Electromagnetically induced transparency in a Zeeman-sublevels Λ-system of cold ^87Rb atoms in free space

We report the experimental investigation of electromagnetically induced transparency （EIT） in a Zeeman-sublevels A-type system of cold 87Rb atoms in free space. We use the Zeeman substates of the hyperfine energy states 52 S 1/2, F =- 2 and 52P3/2, F1 = 2 of 87Rb D2 line to form a A-type EIT scheme. The EIT signal is obtained by scanning the probe light over 1 MHz in 4 ms with an 80 MHz arbitrary waveform generator. More than 97% transparency and 100 kHz EIT window are observed. This EIT scheme is suited for an application of pulsed coherent storage atom clock （Yan B, et al. 2009 Phys. Rev. A 79 063820）.

Electric field intensity measurement by using doublet electromagnetically induced transparency of cold Rb Rydberg atoms

We demonstrate a simple method to measure electric field intensity by using doublet electromagnetically induced transparency(EIT) spectra of cold Rb Rydberg atoms, where the frequency of the coupling laser does not need to be locked. Based on the Stark splitting of the Rb Rydberg state, 10D_(3/2), under electric fields and the corresponding calculated polarizabilities, the real electric field intensity is calculated using the difference in radio-frequency diffraction between two acousto-optic modulators, which acts as a frequency criterion that allows us to measure the electrical field without locking the coupling laser. The value measured by this simple method shows a good agreement with our previous work [Opt.Express 29 1558(2021)] where the frequency of the coupling laser needs to be locked with an additional EIT spectrum based on atom vapor and a proportional–integral–differential feedback circuit. Our presented method can also be extended to the measurement of electric field based on hot Rydberg atom vapor, which has application in industry.

Electromagnetically Induced Transparency in a Cold Gas with Strong Atomic Interactions

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 6/23/2 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 Linclblad equation, we introduce a Rydberg-level dephasing rate γ3 = κ×（P33/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.

Electromagnetically induced transparency of single Λ-type three-level atoms in a high-finesse optical cavity

We study the features of electromagnetically induced transparency（EIT） in a single Λ-type three-level atom placed in a high-finesse cavity under the action of a coupling laser and a probe laser.Our calculations show that three transparency windows appear when the pump strength is large enough.This can be explained by the residual pump in the cavity mostly resulting in energy splitting.The level ｜3 is split into four slightly different energy levels,and interference takes place between the excitation pathways.Furthermore,it is also shown that the frequencies of the EIT windows can be tuned by changing the coupling field detuning 2,and that the reflection profile is very sensitive to the cavity field detuning △c.

Transient electromagnetically induced transparency spectroscopy of^(87)Rb atoms in buffer gas

We study the transient response dynamics of^(87)Rb atomic vapor buffered in 8 torr Ne gas through an electromagnetically induced transparency configured inΛ-scheme.Experimentally,the temporal transmission spectra versus probe detuning by switching on and off the coupling one show complex structures.The transmitted probe light intensity drops to a minimum value when the coupling light turns off,showing a strong absorption.Even at the moment of turning on the coupling light at a subsequent delayed time,the atomic medium shows a fast transient response.To account for the transient switching feature,in the time-dependent optical Bloch equation,we must take the transverse relaxation dephasing process of atomic vapor into account,as well as the fluorescence relaxation along with the optical absorption.This work supplies a technique to quantify the transverse relaxation time scale and to sensitively monitor its variation along the environment by observing the transient dynamics of coherent medium,which is helpful in characterizing the coherent feature of the atomic medium.

Monte Carlo simulations of electromagnetically induced transparency in a square lattice of Rydberg atoms

We study the steady optical response of a square lattice in which all trapped atoms are driven by a probe and a coupling fields into the ladder configuration of electromagnetically induced transparency(EIT).It turns out to be a manybody problem in the presence of van der Waals(vd W)interaction among atoms in the upmost Rydberg state,so Monte Carlo(MC)calculation based on density matrix equations have been done after introducing a sufficiently large cut-off radius.It is found that the absorption and dispersion of EIT spectra depends critically on a few key parameters like lattice dimension,unitary vd W shift,probe Rabi frequency,and coupling detuning.Through modulating these parameters,it is viable to change symmetries of the absorption and dispersion spectra and control on demand depth and position of the transparency window.Our MC calculation is expected to be instructive in understanding many-body quantum coherence effects and in manipulating non-equilibrium quantum phenomena by utilizing vd W interactions of Rydberg atoms.

Laser frequency offset-locking using electromagnetically induced transparency spectroscopy of (85)Rb in magnetic field

We have experimentally offset-locked the frequencies of two lasers using electromagnetically induced transparency（EIT） spectroscopy of ^（85）Rb vapor with a buffer gas in a magnetic field at room temperature. The magnetic field is generated by a permanent magnet mounted on a translation stage and its field magnitude can be varied by adjusting the distance between the magnet and Rb cell, which maps the laser locking frequency to the space position of the magnet. This frequency-space mapping technique provides an unambiguous daily laser frequency detuning operation with high accuracy.A repeatability of less than 0.5 MHz is achieved with the locking frequency detuned up to 184 MHz when the magnetic field varies from 0 up to 80 G.

Rydberg electromagnetically induced transparency and Autler–Townes splitting in a weak radio-frequency electric field

We utilize an electromagnetically induced transparency(EIT) of a three-level cascade system involving Rydberg state in a room-temperature cell, formed with a cesium 6 S_(1/2)–6 P_(3/2)–66 S_(1/2) scheme, to investigate the Autler–Townes(AT)splitting resulting from a 15.21-GHz radio-frequency(RF) field that couples the |66 S_(1/2) → |65 P_(1/2) Rydberg transition.The radio-frequency electric field induced AT splitting, γAT, is defined as the peak-to-peak distance of an EIT-AT spectrum.The dependence of AT splitting γAT on the probe and coupling Rabi frequency, ?_p and ?_c, is investigated. It is found that the EIT-AT splitting strongly depends on the EIT linewidth that is related to the probe and coupling Rabi frequency in a weak RF-field regime. Using a narrow linewidth EIT spectrum would decrease the uncertainty of the RF field measurements.This work provides new experimental evidence for the theoretical framework in [J. Appl. Phys. 121, 233106(2017)].

Simultaneous electromagnetically induced transparency and absorption in thermal atomic medium

A three-level lambda system driven by multicolor control, pump, and probe fields is investigated. The pump and probe fields are derived from the same laser with opposite propagating directions. Due to the Doppler effect, the zero group-velocity atoms face bichromatic fields, while other atoms face trichromatic fields. The atomic medium shows distinct characteristics and exhibits simultaneous electromagnetically induced transparency（EIT） and electromagnetically induced absorption（EIA） at two frequencies. EIT and EIA peaks have a fixed relationship with frequency, which is determined by the Doppler shifts.

Mixture of Electromagnetically Induced Transparency and Autler–Townes Splitting in a Five-Level Atomic System

Discerning electromagnetically induced transparency(EIT) from Autler–Townes splitting(ATS) is a significant issue in quantum optics and has attracted wide attention in various three-level configurations. Here we present a detailed study of EIT and ATS in a five-level atomic system considered to be composed of a four-level Y-type subsystem and a three-level Λ-type subsystem. In our theoretical calculations with standard density matrix formalism and steadystate approximation, we obtain the general analytical expression of the first-order matrix element responsible for the probe-field absorption. In light of the well-known three-level EIT and ATS criteria, we numerically show an intersection of EIT with ATS for the Y-type subsystem. Furthermore, we show that an EIT dip is sandwiched between two ATS dips(i.e., multi-dip mixture of EIT and ATS) in the absorption line for the five-level system, which can be explained by the dressed-state theory and Fano interference.

Talbot effect in nonparaxial self- accelerating beams with electromagnetically induced transparency

In this study,we report on the fractional Talbot ffect of nonpar axial self-accelerating beams in a multilevel electromagnetically induced transparency(EIT)atomic configuration,which,to the best of our knowledge,is the first study on this subject.The Tallbot ffect originates from superposed eigenmodes of the Helmholtz equation and forms in the EIT window in the presence of both linear and cubic susceptibilities.The Talbot ffect can be realized by appropriately selecting the cofficients of the beam components.Our results indicate that the larger the radial difference between beam components,the stronger the interference between them,the smaller the Tallbot angle is.The results of this study can be useful when studying optical imaging.optical measurements,and optical computing.

Quantum storage of optical signals and coherent manipulation of quantum states based on electromagnetically induced transparency

Electromagnetically induced transparency (EIT) techniques are important tools for the storage of the quantum states of light fields in atomic ensembles and for enhancement of the interaction between photons. In this paper, we briefly summarize the recent experimental studies conducted by our group on enhanced cross-phase modulation based on double EIT effects, the quantum interference of stored dual-channel spin-wave excitations and the coherent manipulation of the spin wave vector for the polarization of photons in a single tripod atomic system. The work presented here has potential application in the developing field of quantum information processing.

Vacuum induced transparency and slow light phenomena in a two-level atomic ensemble controlled by a cavity

We study the optical properties of a two-level atomic ensemble controlled by a high-finesse cavity. Even though the cavity is initially in the vacuum state in the absence of external driving, the probe response of the atomic ensemble can be dramatically modified. When the collectively enhanced atom–cavity coupling is strong enough and the cavity decay rate is much smaller than the atomic damping rate, an electromagnetically induced transparency-like coherent phenomenon emerges with a dip absorption for the response of the two-level atoms in the cavity without driving, and thus is called vacuum induced transparency. We also show the slow light with very low group velocity in such an atomic ensemble.

Microwave electrometry with Rydberg atoms in a vapor cell using microwave amplitude modulation

We have theoretically and experimentally studied the dispersive signal of the Rydberg atomic electromagneticallyinduced transparency(EIT)Autler–Townes(AT)splitting spectra obtained using amplitude modulation of the microwave(MW)electric field.In addition to the two zero-crossing points interval△f_(zeros),the dispersion signal has two positive maxima with an interval defined as the shoulder interval△f_(sho),which is theoretically expected to be used to measure a much weaker MW electric field.The relationship of the MW field strength E_(MW)and△f_(sho)is experimentally studied at the MW frequencies of 31.6 GHz and 9.2 GHz respectively.The results show that△f_(sho)can be used to characterize the much weaker E_(MW)than that of△f_(zeros)and the traditional EIT–AT splitting interval△f_(m);the minimum E_(MW)measured by△f_(sho)is about 30 times smaller than that by△f_(m).As an example,the minimum E_(MW)at 9.2 GHz that can be characterized by△f_(sho)is 0.056 mV/cm,which is the minimum value characterized by the frequency interval using a vapor cell without adding any auxiliary fields.The proposed method can improve the weak limit and sensitivity of E_(MW)measured by the spectral frequency interval,which is important in the direct measurement of weak E_(MW).

Sideband-Induced Two-Photon Transparency

We show that it is possible to use a single sideband to induce two-photon transparency in a three-level cascade medium. The medium simultaneously absorbs two photons as a one-step process when the middle level is far off one-photon resonance. A resonant sideband coupling on the upper transition and the two-photon one-step process drive the medium into a trapped state, and the dominant component is the ground state. Thus almost all population is trapped in the ground state and the two-photon absorption is dramatically suppressed. We present a numerical calculation for arbitrary values of the atomic and field parameters and also provide an analytic description for the required conditions.

Thermometry utilizing stored short-wavelength spin waves in cold atomic ensembles

Temperature,as a measure of thermal motion,is a significant parameter characterizing a cold atomic ensemble optical quantum memory.In a cold gas,storage lifetime strongly depends on its temperature and is associated with the spin wave decoherence.Here we experimentally demonstrate a new spin wave thermometry method relying on this direct dependence.The short-wavelength spin waves resulting from the counter-propagating configuration of the control and the probe laser beams make this thermometry highly suitable for probing in situ the atomic motion in elongated clouds as the ones used in quantum memories.Our technique is realized with comparable precision for memories that rely on electromagnetically induced transparency as well as far-detuned Raman storage.

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

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.

Light manipulation by dual channel storage in ultra-cold Rydberg medium

We investigate the light propagation dynamics in ultra-cold Rydberg medium with inverted-Y configuration based on the superatom theory.It is viable to store light information in two types of atomic spin coherence(trivial spin coherence and Rydberg spin coherence),which makes the system a prospective platform for versatile light manipulation.A normal feature is to realize efficient light storage with simultaneous resonant control fields applied.An intriguing feature is to split light into two beams with different intensities and statistical properties if the control fields are applied separately.The beam of light retrieved from the Rydberg spin coherence is severely attenuated and shows anti-bunching character accompanied by the cooperative optical nonlinearity.Moreover,generation and manipulation of beating signal are achievable by applying the non-resonant control fields.

Electromagnetically induced moiré optical lattices in a coherent atomic gas

Electromagnetically induced optical(or photonic)lattices via atomic coherence in atomic ensembles have recently received great theoretical and experimental interest.We here conceive a way to generate electromagnetically induced moiréoptical lattices—a twisted periodic pattern when two identical periodic patterns(lattices)are overlapped in a twisted angle(θ)—in a three-level coherent atomic gas working under electromagnetically induced transparency.We show that,changing the twisted angle and relative strength between the two constitutive sublattices,the moiréBloch bands that are extremely flattened can always appear,resembling the typical flat-band and moiréphysics found in other contexts.Dynamics of light propagation in the induced periodic structures demonstrating the unique linear localization and delocalization properties are also revealed.Our scheme can be implemented in a Rubidium atomic medium,where the predicted moiréoptical lattices and flattened bands are naturally observable.

Extending microwave-frequency electric-field detection through single transmission peak method

The strength of microwave(MW)electric field can be observed with high precision by using the standard electromagnetically induced transparency and Aulter–Towns(EIT-AT)technique,when its frequency is resonant or nearly-resonant with the Rydberg transition frequency.As the detuning of MW field increases,one of the transmission peaks(single peak)is easier to measure due to its increased amplitude.It can be found that the central symmetry point of the two transmission peaks f_(1/2)is only related to the detuning of MW field△_(MW)and central symmetry point f_(0)of resonant MW field,satisfying the relation f_(1/2)=△_(MW)/2+f_(0).Thus,we demonstrate a single transmission peak method that the MW E-field can be determined by interval between the position of single peak and f_(1/2).We use this method to measure continuous frequencies in a band from-200 MHz to 200 MHz of the MW field.The experimental results and theoretical analysis are presented to describe the effectiveness of this method.For 50 MHz<△_(MW)<200 MHz,this method solves the problem that the AT splitting cannot be measured by using the standard EIT-AT techniques or multiple atomic-level Rydberg atom schemes.