Electromagnetically Induced Transparency Signal Research Articles

Utilizing quantum coherence in Cs Rydberg atoms for high-sensitivity room-temperature terahertz detection: a theoretical exploration

In recent years, terahertz (THz) technology has made significant progress in numerous applications; however, the highly sensitive, room-temperature THz detectors are still rare, which is one of the bottlenecks in THz research. In this paper, we proposed a room-temperature electrometry method for THz detection by laser spectroscopy of cesium (Cs133) Rydberg atoms, and conducted a comprehensive investigation of the five-level system involving electromagnetically induced transparency (EIT), electromagnetically induced absorption (EIA), and Autler–Townes (AT) splitting in Cs133 cascades. By solving the Lindblad master equation, we found that the influence of the THz electric field, probe laser, dressing laser, and Rydberg laser on the ground state atomic population as well as the coherence between the ground state and the Rydberg state, plays a crucial role in the transformation and amplitude of the EIT and EIA signals. Temperature and the atomic vapor cell’s dimensions affect the number of Cs133 atoms involved in the detection, and ultimately determine the sensitivity. We predicted the proposed quantum coherence THz detection method has a remarkable sensitivity of as low as 10−9 V m−1 Hz−1/2. This research offers a valuable theoretical basis for implementing and optimizing quantum coherence effects based on Rydberg atoms for THz wave detection with high sensitivity and room-temperature operation.

Enhanced microwave-atom coupling via quadrupole transition-dressed Rydberg atoms

The power broadening of a coupling laser can be converted into two-photon detuning by electromagnetically induced transparency (EIT), resulting in a residual Doppler effect. The residual Doppler effect in a ladder-type EIT in a room-temperature atom ensemble is further amplified through a wavelength mismatch effect between the probe and coupling laser beams, which reduces the atomic coupling of light or microwaves. We measured the Rydberg spectra of the electric dipole (E1) and electric quadrupole (E2) microwave transitions, demonstrating that the reduction in the Rydberg EIT signal can be recovered through far-off-resonance E2 microwave transition dressing and achieving an 8-dB enhancement in the Rydberg EIT signal. The frequency-dependent dressing of the E2 transition enables the shift of the dressed Rydberg states to be tuned, thereby providing a scalable approach to optimize the interaction between the Rydberg state and microwave field.

Effect of laser detuning and Rabi frequency on rubidium Rydberg electromagnetically-induced transparency for atom-based electric field sensing

Atom-based electromagnetic field sensing is a highly precise and sensitive technique for measuring and detecting electromagnetic fields, based on the principles of the Rydberg electromagnetically induced transparency (EIT). In this study, we simulate an atom-based electric field measurement system using a four-level system of rubidium atoms. We solve the steady-state solution of the Lindblad master equation using a Hamiltonian that contains information about rubidium properties and the external electric field. We observe that the splitting of the EIT signal is directly proportional to the intensity of the applied electric field, making it a highly sensitive method for electromagnetic field sensing. In addition, we investigate the effect of laser detuning and Rabi frequency on the linewidth and signal strength of the EIT signal in order to obtain optimal parameters for future experiments. This study provides insights into optimizing the EIT signal for electromagnetic fields detection, with potential benefits for future developments in this field.

Dependence of Rydberg-atom-based sensor performance on different Rydberg atom populations in one atomic-vapor cell

The atomic-vapor cell is a vital component for Rydberg atomic microwave sensors, and impacts on overall capability of Rydberg sensors. However, the conventional analysis approach on effect of vapor-cell length contains two implicit assumptions, that is, the same atomic population density and buffer gas pressure, which make it unable to accurately capture actual response about effect of Rydberg-atom-based sensor performance on different Rydberg atom populations. Here, utilizing a stepped cesium atomic-vapor cell with five different dimensions at the same atomic population density and buffer gas pressure, the height and full width at half maximum of electromagnetically induced transparency (EIT) signal, and the sensitivity of the atomic superheterodyne sensor are comprehensively investigated under conditions of the same Rabi frequencies (saturated laser power). It is identified that EIT signal height is proportional to the cell length, full width at half maximum and sensitivity grow with the increment of cell length to a certain extent. Employing the coherent integration signal theory and atomic linear expansion coefficient method, theoretical analysis of the EIT height and sensitivity are further investigated. The results could shed new light on understanding and design of ultrahigh-sensitivity Rydberg atomic microwave sensors and find promising applications in quantum measurement, communication, and imaging.

A comparative study of electromagnetically induced transparency (EIT) in Λ-, V-, and Ξ-type systems using Laguerre–Gaussian (LG) laser beams

In this paper, a theoretical investigation of electromagnetically induced transparency (EIT) using Laguerre–Gaussian (LG) beams has been carried out for the three canonical atom-laser coupled systems (e.g. [Formula: see text]-, V-, and [Formula: see text]-type) in [Formula: see text]Rb atom. The required optical Bloch equations (OBEs) are derived for each system. The OBEs are analytically solved in steady-state condition under the weak probe field approximation. We have used the iterative perturbative technique to obtain the probe coherence term. The probe response w.r.t. probe detuning for different orders of the orbital angular momentum (OAM) number of both the pump and probe LG beams has been studied. We have also studied the effect of the OAM number on probe response in both Doppler-free and Doppler-broadened mediums. It has been observed that the EIT signal is squeezed for nonzero OAM number of the pump beam with arbitrary OAM number of the probe beam. It is found that for higher-order OAM number, the EIT signal is further squeezed. The modification of the EIT signal is attributed because of the spatial-dependent Rabi frequency. Our study demonstrates that the dynamic of the probe field inside an atomic medium may be controlled by tuning the OAM number of the LG beam.

Noise suppression by differential detection of simultaneous electromagnetically induced transparency and absorption in counterpropagating bichromatic light

Well-established electromagnetically induced transparency (EIT) and absorption (EIA) have been applied to various applications including quantum computing, light storage, and precision measurement. Here, we propose and implement a differential detection scheme based on coexisting EIT and EIA signals in a double-Λ system with counterpropagating bichromatic laser fields, in which a differential coherent population trapping (diff-CPT) signal is extracted with a desired enhanced amplitude and highly suppressed common-mode noise. Compared to that of either EIT or EIA, the observed signal-to-noise ratio of the proposed method’s diff-CPT signal improved by one order of magnitude, which would benefit the implementation of high-performance CPT clocks. This technique may also be applied to magnetometers and precision spectroscopy.

Dephasing of ultracold cesium 80D5/2-Rydberg electromagnetically induced transparency.

We study Rydberg electromagnetically induced transparency (EIT) of a cascade three-level atom involving 80D5/2 state in a strong interaction regime employing a cesium ultracold cloud. In our experiment, a strong coupling laser couples 6P3/2 to 80D5/2 transition, while a weak probe, driving 6S1/2 to 6P3/2 transition, probes the coupling induced EIT signal. At the two-photon resonance, we observe that the EIT transmission decreases slowly with time, which is a signature of interaction induced metastability. The dephasing rate γOD is extracted with optical depth OD = γODt. We find that the optical depth linearly increases with time at onset for a fixed probe incident photon number Rin before saturation. The dephasing rate shows a nonlinear dependence on Rin. The dephasing mechanism is mainly attributed to the strong dipole-dipole interactions, which leads to state transfer from nD5/2 to other Rydberg states. We demonstrate that the typical transfer time τ0(80D) obtained by the state selective field ionization technique is comparable with the decay time of EIT transmission τ0(EIT). The presented experiment provides a useful tool for investigating the strong nonlinear optical effects and metastable state in Rydberg many-body systems.

Deceleration of optical pulses based on electromagnetically induced transparency of Rydberg atoms

Based on the Electromagnetically-Induced-Transparency (EIT) effect of cesium Rydberg atoms, the dispersion of the probe light will experience a drastically change while the absorption is diminished, as the frequency of it is resonated with that of the corresponding atomic transition. In this case, as the light pulse propagates in the atomic medium, the group velocity of the pulse will be slowed. In the cesium atoms 3-ladder-level system (<inline-formula><tex-math id="M2">\begin{document}$ 6{\rm S}_{1/2}\rightarrow6{\rm P}_{3/2}\rightarrow49{\rm D}_{5/2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M2.png"/></alternatives></inline-formula>),the frequency of the probe light is locked at the resonance transition of <inline-formula><tex-math id="M3">\begin{document}$ 6{\rm S}_{1/2}\rightarrow6{\rm P}_{3/2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M3.png"/></alternatives></inline-formula>, while the transmission signal of 852 nm probe light is measured by scanning the coupling light frequency near the transition of <inline-formula><tex-math id="M4">\begin{document}$ 6{\rm P}_{3/2}\rightarrow49{\rm D}_{5/2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20210102_M4.png"/></alternatives></inline-formula>, We observed the EIT phenomenon and explored the relationship between the power of coupling laser and linewidth of the EIT signal. The experimental results show that the linewidth of the EIT signal is proportional to the power of the coupling laser. Then under the two-photon resonance condition, the deceleration of the probe light pulse caused by the steep change of the dispersion curve is observed. We also systematically investigate the influences of coupling optical power and temperature of vapor cell on the slowing down of light pulse. The experimental results show that the weaker the coupled light was, the longer the delay time; and the higher the temperature of the atomic gas chamber was, the more obvious the deceleration effect would be observed, those of which are consistent with the theoretical calculations. The investigation of the deceleration of optical pulses based on the Rydberg Electromagnetically-Induced-Transparency is important for understanding the coherence mechanism of 3-ladder-level system and some potential applications, such as in Rydberg-atom-based electric field metrology. This research provides a new tool for the measurement of pulsed microwave electric field through the optical pulse deceleration effect.

Study of multi-window electromagnetically induced transparency (EIT) and related dispersive signals in V-type systems in the Zeeman sublevels of hyperfine states of 87Rb-D2 line

We have theoretically studied the multi-window electromagnetically induced transparency (EIT) and the related dispersive signals in multi-level V-type systems which are formed by the co-propagating circularly polarized pump (σ −) and probe (σ +) laser fields in the Zeeman sublevels of hyperfine states of 87Rb-D2 line. The optical Bloch equations (OBEs) are derived and numerically solved under the steady-state condition to obtain the probe absorption and dispersion spectra. We present the study of a single-window EIT for the three-level, double-window EIT for the four-level and triple-window EIT for the five-level V-type systems under both Doppler-free and Doppler-broadened conditions. The dispersive signals corresponding to the multi EIT windows for each system are also observed separately. From the knowledge of the slopes of the probe dispersion signals, we have calculated group index (n g) of the medium considering three different V-type schemes. The effect of temperature on the EIT, dispersion and group index profiles is also studied in detail. It is found that the amplitudes of EIT and dispersion signals and also the positive and negative values of n g are decreased as the temperature of the medium increases. To understand the Doppler-broadening effect on the group index profiles, we have considered three different velocity groups of atoms in the calculation of group index profiles. Moreover, the effects of probe intensity variation on the Doppler-broadened EIT and dispersive signals are studied extensively, and the conversions of EIT to EIA and dispersive positive slope to negative slope are observed under strong probe regime. Also, we have investigated the variation of dispersive slope and group index with the variation of probe intensity and probe frequency, respectively, at the multi-frequency position of the multi-window EIT. Finally, the switching between subluminal (slow light) to superluminal (fast light) propagation of light with the variation of both probe intensity and probe frequency is discussed in detail.

Frequency stabilization method for transition to a Rydberg state using Zeeman modulation.

We herein develop and demonstrate a stable frequency-locking scheme for Rydberg atomic experiments. We use the Zeeman effect to modulate the three-level ladder-type Rydberg electromagnetically induced transparency (EIT) signal to lock the laser frequency of the coupling light for transition from its intermediate state to a Rydberg state. The effects of polarization of the probe and coupling lights, and the amplitude of the AC modulated magnetic field ${{\boldsymbol B}_0}$B0 on the EIT and the corresponding dispersive error signal, are both analyzed. The results show that both the EIT signal and dispersive error signal are the strongest when the polarizations of coupling and probe fields are circular and equal. The signal-to-noise ratio of the dispersive error signal increases with ${{\boldsymbol B}_0}$B0. The slope of the dispersive error signal increases first and then decreases with ${{\boldsymbol B}_0}$B0, which is related to the increase of the EIT linewidth caused by the higher ${{\boldsymbol B}_0}$B0. The linewidth of the laser is significantly less than 500 kHz after frequency locking, which satisfies the requirements of most experiments involving Rydberg atoms. The method proposed herein can generally be applied to any cascade system of Rydberg atoms.

Observation of ladder-type electromagnetically induced transparency with atomic optical lattices near a nanofiber

Tapered nanofiber is an efficient tool for enhancing light–matter interactions. Here, we experimentally demonstrate the ladder-type electromagnetically induced transparency (EIT) in one-dimensional atomic lattices near an optical nanofiber (ONF). A typical EIT signal is well fitted from experimental data according to a semiclassical model and implies a transmission nearly 35%. We investigate the dependence of EIT transmission on the coupling power and its saturation condition. In addition, we show a large fraction of the transmission spectral broadening is induced by lattice effects. Our results may pave the road towards generating correlations and entanglement through four-wave mixing with ONFs, which may facilitate the realization of efficient quantum optical networks.

Observation and theoretical simulation of dispersive properties of an electromagnetically induced transparent 87Rb atomic medium

The dispersive properties of 87Rb atomic medium in electromagnetically induced transparency (EIT) have been studied experimentally as well as theoretically. To measure the dispersion signal, a balanced homodyne detection technique was used by forming a Mach–Zehnder interferometer. We studied the system in a Λ-type configuration. From the slope of the dispersive EIT signal, the group index (ng) of the atomic medium, the group velocity () and the time delay () of the light wave through the atomic medium were calculated. We measured the group index of the atomic medium from the dispersion signal and observed that it non-linearly depends on the pump power. This non-linearity signifies that to achieve the maximum reduced group velocity, optimization of the pump power is needed. We got the maximum reduction in the group velocity of the probe beam as m s−1. The corresponding time delay was ns. To support our experimental observation, we have performed a theoretical simulation by taking the semi-classical approach of density matrix formalism of a Λ-type three level system. To get the probe response we solved the optical Bloch equation analytically assuming the Lorentzian velocity distribution of the atom. We have observed that our analytical solution matched exactly with the numerical solution. Our experimental observation of non-linear variation of the group index with the pump Rabi frequency matched quite well with both of our numerical and analytical simulations.

Coupling field dependent quantum interference effects in a Λ-system of 87Rb atom

A Λ-system in D2 line transition of the R87b atom has been investigated for quantum interference effects for different configurations of coupling field. With a traveling wave coupling field (co-propagating with probe field), the probe beam shows the earlier known electromagnetically induced transparency (EIT) effect at the resonance. With a standing wave coupling field (which is co- and counter-propagating with probe beam), the probe EIT gets transformed into an electromagnetically induced absorption (EIA). A variation in coupling beam power has shown that, at high coupling power, EIA signals have much larger amplitude and slope than those of EIT signals with and without applied magnetic field. These EIA signals can be useful for tight laser frequency locking and optical switching.

Electromagnetically induced transparency in Λ-systems of 87Rb atom in magnetic field

ABSTRACTThe electromagnetically induced transparency (EIT) observations in two Λ-systems of 87Rb atom, and have been investigated in detail and the results are found consistent with our proposed theoretical models. The second Λ-system provides EIT signal with higher magnitude than the first system, both in the absence and in the presence of an applied magnetic field. The observed steeper slope of the EIT signal in the presence of the magnetic field can enable one to achieve tight frequency locking of lasers using these EIT signals.

Electromagnetically Induced Transparency (EIT) and Autler-Townes (AT) splitting in the presence of band-limited white Gaussian noise

We investigate the effect of band-limited white Gaussian noise (BLWGN) on electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, when performing atom-based continuous-wave (CW) radio-frequency (RF) electric (E) field strength measurements with Rydberg atoms in an atomic vapor. This EIT/AT-based E-field measurement approach is currently being investigated by several groups around the world as a means to develop a new International System of Units traceable RF E-field measurement technique. For this to be a useful technique, it is important to understand the influence of BLWGN. We perform EIT/AT based E-field experiments with BLWGN centered on the RF transition frequency and for the BLWGN blue-shifted and red-shifted relative to the RF transition frequency. The EIT signal can be severely distorted for certain noise conditions (bandwidth, center frequency, and noise power), hence altering the ability to accurately measure a CW RF E-field strength. We present a model to predict the line shifts and broadenings in the EIT signal in the presence of noise. This model includes AC Stark shifts and on resonance transitions associated with the noise source. The results of this model are compared to the experimental data, and we find very good agreement between the two.

High quality electromagnetically induced transparency spectroscopy of 87Rb in a buffer gas cell with a magnetic field**Project supported by the National Key Basic Research Program of China (Grant No. 2013CB922003) and the National Natural Science Foundation of China (Grant Nos. 91421305, 91121005, 11674359, and 91436106).

We have studied the phenomenon of electromagnetically induced transparency (EIT) of 87Rb vapor with a buffer gas in a magnetic field at room temperature. It is found that the spectral lines caused by the velocity selective optical pump effects get much weaker and wider when the sample cell is mixed with a 5-Torr N2 gas while the EIT signal is kept almost unchanged. A weighted least-square fit is also developed to remove the Doppler broadening completely. This spectral method provides a way to measure the Zeeman splitting with high resolution, for example, the Λ-type EIT resonance splits into four peaks on the D2 line of 87Rb in the thermal 2-cm vapor cell with a magnetic field along the electric field of the linearly polarized coupling laser. The high-resolution spectrum can be used to lock the laser to a given frequency by tuning the magnetic field.

Electromagnetically induced transparency in modulated laser fields

We study electromagnetically induced transparency (EIT) in a room-temperature cesium vapor cell using wavelength-modulated probe laser light. In the utilized cascade level scheme, the probe laser drives the lower transition 6S(F = 4) → 6P (F’ = 5), while the coupling laser drives the Rydberg transition 6P → 57S. The probe laser has a fixed average frequency and is modulated at a frequency of a few kHz, with a variable modulation amplitude in the range of tens of MHz. The probe transmission is measured as a function of the detuning of the coupling laser from the Rydberg resonance. The first-harmonic demodulated EIT signal has two peaks that are, in the case of large modulation amplitude, separated by the peak-to-peak modulation amplitude of the probe laser times a scaling factor , where and are the probe- and coupling-laser wavelengths. The scaling factor is due to Doppler shifts in the EIT geometry. Second-harmonic demodulated EIT signals, obtained with small modulation amplitudes, yield spectral lines that are much narrower than corresponding lines in the modulation-free EIT spectra. The resultant spectroscopic resolution enhancement is conducive to improved measurements of radio-frequency (RF) fields based on Rydberg-atom EIT, an approach in which the response of Rydberg atoms to RF fields is exploited to characterize RF fields. Here, we employ wavelength modulation spectroscopy to reduce the uncertainty of atom-based frequency and field measurement of an RF field in the VHF radio band.

Electromagnetically induced transparency of a cesium Rydberg atom in weak radio-frequency field

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.

Electromagnetically Induced Transparency in a Cold Gas with Strong Atomic Interactions**Supported by the National Basic Research Program of China under Grant No 2012CB921603, Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China under Grant No IRT13076, the State Key Program of the National Natural Science of China under Grant No 11434007, the National Natural Science

Electromagnetically induced transparency (EIT) is investigated in a system of cold, interacting cesium Rydberg atoms. The utilized cesium levels 6S1/2, 6P3/2 and nD5/2 constitute a cascade three-level system, in which a coupling laser drives the Rydberg transition, and a probe laser detects the EIT signal on the 6S1/2 to 6P3/2 transition. Rydberg EIT spectra are found to depend on the strong interaction between the Rydberg atoms. Diminished EIT transparency is obtained when the Rabi frequency of the probe laser is increased, whereas the corresponding linewidth remains unchanged. To model the system with a three-level Lindblad equation, we introduce a Rydberg-level dephasing rate γ3 = κ × (ρ33/Ωp)2, with a value κ that depends on the ground-state atom density and the Rydberg level. The simulation results are largely consistent with the measurements. The experiments, in which the principal quantum number is varied between 30 and 43, demonstrate that the EIT reduction observed at large Ωp is due to the strong interactions between the Rydberg atoms.

Revisiting the four-level inverted-Y system under both Doppler-free and Doppler-broadened conditions: an analytical approach

We report the occurrence of electromagnetically induced transparency (EIT) in the simulated probe response signal for a four-level inverted-Y type system that is being acted upon by a weak coherent probe field, a strong coherent pump field and a coherent repump field. There are two ground energy levels, one intermediate energy level and one uppermost energy level. The weak probe field couples the lowest ground level to the intermediate level whereas the repump field connects the other ground level with the intermediate level. The strong control field couples the intermediate level with the uppermost energy level, thereby forming an inverted-Y type system. The density matrix based theoretical model has been developed and solved analytically for this four-level system and the probe response signal has been simulated at different values of the control and repump Rabi frequencies, control and repump frequency detunings and under both Doppler-free and Doppler-broadened conditions using the parameters of 87Rb D2 transition. Extremely low line width (few tens of kHz) for the EIT signal has been noticed under thermal averaging for copropagating probe, control and repump field configuration. The EIT signal is found to be immune to the variation in the control Rabi frequency.