Coherence Phenomena and Phase Relations in Three Level Systems

Yurii V. Loiko, Carles Serrat

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.

Luis Roa, A. Krügel

Irfan U. Chaudhary, Peter L. Hagelstein

Dmitry V. Kosachiov, Boris G. Matisov, Yu. Rozhdestvensky

The work presented considers a new coherent phenomenon, i.e. the influence of the phases of electromagnetic fields interacting with a multilevel system on the character of excitation of this system. On the basis of analysing the equation for an N-level quantum system density matrix, it was established that in multilevel systems containing a closed contour of transitions, resonantly interacting with the field, stationary populations always depend on the total interaction contour phase Phi . For the simplest multilevel systems, i.e. three-level, the authors have obtained analytical expressions, connecting populations with the relative field phase in such systems. Thus, for a Lambda system, interacting with three resonant electromagnetic fields, it is discovered that, depending on the total phase value of the transition contour, both destruction and successive restoration of a coherent trapping state can take place. The work provides qualitative explanations of phase effects and suggests some possibilities for their application.

Vladimir L. Ermakov, Geoffrey Bodenhausen

It is shown by theory and experiment how coherent superpositions of quantum states in three-level systems can be manipulated by irradiating two connected transitions with two resonant fields with suitably shaped time-dependent amplitudes and phases. Three variants are discussed in detail; (i) adiabatic coherence transfer (ACT) between two transitions, which may be either allowed or forbidden; (ii) nonadiabatic transfer of coherence to a nonirradiated transition by controlled violation of adiabaticity (CVA); (iii) coherence transfer to a nonirradiated transition by antiparallel double resonant irradiation (APDRI). A geometrical representation of these experiments gives a clear physical picture of the phenomena and provides a tool for the development of new methods. The principles are illustrated experimentally by applications to magnetic resonance of deuterium (I=1) in anisotropic phase at high magnetic field, but could also be applied to three level-systems in nuclear quadrupole resonance, optics, and other areas of spectroscopy.

M. M. Al'perin, Ya. D. Klubis