Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation: (a) Self-induced transparency (SIT) solitons and multi-dimensional localized "bullets" propagating at photonic band gap frequencies. These modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. (b) Cross-coupling between pulses exhibiting electromagnetically induced transparency (EIT) and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.
Using the density matrix theory of interaction between light and matter, and relevant parameters of the relaxation rates for a six-level model, we have shown theoretically the possibility of realizing Electromagnetically Induced Transparency (EIT) and Slow Light effects in Pr(+3 ion) doped YSO crystal. In addition, we have presented a simplified method to analyse EIT effect in such a six level atomic system. Finally, we have demonstrated results of numerical calculation and have compared them with experimental measurements reported recently.
Optomechanically induced transparency in the presence of a strong Duffing nonlinearity
Beijing Computational Science Research Center（北京计算科学研究中心）；Department of Physics, Beijing Normal University（北京师范大学物理学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
For Doppler-broadened media operating under double-double electromagnetically induced transparency (EIT) conditions, we devise a scheme to control and reduce the probe-field group velocity at the center of the second transparency window. We derive numerical and approximate analytical solutions for the width of EIT windows and for the group velocities of the probe field at the two distinct transparency windows, and we show that the group velocities of the probe field can be lowered by judiciously choosing the physical parameters of the system. Our modeling enables us to identify three signal-fi…
In this Letter we discuss the possibility of producing Bragg solitons in an electromagnetically induced transparency medium. We show that this coherent medium can be engineered to be a Bragg grating with a large Kerr nonlinearity through proper arrangements of light fields. Unlike in previous studies, the parameters of the medium can be easily controlled through adjusting the intensities and detunings of lasers. Thus this scheme may provide an opportunity to study the dynamics of Bragg solitons. And doing experiments with low power lights is possible.
We present an experimental proposal to achieve a strong photon blockade by employing electromagnetically induced transparency (EIT) with single alkaline-earth-metal atom trapped in an optical cavity. In the presence of optical Stark shift, both second-order correlation function and cavity transmission exhibit asymmetric structures between the red and blue sidebands of the cavity. For a weak control field, the photon quantum statistics for the coherent transparency window (i.e. atomic quasi-dark state resonance) are insensitive to the Stark shift, which should also be immune to the spontaneous …
A strong photon-photon nonlinear interaction is a necessary condition for photon blockade. Moreover, this nonlinearity can also result a bistable behavior in the cavity field. We analyze the relation between detecting field and photon blockade in a superconducting circuit QED system, and show that photon blockade cannot occur when the detecting field is in the bistable regime. This photon blockade is the microwave-photonics analog of the Coulomb blockade. We further demonstrate that the photon transmission through such system can be controlled (from photon blockade to transparency) by the dete…
We consider the quantum effect of slow light dark soliton (SLDS) in a cold atomic gas with defocuing Kerr nonlinearity via electromagnetically induced transparency (EIT). We calculate the quantum fluctuations of the SLDS by solving the relevant non-Hermitian eigenvalue problem describing the quantum fluctuations, and find that only one zero mode is allowed. This is different from the quantum fluctuations of bright solitons, where two independent zero modes occur. We rigorously prove that the eigenmodes, which consist of continuous modes and the zero mode, are bi-orthogonal and constitute a com…
Specific features of nonlinear interference processes at quantum transitions in near- and fully-resonant optically-dense Doppler-broadened medium are studied. The feasibility of overcoming of the fundamental limitation on a velocity-interval of resonantly coupled molecules imposed by the Doppler effect is shown based on quantum coherence. This increases the efficiency of nonlinear-optical processes in atomic and molecular gases that possess the most narrow and strongest resonances. The possibility of all-optical switching of the medium to opaque or, alternatively, to absolutely transparent, or…
Developments in photonic chips have spurred photon based classical and quantum information processing, attributing to the high stability and scalability of integrated photonic devices [1, 2]. Optical nonlinearity [3] is indispensable in these complex photonic circuits, because it allows for classical and quantum light sources, all-optical switch, modulation, and non-reciprocity in ambient environments. It is commonly known that nonlinear interactions are often greatly enhanced in the microcavities [4]. However, the manifestations of coherent photon-photon interaction in a cavity, analogous to …
We report the experimental observation of strong two-color optical nonlinearity in an ultracold gas of $^{85}\mathrm{Rb}$-$^{87}\mathrm{Rb}$ atom mixture. By simultaneously coupling two probe transitions of $^{85}$Rb and $^{87}$Rb atoms to Rydberg states in electromagnetically induced transparency (EIT) configurations, we observe significant suppression of the transparency resonance for one probe field when the second probe field is detuned at $\sim1~\mathrm{GHz}$ and hitting the EIT resonance of the other isotope. Such a cross-absorption modulation to the beam propagation dynamics can be desc…
We study optical bistable behavior of a Rydberg electromagnetically-induced transparency (EIT) atomic medium in a unidirectional optical ring-cavity. Due to strong van del Waal (vdW) interactions between the atoms, both optical nonlinear dispersion and nonlinear absorption coefficients are enhanced substantially. Under the condition of two-photon on resonance, we show that probe one-photon detuning can change the phase of the third order nonlinearity coefficient, which tunes the character of the optical bistability within different ratios of dispersive and absorptive types. This enables the si…
We theoretically investigate the optomechanically induced transparency (OMIT) phenomenon in a N-cavity optomechanical system doped with a pair of Rydberg atoms with the presence of a strong pump field and a weak probe field applied to the Nth cavity. 2N-1(N<10) number OMIT windows can be observed in the output field when N cavities coupled with N mechanical oscillators, respectively. But, the mechanical oscillators coupled with different even-odd label cavities lead to different effect on OMIT. On the other hand, two additional transparent windows (extra resonances) are presented, if two Rydbe…
We report the experimental observation of a cross-Kerr nonlinearity in a free-space medium based on resonantly-excited, interacting Rydberg atoms and electromagnetically induced transparency. The nonlinearity is used to implement cross-phase modulation between two optical pulses. The nonlinear phase written onto the probe pulse is measured to be as large as $8$ mrad per nW of signal power, corresponding to a $χ^{(3)}$ of $10^{-8}\textrm{m}^2/\textrm{V}^2$. Potential applications range from optical quantum information processing to quantum non-demolition measurement of photon number.
We provide a broad outline of the requirements that should be met by components produced for a Quantum Information Technology (QIT) industry, and we identify electromagnetically induced transparency (EIT) as potentially key enabling science toward the goal of providing widely available few-qubit quantum information processing within the next decade. As a concrete example, we build on earlier work and discuss the implementation of a two-photon controlled phase gate and a one-photon phase gate using the approximate Kerr nonlinearity provided by EIT. We rigorously the dependence of the performanc…
We discuss the optical heterodyne detection technique to study the absorption and dispersion of a probe beam propagating through a medium with a narrow resonance. The technique has been demonstrated for Rydberg Electro-magnetically induced transparency (EIT) in rubidium thermal vapor and the optical non-linearity of a probe beam with variable intensity has been studied. A quantitative comparison of the experimental result with a suitable theoretical model is presented. The limitations and the working regime of the technique are discussed.
We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirec…
Kerr-induced nonreciprocal transparency and group delay in a hybrid cavity magnomechanical system
Ibnou Zohr University（伊本·佐赫尔大学）；Princess Nourah bint Abdulrahman University（公主努拉·宾特·阿卜杜勒拉赫曼大学）；Umm Al-Qura University（乌姆古拉大学）；Mohammed V University in Rabat（拉巴特穆罕默德五世大学）；University of Bisha（比沙大学）
The advantage of optical bistability (OB) using three-level electromagnetically induced transparency (EIT) atomic system over the two-level system is its controllability, as absorption, dispersion, and optical nonlinearity in one of the atomic transitions can be modified considerably by the field interacting with nearby atomic transitions. This is due to induced atomic coherences generated in such EIT system. The inclusion of near dipole-dipole (NDD) interaction among atoms further modifies absorption, dispersion, and optical nonlinearity of three-level EIT system and the OB can also be contro…
We present measurements of electromagnetically induced transparency with an ensemble of donor- bound electrons in low-doped n-GaAs. We used optical transitions from the Zeeman-split electron spin states to a bound trion state in samples with optical densities of 0.3 and 1.0. The electron spin dephasing time T* \approx 2 ns was limited by hyperfine coupling to fluctuating nuclear spins. We also observe signatures of dynamical nuclear polarization, but find these effects to be much weaker than in experiments that use electron spin resonance and related experiments with quantum dots.
We propose a novel configuration that utilizes electromagnetically induced transparency (EIT) to tailor a fiber mode propagating inside a thin optical fiber and coherently control its dispersion properties to drastically reduce the group velocity of the fiber mode. The key to this proposal is: the evanescent-like field of the thin fiber strongly couples with the surrounding active medium, so that the EIT condition is met by the medium. We show how the properties of the fiber mode is modified due to the EIT medium, both numerically and analytically. We demonstrate that the group velocity of the…
We introduce two models of quasi-discrete optical systems: an array of waveguides doped by four-level N-type atoms, and a nonlinear checkerboard pattern, formed by doping with three-level atoms of the Λ-type. The dopant atoms are driven by external fields, to induce the effect of the electromagnetically-induced transparency (EIT). These active systems offer advantages and addition degrees of freedom, in comparison with ordinary passive waveguiding systems. In the array of active waveguides, the driving field may adjust linear and nonlinear propagation regimes for a probe signal. The nonlinear …
By mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons via electromagnetically induced transparency, it is now possible to realize a nonlinear optical medium which exhibits a strong optical nonlinearity at the level of individual photons. We review the theoretical concepts and the experimental state-of-the-art of this exciting new field, and discuss first applications in the field of all-optical quantum information processing.
Erbium doped solids are potential candidates for the realization of a quantum memory for photons at telecommunication wavelengths. The implementation of quantum memory proposals in rare earth ion doped solids require spectral tailoring of the inhomogeneous absorption profile by efficient population transfer between ground state levels (spin polarization) using optical pumping. In this article we investigate the limiting factors of efficient optical pumping between ground state Zeeman levels in an erbium doped Y2SiO5 crystal. We introduce two methods to overcome these limiting factors: stimulat…
We study dispersive optical nonlinearities of short pulses propagating in high number density, warm atomic vapors where the laser resonantly excites atoms to Rydberg $P$-states via a single-photon transition. Three different regimes of the light-atom interaction, dominated by either Doppler broadening, Rydberg atom interactions, or decay due to thermal collisions between groundstate and Rydberg atoms, are described. We show that using fast Rabi flopping and strong Rydberg atom interactions, both in the order of gigahertz, can overcome the Doppler effect as well as collisional decay, leading to…
We analyze the nonlinear optical response of a six-level atomic system under a configuration of electromagnetically induced transparency. The giant fifth-order nonlinearity generated in such a system with a relatively large cross-phase modulation effect can produce efficient three-way entanglement and may be used for realizing a three-qubit quantum phase gate. We demonstrate that such phase gate can be transferred to a Toffoli gate, facilitating practical applications in quantum information and computation.
Fiber guided optical signal propagating in a Erbium doped nonlinear resonant medium is known to produce cleaner solitonic pulse, described by the self induced transparency (SIT) coupled to nonlinear Schroedinger equation. We discover two new possibilities hidden in its integrable structure, for amplification and control of the optical pulse. Using the variable soliton width permitted by the integrability of this model, the broadening pulse can be regulated by adjusting the initial population inversion of the opant atoms. The effect can be enhanced by another innovative application of its const…
Quantum coherent control of slow light for all-optical switching is investigated in a multi-level system of solids for an understanding of self-induced ultraslow light. In an optical population shelving system of a rare-earth doped solid, dynamics of the slow light are presented by using a third optical field controlling shelved atom population. Unlike two-photon coherence-based delayed all-optical switching utilizing electromagnetically induced transparency, the present method relies on one-photon coherence controlling shelved atom population.
We analyze the nonlinear optical response of a five-level system under a novel configuration of electro-magnetically induced transparency. We show that a giant Kerr nonlinearity with a relatively large cross-phase modulation coefficient that occurs in such system may be used to produce an efficient photon-photon entanglement. We demonstrate that such photon-photon entanglement is practically controllable and hence facilitates promising applications in quantum information and computation.
Electromagnetically induced transparency (EIT) and EIT-like effects have been investigated in a wide variety of coupled resonant systems. Here, a classification of the phase characteristics of the EIT-like spectral responses is presented. Newly identified phase responses reveal unexplored operation regimes of EIT-like systems. Taking advantage of the new phase regimes, one can obtain group delay, dispersion and nonlinearity properties greatly enhanced by almost one order of magnitude, compared to the traditionally constructed EIT-like devices, which breaks the fundamental limitation (e.g., del…
We predict a resonant enhancement of the nonlinear optical response of an interacting Rydberg gas under conditions of electromagnetically induced transparency. The enhancement originates from a two-photon process which resonantly couples electronic states of a pair of atoms dressed by a strong control field. We calculate the optical response for the three-level system by explicitly including the dynamics of the intermediate state. We find an analytical expression for the third order susceptibility for a weak classical probe field. The nonlinear absorption displays the strongest resonant behavi…
Quantum light-matter interfaces (QLMIs) connecting stationary qubits to photons will enable optical networks for quantum communications, precise global time keeping, photon switching, and studies of fundamental physics. Rare-earth-ion (REI) doped crystals are state-of-the-art materials for optical quantum memories and quantum transducers between optical photons, microwave photons and spin waves. Here we demonstrate coupling of an ensemble of neodymium REIs to photonic nano-cavities fabricated in the yttrium orthosilicate host crystal. Cavity quantum electrodynamics effects including Purcell en…
When Th nuclei are doped in CaF$_2$ crystals, a set of electronic defect states appears in the crystal bandgap which would otherwise provide complete transparency to vacuum-ultraviolet radiation. The coupling of these defect states to the 8 eV $^{229m}$Th nuclear isomer in the CaF$_2$ crystal is investigated theoretically. We show that although previously viewed as a nuisance, the defect states provide a starting point for nuclear excitation via electronic bridge mechanisms involving stimulated emission or absorption using an optical laser. The rates of these processes are at least two orders …
We propose a new method to produce self- and cross-Kerr photonic nonlinearities, using light-induced Stark shifts due to the interaction of a cavity mode with atoms. The proposed experimental set-up is considerably simpler than in previous approaches, while the strength of the nonlinearity obtained with a single atom is the same as in the setting based on electromagnetically induced transparency. Furthermore our scheme can be applied to engineer effective photonic nonlinear interactions whose strength increases with the number of atoms coupled to the cavity mode, leading to photon-photon inter…
Controlling the interaction between localized optical and mechanical excitations has recently become possible following advances in micro- and nano-fabrication techniques. To date, most experimental studies of optomechanics have focused on measurement and control of the mechanical subsystem through its interaction with optics, and have led to the experimental demonstration of dynamical back-action cooling and optical rigidity of the mechanical system. Conversely, the optical response of these systems is also modified in the presence of mechanical interactions, leading to strong nonlinear effec…
Electromagnetically-induced transparency (EIT) has been proposed as a way to greatly enhance cross-phase modulation, with the possibility of leading to few-photon-level optical nonlinearities. This enhancement grows as the transparency window width, Δ_EIT, is narrowed. Decreasing Δ_EIT, however, increases the response time of the effect, suggesting that for pulses of a given duration, there could be a fundamental limit to the strength of the nonlinearity. We show that in the regimes of most practical interest - narrow EIT windows perturbed by short signal pulses- the enhancement offered by EIT…
We theoretically study high-order optomechanically-induced transparency (OMIT) process in a nonlinear Kerr resonator. A frequency shift induced by the Kerr effect, is identified for the optical cavity mode, which results in asymmetric OMIT windows of the signal and its higher-order sidebands. We also find that both the sideband amplitude and its associated group delay sensitively depend on the strength of the Kerr nonlinearity. This indicates the possibility to enhance or steer the performance of OMIT devices with various nonlinear optical cavities.
We show that an ensemble of organic dye molecules with permanent electric dipole moments embedded in a microcavity can lead to strong optical nonlinearities at the single photon level. The strong long-range electrostatic interaction between chromophores due to their permanent dipoles introduces the desired nonlinearity of the light-matter coupling in the microcavity. We obtain the absorption spectra of a weak probe field under the influence of strong exciton-photon coupling with the cavity field. Using realistic parameters, we demonstrate that a single cavity photon can significantly modify th…
We develop a theoretical description of Coulomb interactions between trions (charged excitons) that define a nonlinear optical response in doped two-dimensional semiconductors. First, we formulate a microscopic theory of trion-trion interactions based on composite nature of these particles, and account for all possible exchange processes. Next, we calculate numerically the trion binding energies and corresponding three-body wavefunctions using a basis set with high expressivity. Then, using the obtained wavefunctions we calculate the matrix elements of two-trion scattering, and compare the con…
The extraordinary properties of resonant four-wave mixing of backward waves in doped negative-index materials are investigated. The feasibility of independent engineering of negative refractive index and nonlinear optical response as well as quantum control of the nonlinear propagation process in such composites is shown due to the coherent energy transfer from the control to the signal field. Laser-induced transparency, quantum switching, frequency-tunable narrow-band filtering, amplification, and realizing a miniature mirrorless optical parametric generator of the entangled backward and ordi…
