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Physical Review A

Ultrashort pulse control of space-dependent excitations in a three-level system

Yu. V. Loiko, Carles Serrat, Ramon A. Vilaseca, V. Ahufinger, J. Mompart, R. Corbalán

Published Feb 1, 2007• 11 citations
Publisher

Abstract

Coherent control of regions with spatial excitation of populations and coherence between two lower states in three-level $\ensuremath{\Lambda}$-type quantum systems mediated by the self-induced transparency (SIT) phenomenon is theoretically investigated with one- and two-color ultrashort pulses and with pulse sequences beyond the slowly varying envelope (SVEA) and rotating wave (RWA) approximations. The effects of different parameters characterizing the pulses and the medium on the location as well as the width of such excited regions have been studied numerically by means of the finite-difference time-domain (FDTD) method. It has been determined that with a scheme of two-pulse excitation one can effectively control the position at which the region is written and its width. In particular, the position of the excited region can be controlled by the area of the pulses. We find that the maximum value of the population transferred to the lower excited state depends on the detuning of the pulses with respect to the one-photon resonances, and that both position and width of the region also depend on the temporal duration of the pulses. We show how after the excited region is written, its position can be shifted by additional pulses. On the basis of numerical results, scaling laws are formulated for the reported phenomena. With such control, the width of the region excited inside the medium can be reduced to the order of the wavelength of the light.

DOI
10.1103/physreva.75.023801

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Coherent control of regions with spatial excitation of populations and coherence between two lower states in three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type quantum systems mediated by the self-induced transparency (SIT) phenomenon is theoretically investigated with one- and two-color ultrashort pulses and with pulse sequences beyond the slowly varying envelope (SVEA) and rotating wave (RWA) approximations. The effects of different parameters characterizing the pulses and the medium on the location as well as the width of such excited regions have been studied numerically by means of the finite-difference time-domain (FDTD) method. It has been determined that with a scheme of two-pulse excitation one can effectively control the position at which the region is written and its width. In particular, the position of the excited region can be controlled by the area of the pulses. We find that the maximum value of the population transferred to the lower excited state depends on the detuning of the pulses with respect to the one-photon resonances, and that both position and width of the region also depend on the temporal duration of the pulses. We show how after the excited region is written, its position can be shifted by additional pulses. On the basis of numerical results, scaling laws are formulated for the reported phenomena. With such control, the width of the region excited inside the medium can be reduced to the order of the wavelength of the light.
Propagation of single- and two-color hyperbolic secant femtosecond laser pulses in a three-level $\ensuremath{\Lambda}$-type quantum system is investigated by solving the Maxwell and density matrix equations with the finite-difference time-domain and Runge-Kutta methods. As a first study of our modeling, we simulate pulse self-induced transparency (SIT) in two-level systems and see how this phenomenon can be controlled by manipulating the initial relative phase between the SIT pulse and a second control pulse, provided the ratio between both pulse frequencies obeys the relation ${\ensuremath{\omega}}_{1}∕{\ensuremath{\omega}}_{2}=3$. We then examine frequency down-conversion processes that are observed with single- and two-color pulses the envelope area of which is equal to or a multiple of $2\ensuremath{\pi}$, for pulse frequencies close to resonance with the transitions of a three-level $\ensuremath{\Lambda}$ medium. Also, phase-sensitive phenomena are discussed in the case of two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ pulses propagating resonantly in the three-level system. In particular, possibilities for such coherent control are found for frequency down-conversion processes when the ratio of the frequencies of optical transitions is ${\ensuremath{\omega}}_{13}∕{\ensuremath{\omega}}_{12}=3$. The conditions for quantum control of four-wave mixing processes are also examined when the pulse frequencies of two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ pulses are far from any resonance of the three-level system. We demonstrate the possibility to cancel the phase sensitivity of the four-wave coupling in a $\ensuremath{\Lambda}$-type system by competition effects between optical transitions.
Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrodinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.
We study the effects of dispersion in carrier waves on the properties of soliton self--induced transparency (SIT) in two level media. We found substantial impact of dispersion effects on typical SIT soliton features. For example, the degree of SIT pulse velocity slowing down (acceleration) is determined by the ratio of the incoming pulse frequency over atomic transition frequency - x=ω/ω0x=ω/ω_0x=ω/ω0​. Specifically, an immediate pulse stopping is predicted for absorbing media when pulse duration time exceeds some critical value. In the sharp line limit stopping may emerge only for frequency ratio above unity, while for the inhomogeneously broadened systems it appears irrespective of the value of xxx. Analysis performed on the basis of Mcall\& Hahn \textit{Area theorem} implies that pulse stopping is achieved when Ber's absorption coefficient approaches infinity, that is, pulse energy is fully absorbed in the medium. In the case of amplifying media super-luminal motion is predicted as in the case of resonance. However, there is a lowest value in the frequency ratio below which the pulse velocity tends to the sub-luminal region. These new features of the SIT phenomenon open novel ways on how it may be exploited for the control of electromagnetic wave radiation in two-level media. This may be achieved by varying frequency ratio.
A critical dependence of the quantum interference on the optical Stark spectral shift produced when two-color laser pulses interact with a two-level medium is observed. The four-wave mixing of two ultrashort phase-locked $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ laser pulses propagating coherently in a two-level system depends on the pulses' relative phase. The phase dominating the efficiency of the coupling to the anti-Stokes Raman component is found to be determined by the sign of the total ac Stark shift induced in the system, in such a way that the phase sensitivity disappears precisely where the ac Stark effect due to both pulses is compensated. A coherent control scheme based on this phenomenon can be contemplated as the basis for nonlinear optical spectroscopy techniques.
A theoretical investigation on the coherent control of optical transient four-wave mixing interactions in two-level systems with two intense few-cycle propagating laser pulses of central angular frequencies $\ensuremath{\omega}$ and $3\ensuremath{\omega}$ is reported. By numerically solving the full Maxwell-Bloch equations beyond the slowly varying envelope and rotating-wave approximations in the time domain, the nonlinear coupling to the optical field at frequency $5\ensuremath{\omega}$ is found to depend critically on the initial relative phase $\ensuremath{\phi}$ of the propagating pulses: the coupling is enhanced when the pulses interfere constructively in the center $(\ensuremath{\phi}=0)$, while it is nearly suppressed when they are out of phase $(\ensuremath{\phi}=\ensuremath{\pi})$.