The transfer mechanism from the amplitude noise of the coupling light to the phase noise of the probe light in a Rydberg electromagnetic induced transparency effect derived from a ladder-type system including 6S1/2↔6P3/2↔62D5/2 of Cs atoms is demonstrated by using Mach-Zehnder interferometer and balanced homodyne detection technology. In our experiments, the transmission signal of 852 nm probe light is measured by scanning the coupling light frequency nearby the transition from 6P3/2 to 62D5/2 Rydberg state, while the frequency of the probe light is locked at the resonance transition of the 6S1/2↔6P3/2. The relative phase stability of two arms of Mach-Zehnder interferometer, which is constructed with the first order diffraction light of probe light through an acoustic-optic modulator, is accomplished by the controlled piezoelectric ceramic with the PID feedback loop. The interferences between the probe light and the reference light of Mach-Zehnder interferometer under the different relative phases are observed. The interference spectrum of probe light is in good agreement with the theoretical simulation result of the ladder-type three-level system. Therefore, we study the transfer characteristics from the frequency noise of coupling light to the phase noise of probe light when coupling light frequency resonance happens at the transition 6P3/2↔62D5/2. We find the significant suppression of the phase noise of probe light at the higher frequency noise. Moreover, we observe the characteristics of the phase noise of the probe light varying with the power of the coupling light under the different detuning degrees of coupling light. In the red detuning side, the transferred phase noise of probe light decreases with the increase of coupling light power, which is different significantly from the scenario under the blue detuning condition. The ions produced in the ionization process of Rydberg atoms will form the local electric field that would cause the energy level of Rydberg states to shift. The investigation of the noise transfer between the coupling light and probe light in the Rydberg electromagnetically induced transparency effect is important for understanding the coherence mechanism of ladder-type system and the some potential applications, such as in Rydberg-atom-based electric field metrology.
The transfer mechanism from the amplitude noise of the coupling light to the phase noise of the probe light in a Rydberg electromagnetic induced transparency effect derived from a ladder-type system including 6S1/2↔6P3/2↔62D5/2 of Cs atoms is demonstrated by using Mach-Zehnder interferometer and balanced homodyne detection technology. In our experiments, the transmission signal of 852 nm probe light is measured by scanning the coupling light frequency nearby the transition from 6P3/2 to 62D5/2 Rydberg state, while the frequency of the probe light is locked at the resonance transition of the 6S1/2↔6P3/2. The relative phase stability of two arms of Mach-Zehnder interferometer, which is constructed with the first order diffraction light of probe light through an acoustic-optic modulator, is accomplished by the controlled piezoelectric ceramic with the PID feedback loop. The interferences between the probe light and the reference light of Mach-Zehnder interferometer under the different relative phases are observed. The interference spectrum of probe light is in good agreement with the theoretical simulation result of the ladder-type three-level system. Therefore, we study the transfer characteristics from the frequency noise of coupling light to the phase noise of probe light when coupling light frequency resonance happens at the transition 6P3/2↔62D5/2. We find the significant suppression of the phase noise of probe light at the higher frequency noise. Moreover, we observe the characteristics of the phase noise of the probe light varying with the power of the coupling light under the different detuning degrees of coupling light. In the red detuning side, the transferred phase noise of probe light decreases with the increase of coupling light power, which is different significantly from the scenario under the blue detuning condition. The ions produced in the ionization process of Rydberg atoms will form the local electric field that would cause the energy level of Rydberg states to shift. The investigation of the noise transfer between the coupling light and probe light in the Rydberg electromagnetically induced transparency effect is important for understanding the coherence mechanism of ladder-type system and the some potential applications, such as in Rydberg-atom-based electric field metrology.
Rydberg atoms, with large principal quantum number n, have been widely investigated in recent years due to their peculiar properties, such as big sizes, long lifetimes and strong interactions with fields and other Rydberg atoms. Rydberg atoms are very sensitive to external fields due to their large polarizabilities scaling as n7.These make Rydberg atoms an ideal candidate for the quantum information, the many-body interaction, etc.In this work, we investigate the Rydberg atoms using electromagneticlly induced transparency (EIT) in a ladder three-level system. The EIT is a quantum interference effect between two excitation path-ways driven by two laser fields. The main idea is performed in a room temperature cesium vapor cell, where the probe laser frequency is modulated. The ground state (6P1/2), excited state (6P3/2), and Rydberg state (nS1/2) constitute a Rydberg three-level system, in which the probe laser is fixed to the 6S1/2 (F = 4)6P3/2 (F = 5) transition by saturated absorption spectrum technique, whereas the coupling laser is scanned across the 6P3/249S1/2 transition. We detect the demodulated EIT signal with the lock-in amplifier (SR830). The modulated EIT signal shows a two-peak structure. The measured spacing between two peaks increases with the frequency detuning, caused by the modulation amplitude, and half the spacing between the peak-to-peak is nearly 1.67 times the modulation amplitude of the probe laser; the measured result shows that the splitting is independent of the modulation frequency. The experimental results are in agreement with the theoretical calculations. The results in our work can be used for real-time monitoring of the laser-line profiles and the fluctuation of laser frequency.
The double resonance phenomenon of EIT is studied through the ladder three-level Rydberg system. A probe laser with the wavelength λp=852.35 nm is used to coupling the ground state 6S1/2 to the middle state 6P3/2, and a coupling laser with the wavelength λc=509.08 nm is implemented to couple the state 6P3/2 to the Rydberg state 62D5/2. A special optical scheme is designed, in which the co-propagating and counter-propagating configurations are both used. As a result, the double resonance of electromagnetically induced transparency (EIT) with the Rydberg atom is observed. By comparing the distance between the double peaks, it is found that the double resonance phenomenon comes from the Doppler effect, and the distance between the two resonance peaks in the absorption spectrum is related to the detuning of the resonant lasers.
The conversion of the modulation signal from the coupling light to the probe light and the conversion of the additional phase noise from the coupling light to the amplitude noise of the probe light in the electromagnetically induced transparency (EIT) spectrum of the cesium atomic ladder type three level system were investigated by detecting the probe light output noise spectrum. It was demonstrated that frequency stabilization via external modulation can effectively avoid the transfer of modulation noise. In the experiment, two frequency stabilization methods external modulation transfer spectroscopy and internal modulation transfer spectroscopy were employed to achieve the frequency stabilization of the coupling light. The probe light noise spectra at the frequency stabilized output terminal and the detection output terminal were measured under both methods.
We established a theoretical model for the ladder-type EIT laser frequency stabilization method based on the analysis of the system response. By using the method of deriving the density matrix equations, we obtained the density matrix elements of the three-level system and subsequently derived the system’s response function. Based on this, we revealed the complex interference mechanism of the modulated probe light in the atomic medium. Through quantitative analysis of this process, we obtained the output signal, which carries information about the frequency offset of the coupling light, after the probe light passes through the atomic medium. The error signal obtained after demodulation can then serve as the reference signal for the closed-loop feedback system. To make the error signal more intuitively reflect its variation with the coupling light frequency offset, we introduced the equivalent transfer of the modulation frequency based on the locking relationship between the probe light detuning and the coupling light detuning. This paper provides a deep analysis of the impact of the probe light modulation frequency on the error signal and experimentally validates our theoretical analysis results. Finally, we select a modulation frequency of 10 MHz to lock the coupling light and compare the Allan variance before and after locking. The minimum value of σ ( τ ) was reduced from 4.62×10 −10 before locking to 1.70×10 −10 after locking.
Rydberg atoms, with large principal quantum number, exhibit certain properties, such as long lifetimes and strong interactions with fields and other atoms, which have been extensively investigated recently. One of the properties is the electromagnetically induced transparency (EIT) of Rydberg ladder system, which can be used to measure the radio frequency (RF) field with high sensitivity. In this paper, we investigate the quantum coherent effect of cesium Rydberg atom in a three-level ladder system involving the ground state (6S1/2), the excited state (6P3/2) and 49S1/2 Rydberg state in room temperature vapor cell. The probe laser (852 nm) drives the transition of 6S1/2(F=4)→6P3/2(F'=5), while the coupling laser (510 nm) couples the Rydberg transition of 6P3/2 (F'=5)→nS1/2. A typical electromagnetically induced transparency spectrum is obtained when the weak probe laser is scanned through the transition of 6S1/2(F=4)→6P3/2(F'=5) and the coupling laser tuning to Rydberg transition. The two-photon RF spectra are observed when the RF field with a frequency of ～16.9 GHz couples the Rydberg transition of 49S1/2→47D3/2, where the EIT signal is split into two EIT peaks due to the interaction between the RF field and Rydberg atoms. The dependences of EIT splitting on the power of RF field are investigated. The results show that the EIT splitting increases with the power of RF field, which can inversely be used to measure the RF field with a higher spatial resolution in the future.
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.