This paper presents a wide-ranging theoretical and experimental study of non-adiabatic transient phenomena in a $Λ$ EIT system when a strong coupling field is rapidly switched on or off. The theoretical treatment uses a Laplace transform approach to solve the time-dependent density matrix equation. The experiments are carried out in a Rb$^{87}$ MOT. The results show transient probe gain in parameter regions not previously studied, and provide insight into the transition dynamics between bare and dressed states.
We present an efficient and convenient scheme to entangle multiple optical fields via electromagnetically induced transparency in an atomic ensemble. The atomic spin wave, produced through electromagnetically induced transparency in the Lambda-type configuration in an atomic ensemble, can be described by a Bose operator and acts as the entangler. By using the entangler, any desired number of nondegenerate narrow-band continuous-variable entangled fields, in principle, can be generated through stimulated Raman scattering processes, which holds great promise for applications in scalable quantum …
In this work we reproduce the phenomenology of the electromagnetically induced transparency and dynamic Stark effect in a dissipative system composed by two coupled bosonic fields under linear and nonlinear amplification process. Such a system can be used as a quantum switch in networks of oscillators.
The electromagnetically induced transparency (EIT) phenomenon in a four level atomic system with tripod configuration is studied. The results show that this configuration is equivalent to the combination of two single three-level $Λ$ configurations, which, under certain conditions, results in the so-called double-EIT (DEIT) phenomenon. The properties of the double transparency windows for DEIT are discussed in detail and the possible experimental scheme is proposed.
We describe how electromagnetically induced transparency may be used to construct a non-traditional near-ideal quantum heat engine as constrained by the Second Law. The engine is pumped by a thermal reservoir that may be either hotter or colder than that of an exhaust reservoir, and also by a monochromatic laser. As output, it produces a bright narrow emission at line center of an otherwise absorbing transition.
We theoretically investigate the phenomenon of voltage-controlled intracavity electromagnetically induced transparency with asymmetric double quantum dot system. The impact of voltage on frequency pulling and cavity linewidth narrowing are discussed. The linewidth and position of the cavity transmission can be engineered by the bias voltage. The scheme may be useful in integrated electro-optical device in quantum information process.
We consider the dynamics of intracavity electromagnetically induced transparency (EIT) in an ensemble of strongly interacting Rydberg atoms. By combining the advantage of variable cavity lifetimes with intracavity EIT and strongly interacting Rydberg dark-state polaritons, we show that such intracavity EIT system could exhibit very strong photon blockade effect.
Electromagnetically-induced transparency has become an important tool to control the optical properties of dense media. However, in a broad class of systems, the interplay between inhomogeneous broadening and the existence of several excited levels may lead to a vanishing transparency. Here, by identifying the underlying physical mechanisms resulting in this effect, we show that transparency can be strongly enhanced. We thereby demonstrate a 5-fold enhancement in a room-temperature vapor of alkali-metal atoms via a specific shaping of the atomic velocity distribution.
The rigorous dark-sate conditions, i.e., two-photon resonance, for a Lambda-type electromagnetically induced transparency (EIT) are extended with the system controlled by a microwave field. The extended dark-states are found to be extremely sensitive to the phase of the microwave field in a narrow interval. However, the dark-state is no longer the requirement for EIT in this scheme and EIT without dark states is present.
A cooling scheme for trapped atoms is proposed, which combines cavity-enhanced scattering and electromagnetically induced transparency. The cooling dynamics exploits a three-photon resonance, which combines laser and cavity excitations. It is shown that relatively fast ground-state cooling can be achieved in the Lamb-Dicke regime and for large cooperativity. Efficient ground-state cooling is found for parameters of ongoing experiments.
We experimentally and theoretically analyze the transmission of continuous-wave and pulsed squeezed vacuum through rubidium vapor under the conditions of electromagnetically induced transparency. Frequency- and time-domain homodyne tomography is used to measure the quadrature noise and reconstruct the quantum states of the transmitted light. A simple theoretical model explains the spectrum and degradation of the transmitted squeezing with high precision.
We report an absorption spectroscopy experiment and the observation of electromagnetically induced transparency from a single trapped atom. We focus a weak and narrowband Gaussian light beam onto an optically cooled Barium ion using a high numerical aperture lens. Extinction of this beam is observed with measured values of up to 1.3 %. We demonstrate electromagnetically induced transparency of the ion by tuning a strong control beam over a two-photon resonance in a three-level lambda-type system. The probe beam extinction is inhibited by more than 75 % due to population trapping.
We present a classical analog for Electromagnetically Induced Transparency (EIT). In a system of just two coupled harmonic oscillators subject to a harmonic driving force we can reproduce the phenomenology observed in EIT. We describe a simple experiment performed with two linearly coupled RLC circuits which can be taught in an undergraduate laboratory class.
We demonstrate electromagnetically induced transparency (EIT) in a sample of rubidium atoms, trapped in an optical dipole trap. Mixing a small amount of $σ^-$-polarized light to the weak $σ^+$-polarized probe pulses, we are able to measure the absorptive and dispersive properties of the atomic medium at the same time. Features as small as 4 kHz have been detected on an absorption line with 20 MHz line width.
We theoretically study a parallel optical configuration which includes N periodically coupled whispering-gallery-mode resonators. The model shows an obvious effect which has a direct analogy with the phenomenon of multiple electromagnetically induced transparency in quantum systems. The numerical simulations illuminate that the frequency transparency windows are sharp and highly transparent. We also briefly discuss the experimental feasibility of the current scheme in two practical systems, microrings and microdisks.
We study the effect of inter-band interactions in the absorption profile of a semi-classical model describing electromagnetically induced transparency. We develop a consistent approach using a non-hermitian Hamiltonian to model particle decay. This allow us to characterize the system response for different number of particles so that the effect of particle-interaction on the transmission profile can be studied over a wide range of characteristic parameters.
We analyze the influence of dipole-dipole interactions in an electromagnetically induced transparency setup at high density. We show both analytically and numerically that the polarization contribution to the local field strongly modulates the phase of a weak pulse. We give an intuitive explanation for this local field induced phase modulation and show that it distinctively differs from the nonlinear self-phase modulation a strong pulse experiences in a Kerr medium.
The electromagnetically induced transparency (EIT) in an $N$ configuration is studied under both resonant and off-resonant conditions. In a certain off-resonant condition the dark state of the four level system, which is almost the same as the resonant dark state in $Λ$ configuration, is rebuilt. The actual system with damping is examined using optical Bloch equation, both numerically and analytically. Based on this detuned dark state, some new applications with frequency shifts can be realized.
The long-lived singlet states are useful to study a variety of interesting quantum phenomena. In this work we study electromagnetically induced transparency using a two-qubit system. The singlet state acts as a `dark state' which does not absorb a probe radiation in the presence of a control radiation. Further we demonstrate that the simultaneous irradiation of probe and control radiations acts as a dynamical decoupling preserving the singlet state at higher correlation for longer durations.
We propose a feasible scheme of quantum state storage and manipulation via electromagnetically induced transparency (EIT) in flexibly $united$ multi-ensembles of three-level atoms. For different atomic array configurations, one can properly steer the signal and the control lights to generate different forms of atomic entanglement within the framework of linear optics. These results shed new light on designing the versatile quantum memory devices by using, e.g., an atomic grid.
Propagation of two dimensional pulses in electromagnetically induced tranparency media in the case of perpendicular storing and retrieving pulses has been analyzed. It has been shown that propagation control of the pulses in optically thick media can be used for producing interchange between pulse time-shape and intensity profile distribution. A simple obvious analytical solution for the retrieved new field has been obtained.
A probe light in a squeezed vacuum state was injected into cold 87 $Rb atoms with an intense control light in a coherent state. A sub-MHz window was created due to electromagnetically induced transparency, and the incident squeezed vacuum could pass through the cold atoms without optical loss, as was successfully monitored using a time-domain homodyne method.
Autler-Townes splitting (ATS) and electromagnetically-induced transparency (EIT) both yield transparency in an absorption profile, but only EIT yields strong transparency for a weak pump field due to Fano interference. Empirically discriminating EIT from ATS is important but so far has been subjective. We introduce an objective method, based on Akaike's information criterion, to test ATS vs. EIT from experimental data and determine which pertains. We apply our method to a recently reported induced-transparency experiment in superconducting circuit quantum electrodynamics.
Electromagnetically-induced transparency and light storing are studied in the case of a medium of atoms in a double Lambda configuration, both in terms of dark- and bright-state polatitons and atomic susceptibility. It is proven that the medium can be made transparent simultaneously for two pulses following their self-adjusting so that a condition for an adiabatic evolution has become fulfilled. Analytic formulas are given for the shapes and phases of the transmitted/stored pulses. The level of transparency can be regulated by adjusting the heights and phases of the control fields.
We report on the all-optical detection of Rydberg states in a effusive atomic beam of strontium atoms using electromagnetically induced transparency (EIT). Using narrow-linewidth CW lasers we obtain an EIT linewidth of 5 MHz. To illustrate the high spectroscopic resolution offered by this method, we have measured isotope shifts of the 5s18d ^1D_2 and 5s19s ^1S_0 Rydberg states. This technique could be applied to high-resolution, non-destructive measurements of ultra-cold Rydberg gases and plasmas.
Ground state laser cooling of a single trapped ion is achieved using a technique which tailors the absorption profile for the cooling laser by exploiting electromagnetically induced transparency in the Zeeman structure of a dipole transition. This new method is robust, easy to implement and proves particularly useful for cooling several motional degrees of freedom simultaneously, which is of great practical importance for the implementation of quantum logic schemes with trapped ions.
We have succeeded in observing ultraslow propagation of squeezed vacuum pulses with electromagnetically induced transparency. Squeezed vacuum pulses (probe lights) were incident on a laser cooled 87Rb gas together with an intense coherent light (control light). A homodyne method sensitive to the vacuum state was employed for detecting the probe pulse passing through the gas. A delay of 3.1us was observed for the probe pulse having a temporal width of 10 us.
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.
We report electromagnetically induced transparency using quantized fields in optomechanical systems. The weak probe field is a narrow band squeezed field. We present a homodyne detection of EIT in the output quantum field. We find that the EIT dip exists even though the photon number in the squeezed vacuum is at the single photon level. The EIT with quantized fields can be seen even at temperatures of the order of 100 mK paving the way for using optomechanical systems as memory elements.
We investigate a hybrid optomechanical system comprised of a mechanical oscillator and an atomic 3-level ensemble within an optical cavity. We show that a suitably tailored cavity field response via Electromagnetically Induced Transparency (EIT) in the atomic medium allows for strong coupling of the mechanical mirror oscillations to the collective atomic ground-state spin. This facilitates ground-state cooling of the mirror motion, quantum state mapping and robust atom-mirror entanglement even for cavity widths larger than the mechanical oscillator frequency.
Electromagnetically induced transparency (EIT) is observed in gaseous 4He at room temperature. Ultra-narrow (less than 10 kHz) EIT windows are obtained for the first time for purely electronic spins in the presence of Doppler broadening. The positive role of collisions is emphasized through measurements of the power dependence of the EIT resonance. Measurement of slow light opens up possible ways to applications.
By solving the self-consistent system of Maxwell and density matrix equations to the first order with respect to nonadiabaticity, we obtain an analytical solution for the probe pulse propagation. The conditions for efficient storage of light are analyzed. The necessary conditions for optical propagation distance has been obtained.
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 report experimental investigationd of optical pulse group velocity reduction and probe pulse regeneration using a Raman scheme. The new scheme which does not rely on the on-one-photon resonance electromagnetically induced transparency (EIT), has many advantages over the conventional method which critically relys on the transparency window created by an EIT process. We demonstrate significant reduction of group velocity, less probe field loss, reduced probe pulse distortion, and high probe pulse regeneration efficiency.
We have measured the photon statistics of pump and probe beams after interaction with Rb atoms in a situation of Electromagnetically Induced Transparency. Both fields present super-poissonian statistics and their intensities become correlated, in good qualitative agreement with theoretical predictions in which both fields are treated quantum-mechanically. The intensity correlations measured are a first step towards the observation of entanglement between the fields.
We identify form-stable coupled excitations of light and matter (``dark-state polaritons'') associated with the propagation of quantum fields in Electromagnetically Induced Transparency. The properties of the dark-state polaritons such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and ``trapped'' in which case their shape and quantum state are mapped onto metastable collective states of matter. Possible applications of this r…
We obtain a partial differential equation for a pulse travelling inside a Bose-Einstein condensate under conditions of electromagnetically induced transparency. The equation is valid for a weak probe pulse. We solve the equation for the case of a three-level BEC in $Λ$ configuration with one of its ground state spatial profiles initially constant. The solution characterizes, in detail, the effect that the evolution of the condensate wave function has on pulse propagation, including the process of stopping and releasing it.
We examine in detail an alternative method of retrieving the information written into an atomic ensemble of three-level atoms using electromagnetically induced transparency. We find that the behavior of the retrieved pulse is strongly influenced by the relative collective atom-light coupling strengths of the two relevant transitions. When the collective atom-light coupling strength for the retrieval beam is the stronger of the two transitions, regeneration of the stored pulse is possible. Otherwise, we show the retrieval process can lead to creation of soliton-like pulses.
We experimentally demonstrate electromagnetically induced transparency and light storage with ultracold 87Rb atoms in a Mott insulating state in a three dimensional optical lattice. We have observed light storage times of about 240 ms, to our knowledge the longest ever achieved in ultracold atomic samples. Using the differential light shift caused by a spatially inhomogeneous far detuned light field we imprint a "phase gradient" across the atomic sample, resulting in controlled angular redirection of the retrieved light pulse.
The effect of inhomogeneous coupling between three-level atoms and external light fields is studied in the electromagnetically induced transparency (EIT) quantum memory techqnique. By introducing a subensemble-atomic system to deal with present inhomogeneous coupling case, we find there is a non-symmetric dark-state subspace (DSS) that allows the EIT quantum memory technique to function perfectly. This shows that such memory scheme can work ideally even if the atomic state is very far from being a symmetric one.
We describe how electromagnetically induced transparency can arise in quadratically coupled optomechanical systems. Due to quadratic coupling the underlying optical process involves a two phonon process in optomechanical system and this two phonon process makes the mean amplitude, which plays the role of atomic coherence in traditional EIT, zero. We show how the fluctuation in displacement can play a role similar to atomic coherence and can lead to EIT-like effects in quadratically coupled optomechanical systems. We show how such effects can be studied using the existing optomechanical systems…
We show that a quasi-perfect quantum state transfer between an atomic ensemble and fields in an optical cavity can be achieved in Electromagnetically Induced Transparency (EIT). A squeezed vacuum field state can be mapped onto the long-lived atomic spin associated to the ground state sublevels of the Lambda-type atoms considered. The EIT on-resonance situation show interesting similarities with the Raman off-resonant configuration. We then show how to transfer the atomic squeezing back to the field exiting the cavity, thus realizing a quantum memory-type operation.
We experimentally investigate electromagnetically-induced transparency (EIT) created on an inhomogeneously broadened 5S_1/2-5P_1/2 transition in rubidium vapor using a control field of a complex temporal shape. A comb-shaped transparency spectrum enhances the delay-bandwidth product and the light storage capacity for a matched probe pulse by a factor of about 50 compared to a single EIT line [D. D. Yavuz, Phys. Rev. A 75, 031801 (2007)]. If the temporal mode of the control field is slowly changed while the probe is propagating through the EIT medium, the probe will adiabatically follow, provid…
We study single photon transport in a one-dimensional disordered lattice of three-level atoms coupled to an optical waveguide. In particular, we study atoms of Λ-type that are capable of exhibiting electromagnetically induced transparency (EIT) and separately consider disorder in the atomic positions and transition frequencies. We mainly address the question of how preferential emission into waveguide modes (chirality) can influence the formation of spatially localized states. Our work has relevance to experimental studies of cold atoms coupled to nanoscale waveguides and has possible applicat…
We study the propagation of a weak probe field through an optomechanical system in which $N$ nearly degenerate mechanical membranes are inside a Febry-Perot cavity, and couple dispersively to an intracavity field. We derive a general analytical expression for the output probe field. We show that the in-phase quadrature of the output probe field can exhibit multiple electromagnetically induced transparency with at most $N$ narrow transparency windows. We find that the superluminal light can be achieved with at most $N$ different negative group velocities at the transparency windows. Moreover, b…
We report the observation of Electromagnetically Induced Transparency (EIT) of a mechanical field, where a superconducting artificial atom is coupled to a 1D-transmission line for surface acoustic waves. An electromagnetic microwave drive is used as the control field, rendering the superconducting transmon qubit transparent to the acoustic probe beam. The strong frequency dependence of the acoustic coupling enables EIT in a ladder configuration due to the suppressed relaxation of the upper level. Our results show that superconducting circuits can be engineered to interact with acoustic fields …
Dissipation-free photon-photon interaction at the single photon level is studied in the context of cavity electromagnetically induced transparency (EIT). For a single multilevel atom exhibiting EIT in the strong cavity-coupling regime, the anharmonicity of the atom-cavity system has an upper bound determined by single atom-photon coupling strength. Photon blockade is inferred to occur for both single and multi-atom cases from the behaviour of transition rates between dressed states of the system. Numerical calculations of the second order coherence function indicate that photon antibunching in…
We suggest a multiatom cavity quantum electrodynamics system for the weak magnetic field detection based on Faraday rotation with intracavity electromagnetically induced transparency. Our study demonstrates that the collective coupling between the cavity modes and the atomic ensemble can be used to improve the sensitivity. With single probe photon input, the sensitivity is inversely proportional to the number of atoms, and the sensitivity with 0.7(5)~nT/$\sqrt{\rm Hz}$ could be attained. With multiphoton measurement, our numerical calculations show that the magnetic field sensitivity can be im…
We study the effects of the four-wave mixing (4WM) in a quantum memory scheme based on electromagnetically induced transparency (EIT). We treat the problem of field propagation on the quantum mechanical level, which allows us to calculate the fidelity for propagation for a quantum light pulse such as a single photon. While 4WM can be beneficial for classical, all-optical information storage, the quantum noise associated with the signal amplification and idler generation is in general detrimental for a quantum memory. We identify a range of parameters where 4WM makes a single photon quantum mem…
The slow light effects of an amplitude modulated Gaussian (AMG) pulse in a cesium atomic vapor are presented. In a single-$Λ$ type electromagnetically induced transparency (EIT) medium, more severe distortion is observed for an AMG pulse than a Gaussian one. Using Fourier spectrum analysis, we find that the distortion, as well as the loss, is dominantly caused by linear absorption than dispersion. Accordingly, a compensation method is proposed to reshape the slow light pulse based on the transmission spectrum. In addition, we find a novel way to obtain simultaneous slow and fast light.
Interest in lossless nonlinearities has focussed on the the dispersive properties of $Λ$ systems under conditions of electromagnetically induced transparency (EIT). We generalize the lambda system by introducing further degenerate states to realize a `Chain $ Λ$' atom where multiple coupling of the probe field significantly enhances the intensity dependent dispersion without compromising the EIT condition.
We present a theory of electromagnetically induced transparency in a cold ensemble of strongly interacting Rydberg atoms. Long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our model is computationally very efficient and is in quantitative agreement with the results of recent …
The transmission of a probe field experiencing electromagnetically induced transparency and optical switching in an atomic medium enclosed in an optical cavity is investigated. Using a semiclassical input-output theory for the interaction between an ensemble of four-level atoms and three optical cavity fields coupled to the same spatial cavity mode, we derive the steady-state transmission spectra of the probe field and discuss the dynamics of the intracavity field buildup. The analytical and numerical results are in good agreement with recent experiments with ion Coulomb crystals [M. Albert et…
We consider the dynamical behavior of a nanomechanical mirror in a high-quality cavity under the action of a coupling laser and a probe laser. We demonstrate the existence of the analog of electromagnetically induced transparency (EIT) in the output field at the probe frequency. Our calculations show explicitly the origin of EIT-like dips as well as the characteristic changes in dispersion from anomalous to normal in the range where EIT dips occur. Remarkably the pump-probe response for the opto mechanical system shares all the features of the Lambda system as discovered by Harris and collabor…
We report an experimental investigation of electromagnetically induced transparency in a multi-level cascade system of cold atoms. The absorption spectral profiles of the probe light in the multi-level cascade system were observed in cold Rb-85 atoms confined in a magneto-optical trap, and the dependence of the spectral profile on the intensity of the coupling laser was investigated. The experimental measurements agree with the theoretical calculations based on the density matrix equations of the rubidium cascade system.
We report characterization of electromagnetically induced transparency (EIT) resonances in the D1 line of Rb-87 under various experimental conditions. The dependence of the EIT linewidth on the power of the pump field was investigated, at various temperatures, for the ground states of the lambda-system associated with different hyperfine levels of the atomic 5S_1/2 state as well as magnetic sublevels of the same hyperfine level. Strictly linear behavior was observed in all cases. A theoretical analysis of our results shows that dephasing in the ground state is the main source of decoherence, w…
The interaction of a weak probe laser with an inverted-Y type four-level atomic system driven by two additional coherent fields is investigated theoretically. 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 electromagnetically induced transparency windows depending on the amplitude and the detuning of the coupling lasers. The corresponding index of refraction associated with the group velocity of the probe laser can be controlled at both transparency windows by the coupling fields. Th…
The broadband parametric fluorescence pulse (probe light) with center frequency resonant on 87Rb D1 line was injected into a cold atomic ensemble with coherent light (control light). Due to the low gain in the parametric down conversion process, the probe light was in a highly bunched photon-pair state. By switching off the control light, the probe light within the electromagnetically induced transparency window was mapped on the atoms. When the control light was switched on, the probe light was retrieved and frequency filtered storage was confirmed from the superbunching effect and an increas…
We propose a scheme to realize parity-time (PT) symmetry via electromagnetically induced transparency (EIT). The system we consider is an ensemble of cold four-level atoms with an EIT core. We show that the cross-phase modulation contributed by an assisted field, the optical lattice potential provided by a far-detuned laser field, and the optical gain resulted from an incoherent pumping can be used to construct a PT-symmetric complex optical potential for probe field propagation in a controllable way. Comparing with previous study, the present scheme uses only a single atomic species and hence…
