Electromagnetically Induced Transparency Spectra Research Articles

Electromagnetically induced transparency spectra of cesium Rydberg atoms decorated by radio-frequency fields

<sec>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. </sec><sec>In this work, by selecting probe light (852 nm), dressed light (1470 nm), and coupled light (780 nm), the Rydberg state (49<i>P</i><sub>3/2</sub>) 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.</sec><sec>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.</sec>

Electromagnetically Induced Transparency Spectra of 6Li Rydberg Atoms

Rydberg atoms possess highly excited valence electrons that are far away from atomic cations. Compared with ground states, Rydberg states are excited states with a high principal quantum number n that exhibit large electric dipole moments and have a variety of applications in quantum information processing. In this communication, we report the measurement of the 6Li Rydberg excitation spectrum by ladder-type electromagnetically induced transparency (EIT) in a vapor cell. The 2p→ns/nd EIT spectra were recorded by sweeping the frequency of an ultraviolet Rydberg pumping laser while keeping the probing laser resonant to the 2s→2p transition. All lasers were locked on an ultrastable optical Fabry-Pérot cavity and measured by an optical frequency comb. Our results provide valuable information to precisely determine quantum defects and enable novel experiments with Rydberg-dressed ultracold Fermi gases.

Application of kernel principal component analysis for optical vector atomic magnetometry

Vector atomic magnetometers that incorporate electromagnetically induced transparency (EIT) allow for precision measurements of magnetic fields that are sensitive to the directionality of the observed field by virtue of fundamental physics. However, a practical methodology of accurately recovering the longitudinal angle of the local field through observations of EIT spectra has not been established. In this work, we address this problem of angle determination with an unsupervised machine learning algorithm utilizing nonlinear dimensionality reduction. The proposed algorithm was developed to interface with spectroscopic measurements from an EIT-based atomic rubidium magnetometer and uses kernel principal component analysis (KPCA) as an unsupervised feature extraction tool. The resulting KPCA features allow each EIT spectrum measurement to be represented by a single coordinate in a new reduced dimensional feature space, thereby streamlining the process of angle determination. A supervised support vector regression (SVR) machine was implemented to model the resulting relationship between the KPCA projections and field direction. If the magnetometer is configured so that the azimuthal angle of the field is defined with a polarization lock, the KPCA-SVR algorithm is capable of predicting the longitudinal angle of the local magnetic field within 1 degree of accuracy and the magnitude of the absolute field with a resolution of 70 nT. The combined scalar and angular sensitivity of this method make the KPCA-enabled EIT magnetometer competitive with conventional vector magnetometry methods. © 2023. All rights reserved.

Investigating electromagnetically induced transparency spectral lineshape distortion due to non-uniform fields in Rydberg-atom electrometry

We investigate the effects of spatially non-uniform radio-frequency electric (E) field amplitudes on the spectral line shapes of electromagnetically induced transparency (EIT) signals in Rydberg atomic systems used in electrometry (i.e., the metrology of E-field strengths). Spatially non-uniform fields distort the EIT spectra from that of an ideal case, and understanding this distortion is important in the development of Rydberg atom-based sensors, as these distortions can limit accuracy and sensitivity. To characterize this distortion, we present a model that approximates the atom vapor as multi-layered media and then uses Beer’s law to combine the absorption through its many discrete thin segments. We present a set of expected line distortions caused by various RF electric-field distributions found in practice. This provides an intuitive diagnostic tool for experiments. We compare this model to measured experimental atomic spectra in both two-photon and three-photon excitation schemes in the presence of non-uniform radio-frequency fields. We show that we can accurately model and reproduce the EIT lineshape distortion observed in these experimental data.

Polarization-independent tunable terahertz slow light with electromagnetically induced transparency metasurface

Tunable slow light systems have gained much interests recently due to their efficient control of strong light–matter interactions as well as their huge potential for realizing tunable device applications. Here, a dynamically tunable polarization independent slow light system is experimentally demonstrated via electromagnetically induced transparency (EIT) in a terahertz (THz) metasurface constituted by plus and dimer-shaped resonators. Optical pump-power dependent THz transmissions through the metasurface samples are studied using the optical pump THz probe technique. Under various photoexcitations, the EIT spectra undergo significant modulations in terms of its resonance line shapes (amplitude and intensity contrast) leading to dynamic tailoring of the slow light characteristics. Group delay and delay bandwidth product values are modulated from 0.915 ps to 0.42 ps and 0.059 to 0.025 as the pump fluence increases from 0 to 62.5 nJ cm−2. This results in tunable slow THz light with group velocities ranging from 2.18 × 105 m s−1 to 4.76 × 105 m s−1, almost 54% change in group velocity. The observed tuning is attributed to the photo-induced modifications of the optoelectronic properties of the substrate layer. The demonstrated slow light scheme can provide opportunities for realizing dynamically tunable slow light devices, delay lines, and other ultrafast devices for THz domain.

Temporal profile of biphotons generated from a hot atomic vapor and the spectrum of electromagnetically induced transparency

We systematically studied the temporal profile of biphotons, i.e., pairs of time-correlated single photons, generated from a hot atomic vapor via the spontaneous four-wave mixing process. The measured temporal width of biphoton wave packet or two-photon correlation function against the coupling power was varied from about 70 to 580 ns. We derived an analytical expression of the biphoton's spectral profile in the Doppler-broadened medium. The analytical expression reveals that the spectral profile is mainly determined by the effect of electromagnetically induced transparency (EIT), and behaves like a Lorentzian function with a linewidth approximately equal to the EIT linewidth. Consequently, the biphoton's temporal profile influenced by the Doppler broadening is an exponential-decay function, which was consistent with the experimental data. Employing a weak input probe field of classical light, we further measured the EIT spectra under the same experimental conditions as those in the biphoton measurements. The theoretical predictions of the biphoton wave packets calculated with the parameters determined by the classical-light EIT spectra are consistent with the experimental data. The consistency demonstrates that in the Doppler-broadened medium, the classical-light EIT spectrum is a good indicator for the biphoton's temporal profile. Besides, the measured biphoton's temporal widths well approximated to the predictions of the analytical formula based on the biphoton's EIT effect. This study provides an analytical way to quantitatively understand the biphoton's spectral and temporal profiles in the Doppler-broadened medium.

Metal-graphene hybrid terahertz metamaterial based on dynamically switchable electromagnetically induced transparency effect and its sensing performance

A dynamically switchable electromagnetically induced transparency (EIT) based on metal-graphene hybrid metamaterial is proposed. The EIT metamaterial consists of two split-ring resonator (SRRs) and two orthogonal cut-wires (CWs) with different length. The EIT metamaterial illuminated by y-polarized and x-polarized incident waves exhibits two different EIT effects, which can be explained by multipole scattering theory and three-dimensional schematic diagrams. The simulated EIT spectra are almost identical to the theoretical EIT spectra calculated by the two-particle model. Two EIT effects and theirs group delays can be dynamically tunable by manipulating the Fermi level of graphene on two SRRs. Moreover, EIT metamaterial shows good sensing performance with the sensitivities of 0.185 THz/RIU and 0.160 THz/RIU in the x and y polarization directions, respectively. Our EIT metamaterial realizes dynamically switchable EIT effect and provides a novel approach for applications in slow light devices and sensors.

Monte Carlo simulations of electromagnetically induced transparency in a square lattice of Rydberg atoms* *Project supported by the National Natural Science Foundation of China (Grant No. 12074061).

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 many-body problem in the presence of van der Waals (vdW) 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 vdW 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 vdW interactions of Rydberg atoms.

Wideband reciprocity tunable electromagnetically induced transparency in complementary graphene metasurface

A reciprocity electromagnetically induced transparency (EIT) effect can be obtained in the complementary graphene metasurface structure. The EIT spectra can be obtained whether the excitation was input from a positive or reverse direction. The transmission of the structure which consisted of a graphene square (GS) and the graphene circle of hollowed air square (GCHAS) placed on the top and bottom of the polyimide layer was discussed. A wideband EIT window was found in the structure of GCHAS as bright mode and GS as dark mode by the finite integration time domain method. The EIT effect can be tuned by the chemical potential, the electron-phonon relaxation time of graphene, and the widths of GCHAS and GS, respectively. The polarization insensitive EIT effect can be obtained. The transmission mechanism is interpreted by giving the electric and magnetic field distributions at certain frequencies. The effective permittivity of the structure was calculated by method of inversion. These results can be applied for many areas, such as wideband wavelength slow-light devices, active plasmon switching and bidirectional devices.

Interplay between optical pumping and Rydberg EIT in magnetic fields.

We perform Zeeman spectroscopy on a Rydberg electromagnetically induced transparency (EIT) system in a room-temperature Cs vapor cell, in magnetic fields up to 50 Gauss. The magnetic interactions of the |6S1/2 Fg = 4> ground, |6P3/2 Fe = 5> intermediate, and |33S1/2> Rydberg states that form the ladder-type EIT system are in the linear Zeeman, quadratic Zeeman, and the Paschen-Back regimes, respectively. We explain the dependence of Rydberg EIT spectra on the magnetic field and polarization. The asymmetry of the EIT spectra, which is caused by the quadratic Zeeman effect of the intermediate state, becomes paramount in magnetic fields ≥40 Gauss. We investigate the interplay between Rydberg EIT, which reduces photon scattering, and optical pumping, which relies on photon scattering. We employ a quantum Monte Carlo wave-function approach to quantitatively model the spectra and their asymmetry behavior. Simulated spectra are in good agreement with the experimental data.

Transition from electromagnetically induced transparency to Autler–Townes splitting in cold cesium atoms

Electromagnetically induced transparency (EIT) and Autler–Townes splitting (ATS) are two similar yet distinct phenomena that modify the transmission of a weak probe field through an absorption medium in the presence of a coupling field, featured in a variety of three-level atomic systems. In many applications it is important to distinguish EIT from ATS splitting. We present EIT and ATS spectra in a three-level cascade system, involving cold cesium atoms in the Rydberg state. The EIT linewidth, γEIT, defined as the full width at half maximum of the transparency window, and the ATS splitting, γATS, defined as the peak-to-peak distance between AT absorption peaks, are used to delineate the EIT and ATS regimes and to characterize the transition between the regimes. In the cold-atom medium, in the weak-coupler (EIT) regime γEIT ≈ A + B( + , where Ωc and Ωp are the coupler and probe Rabi frequencies, Γeg is the spontaneous decay rate of the intermediate 6P3/2 level, and parameters A and B that depend on the laser linewidth. We explore the transition into the strong-coupler (ATS) regime, which is characterized by the relation γATS ≈ Ωc. The experiments are in agreement with numerical solutions of the Master equation. Our analysis accounts for non-ideal conditions that exist in typical realizations of Rydberg-EIT, including laser-frequency jitter, Doppler mismatch of the utilized two-color Rydberg EIT system, and strong probe fields. The obtained criteria to distinguish cold-atom EIT from ATS are readily accessible and applicable in practical implementations.

Coherence effects in electromagnetically induced transparency in V-type systems of 87Rb.

We present a theoretical and experimental study of electromagnetically induced transparency (EIT) in V-type systems of 87Rb atoms. We calculate accurate lineshapes of V-type EIT spectra by solving density matrix equations considering all the magnetic sublevels involved. The calculated spectra demonstrate consistency with the experimental results. We identify the coherence effect in the calculated EIT spectra, and determine that the coherence effect exists only in the cycling transition. We explain the reason for the suppression of the coherence effect in open transitions using an analytical calculation of the spectra for a simple V-type three-level atomic system.

Conversion between EIT and Fano spectra in a microring-Bragg grating coupled-resonator system

A conversion between the electromagnetically induced transparency (EIT) transmission and Fano transmission is theoretically and experimentally demonstrated in an all-pass microring-Bragg grating (APMR-BG) coupled-resonator system. In this work, the coupling between the two resonators (the microring resonator and the Fabry-Perot resonator formed by two Bragg gratings) gives rise to the EIT and Fano transmissions. The resonant status strongly depends on the round-trip attenuation of the microring and the coupling strength. By tuning the coupling strength, the EIT and Fano transmissions can be controlled and converted. The device performance has been theoretically calculated and analyzed with a specially developed numerical model based on the transfer matrix method. The APMR-BG coupled-resonator systems with different gap widths were designed, fabricated, and characterized on a silicon-on-insulator (SOI) platform. The conversion of resonance was experimentally observed and verified. In addition, this on-chip system has the advantage of a small footprint, and the fabrication process is compatible with the planar waveguide fabrication process.

Paschen-Back effects and Rydberg-state diamagnetism in vapor-cell electromagnetically induced transparency

We report on rubidium vapor-cell Rydberg electromagnetically induced transparency (EIT) in a 0.7~T magnetic field where all involved levels are in the hyperfine Paschen-Back regime, and the Rydberg state exhibits a strong diamagnetic interaction with the magnetic field. Signals from both $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ are present in the EIT spectra. This feature of isotope-mixed Rb cells allows us to measure the field strength to within a $\pm 0.12$\% relative uncertainty. The measured spectra are in excellent agreement with the results of a Monte Carlo calculation and indicate unexpectedly large Rydberg-level dephasing rates. Line shifts and broadenings due to small inhomogeneities of the magnetic field are included in the model.

Electromagnetically induced transparency with superradiant and subradiant states

We construct the electromagnetically induced transparency (EIT) by dynamically coupling a superradiant state with a subradiant state. The superradiant and subradiant states with enhanced and inhibited decay rates act as the excited and metastable states in EIT, respectively. Their energy difference determined by the distance between the atoms can be measured by the EIT spectra, which renders this method useful in subwavelength metrology. The scheme can also be applied to many atoms in nuclear quantum optics, where the transparency point due to counter-rotating wave terms can be observed.

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.

Radiation-Pressure Effects in Cold-Atom Absorption Spectroscopy and Electromagnetically Induced Transparency

Radiation pressure due to the interaction between a probe light and cold atoms is investigated in a standard cesium magneto-optical trap. The radiation pressure alters the absorption spectroscopy of cold atoms, leading to line shapes and linewidths after resonant interaction that are different for positive and negative probe chirps. The difference is attributed to the radiation pressure of the probe laser, due to which atoms become accelerated at the resonance. The effect of the radiation pressure is also seen in electromagnetically induced transparency (EIT) involving an excited Rydberg level. The density matrix equation accounting for the radiation pressure is used to simulate the experiments. The simulations agree well with the measurements both for absorption and EIT spectra. We find that the effect of the radiation pressure is reduced at low probe intensities, and can be neglected when the probe intensity is smaller than Isat/2 .

Measurement of the fine structure of cesium Rydberg state

The spectra of Rydberg atoms are of great significance for studying the energy levels of Rydberg atoms and the interaction between neutral atoms, especially, the high-precision spectra of Rydberg atoms can be used to measure the energy level shifts of Rydberg atoms resulting from the dipole-dipole interactions in room-temperature vapor cells. In this paper we report the preparation of cesium Rydberg states based on the cascaded two-photon excitation of 509 nm laser and 852 nm laser in opposite, and the measurements of the fine structure of cesium Rydberg states. In this experiment, the 509 nm laser is generated by the cavity-enhanced second-harmonic generation from 1018 nm laser with a periodically-poled KTP crystal and has a maximum power of about 1 W, and the 852 nm probe laser is provided by an external-cavity diode laser with a maximum output power of 5 mW and a typical linewidth of 1 MHz. By scanning the frequency of 509 nm coupling laser, it is presented that the Doppler-free spectra based on electromagnetically-induced transparency (EIT) of 509 nm coupling laser and 852 nm probe laser. The velocity-selective EIT spectra are used to study the spectral splitting of 6S1/26P3/257S(D) ladder-type system of cesium Rydberg atoms in a room-temperature vapor cell. The powers of 852 nm probe laser and 509 nm coupling laser are 0.3 upW and 200 mW, respectively. Their waist radii are both approximately 50 m. The intervals of hyperfine splitting of the intermediate state 6P3/2(F'=3, 4, 5) and fine splitting of 57D3/2 and 57D5/2 Rydberg states are measured by a frequency calibrating. Concretely, the velocity-selective spectrum with a radio frequency (RF) modulation of 30 MHz is used as a reference to calibrate the Rydberg fine-structure states in the hot vapor cell, where the RF frequency precision is smaller than a hertz on long time scales and the EIT linewidth is smaller than 13 MHz. The experimental value of the fine structure splitting of 57D3/2 and 57D5/2 Rydberg states is (354.72.5) MHz, that is in consistence with the value of 346.8 MHz calculated by Rydberg-Ritz equation and quantum defects of 57D3/2 and 57D5/2 Rydberg states. The experimental values of hyperfine splitting of intermediate state 6P3/2(F'=3, 4, 5) are also coincident with the theoretical calculated values. The dominant discrepancy existing between the experimental and calculated results may arise from the nonlinear correspondence of the PZT while the 509 nm wavelength cavity is scanned, and the measurement accuracy influenced by the spectral linewidth. The velocity-selective spectroscopy technique can also be used to measure the energy level shifts caused by the interactions of 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.