Perturbing an electromagnetically induced transparency in aΛsystem using a low-frequency driving field. I. Three-level system

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 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.

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.

In this paper, we study the effects of Rabi frequencies and multi-path radiation on the electromagnetically induced transparency (EIT) and the inversionless gain in a ladder- four-level system driven by two-coherent fields- The Rabi frequencies of the field-driven transition from the upper level to middle levels play an important role for the realization of the ultra-narrow EIT and inversionless gain- Different excitation mechanism can change the position of the EIT- The action of the spontaneous alignment of the dipole moment is investigated- The explanation for the numerical results is presented using the theory of dressed state

Role of dressed-state interference in electromagnetically induced transparency

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.

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.

EIT line shape in an open and partially closed multilevel V-type system

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 present a realization of a magnetic sensor based on electromagnetically induced transparency (EIT) resonances observed in hot Rb vapor using lin$\parallel$lin polarized dichromatic light and evaluate scalar and vector capabilities of the sensor for measuring Earth-like magnetic fields. We demonstrate scalar measurement sensitivity of 2 pT/Hz^1/2 in the 1-100~Hz spectral frequency band using a cm^3 Rb vapor cell, significantly improving the performance for such a configuration if compared with earlier measurements of large magnetic fields. By using a single linearly polarized dichromatic optical field, we are also able to determine the direction of the magnetic field with respect to the light propagation direction and polarization, taking advantage of the symmetries of the interaction scheme. We accomplish that by combining the polarization-sensitive transmission measurements and sparse sensing machine learning techniques. A path for further improvement of the sensitivity and elimination of systematic effects, such as heading error, is discussed.

In this chapter, a simple photonic device consisting of two dangling side resonators grafted at two sites (U-shape) or at the same site (cross-shape) along a waveguide is designed in order to obtain sharp resonant states inside the transmission gaps without introducing any defects in the structure. This results from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or placed between two zeros of transmission, the so-called Fano resonances. A general analytic expression for the transmission coefficient is given for various systems of this kind. The amplitude of the transmission is obtained following the Fano form. The full width at half maximum of the resonances and the asymmetric Fano parameter are discussed explicitly as functions of the geometrical parameters of the system. In addition to the usual asymmetric Fano resonance, we show that this system may exhibit an electromagnetic induced transparency (EIT) resonance, as well as a particular case where such resonances collapse in the transmission coefficient, giving rise to the so-called bound in continuum (BIC) states. Also, we give a comparison between the phase of the determinant of the scattering matrix, the so-called Friedel phase, and the phase of the transmission amplitude. By taking into account the loss in the waveguides, we show that at the transmission resonance, the transmission (reflection) increases (decreases) as a function of the detuning δ between the lengths of the two stubs, whereas the absorption goes through a maximum around 0.5 for a threshold value δth, giving rise to electromagnetic induced absorption (EIA) resonance, which depends on the attenuation in the system and then falls to zero. The effect of the boundary conditions at the end of the resonators on the EIA resonance is also discussed. The analytical results are obtained by means of the Green's function method, whereas the experiments are carried out using coaxial cables in the radio-frequency regime. These results should have important consequences for designing integrated devices such as narrow-frequency optical or microwave filters and high-speed switches. This system is proposed as a simpler alternative to coupled microresonators.

We develop a classical model of the recently popular parametric effect of electromagnetically induced transparency (EIT), i.e., the formation of a “transparency window” inside a resonance absorption line of a three-level quantum system, which is accompanied by a record strong slowing of the probe wave. Based on this model, we consider the EIT effect for electromagnetic waves at frequencies of the electron-cyclotron resonance in a cold plasma. The parametric (three-wave) interaction of two electromagnetic modes (the frequency of one of these modes is equal to the electron gyrofrequency) with the electrostatic mode is considered. It is shown that the resonance growth in the electron oscillations at the gyrofrequency can be damped due to the parametric coupling with the collective electrostatic oscillations. Similar to analogous quantum systems, the group slowing of the probe electron-cyclotron wave in the transparency window takes place in the case considered.

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.

We propose a scheme for controlling coherent photon absorption by electromagnetically induced transparency (EIT) in a three-level atom-cavity system. Coherent perfect absorption (CPA) occurs when time-reversed symmetry of lasing process is obtained with the destructive interference at the cavity interfaces. The frequency range of CPA is generally dependent on the decay rates of the cavity mirrors. The smaller decay rate of the cavity mirror causes the wider frequency range of CPA, and the needed intensity of the probe fields is larger to satisfy CPA condition for a given frequency. Although Rabi frequency of the control laser has little effect on the frequency range of CPA, with EIT-type quantum interference, the CPA mode is tunable by the control laser. In addition, with the relative phase, the probe fields can be perfectly transmitted and/or reflected. Therefore, the system can be used as a controllable coherent perfect absorber or transmitter (reflector), and our work may have practical applications in optical logic devices.

We consider an optomechanical cavity made by two moving mirrors which contain a Kerr-down-conversion nonlinear crystal. We show that the coherent oscillations of the two mechanical oscillators can lead to splitting in the electromagnetically induced transparency (EIT) resonance and the appearance of an absorption peak within the transparency window. In this configuration, the coherent-induced splitting of EIT is similar to driving a hyperfine transition in an atomic $\ensuremath{\Lambda}$-type three-level system by a radio-frequency or microwave field. Also, we show that the presence of nonlinearity provides an additional flexibility for adjusting the width of the transparency windows. The combination of an additional mechanical mode and the nonlinear crystal suggests new possibilities for adjusting the resonance frequency, the width and the spectral positions of the EIT windows, as well as the enhancement of the absorption peak within the transparency window.