Electromagnetically induced transparency and dark fluorescence in a cascade three-level diatomic lithium system

We study the steady optical response of a five-level atomic system in the parametric region where resonant two-photon transitions are much stronger than far-detuned single-photon transitions. We find that the concurrent absorption of two weak probe fields can be well suppressed in a narrow spectral region to attain electromagnetically induced transparency (EIT) via quantum destructive interference between different two-photon transition pathways. To gain a deeper insight into relevant physics, we adiabatically reduce this five-level system with trivial single-photon transitions into a three-level system with vanishing single-photon transitions by deriving an effective Hamiltonian. The two systems have almost the same two-photon absorption spectra exhibiting typical EIT features but are a little different in fine details. This means that most characteristics of two-photon quantum destructive interference are reserved after the adiabatic elimination approximation. In addition, we verify by numerical calculations that the two-photon EIT spectra are insensitive to the dipole-dipole interaction of cold Rydberg atoms when the uppermost level has a high principle quantum number.

We propose a multifunction phase-shifting manipulator with low noise at a single-photon level,by using a threelevel atomic scheme.This three-level system interacts with a strong pumping field and a weak probe field with a large detuning.Due to this large detuning,two lower states can be coherently prepared prior to the injection of the pump and probe fields.In our configuration,the duration of the pumping field is much longer than that of the probe field. By solving the Heisenberg-Langevin equations of our system under the steady state approximation,we calculate the linear susceptibility of the system and examine the quantum noise properties of the probe field in detail.We show that this scheme,which rests on the process of two-wave mixing with initial atomic coherence,exhibits many interesting properties that neither typical electromagnetically induced transparency (EIT) schemes nor active Raman gain (ARG) schemes possess.Although both EIT-and ARG-based schemes have been widely investigated in atomic medium,the direct generalizations of these schemes to the single/few photon limit prove to be more problematic.The low fidelity due to the significant probe-field attenuation in EIT medium and the large quantum noise due to the amplification of the probe field in an active Raman gain medium are the main obstacles that prohibit a high-fidelity,low-noise phase shifter from being realized in the single/few photon limit.Physically,this scheme can be viewed as a hybrid scheme in which two processes of different physical principles are allowed to interfere with each other to achieve many desired functionalities. For instance,it can be used as a lossless two-photon-broadband phase-shifter with suitable system parameters.It can also be used as an attenuator/amplifier and a total transparency with a zero phase shift.In particular,we show that by locking the pump field intensity and the two-photon detuning simultaneously a flat constant π-phase shift can be realized with unit probe fidelity in a broad probe field frequency range.Applying the quantum regression theorem,we calculate the noise spectrum of the outgoing probe field as a large phase shift is achieved,and show that this two-photon-insensitive π-phase shift may significantly reduce the quantum noise fluctuations associated with a Raman gain process,and have a lot of potential applications for quantum information processing and optical telecommunication.The realization of this broadband π-phase-shift with significantly reduced quantum noise fluctuations makes this scheme attractive for the realization of low-noise phase-gate/polarization-gate at single-photon level.

We investigate, both theoretically and experimentally, the cross-Kerr nonlinearity generated in a four-level tripod system in the 87Rb D1 line. The system exhibits simultaneous electromagnetically induced transparency (EIT) windows for two weak (probe and trigger) fields and the enhanced cross-Kerr nonlinearity by EIT. The cross-Kerr nonlinear phase shifts for probe (trigger) field are measured at several different intensities of trigger (probe) field. The results show that large cross-phase modulation (XPM) coefficients can be achieved at low light intensities.

In this paper, we consider a scheme for electromagnetically induced grating (EIG) in a three-level ladder-type system. A microwave field of finite bandwidth making a standing-wave pattern is applied on lower levels. In addition, we have also introduced an indirect pump in our system. A weak probe field is then applied to study the effects of phase diffusion associated with the microwave control field on EIG. It is found that phase diffusion associated with the strong microwave control field strongly affect the diffraction. We have incorporated the effect of different system parameters such as the strength of the microwave field, indirect pumping mechanism, interaction length, and detuning in the weak probe field. Interestingly, the stronger microwave control field retrieves the loss in diffraction intensity caused by the phase diffusion. Our results show that the introduction of detuning in the optical probe field results in the enhancement of the phase grating effect. Furthermore, our results show that an optimized indirect pump field can slightly improve the first-order diffraction intensities both in the absence and presence of phase diffusion.

Comparison of steady and transient optical responses between a four-level Tripod system and a three-level Lambda system

Role of dressed-state interference in electromagnetically induced transparency

Electromagnetically induced transparency (EIT) is a well-known phenomenon due in part to its applicability to quantum devices such as quantum memories and quantum gates. EIT is commonly modeled with a three-level lambda system; however, this simplified model does not capture all the physics of EIT experiments with real systems. We present a theoretical study of the effect of two closely-spaced excited states on EIT and off-resonance Raman transitions. In addition to the expected broadening of the EIT resonance and reduction in EIT transparency due to multiple excited states, we find some unexpected and interesting results. A comparison with a model that does not allow for coupling of the excited states shows that the coherent interaction of the fields with two excited states whose separation is smaller than their Doppler broadened linewidth can enhance the EIT transparency under some conditions and can enhance and shift the resonance frequency of off-resonance Raman absorption. Furthermore, through a dressed state analysis of the full four-level system, we find that the underlying mechanism for the reduction in EIT transparency is a shift in the two-photon resonance due to unequal dipole moments of the transitions coupled by the control field. Complete transparency can only be recovered for systems with equal dipole moments or when the separation between the two excited states is at least of the order of the Doppler width. To support our theoretical study, we present experimental EIT measurements in the D1 lines of 85Rb and 87Rb that agree with our predictions of an enhancement or reduction of EIT transparency under specific conditions. The experimental results also verify the roles that the dipole moments and the separation between the two excited states have on recovering the EIT transparency.

We study electromagnetically-induced transparency (EIT) of a probe field in a Doppler- broadened five-level K-type atomic system driven by three strong laser (coupling) fields. Effect of wave-vector mismatch occurring when the coupling field frequency is higher than that of the probe field frequency (λc < λp) are considered. Under the influence of the coherent coupling fields, the steady-state linear susceptibility of the probe laser shows that the system can have single or double or triple EIT windows depending on the amplitude and detuning of the coupling fields.

Cavity optomechanical systems have become a topic of great interest in recent years, and the coupled-cavity model is also a classic theoretical framework. This paper aims to construct a coupledcavity optomechanical system to study induced transparency, Fano resonance, and fast-slow light effects in such a system. By transferring phenomena typically studied in a single optical cavity to a coupled-cavity system, we analyze specific phenomena detected in optical and microwave cavities, such as transmission and absorption spectra, to investigate induced transparency. We also examine Fano resonance in the model by varying detuning, and study fast-slow light effects through group velocity. This paper first constructs the corresponding physical model, as shown in Figure 1. Based on the theoretical model, a reasonable Hamiltonian is proposed. By introducing appropriate dissipation and fluctuation noise terms, the Langevin equations of motion are derived. Next, the Langevin equations are linearized, and the resonant terms are retained to obtain &lt;i&gt;O&lt;/i&gt;&lt;sub&gt;+&lt;/sub&gt; . The amplitude of the field modes is then derived using the input-output relations. Following the experimental data from referenced literature, a numerical simulation program is implemented in Mathematica. By substituting the relevant parameters and performing calculations, the results are obtained through simulation. For the first time, the interactions among photons, magnons, microwaves, and phonons— as well as the interplay between photons in the two cavities—are investigated in a coupled cavity optomagnomechanical system. Electromagnetically induced transparency (EIT), Fano resonance, and fast-slow light effects are studied in this coupled-cavity optomagnomechanical framework. Phenomena typically examined in a single optical cavity are extended to the coupled-cavity system, with specific observations analyzed separately in the optical and microwave cavities. When &lt;i&gt;δ&lt;/i&gt;=&lt;i&gt;ω&lt;/i&gt;&lt;i&gt;&lt;sub&gt;b&lt;/sub&gt;&lt;/i&gt;, the absorption spectrum splits, and the absorption peak decreases from its maximum to its minimum. This phenomenon arises from the disruption of quantum interference effects. The resonance condition suppresses the generation of Fano resonance. At the resonant frequency &lt;i&gt;ω&lt;/i&gt;&lt;i&gt;&lt;sub&gt;0&lt;/sub&gt;&lt;/i&gt;, the group delay is greater than zero, indicating slow-light propagation, and this effect is enhanced with increasing coupling strength. Additionally, a group delay of τ is achieved. Meanwhile, on either side of the resonant frequency, the group delay peaks exhibit a decreasing positive value and an increasing negative value, respectively, signifying a gradual weakening of the slow-light effect and a corresponding enhancement of the fast-light effect. This paper investigates the MIT, MMIT, and OMIT windows in a coupled-cavity optomagnomechanical (OMM) system under a strong control field and weak probe field. The MMIT phenomenon is observed through nonlinear phonon-magnon interactions. Additionally, the photon-magnon interaction in the microwave cavity leads to MIT, while OMIT is achieved via the radiation pressure interaction between photons and nonlinear phonons in the optical cavity. The frequency of the probe field is tuned to interact with both the microwave and optical cavities. When the probe field couples with the microwave cavity, its absorption at the resonant frequency is significantly suppressed under optomechanical coupling, resulting in a pronounced optical switching effect on transmission. We analyze the asymmetric Fano resonance phenomenon, which reflects the existence of quantum interference mechanisms within the system and influences the fast- and slow-light conversion processes. Furthermore, by selecting appropriate coupling parameters, not only can the fast- and slow-light effects be enhanced, but dynamic switching between them can also be achieved.

The electromagnetically induced transparency (EIT) with a (near-)resonant chaotic (amplitude-phase fluctuating, Gaussian-Markovian) coupling field is studied theoretically. The Fourier transform of the steady-state EIT spectrum, which determines a nonstationary probe absorption, is also considered. This quantity equals the average diagonal element of the (reduced) evolution operator of the coupled transition (the evolution function). The exact solution in the form of a continued fraction is obtained and used to perform numerical calculations. Moreover, a number of approximate analytical results are obtained, which, together with the results of previous publications, describe the EIT and the evolution function in all possible regimes. In particular, in the constructive-interference case the EIT increases with the coupling-field bandwidth ν at sufficiently small ν. For a strong field, the maximum of the transparency as a function of ν is less than that for a monochromatic field of the same average intensity. In contrast, for a weak field, there is a range of ν values, where the field fluctuations do not affect the EIT. The latter result is shown to hold for a broad class of stochastic fields.

For the cavity-based electromagnetically induced transparent (EIT), as the coherent driving field is enhanced by the optical cavity, the weak probe field can propagate through the atomic ensemble without absorption even if the driving field is weak. The extreme case of vacuum in the cavity is called "vacuum-induced transparency" (VIT) to distinguish it from the cavity EIT. Here we construct a new kind of cavity made of Metamaterials, i.e. ε-negative (EN) and μ-negative (MN) slabs, and study the VIT phenomena of the atomic ensemble doped within it. When the impedances of the MN and EN slabs are matched to each other and the dissipation of the material is small, it behaves as a surface plasmon cavity with a huge Q factor. And the VIT phenomenon in this cavity appears. By adjusting the position of atoms, the coupling strength between the atom and the structure could be changed. Two kinds of extremes of VIT, the coherent population trapping (CPT) and the Autler-Townes splitting (ATS), can be achieved in this system easily. Our proposal could be used in the realization of ultra-strong coupling and integrated devices on quantum memory or optical switch.

In this work we present a theoretical frame work to identify the role and the nature of interference between Autler-Townes (AT) peaks (or dressed states) in generic multi-level system. The destructive interference between the AT peaks, gives rise to sharp transparency window known as electromagnetically induced transparency (EIT). In the three-level system, the two AT peaks interferes pair-wise with each other, almost similar to the two-slit interference. In the four-level system, the interference between the three AT peaks is also pair-wise analogous to three-slit interference but has a bit more complicated nature of interference. However, in many practical situations in atomic systems only the simple form of interference similar to three-level system dominates. In the three-level system, the nature of interference (i.e. constructive, destructive or zero/no interference) between the two AT peaks is purely determined by the natural decay rate of the states coupled by the control laser. However, in four-level system the nature of interference between the two extreme AT peaks can be tuned from constructive to destructive by tuning the power of the control laser.

The behavior of multilevel atomic ensembles (e.g., alkali-metal atoms) can be influenced significantly by the intensity of a driving field (or controlling/coupling field). The phase coherence between two transition pathways driven by a probe light and a driving field can lead to the effect known as electromagnetically induced transparency (EIT). In EIT, the probe light can pass through a three-level alkali-metal atomic vapor without absorption or reflection when two coherent resonances (transition pathways driven by the driving and probe fields) are present and the linewidths of the transparency windows are sufficiently narrow. The optical characteristics of atomic systems can also be affected by the Doppler broadening of the absorption profile in a spectroscope. Our analysis indicates that both broadenings (related to the transitions excited by the driving and probe fields) can be expanded, leading to an increase in the transmittance and reflectance broadenings when a coupling field with adaptive strength is applied; the corresponding temperature would, thus, be implemented and readable. We show that the most suitable preparation for temperature sensing via an EIT vapor is to provide 80 times the spontaneous decay rate (SDR) of the excited atomic levels. This configuration results in reflectance and transmittance values that range between zero and one and cover a temperature range of 0 K to 600 K. As an example, we demonstrate the integration of specialized coating technologies with EIT ensembles for temperature sensing in the range of dozens of kelvins at and above room temperature. A key advantage of this temperature-sensing system is its ability to use adaptive resonant visible light as the probe field. This novel approach may find applications in providing unprecedented levels of precision and control in temperature sensing for coating processes and in the design of other photonic or optical devices. It can also be used to determine the temperature-dependent behavior of the specific heat of alkali-metal solids and gases (including the latent heats of vaporization or sublimation of alkali-metal solids) through the reflection and transmission spectra of the vaporized EIT atomic vapors.

Optical-optical double resonance (OODR) spectroscopy is a powerful tool for the experimental assignment of highly-excited molecular states, which in turn is needed for verification of the accuracy of theoretical predictions of high-temperature spectra observed in exoplanets and in combustion environments. Previous implementations of OODR used either continuous wave (cw) lasers, which limit the number of transitions that can be detected, or pulsed lasers, which limit the spectral resolution. Recently, we demonstrated OODR with a cw pump and a frequency comb probe and applied it to the detection and assignment of methane transitions in the 3ν 3 ← ν 3 range with sub-Doppler resolution over 200 cm -1 of bandwidth [1] . The pump [see Fig. 1(a) ] was a 1 W 3.3 µm idler of a cw optical parametric oscillator (cw-OPO), stabilized to the Lamb dip in a selected CH 4 transition in the ν 3 band using a signal from a reference cell. The probe was an amplified fully-stabilized Er:fiber comb ( f rep = 250 MHz), whose center wavelength was shifted to 1.67 µm using a soliton self-frequency shift fiber (SSSF). The sample of pure CH 4 was contained in an 80-cm-long single-pass cell cooled by liquid nitrogen. The probe spectra were detected using a Fourier transform spectrometer (FTS) with comb-mode-limited resolution [2] , and the final interleaved spectra had 2 MHz sampling point spacing. Figure 1(b) shows the 3ν 3 ← ν 3 R(1) transition at 6046.36008(5) cm -1 , detected with the pump on the ν 3 R(0) line. We measured, fit and assigned 36 probe transitions with the pump tuned to 9 different transitions. Figure 1(d) shows a comparison of the probe transition wavenumbers to predictions from the TheoReTS database [3] , demonstrating agreement within 1 cm -1 .

Electromagnetically induced transparency (EIT) resonance in a $\ensuremath{\Lambda}$ configuration is obtained when the frequencies of two fields are close to resonance with two of the transitions and their frequency difference matches the frequency of the third transition. In this situation the spectrum of one swept field as a probe gives a simple transparency feature. However, when an additional field drives the third transition the EIT feature associated with the probe is split. This perturbed EIT is illustrated for both single and bichromatic driving fields. In the single-driving-field case a density matrix treatment is shown to be in reasonable agreement with experiment, and in both single and bichromatic cases the structure in the spectrum can be explained using the dressed-state formalism. The dressed states can also be used to account for subharmonic resonances observed in the strong-probe regime.