Electromagnetically induced transparency in a five-levelΛsystem dominated by two-photon resonant transitions

We investigate the steady optical response of a coherently driven five-level M-type atomic system in three different situations. When all three coupling fields have the same zero detuning, we just find one deep transparency window accompanied by a steep normal dispersion in the probe absorption and dispersion spectra. When two coupling fields are detuned from the relevant transitions to the same extent, however, a second deep transparency window may be observed in the presence of a narrow absorption line of linewidth ∼ 50 kHz. In this case, two single-photon far-detuned transitions can be replaced by a two-photon resonant transition, so the five-level M system in fact reduces into a four-level quasi-Λ system. Finally, we note that no deep transparency windows and no narrow absorption lines can be found when all three coupling fields have unequal detunings.

The difference in the static electric dipole polarizabilities of the and Rydberg levels in helium has been eliminated by dressing the atom with a microwave field near resonant with the single-photon transition. For an amplitude dressing field, detuned by from the zero-field transition frequency, the dc Stark shift of the two-photon transition between these states remained within for electric fields up to . This transition was probed by single-color two-photon microwave spectroscopy, and by two-color two-photon spectroscopy with one strong additional dressing field and a weak probe field. For all measurements, the transition frequencies and Stark shifts were compared, and found to be in excellent quantitative agreement with the results of Floquet calculations of the energy-level structure of the Rydberg states in the presence of the dressing fields and applied dc electric fields. The two-color microwave dressing scheme demonstrated, with one field applied to null the differential polarizability of the Rydberg–Rydberg transition, and the second exploited to allow the two-photon transition to be employed to achieve tunable absorption of single-photons from a weak probe field, will facilitate improved coherence times and tunable single-photon absorption in hybrid cavity QED experiments with Rydberg atoms and superconducting microwave circuits.

Following our previous brief report [Phys. Rev. Lett. 88, 173003 (2002)], we report here a detailed study of electromagnetically induced transparency (EIT) and dark fluorescence in a cascade three-level diatomic lithium system using optical-optical double resonance (OODR) spectroscopy for both resonance and off resonance coupling. When a strong coupling laser couples the intermediate state $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(v=13,J=14)$ to the upper state $G\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}_{g}(v=11,J=14)$ of $^{7}\mathrm{Li}_{2}$, the fluorescence from both $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ and $G\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}_{g}$ states was drastically reduced as the weak probe laser was tuned through the resonance transition between the ground state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}(v=4,J=15)$ and the excited state $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(v=13,J=14)$. The strong coupling laser makes an optically thick medium transparent for the probe transition. In addition, the fact that fluorescence from the upper state $G\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}_{g}(v=11,J=14)$ was also dark when both lasers were tuned at resonance implies that the molecules were trapped in the ground state. We used density matrix methods to simulate the response of an open molecular three-level system to the action of a strong coupling field and a weak probe field. The analytical solutions were obtained under the steady-state condition. We have incorporated the magnetic sublevel $(M)$ degeneracy of the rotational levels in the line shape analysis and report $\ensuremath{\mid}M\ensuremath{\mid}$ dependent line shape splitting. Our theoretical calculations are in excellent agreement with the observed fluorescence spectra. We show that the coherence is remarkably preserved even when the coupling field was detuned far from the resonance.

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.

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.

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 <i>O</i><sub>+</sub> . 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 <i>δ</i>=<i>ω</i><i><sub>b</sub></i>, 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 <i>ω</i><i><sub>0</sub></i>, 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.

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.

Role of dressed-state interference in electromagnetically induced 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.

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.

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.

Light shift is important and inevitably affects the long-term stability of an atomic clock. In this work, considering two unbalanced branches of the spontaneous decay rate in a three-level system, we studied the frequency shifts of electromagnetically induced transparency (EIT) and coherent population trapping (CPT) clocks operating under the pulse sequence regime by numerically solving the Liouville density matrix equations. The results show that the frequency shifts are larger when the two branches of spontaneous emission rate are not equal compared to the equal case. In addition, in EIT-Ramsey, the effect of the unbalanced branches of the spontaneous decay rate and relaxations of low-energy states on the frequency shift is greater than that of Rabi frequency. In CPT-Ramsey, the relaxations of low-energy states play a dominant role in frequency shift.

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.

We report an experimental observation of Autler-Townes doublet splitting in electromagnetically induced transparency (EIT) resonance. The splitting is introduced by a coherent microwave field, which perturbs a three-level A-type EIT system through an auxiliary level. The doublet splitting of EIT resonance is demonstrated in two cases, where the microwave field shares a common lower level with coupled or probe transition, respectively. The dependence of doublet splitting on microwave field intensity and detuning is measured. This may provide a feasible way of manipulating the atomic states with both laser and microwave field.

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.