We analyze the effects of partial coherence of ground state preparation on two-pulse propagation in a three-level $Λ$ medium, in contrast to previous treastments that have considered the cases of media whose ground states are characterized by probabilities (level populations) or by probability amplitudes (coherent pure states). We present analytic solutions of the Maxwell-Bloch equations, and we extend our analysis with numerical solutions to the same equations. We interpret these solutions in the bright/dark dressed state basis, and show that they describe a population transfer between the bright and dark state. For mixed-state $Λ$ media with partial ground state phase coherence the dark state can never be fully populated. This has implications for phase-coherent effects such as pulse matching, coherent population trapping, and electromagnetically induced transparency (EIT). We show that for partially phase-coherent three-level media, self induced transparency (SIT) dominates EIT and our results suggest a corresponding three-level area theorem.
We investigate the problem of propagation of three-component resonant light pulses with adiabatically varying amplitudes through a medium consisting of atoms with the tripod level configuration. By means of both analytic and numerical methods we found the two modes of shape-preserving pulse propagation. The pulse propagation velocity is found to be either equal to the speed of light or significantly slowed down, depending on a particular propagation mode.
We investigate propagation of a pulse pair in a three-level medium under the adiabatic following condition for the general case of unequal oscillator strengths. Exact analytical solutions to the propagation equations have been obtained. It is shown that propagation dynamics strongly depends on the relationship between oscillator strengths. The adiabaticity criterion for the interaction of pulses with three-level media has been derived and analyzed in detail.
The prospect of self-consistent propagation of more than two pulses contemporaneously through multi-resonant media raises open questions: whether soliton solutions exist, and whether a useful generalization of two-level pulse Area can be found. We answer these questions positively for the case of four pulses interacting in combined V and Lambda fashion with an idealized pair of atomic D-lines.
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.
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.
We have observed the ultraslow propagation of matched pulses in nondegenerate four-wave mixing in a hot atomic vapor. Probe pulses as short as 70 ns can be delayed by a tunable time of up to 40 ns with little broadening or distortion. During the propagation, a probe pulse is amplified and generates a conjugate pulse which is faster and separates from the probe pulse before getting locked to it at a fixed delay. The precise timing of this process allows us to determine the key coefficients of the susceptibility tensor. The presence of gain in this system makes this system very interesting in th…
The photon density operator function is used to calculate light beam propagation through turbulent atmosphere. A kinetic equation for the photon distribution function is derived and solved using the method of characteristics. Optical wave correlations are described in terms of photon trajectories that depend on fluctuations of the refractive index. It is shown that both linear and quadratic disturbances produce sizable effects for long-distance propagation. The quadratic terms are shown to suppress the correlation of waves with different wave vectors. We examine the intensity fluctuations of p…
We investigate the causal propagation of the pulse through dispersive media by very precise numerical solution of the coupled Maxwell-Bloch equations without any approximations about the strength of the input field. We study full nonlinear behavior of the pulse propagation through solid state media like ruby and alexandrite. We have demonstrated that the information carried by the discontinuity, {\it i.e}, front of the pulse, moves inside the media with velocity $c$ even though the peak of the pulse can travel either with sub-luminal or with super-luminal velocity. We extend the argument of Le…
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 develop models for the propagation of intense pulses in solid state media which can have either saturated absorption or exhibit reverse absorption . We show that the experiments of Bigelow {\it et al.}[Phys. Rev. Lett. {\bf 90}, 113903 (2003); Science {\bf 301}, 200 (2003).] on subluminal propagation in Ruby and superluminal propagation in Alexandrite are well explained by modelling them as three level and four level systems coupled to Maxwell equations. We present results well beyond the traditional pump-probe approach.
The response of an arbitrary closed quantum system to a partially coherent electric field is investigated, with a focus on the transient coherences in the system. As a model we examine, both perturbatively and numerically, the coherences induced in a three level $V$ system. Both rapid turn-on and pulsed turn-on effects are investigated. The effect of a long and incoherent pulse is also considered, demonstrating that during the pulse the system shows a coherent response which reduces after the pulse is over. Both the pulsed scenario and the thermally broadened CW case approach a mixed state in …
Using a microscopic master equation to account for the environmental effects, we compute the decoherence culminated during the propagation of a microwave pulse of arbitrary shape through a superconducting qubit. It is shown that the qubit decoherence vanishes and the pulse shape remains absorption-free when the latter adopts a soliton shape with $nπ$ area. Otherwise, the environmental feedback decelerates the velocity of the soliton envelop and induces an monotonic increase of phase in the microwave. A pulse of non-$nπ$ area thus ramifies into a transparent part that travels decoherence-free a…
We consider the simultaneous propagation of a pair of Raman-resonant, frequency-modulated (chirped) laser pulses in an optically thick medium, modeled by an ensemble of $Λ$-atoms. A self-organization ('matching`) effect is shown for the chirped pulse pair, which leads to a quasi-lossless propagation. Furthermore, we demonstrate that a well-defined coherent superposition of the atomic ground states and, correspondingly, a coherence is robustly created in the medium that can be controlled by amplitudes of the laser pulses. The proposed scheme can be applied to substantially increase the efficien…
We investigate the role of non-uniform spatial density profiles of trapped atomic Bose-Einstein condensates in the propagation of Raman-matched laser pulses under conditions for electromagnetically induced transparency (EIT). We find that the sharp edged axial density profile of an interacting condensate (due to a balance between external trap and repulsive atomic interaction) is advantageous for obtaining ultra slow averaged group velocities. Our results are in good quantitative agreement with a recent experiment report [Nature {\bf 397}, 594 (1999)].
The modification of initially entangled light pulses passing through dispersive and absorbing four-port devices is studied, using recently obtained results on quantum state transformations [Phys. Rev. A 59, 4716 (1999)]. The fidelity and indices of quantum correlations based on the von Neumann entropy are calculated. Their dependence on both the pulse shape and the four-port device parameters is studied. It is shown, that due to dispersion and absorption the quantum correlations are reduced substantially for large initial entanglement.
Using a single channel active Raman gain medium we show a $(220\pm 20)$ns advance time for an optical pulse of $τ_{FWHM}=15.4 μ$s propagating through a 10 cm medium, a lead time that is comparable to what was reported previously. In addition, we have verified experimentally all the features associated with this single channel Raman gain system. Our results show that the reported gain-assisted superluminal propagation should not be attributed to the interference between the two frequencies of the pump field.
Propagation of a two-photon pulse in a waveguide coupled to a two-level system (TLS) is studied. The pulse is formed by two spatially separated identical wavepackets. A set of equations governing the dynamics of the photon distribution in the configuration-momentum space is derived and solved. It is shown that the distribution function can be negative that manifests its quasiprobability nature. A spectrum of the reflected light is found to be narrower than that of the transmitted light that features a pronounced filtering effect. Average numbers of the transmitted and reflected photons and the…
Nonlinear effects in pulse propagation through a medium consisting of four-level double-$Λ$-type systems are studied theoretically. We apply three continous-wave driving fields and a pulsed probe field such that they form a closed interaction loop. Due to the closed loop and the finite frequency width of the probe pulses the multiphoton resonance condition cannot be fulfilled, such that a time-dependent analysis is required. By identifying the different underlying physical processes we determine the parts of the solution relevant to calculate the linear and nonlinear response of the system. We…
We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda ($Λ$) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional $Λ$- or $N$-type atom-light couplings providing the EIT or absorption, respectively. Thus the atomic system can experi…
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.
We investigate orbital alignment dynamics within the valence shell of atoms in coherently excited $j=3/2,1/2$ fine-structure manifolds generated by short-pulse photodetachment of F$^-$, Cl$^-$ and Br$^-$ anions. Using Keldysh-type theory, we calculate the density matrix of the residual atoms generated by few-cycle pulses, whose elements determine the populations and coherence among the electronic states. Our calculations demonstrate that the degree of atomic coherence can be represented by a near universal function of the ratio between the pulse duration $\tildeτ_p$ and the beat period $τ_{j'j…
We study propagation of short laser pulses in a Bose-Einstein condensate taking into account dispersive effects under the conditions for electromagnetically induced transparency. We calculate dispersion coefficients using typical experimental parameters of slow-light schemes in condensates. By numerically propagating the laser pulse, and referring to theoretical estimations, we determine the conditions for which dispersion starts to introduce distortions on the pulse shape.
We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly-varying-envelope approximations. The method of solution is based on the Maxwell--Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pu…
Pulse propagation is studied in an EIT medium with the control field having a periodically varying phase (chirp). Based both on numerical calculations and on an approximate approach neglecting absorption and nonadiabatic effects, it is shown that transparency occurs for probe pulses having a sufficiently narrow envelope and an appropriately suited chirp. For other chirped pulses the evolution of their spectra along a sample is studied. Using a projection method one can divide a pulse into a part for which the medium is transparent and a rest for which it is opaque.
We focus on the propagation properties of a single-cycle laser pulse through a two-level medium by numerically solving the full-wave Maxwell-Bloch equations. The counter-rotating terms in the spontaneous emission damping are included such that the equations of motion are slightly different from the conventional Bloch equations. The counter-rotating terms can considerably suppress the broadening of the pulse envelope and the decrease of the group velocity rooted from dispersion. Furthermore, for incident single-cycle pulses with envelope area 4$π$, the time-delay of the generated soliton pulse …
Group velocity control is demonstrated for x-ray photons of 14.4 keV energy via a direct measurement of the temporal delay imposed on spectrally narrow x-ray pulses. Sub-luminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of ${}^{57}$Fe Mössbauer nuclei embedded in a thin film planar x-ray cavity. The direct detection of the temporal pulse delay is enabled by generating frequency-tunable spectrally narrow x-ray pulses from broadband pulsed synchrotron radiation. Our theoretical model is in good agreement with the experimental data.
We examine fully coherent two-pulse propagation in a lambda-type medium, under two-photon resonance conditions and including inhomogeneous broadening. We examine both the effects of short pulse preparation and the effects of medium preparation. We contrast cases in which the two pulses have matched envelopes or not, and contrast cases in which ground state coherence is present or not. We find that an extended interpretation of the Area Theorem for single-pulse self-induced transparency (SIT) is able to unify two-pulse propagation scenarios, including some aspects of electromagnetically-induced…
We investigate the spatio-temporal evolution of a Gaussian probe pulse propagating through a four-level $N$-type atomic medium. At two-photon resonance of probe-and control fields, weaker probe pulses may propagate through the medium with low absorption and pulse shape distortion. In contrast, we find that increasing the probe pulse intensity leads to a splitting of the initially Gaussian pulse into a sequence of subpulses in the time domain. The number of subpulses arising throughout the propagation can be controlled via a suitable choice of the probe and control field parameters. Employing a…
We study the propagation and amplification of a microwave field in a four-level cascade quantum system which is realized in a superconducting phase quantum circuit. It is shown that by increasing the microwave pump tones feeding the system, the normal dispersion switches to the anomalous and the gain-assisted superluminal microwave propagation is obtained in this system. Moreover, it is demonstrated that the stimulated microwave field is generated via four-wave mixing without any inversion population in the energy levels of the system (amplification without inversion) and the group velocity of…
Existence of self-similar, superposed pulse-train solutions of the nonlinear, coupled Maxwell-Schrödinger equations, with the frequencies controlled by the oscillator strengths of the transitions, is established. Some of these excitations are specific to the resonant media, with energy levels in the configurations of $Λ$ and $N$ and arise because of the interference effects of cnoidal waves, as evidenced from some recently discovered identities involving the Jacobian elliptic functions. Interestingly, these excitations also admit a dual interpretation as single pulse-trains, with widely differ…
We investigate the evolution of extreme ultraviolet (XUV) spectral lineshapes in an optically-thick helium gas under near-infrared (IR) perturbation. In our experimental and theoretical work, we systematically vary the IR intensity, time-delay, gas density and IR polarization parameters to study lineshape modifications induced by collective interactions, in a regime beyond the single atom response of a thin, dilute gas. In both experiment and theory, we find that specific features in the frequency-domain absorption profile, and their evolution with propagation distance, can be attributed to th…
