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Optics Continuum

Properties and utilization in time-dependent Rydberg EIT

Zhengmao Jia, Qianzhu Li, Yingfan Wang, Yu You, Bing Chen, Yandong Peng

Published Nov 29, 2023• 7 citations
Publisher

Abstract

Transient response of four-level cold Rb atoms with light and microwave (MW) fields is investigated via electromagnetically induced transparency (EIT) theoretically. The local control laser acts as a switch. When the control field is weak, the population transition channel from state 53 D 5/2 to state 5 S 1/2 is closed, which leads to that the transient absorption for the probe field monotonically decreases to its steady state. Nevertheless, when the control field becomes strong, the transition channel is open, which gives rise to that the transient absorption for the probe laser will be oscillatorily damped to the steady-state value, and transient negative absorption appears. A third MW field can induce splitting of the time-dependent EIT transmission spectrum, and the stable splitting distance shows a linear dependence on the continuous MW electric (E) field strength. Furthermore, the simulation results show that the temporal medium transmission signals are sensitive to the E-field strength of local MW pulse, and can be used to sense pulsed MW fields.

DOI
10.1364/optcon.506054

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Rydberg dark states in external fields

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We initially discuss the theory of three-level systems using the dressed state formalism. One of the dressed states, containing a ground state and a Rydberg state, does not couple with the probe laser; thus, the medium becomes transparent to the latter. This phenomenon is known as electro- magnetically induced transparency (EIT) and this dressed state is known as a Rydberg dark state. We show that EIT can be used to extract the reduced dipole matrix element for transitions to a Rydberg state. However, a prob- lem with three-level Rydberg EIT in a vapour cell is the occurrence of space charges caused by photoelectric ionisation of Rb metal deposited inside the cell. To avoid this problem, we consider adding a third laser resonant with a fourth level. This is to avoid using the laser whose wavelength is less than the threshold wavelength. In cold atoms, the effect of the third laser is to split the usual EIT resonance into a doublet. In thermal atoms, we observe narrow features due to electromagnetically induced absorption and electro- magnetically induced transparency in the Doppler-free configuration. Next we consider the action of a far off-resonance radio frequency (rf) field in the three-level system. We demonstrate the formation of rf-dressed EIT reso- nances in a thermal Rb vapour and show that such states exhibit enhanced sensitivity to dc electric fields compared to their bare counterparts. Fitting the corresponding EIT profile enables precise measurements of the dc field in- dependent of laser frequency fluctuations. We further investigate the theory of rf-dressed Rydberg EIT using the Floquet approach in order to understand the formation of the sideband structure of the Rydberg state. We find that if the time scale of the rf interaction is much shorter than that of the system evolution and decoherence, the sideband structure is well resolved. We also show that the intermediate state exhibits a sideband structure, induced by the Rydberg state, when the Rabi frequency of coupling laser is larger than twice the modulation frequency. Finally we consider resonant microwave cou- pling between the Rydberg states which leads to an Autler-Townes splitting of the EIT resonance in cold atoms. This splitting can be employed to vary the group index by ±10^5 allowing independent control of the absorptive and dispersive properties of the medium, i.e., one can switch the transparency of the medium or control the group velocity of a pulse propagation by tuning on and off the microwave field.

•Jan 1, 2011•5 citations
Transient response of four-level cold Rb atoms with light and microwave (MW) fields is investigated via electromagnetically induced transparency (EIT) theoretically. The local control laser acts as a switch. When the control field is weak, the population transition channel from state 53 D 5/2 to state 5 S 1/2 is closed, which leads to that the transient absorption for the probe field monotonically decreases to its steady state. Nevertheless, when the control field becomes strong, the transition channel is open, which gives rise to that the transient absorption for the probe laser will be oscillatorily damped to the steady-state value, and transient negative absorption appears. A third MW field can induce splitting of the time-dependent EIT transmission spectrum, and the stable splitting distance shows a linear dependence on the continuous MW electric (E) field strength. Furthermore, the simulation results show that the temporal medium transmission signals are sensitive to the E-field strength of local MW pulse, and can be used to sense pulsed MW fields.
An analytical model of an electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting spectrum with a four-level Rydberg atom was presented, and equations were derived to explain the dependence of the transient absorption for a probe laser on light and microwave (MW) fields. The analytical solution of absorption for the probe laser Im [ χ ( t )] shows that it depends on the spontaneous decay rate from level |2〉 to level |1〉, Rabi frequencies of the control and MW fields. For 87 Rb atoms, a stronger control laser shortens the steady-state time window and a stronger MW field will lead to a higher oscillation frequency shown in analytical and numerical results. The time-dependent EIT-AT splitting spectrum is also investigated, and the stable splitting distance shows a linear dependence on the continuous MW E-field strength.
Abstract We present the electromagnetically induced transparency (EIT) spectra of cold Rydberg four-level cascade atoms consisting of the 6S1/2 → 6P3/2 → 7S1/2 → 60P3/2 scheme. A coupling laser drives the Rydberg transition, a dressing laser couples two intermediate levels and a weak probe laser probes the EIT signal. We numerically solve the Bloch equations and investigate the dependence of the probe transmission rate signal on the coupling and dressing lasers. We find that the probe transmission rate can display an EIT or electromagnetically induced absorption (EIA) profile, depending on the Rabi frequencies of the coupling and dressing lasers. When we increase the Rabi frequency of the coupling laser and keep the Rabi frequency of the probe and dressing laser fixed, flipping of the EIA to EIT spectrum occurs at the critical coupling Rabi frequency. When we apply a microwave field coupling the transition 60P3/2 → 61S1/2, the EIT spectrum shows Autler–Townes splitting, which is employed to measure the microwave field. The theoretical measurement sensitivity can be 1.52 × 10−2 nV⋅cm−1⋅Hz−1/2 at the EIA–EIT flipping point.
Abstract A scheme for measuring microwave (MW) electric (E) fields is proposed based on bichromatic electromagnetically induced transparency (EIT) in Rydberg atoms. A bichromatic control field drives the excited state transition, whose absorption shows three EIT windows. When a MW field drives the Rydberg transition, the EIT windows split and six transmission peaks appear. It is interesting to find that the peak-to-peak distance of transmission spectrum is sensitive to the MW field strength, which can be used to measure MW E-field. Simulation results show that the measurement accuracy could be increased by about 4 times, and the minimum detectable strength of the MW E-field may be improved by about 3 times compared with the common EIT scheme. After the Doppler averaging, the minimum detectable MW E-field strength is about 5 times larger than that without Doppler effect. Also, we investigate other effects on the sensitivity of the system.
We study theoretically laser excitation of Rydberg triplet states of strontium atoms in the presence of weak microwave (MW) fields. Starting from the ground state 5s21S05{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}5s21S0​, the Rydberg excitation is realized through the metastable, triplet 5s5p3P15s5{p}^{3}{P}_{1}5s5p3P1​ state, whose decay rate ${\ensuremath{\gamma}}_{2}$ is $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}7.5$ kHz, much smaller than the one in the singlet state or alkali-metal atoms. The influences of ${\ensuremath{\gamma}}_{2}$ on the transparency and absorption spectrum in the electromagnetically induced transparency (EIT), and electromagnetically induced absorption (EIA) regime are examined. Narrow transparent windows (EIT) or absorption peaks (EIA) are found, whose distance in the spectrum depends on the Rabi frequency of the weak MW field. It is found that the spectrum exhibits higher contrast than using the singlet state or alkali-metal atoms in typical situations. Using the metastable intermediate state, we find that the resonance fluorescence of Sr gases exhibits very narrow peaks, which are modulated by the MW field. When the MW field is weaker than the probe and control light, the spectrum distance of these peaks is linearly proportional to ${\mathrm{\ensuremath{\Omega}}}_{m}$. This allows us to propose an alternative way to sense very weak MW fields through resonance fluorescence. Our study shows that the Sr triplet state could be used to develop the Rydberg MW electrometry that gains unique advantages.
We present an electromagnetically induced transparency and Aulter-Townes (EIT-AT) spectrum of a Rydberg three-level atom that is dressed with a microwave field in a room-temperature cesium cell. The EIT is a quantum coherent effect produced by the interaction of atoms with electromagnetic waves, which leads to the decrease of the absorption for a weak resonant probe laser. AT splitting refers to the phenomenon, that the absorption line splits when an electromagnetic field that is in resonance or near resonance acts on the transition of atoms. Rydberg atoms are extremely sensitive to an external electric field due to their large polarizabilities and microwave transition dipole moments, which can be used to measure the external field. In this work, a Rydberg three-level EIT is used to detect Rydberg atom and AT splitting induced by the microwave field. Cesium levels 6S1/2, 6P3/2 and 50S1/2 constitute a Rydberg three-level system, in which a weak probe laser locking to the transition from 6S1/2 to 6P3/2 couples ground-state transition and the strong coupling laser resonates on the Rydberg transition from 6P2/3 to 50S1/2. The two Rydberg levels 50S1/2 and 50P1/2 are coupled with the microwave field at a frequency of 30.852 GHz, leading to the AT splitting of EIT line and forming an EIT-AT spectrum, which is used to measure the electric field amplitude of microwave. In order to further study the EIT-AT splitting characteristics of the Rydberg levels, we carry out a series of measurements by changing the microwave field. The experimental results show a broadened EIT-AT signal for the weak field range and the four-peak spectrum for the strong field, which is attributed to the inhomogeneity of the microwave field. The microwave in cesium cell, emitted by a function generator, shows inhomogeneous behavior such that the atoms interacting with the laser field experience the different fields, leading to the line broadened and multi-peak EIT-AT spectra. For the microwave transition of nS1/2-nP1/2 in this paper, a pair of EIT-AT lines should be obtained for an electric field value. The broadening of the EIT-AT spectrum and the multi-peak structure here are due to the inhomogeneity of the microwave field measurement. We propose a method to increase the spatial resolution by reducing the length of cesium cell. The result in this work provides a method of measuring the field amplitude and monitoring the distribution of microwave electric field, meanwhile the spatial resolution of the measurements can be improved by reducing the size of the cell.
We initially discuss the theory of three-level systems using the dressed state formalism. One of the dressed states, containing a ground state and a Rydberg state, does not couple with the probe laser; thus, the medium becomes transparent to the latter. This phenomenon is known as electro- magnetically induced transparency (EIT) and this dressed state is known as a Rydberg dark state. We show that EIT can be used to extract the reduced dipole matrix element for transitions to a Rydberg state. However, a prob- lem with three-level Rydberg EIT in a vapour cell is the occurrence of space charges caused by photoelectric ionisation of Rb metal deposited inside the cell. To avoid this problem, we consider adding a third laser resonant with a fourth level. This is to avoid using the laser whose wavelength is less than the threshold wavelength. In cold atoms, the effect of the third laser is to split the usual EIT resonance into a doublet. In thermal atoms, we observe narrow features due to electromagnetically induced absorption and electro- magnetically induced transparency in the Doppler-free configuration. Next we consider the action of a far off-resonance radio frequency (rf) field in the three-level system. We demonstrate the formation of rf-dressed EIT reso- nances in a thermal Rb vapour and show that such states exhibit enhanced sensitivity to dc electric fields compared to their bare counterparts. Fitting the corresponding EIT profile enables precise measurements of the dc field in- dependent of laser frequency fluctuations. We further investigate the theory of rf-dressed Rydberg EIT using the Floquet approach in order to understand the formation of the sideband structure of the Rydberg state. We find that if the time scale of the rf interaction is much shorter than that of the system evolution and decoherence, the sideband structure is well resolved. We also show that the intermediate state exhibits a sideband structure, induced by the Rydberg state, when the Rabi frequency of coupling laser is larger than twice the modulation frequency. Finally we consider resonant microwave cou- pling between the Rydberg states which leads to an Autler-Townes splitting of the EIT resonance in cold atoms. This splitting can be employed to vary the group index by ±10^5 allowing independent control of the absorptive and dispersive properties of the medium, i.e., one can switch the transparency of the medium or control the group velocity of a pulse propagation by tuning on and off the microwave field.