through a pair of parallel-placed copper plates leads to modulation of the Rydberg state by virtue of Stark effect where the frequency and strength of the sidebands quantify the RF electric field present. The variation of the strength of the EIT peak and the sidebands with RF voltage is observed to vary as a function of the Bessel function of modulation index. It provides an estimate of the atomic polarizability in the medium, which for $54S_{1/2}$ state, is found to be $(h)\cdot1.01\times10^8$ $\text{Hz/(V/cm)}^2$.

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The large electric dipole moment of the Rydberg atom allows for strong coupling with weak electric fields, and is widely used in electric field measurements because of its reproducibility, precision and stability. The combination of Rydberg atoms and electromagnetically induced transparency (EIT) technology has been used for detecting and characterizing radio-frequency (RF) electric fields. In this work, by selecting probe light (852 nm), dressed light (1470 nm), and coupled light (780 nm), the Rydberg state (49P3/2) of Cs atom is prepared by using a three-photon excitation scheme through using all-infrared light excitation of Rydberg atoms. We experimentally observe the EIT spectra of the Rydberg states decorated by radio-frequency electric fields, which optically detects Rydberg atoms. The effect of the amplitude and frequency of the RF electric field on the spectrum is explored in light of changes in the EIT spectrum. The results show that in the region of weak electric field, only the ac Stark energy shift and spectral broadening occur. As the electric field is further enhanced, the sideband phenomenon occurs in both the primary peak and secondary peak of the EIT. In the region of strong field, the Rydberg energy level produces a series of Floquet states with higher-order terms, as well as state shifting and mixing, resulting in asymmetry in the spectra of the EIT sideband peaks. The effect of frequency on the shielding effect of the Cs vapor cell is further discussed based on the shift of the main peak of the EIT. The demodulation of the electric field in a range of 50 Hz–1 kHz with a fidelity of 95% is achieved by modulating the low-frequency electric field to the RF electric field. The results can provide valuable references for spectral detection and traceable measurements of low-frequency electric fields.

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Rydberg atoms are highly excited atoms with large principal quantum number n, big sizes (~n2) and long lifetimes (~n3). Rydberg atoms are very sensitive to an external field due to the large polarizabilities of Rydberg atoms (~n7). Electromagnetically induced transparency (EIT) of Rydberg atom provides an ideal method to detect Rydberg atoms without destroying atoms, and can be used to measure the external direct current and radio frequency (RF) field. In this paper, we study the EIT effect of a cesium ladder-type three-level atom involving Rydberg state exposed to a weak RF field. The ground state (6S1/2), the excited state (6P3/2) and Rydberg state (48D5/2) constitute the Rydberg three-level system, in which the probe laser couples 6S1/2(F=4)6P3/2(F'=5) transition, whereas the coupling laser scans across the 6P3/248D5/2 Rydberg transition. The coupling laser (510 nm laser, propagating in the z-axis direction and linear polarization in the y-axis direction) and the probe laser (852 nm laser, linear polarization in the y-axis direction) counter-propagate through a 50-mm-long cesium vapor cell at room temperature, yielding Rydberg EIT spectra. Rydberg EIT signal is detected as a function of the detuning of the coupling laser. When a weak RF (80 MHz) electric field polarized in the x-axis direction is applied to a pair of electrode plates located on both sides of the cesium cell, the EIT spectrum of Rydberg 48D5/2 shows the Stark splitting and the even order harmonic sidebands. The experimental results are analyzed by using the Floquet theory. The simulation results accord well with the experimentally measured results. Furthermore, we also investigate the influence of the self-ionization effect of Rydberg atom on the Stark spectrum by changing the RF frequency. We put forward a proposal to avoid the effect of ionization by placing electrode plates in the cesium cell. In the weak RF-field domain, mj=5/2 Stark line crosses mj=1/2, 3/2 sidebands, these cross points provide an antenna-free method of accurately calibrating the RF electric field based on Rydberg atoms.

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Atom-based power-frequency electric field measurement using the radio-frequency-modulated Rydberg spectroscopy

Weixin Liu, Linjie Zhang, Tao Wang

The radio-frequency modulated electromagnetically induced transparency (EIT) in a ladder three-level system with Rydberg state is studied. Under the influence of a fast radio-frequency field, the EIT peak splits into a series of sidebands. When attaching a power-frequency electric field directly to the fast radio-frequency field, the odd-order sidebands of the Rydberg-EIT oscillate sensitively with the power-frequency field. The oscillation frequency is equal to twice the power frequency; the oscillation amplitude is monotonically increasing with the amplitude of the power-frequency field when the change of Stark-shift is smaller than the radio frequency. Our work paves the way for measurement of power-frequency electric field based on Rydberg atoms.

Chinese Physics B•Nov 29, 2022•16 citations
In this work, we demonstrate the generation of sidebands in electromagnetically induced transparency (EIT) signal due to frequency modulation of Rydberg states in 87Rb^{87}\text{Rb}87Rb thermal vapor. An oscillating radio-frequency (RF) electric field generated through a pair of parallel-placed copper plates leads to modulation of the Rydberg state by virtue of Stark effect where the frequency and strength of the sidebands quantify the RF electric field present. The variation of the strength of the EIT peak and the sidebands with RF voltage is observed to vary as a function of the Bessel function of modulation index. It provides an estimate of the atomic polarizability in the medium, which for 54S1/254S_{1/2}54S1/2​ state, is found to be (h)⋅1.01×108(h)\cdot1.01\times10^8(h)⋅1.01×108 Hz/(V/cm)2\text{Hz/(V/cm)}^2Hz/(V/cm)2.
In this work, we demonstrate the generation of sidebands in electromagnetically induced transparency (EIT) signal due to frequency modulation of Rydberg states in 87Rb^{87}\text{Rb}87Rb thermal vapor. An oscillating radio-frequency (RF) electric field generated through a pair of parallel-placed copper plates leads to modulation of the Rydberg state by virtue of Stark effect where the frequency and strength of the sidebands quantify the RF electric field present. The variation of the strength of the EIT peak and the sidebands with RF voltage is observed to vary as a function of the Bessel function of modulation index. It provides an estimate of the atomic polarizability in the medium, which for 54S1/254S_{1/2}54S1/2​ state, is found to be (h)⋅1.01×108(h)\cdot1.01\times10^8(h)⋅1.01×108 Hz/(V/cm)2\text{Hz/(V/cm)}^2Hz/(V/cm)2.
In this work, we demonstrate the generation of sidebands in electromagnetically induced transparency (EIT) signal due to frequency modulation of Rydberg states in 87Rb^{87}\text{Rb}87Rb thermal vapor. An oscillating radio-frequency (RF) electric field generated through a pair of parallel-placed copper plates leads to modulation of the Rydberg state by virtue of Stark effect where the frequency and strength of the sidebands quantify the RF electric field present. The variation of the strength of the EIT peak and the sidebands with RF voltage is observed to vary as a function of the Bessel function of modulation index. It provides an estimate of the atomic polarizability in the medium, which for 54S1/254S_{1/2}54S1/2​ state, is found to be (h)⋅1.01×108(h)\cdot1.01\times10^8(h)⋅1.01×108 Hz/(V/cm)2\text{Hz/(V/cm)}^2Hz/(V/cm)2.
This study demonstrates the frequency modulation of Rydberg states in 87Rb thermal vapor leading to the production of sidebands in electromagnetically induced transparency (EIT) signal. The modulation is provided externally through radio-frequency (RF) electric fields from a parallel-plate capacitor. The modified EIT signal is detected via the conventional lock-in amplified EIT setup. We assess the strengths of the peaks in the modulated EIT spectrum and compare them to a mathematical model based on Floquet theory. The relationship between the strength of the EIT peaks and the RF voltage is identified as a function of the Bessel function of the modulation index.
The large electric dipole moment of the Rydberg atom allows for strong coupling with weak electric fields, and is widely used in electric field measurements because of its reproducibility, precision and stability. The combination of Rydberg atoms and electromagnetically induced transparency (EIT) technology has been used for detecting and characterizing radio-frequency (RF) electric fields. In this work, by selecting probe light (852 nm), dressed light (1470 nm), and coupled light (780 nm), the Rydberg state (49P3/2) of Cs atom is prepared by using a three-photon excitation scheme through using all-infrared light excitation of Rydberg atoms. We experimentally observe the EIT spectra of the Rydberg states decorated by radio-frequency electric fields, which optically detects Rydberg atoms. The effect of the amplitude and frequency of the RF electric field on the spectrum is explored in light of changes in the EIT spectrum. The results show that in the region of weak electric field, only the ac Stark energy shift and spectral broadening occur. As the electric field is further enhanced, the sideband phenomenon occurs in both the primary peak and secondary peak of the EIT. In the region of strong field, the Rydberg energy level produces a series of Floquet states with higher-order terms, as well as state shifting and mixing, resulting in asymmetry in the spectra of the EIT sideband peaks. The effect of frequency on the shielding effect of the Cs vapor cell is further discussed based on the shift of the main peak of the EIT. The demodulation of the electric field in a range of 50 Hz–1 kHz with a fidelity of 95% is achieved by modulating the low-frequency electric field to the RF electric field. The results can provide valuable references for spectral detection and traceable measurements of low-frequency electric fields.
Rydberg atoms are highly excited atoms with large principal quantum number n, big sizes (~n2) and long lifetimes (~n3). Rydberg atoms are very sensitive to an external field due to the large polarizabilities of Rydberg atoms (~n7). Electromagnetically induced transparency (EIT) of Rydberg atom provides an ideal method to detect Rydberg atoms without destroying atoms, and can be used to measure the external direct current and radio frequency (RF) field. In this paper, we study the EIT effect of a cesium ladder-type three-level atom involving Rydberg state exposed to a weak RF field. The ground state (6S1/2), the excited state (6P3/2) and Rydberg state (48D5/2) constitute the Rydberg three-level system, in which the probe laser couples 6S1/2(F=4)6P3/2(F'=5) transition, whereas the coupling laser scans across the 6P3/248D5/2 Rydberg transition. The coupling laser (510 nm laser, propagating in the z-axis direction and linear polarization in the y-axis direction) and the probe laser (852 nm laser, linear polarization in the y-axis direction) counter-propagate through a 50-mm-long cesium vapor cell at room temperature, yielding Rydberg EIT spectra. Rydberg EIT signal is detected as a function of the detuning of the coupling laser. When a weak RF (80 MHz) electric field polarized in the x-axis direction is applied to a pair of electrode plates located on both sides of the cesium cell, the EIT spectrum of Rydberg 48D5/2 shows the Stark splitting and the even order harmonic sidebands. The experimental results are analyzed by using the Floquet theory. The simulation results accord well with the experimentally measured results. Furthermore, we also investigate the influence of the self-ionization effect of Rydberg atom on the Stark spectrum by changing the RF frequency. We put forward a proposal to avoid the effect of ionization by placing electrode plates in the cesium cell. In the weak RF-field domain, mj=5/2 Stark line crosses mj=1/2, 3/2 sidebands, these cross points provide an antenna-free method of accurately calibrating the RF electric field based on Rydberg atoms.
The radio-frequency modulated electromagnetically induced transparency (EIT) in a ladder three-level system with Rydberg state is studied. Under the influence of a fast radio-frequency field, the EIT peak splits into a series of sidebands. When attaching a power-frequency electric field directly to the fast radio-frequency field, the odd-order sidebands of the Rydberg-EIT oscillate sensitively with the power-frequency field. The oscillation frequency is equal to twice the power frequency; the oscillation amplitude is monotonically increasing with the amplitude of the power-frequency field when the change of Stark-shift is smaller than the radio frequency. Our work paves the way for measurement of power-frequency electric field based on Rydberg atoms.