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.
A method is proposed to produce atomic ensembles with sub-Poissonian atom number distributions. The method consists of removing the excess atoms using the interatomic interactions induced by Rydberg dressing. The selective removal of atoms occurs via spontaneous decay into untrapped states using an electromagnetically induced transparency scheme. Ensembles with the desired number of atoms can be produced almost deterministically. Numerical simulations predict a strong reduction of the atom number fluctuations, with the variance twenty times less than the Poisson noise level (the predicted Fano…
We present a novel quantum phenomenon named electromagnetically induced entanglement in the conventional Lambda-type three-level atomic system driven by a strong pump field and a relatively weak probe field. Nearly perfect entanglement between the pump and probe fields can be achieved with a low coherence decay rate between the two lower levels, high pump-field intensity, and large optical depth of the atomic ensemble. The physical origin is quantum coherence between the lower doublet produced by the pump and probe fields, similar to the well-known electromagnetically induced transparency. Thi…
We consider a hybrid atom-optomechanical system incorporating N identical $Λ$-type atoms. The system is subjected to dual optical and phononic drives. We show that by exploiting the optomechanical linear and quadratic interactions, multiple electromagnetic transparency windows are attained. Furthermore, owing to the incorporated mechanical pump, the transparency windows are controlled and tuned. For instance, by adjusting the phase of the external mechanical pump, additional controlling parameters are enabled, and the absorption/emission profiles are enhanced. Our present study provides an eff…
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.
The propagation of a pair of quantized fields inside a medium of three-level atoms in $Λ$ configuration is analyzed. We calculate the stationary quadrature noise spectrum of the field after propagating through the medium in the case where the field has a general (but small) noise spectrum and the atoms are in a coherent population trapping state and show electromagnetically induced transparency (EIT). Although the mean values of the field remain unaltered as the field propagates, there is an oscillatory interchange of noise properties between the probe and pump fields. Also, as the field propa…
We describe the effect of thermal motion and buffer-gas collisions on a four-level closed N system interacting with strong pump(s) and a weak probe. This is the simplest system that experiences electromagnetically induced absorption (EIA) due to transfer of coherence via spontaneous emission from the excited to ground state. We investigate the influence of Doppler broadening, velocity-changing collisions (VCC), and phase-changing collisions (PCC) with a buffer gas on the EIA spectrum of optically active atoms. In addition to exact expressions, we present an approximate solution for the probe a…
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 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…
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…
In the present work the model of a single-atom laser generating in the regime when incoherent pumping rate coincides with the cavity decay rate is theoretically investigated. Using the stationary equation for the phase averaged Glauber P function the analytical expressions for mean number of photons and its dispersion are obtained. In the limiting case of the strong-coupling regime the exact expression for the photon number distribution function is found. Obtained results describe the sub-Poissonian photon statistics and show an increase in mean number of photons to non-zero value when the pum…
We analyze the propagation of a pair of quantized fields inside a medium of three-level atoms in $Λ$ configuration. We calculate the stationary quadrature noise spectrum of the field after propagating through the medium, in the case where the probe field is in a squeezed state and the atoms show electromagnetically induced transparency (EIT). We find an oscillatory transfer of the initial quantum properties between the probe and pump fields which is most strongly pronounced when both fields have comparable Rabi frequencies. This implies that the quantum state measured after propagation can be …
We have observed CW lasing without inversion in a gas of hot rubidium atoms in an optical cavity under conditions of electromagnetically-induced transparency (EIT). The medium is pumped coherently and resonantly by a single ``coupling'' beam which also produces EIT in the lasing transition. The steady-state intensity exhibits thresholds as a function of the atomic density and the strength of the coupling beam. A theoretical model for an effective three-level lambda system indicates that gain without inversion is possible in this system if the two ground states are coupled by depolarizing colli…
Lasers essentially consist of single-mode optical cavities containing two-level atoms with a supply of energy called the pump and a sink of energy, perhaps an optical detector. The latter converts the light energy into a sequence of electrical pulses corresponding to photo-detection events. It was predicted in 1984 on the basis of Quantum Optics and verified experimentally shortly thereafter that when the pump is non-fluctuating the emitted light does not fluctuate much. Precisely, this means that the variance of the number of photo-detection events observed over a sufficiently long period of …
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.
We investigate theoretically the optical properties of an atomic gas which has been cooled by the laser cooling method velocity-selective coherent population trapping. We demonstrate that the application of a weak laser pulse gives rise to a backscattered pulse, which is a direct signal for the entanglement in the atomic system, and which leads to single-particle entanglement on the few-photon level. If the pulse is applied together with the pump lasers, it also displays the phenomenon of electromagnetically induced transparency. We suggest that the effect should be observable in a gas of Rubi…
We present a theoretical model for electromagnetically induced transparency (EIT) in vapor, that incorporates atomic motion and velocity-changing collisions into the dynamics of the density-matrix distribution. Within a unified formalism we demonstrate various motional effects, known for EIT in vapor: Doppler-broadening of the absorption spectrum; Dicke-narrowing and time-of-flight broadening of the transmission window for a finite-sized probe; Diffusion of atomic coherence during storage of light and diffusion of the light-matter excitation during slow-light propagation; and Ramsey-narrowing …
We theoretically demonstrate the mechanically mediated electromagnetically induced transparency in a two-mode cavity optomechanical system, where two cavity modes are coupled to a common mechanical resonator. When the two cavity modes are driven on their respective red sidebands by two pump beams, a transparency window appears in the probe transmission spectrum due to destructive interference. Under this situation the transmitted probe beam can be delayed as much as 4 us, which can be easily controlled by the power of the pump beams. In addition, we also investigate the amplification of the tr…
The interaction of a quantized field with three-level atoms in $Λ$ configuration inside a two-mode cavity is analyzed in the small noise approximation. The atoms are in a two-photon detuning with respect to the carriers of the field. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is a squeezed state and the input pump field is a coherent state. The mean value of the field is unaltered in all the analysis: the atoms shows electromagnetically induced transparency (EIT). The effect of the atoms' base level decoherence …
Electromagnetically induced transparency (EIT) has usually been demonstrated by using three-level atomic systems. In this paper, we theoretically proposed an efficient method to realize EIT in microwave regime through a coupled system consisting of a flux qubit and a superconducting LC resonator with relatively high quality factor. In the present composed system, the working levels are the dressed states of a two-level flux qubit and the resonators with a probe pump field. There exits a second order coherent transfer between the dressed states. By comparing the results with those in the conven…
The temporal evolution of electromagnetically induced transparency (EIT) and absorption (EIA) coherence resonances in pump-probe spectroscopy of degenerate two-level atomic transition is studied for light intensities below saturation. Analytical expression for the transient absorption spectra are given for simple model systems and a model for the calculation of the time dependent response of realistic atomic transitions, where the Zeeman degeneracy is fully accounted for, is presented. EIT and EIA resonances have a similar (opposite sign) time dependent lineshape, however, the EIA evolution is…
We experimentally demonstrate coherent amplification of probe field in a tripod-type atoms driven by strong coupling, signal and weak probe fields. We suppress linear and nonlinear atomic absorptions for resonant and near resonant probe via double electromagnetically induced transparency (DEIT). Combining these advantages of suppressed absorption along with temperature- or atomic-density-controlled transfer of population(ToP) between hyperfine ground states, we can induce near-resonant amplification of probe through stimulated Raman scattering(SRS) pumped by low-intensity signal field. The inc…
Dicke narrowing is a phenomena that dramatically reduces the Doppler width of spectral lines, due to frequent velocity-changing collisions. A similar phenomena occurs for electromagnetically induced transparency (EIT) resonances, and facilitates ultra-narrow spectral features in room-temperature vapor. We directly measure the Dicke-like narrowing by studying EIT line-shapes as a function of the angle between the pump and the probe beams. The measurements are in good agreement with an analytic theory with no fit parameters. The results show that Dicke narrowing can increase substantially the to…
The interaction of a quantized field with three-level atoms in $Λ$ configuration inside a two mode cavity is analyzed. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is in a squeezed state and the atoms show electromagnetically induced transparency (EIT). If the Rabi frequencies of both dipole transitions of the atoms are different from zero, we show that the output probe field have four maxima of squeezing absorption. We show that in some cases two of these frequencies can be very close to the transition frequency …
Quiet (or sub-Poissonian) oscillators generate a number of dissipation events whose variance is less than the mean. It was shown in 1984 by Golubev and Sokolov that lasers driven by regular pumps are quiet in that sense. The purpose of this paper is to show that, as long as the laser-detector system is strictly stationary, quantization of the optical field is not required to explain such phenomena. The theory presented here is semi-classical, yet exact. Previous theories considering excited-state atoms regularly-injected in resonators, on the other hand, do require in principle light quantizat…
From the microscopic quantum Langevin equations (QLEs) we derive the effective semiconductor QLEs and the associated noise correlations which are valid at a low-injection level and in real devices. Applying the semiconductor QLEs to semiconductor light-emitting devices (LEDs), we obtain a new formula for the Fano factor of photons which gives the photon-number statistics as a function of the pump statistics and several parameters of LEDs. Key ingredients are non-radiative processes, carrier-number dependence of the radiative and non-radiative lifetimes, and multimodeness of LEDs. The formula i…
We investigate experimentally the absorptive and dispersive properties of triple-resonant optical parametric amplifier OPA for the degenerate subharmonic field. In the experiment, the subharmonic field is utilized as the probe field and the harmonic wave as the pump field. We demonstrate that EIT-like effect can be simulated in the triple-resonant OPA when the cavity line-width for the harmonic wave is narrower than that for the subharmonic field. However, this phenomenon can not be observed in a double-resonant OPA. The narrow transparency window appears in the reflected field. Especially, in…
High degrees of intensity correlation between two independent lasers were observed after propagation through a rubidium vapor cell in which they generate Electromagnetically Induced Transparency (EIT). As the optical field intensities are increased, the correlation changes sign (becoming anti-correlation). The experiment was performed in a room temperature rubidium cell, using two diode lasers tuned to the $^{85}$Rb $D_2$ line ($λ= 780$nm). The cross-correlation spectral function for the pump and probe fields is numerically obtained by modeling the temporal dynamics of both field phases as dif…
We present a realistic theoretical treatment of a three-level $Λ$ system in a hot atomic vapor interacting with a coupling and a probe field of arbitrary strengths, leading to electromagnetically-induced transparency and slow light under the two-photon resonance condition. We take into account all the relevant decoherence processes including col5Blisions. Velocity-changing collisions (VCCs) are modeled in the strong collision limit effectively, which helps in achieving optical pumping by the coupling beam across the entire Doppler profile. The steady-state expressions for the atomic density-ma…
Here we demonstrate that photocurrent noise reduction below the standard quantum limit and modal anticorrelation can arise in two mode coupled two-VECSEL system with common pump. This effect occurs due to correlated loss of laser modes. It is possible to suppress noise below the standard quantum limit even for Poissonian coherent pumping, whereas the regularity of the pump can be harmful for non-classicality.
We propose to pump semiconductor quantum dots with surface acoustic waves which deliver an alternating periodic sequence of electrons and holes. In combination with a good optical cavity such regular pumping could entail anti-bunching and sub-Poissonian photon statistics. In the bad-cavity limit a train of equally spaced photons would arise.
Laser induced line narrowing effect, discovered more than thirty years ago, can also be applied to recent studies in high resolution spectroscopy based on electromagnetically induced transparency. In this paper we first present a general form of the transmission width of electromagnetically induced transparency in a homogeneously broadened medium. We then analyze a Doppler broadened medium by using a Lorentzian function as the atomic velocity distribution. The dependence of the transmission linewidth on the driving field intensity is discussed and compared to the laser induced line narrowing e…
We performed an experiment to observe the storages of an input probe field and an idler field generated through an off-axis four-wave mixing (FWM) process via a double-lambda configuration in a cold atomic ensemble. We analyzed the underlying physics in detail and found that the retrieved idler field came from two parts if there was no single-photon detuning for pump pulse: part 1 was from the collective atomic spin (the input probe field, the coupling field and the pump field combined to generate the idle field through FWM, then the idler was stored through electromagnetically induced transpa…
Interfacing light and matter at the quantum level is at the heart of modern atomic and optical physics and enables new quantum technologies involving the manipulation of single photons and atoms. A prototypical atom-light interface is electromagnetically induced transparency, in which quantum interference gives rise to hybrid states of photons and atoms called dark-state polaritons. We have observed individual dark-state polaritons as they propagate through an ultracold atomic gas involving Rydberg states. Strong long-range interactions between Rydberg atoms give rise to an effective interacti…
The absorption and dispersion of probe light is studied in an unified framework of three-level system, with coherent laser driving and incoherent pumping and relaxation. The electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are studied in details. In the phase diagram of the unified three-level system, there are distinct parameter regimes corresponding to different lineshapes and mechanisms, and the incoherent transition could control the cross-over between EIT and ATS. The incoherent control of the three-level system enables the investigation of various phenomen…
We show the pulse matching phenomenon can be obtained in the general multi-level system with electromagnetically induced transparency (EIT). For this we find a novel way to create tightly localized stationary pulses by using counter-propagating pump fields. The present process is a spatial compression of excitation so that it allows us to shape and further intensify the localized stationary pulses, without using standing waves of pump fields or spatially modulated pump fields.
We present a study of manipulating the multiphoton blockade phenomenon in a single mode cavity with two ladder-type three-level atoms. Combining the cavity QED with electromagnetically induced transparency technique, we show that it is possible to actively manipulate the photon blockade when two atoms are in phase radiations. As a result, the two-photon blockade can be changed to three-photon blockade by changing the control field Rabi frequency. In the case of out-phase radiations, we show that the three-photon blockade can be improved with enhanced mean photon number. In addition, we show th…
For a transition $F_e=0\leftrightarrow F_g=1$ driven by a linearly polarized light and probed by a circularly light, quantum coherence effects are investigated. Due to the coherence between the drive Rabi frequency and Zeeman splitting, electromagnetically induced transparency, electromagnetically induced absorption, and the transition from positive to negative dispersion are obtained, as well as the populations coherently oscillating in a wide spectral region. At the zero pump-probe detuning, the subluminal and superluminal light propagation is predicted. Finally, coherent population trapping…
Optical parametric process occurring in a nonlinear planar waveguide can serve as a source of light with nonclassical properties. Properties of the generated fields are substantially modified by scattering of the nonlinearly interacting fields in a photonic band-gap structure inside the waveguide. A quantum model of linear operator amplitude corrections to amplitude mean-values provides conditions for an efficient squeezed-light generation as well as generation of light with sub-Poissonian photon-number statistics. Destructive influence of phase mismatch of the nonlinear interaction can fully …
We investigate the controllability of electromagnetically induced transparency (EIT) and Fano resonances in hybrid optomechanical system which is composed of cigar-shaped Bose-Einstein condensate (BEC) trapped inside high-finesse Fabry-Pérot cavity driven by a single mode optical field along the cavity axis and a transverse pump field. Here, transverse optical field is used to control the phenomenon of EIT in the output probe laser field. The output probe laser field can efficiently be amplified or attenuated depending on the strength of transverse optical field. Furthermore, we demonstrate th…
Electromagnetically induced transparency (EIT) has mainly been modelled for three-level systems. In particular, a considerable interest has been dedicated to the Lambda-configuration, with two ground states and one excited state. However, in the alkali-metal atoms, which are commonly used, hyperfine interaction in the excited state introduces several levels which simultaneously participate in the scattering process. When the Doppler broadening is comparable with the hyperfine splitting in the upper state, the three-level Lambda model does not reproduce the experimental results. Here we theoret…
We study the intensity-intensity correlations of the radiation emitted on probe transition in a three level cascade electromagnetically induced transparency (EIT) scheme. By applying an incoherent pump, we also monitor further changes in the characteristics of the emitted radiation. It is found that application of even a very weak incoherent pump can significantly alter the characteristics of the emitted radiation, even though the EIT characteristics remain unaltered. Our study demonstrates that for certain range of parameter values, the two photon correlation function in the probe transition …
We theoretically investigate the analog of electromagnetically induced transparency, absorption and parametric amplification in a hybrid opto-electromechanical system consisting of an optical cavity and a microwave cavity coupled to a common nanomechanical resonator. When the two cavity modes are driven on their respective red sidebands by two pump beams and a probe beam is applied to the optical cavity to monitor the optical response of the hybrid system, we find that a transparency window appears in the probe transmission spectrum due to destructive interference. When the optical cavity is p…
We present and investigate an analogue model for a controllable photon geberation via the dynamical Casimir effect (DCE) in a cavity containing a degenerate optical amplifier (OPA) which is pumed by an amplitude-modulated field. The time modulation of the pump field in the model OPA system is equivalent to a periodic modulation of the cavity length, which is responsible for the generation of the Casimir radiation. By taking into account the rapidly oscillating terms of the modulation frequency, the effects of the corresponding counter-rotating terms (CRTs) on the analogue Casimir radiation eme…
We report on the generation of photon pairs in the 1550-nm band suitable for long-distance fiber-optic quantum key distribution. The photon pairs were generated in a periodically poled lithium niobate waveguide with a high conversion-efficiency. Using a pulsed semiconductor laser with a pulse rate of 800 kHz and a maximum average pump power of 50 muW, we obtained a coincidence rate of 600 s^-1. Our measurements are in agreement with a Poissonian photon-pair distribution, as is expected from a comparison of the coherence time of the pump and of the detected photons. An average of 0.9 photon pai…
We demonstrate the analogue of electromagnetically induced transparency in a room temperature cavity optomechanics setup formed by a thin semitransparent membrane within a Fabry-Pérot cavity. Due to destructive interference, a weak probe field is completely reflected by the cavity when the pump beam is resonant with the motional red sideband of the cavity. Under this condition we infer a significant slowing down of light of hundreds of microseconds, which is easily tuned by shifting the membrane along the cavity axis. We also observe the associated phenomenon of electromagnetically induced amp…
We investigate electromagnetically induced transparencies with two transverse Bose-Einstein condensates in four-mirror optical cavity, driven by a strong pump laser and a weak probe laser. The cavity mode, after getting split from beam splitter, interacts with two independent Bose-Einstein Condensates transversely trapped in the arms of the cavity along $x$-axis and $y$-axis. The interaction of intra-cavity optical mode excites momentum side modes in Bose-Einstein Condensates, which then mimic as two atomic mirrors coupled through cavity field. We show that the probe field photons transition t…
Using two different criteria for continuous variable systems we demonstrated that pump and probe beams became quantum correlated in a situation of Electromagnetically Induced Transparency in a sample of Rb atoms. Our result combines two important features for practical implementations in the field of quantum information processing. Namely, we proved the existence of entanglement between two macroscopic light beams, and this entanglement is intrinsically associated to a strong coherence in an atomic medium.
A new configuration for observation of magneto-optical subnatural-linewidth resonances of electromagnetically induced absorption (EIA) in alkali vapor has been verified experimentally. The configuration includes using two counter-propagating pump and probe light waves with mutually orthogonal linear polarizations, exciting an open optical transition of an alkali atom in the presence of a buffer gas. The main advantage of the novel observation scheme consists in the possibility of obtaining simultaneously high-contrast and quite narrow nonlinear signals. Here a 2.5-cm long rubidium-87 vapor cel…
We propose a scheme to generate double electromagnetically induced transparency and optimal cross-phase modulation for two slow, copropagating pulses with matched group velocities in a single species of atom, namely 87 Rb. A single pump laser is employed and a homogeneous magnetic field is utilized to avoid cancellation effects through the nonlinear Zeeman effect. We suggest a feasible preparational procedure for the atomic initial state to achieve matched group velocities for both signal fields.
We present a full quantum analysis of resonant forward four-wave mixing based on electromagnetically induced transparency (EIT). In particular, we study the regime of efficient nonlinear conversion with low-intensity fields that has been predicted from a semiclassical analysis. We derive an effective nonlinear interaction Hamiltonian in the adiabatic limit. In contrast to conventional nonlinear optics this Hamiltonian does not have a power expansion in the fields and the conversion length increases with the input power. We analyze the stationary wave-mixing process in the forward scattering co…
Vector magnetometry was studied using the electromagnetically induced transparency (EIT) with linear $\perp$ linear ($lin \perp lin$) polarization of the probe and the pump beams in $^{87}Rb$ - $D_2$ transition. The dependence of the EIT on the direction of the quantization axis and the relative orientation of the polarization of the applied electric fields was studied experimentally. We have shown that from the relative strengths of the $σ$ and $π$ EIT peaks, the direction of the magnetic field can be found. Moreover from the relative separation between the $σ$ and $π$ EIT peaks, the strength…
Electromagnetically-induced transparency (EIT) exploits quantum coherence to burn subnatural linewidth holes within a spectral line. We investigate the less explored properties of EIT to effect absorptive nonlinear processes without restrictions on the relative intensities of pump and probe fields. We show that a three-level medium under imperfect EIT conditions can generate a form of bleaching that is qualitatively similar to two-state saturable absorption. This scheme has the advantages of greater sensitivity to signal intensity and controllability over its bleaching intensity level post-fab…
Statistical properties of optical fields in nonlinear couplers composed of two waveguides in which Raman or Brillouin processes (with classical pumping) are in operation and which are mutually connected through the Stokes and/or anti-Stokes linear interactions are investigated within the framework of generalized superposition of coherent fields and quantum noise. Heisenberg equations describing the couplers are solved both analytically under special conditions and numerically in general cases. Regimes for nonclassical properties of optical fields, such as sub-Poissonian photon-number statistic…
A full quantum theory beyond the mean-field regime is developed for an exciton polariton condensate, to gain a complete understanding of quantum fluctuations. We find analytical solution for the polariton density matrix, showing the polariton nonlinearity causing fast relaxation correlated with the pump so as to yield the condensation at threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian and to a nonclassical distribution beyond the understandin…
