Multiple Color Electromagnetically Induced Switching Using a Five-Level Atomic Medium

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.

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.

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.

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.

We propose a scheme to construct a two-dimensional Aubry-Andr\'e (AA) model and realize two-dimensional AA localization of light waves via electromagnetically induced transparency (EIT). The system we suggest is a cold, resonant atomic gas with an $N$-type level configuration and interacting with probe, control, assisted, and far-detuned laser fields. We show that under EIT conditions the probe-field envelope obeys a modified nonlinear Schr\"odinger equation with a quasiperiodic potential, which becomes a two-dimensional nonlinear AA model when the system parameters are suitably chosen. The quasiperiodic potential is obtained by the cross-phase modulation of the assisted field and the Stark shift of the far-detuned laser field. In addition, the cubic nonlinearity term appearing in the model is contributed by the self-phase modulation of the probe field. We demonstrate that the system can be used to not only realize various two-dimensional AA localizations of light waves, but also to display nonlinearity and dimensionality effects on the AA localizations.

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.

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.

I will review recent progresses on the realization and application of electromagnetically induced transparency in semiconductors. The emphasis will be on the use of electron spin coherence in quantum well structures. Electromagnetically induced transparency (EIT) exploits destructive quantum interference induced by a nonradiative quantum coherence to make an otherwise opaque medium transparent. EIT and EIT-related processes provide a powerful and effective mechanism for controlling and manipulating light. While most EIT studies have thus far been carried out in atomic or atomic-like systems, the basic concept of EIT can also be applied to optical excitations in semiconductors. In this talk, I will discuss recent progresses on EIT studies in semiconductors. There are two major obstacles for realizing EIT and, more generally, for coherent manipulation of quantum coherences in semiconductors. First of all, with the exception of electron spin coherence, quantum coherences in semiconductors are typically short lived and are extremely fragile against dynamic processes such as carrier-carrier and carrier-phonon scattering. Secondly, coherent nonlinear optical processes in semiconductors are profoundly modified by manybody Coulomb interactions between carriers. I will discuss various EIT schemes that have been used to take advantage of the robust electron spin coherence in semiconductors and to harness effects of inherent manybody Coulomb interactions.

We investigate linear and nonlinear Faraday effects in a room-temperature, coherently driven four-level active-Raman-gain (ARG) medium. By using the multiple-scale method, we derive two nonlinear coupled envelope equations governing the dynamics of left- and right-polarized components of a linearly polarized probe field. Under the weak probe field approximation, we demonstrate a factor of four increase of the Faraday rotation angle by the linear and nonlinear response of the ARG scheme without probe field loss. We further compare this ARG system with an $M$-type five-state electromagnetically induced transparency (EIT) scheme and demonstrate the superiority of the ARG scheme over the conventional EIT scheme.

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.

Based on electromagnetically induced transparency (EIT), we investigate an all-optical grating structure to realize polarization-dependent multiple beam splitting in the Raman-Nath limit. To optimize the grating performance, higher excited state [e.g., nS1/2 (n ≥ 6)] of ultracold 87Rb atoms is employed to construct a five-level Ξ-Λ system sharing one common populated ground state. A principal advantage of our proposed scheme is that the σ± components of a linearly polarized weak probe field can be decoupled and thus be independently diffracted with high efficiency in both one and two dimensions by exploiting different quasi-standing waves as the two strong coupling fields in the Ξ and Λ configurations. Such an all-optical polarization-sensitive operation could greatly enhance the tunability and capacity of all-optical multiplexing, interconnecting, and networking in free space for both classical and quantum applications.

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.

Since discrete multilevel transitions of quantum-dot molecules driven by external electromagnetic fields can exhibit quantum coherence effects, such an optical characteristic can be utilized to control propagation of electromagnetic wave through a quantum-dot molecule dielectric film. Since inner-dot tunneling in quantum-dot molecules can be controlled by a gate voltage, destructive quantum coherence among multilevel transitions in quantum-dot molecule would give rise to EIT (electromagnetically induced transparency). In this report, we shall investigate controllable on- and off-resonance tunneling effects of an incident electromagnetic wave through such a quan-tum-dot-molecule dielectric film, of which the optical response is tuned by the switchable gate voltage. We have found from the theoretical mechanism that a high gate voltage can cause the EIT phenomenon of quan-tum-dot-molecule systems, and under the condition of on-resonance light tunneling through the thin film, the probe field will propagation without loss if the probe frequency detuning is zero. By taking advantage of these effects sensitive to the tunable gate voltage, such quantum coherence would be inte-grated in certain photonic structures, and some devices such as photonic switching and transistors can be designed. Transient evolution of optical characteristics in the quantum-dot-molecule dielectric film (once the tunable gate voltage is turned on or off) is also considered in this report.

We present the results of a theoretical study of the output amplitude noises of a four-level atomic system in vee + ladder configuration. The difference and connection of electromagnetically induced transparency and Autler–Townes splitting effects are investigated theoretically. The output amplitude noise of the probe field of two effects were compared, the quantum properties of the input field of the thin medium and the thick medium under Autler–Townes splitting or electromagnetically induced transparency (EIT) condition are maintained, the higher fidelity is obtained in the storage of the thick medium under the condition of EIT in non-classical states. The noise characteristics of the squeezed vacuum field after four-level coherent medium are studied; the noise of the output field is lowest when the detection light is far away from detuning. The double split of EIT window was made by the dynamic Stark splitting on the ground state of control field, the quantum properties of the input field in the strong-control field and strong-coupling field were maintained. The output noise spectrum is divided with the increase in the field strength, the maximum output squeezing is far away from the resonance.

The propagation of a probe field through a four-level Y-type atomic system is described in the presence of two additional coherent radiation fields, namely, the control field and the coupling field. An expression for the probe response is derived analytically from the optical Bloch equations under steady state condition to study the absorptive properties of the system under probe field propagation through an ensemble of stationary atoms as well as in a Doppler broadened atomic vapor medium. The most striking result is the conversion of electromagnetically induced transparency (EIT) into electromagnetically induced absorption (EIA) as we start switching from weak probe regime to strong probe regime. The dependence of this conversion on residual Doppler averaging due to wavelength mismatch is also shown by choosing the coupling transition as a Rydberg transition.