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Physical Review A

Propagation dynamics of a temporally, amplitude- and group-velocity-matched two-mode ultraslow wave in a three-level Λ system

L. Deng, M. G. Payne, E. W. Hagley

Published Dec 1, 2004• 7 citations
Publisher

Abstract

We investigate the propagation dynamics of a two-mode probe field traveling with ultraslow group velocities. We show that a strong cross-beam coupling occurs between the two modes of the probe wave in the presence of a two-mode control laser field that maintains two-photon resonance excitations in a three-level system. In the adiabatic limit and under appropriate conditions, both modes can travel with matched temporal profiles, amplitudes, and greatly reduced group velocities, and one mode can grow and take on features of the other mode. When only one mode of probe field is injected, the generation and growth of the second mode has the characteristics of four-wave mixing, resulting in a tunable, ultraslow four-wave mixing field with nearly 100% photon flux conversion efficiency. We further show a type of induced transparency resulting from an efficient one- and three-photon destructive interference. This is to be contrasted with the conventional one-mode, three-level electromagnetically induced transparency where the interference involves two one-photon pathways.

DOI
10.1103/physreva.70.063813

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Physical Review A•Sep 14, 2007•44 citations
We investigate the propagation dynamics of a two-mode probe field traveling with ultraslow group velocities. We show that a strong cross-beam coupling occurs between the two modes of the probe wave in the presence of a two-mode control laser field that maintains two-photon resonance excitations in a three-level system. In the adiabatic limit and under appropriate conditions, both modes can travel with matched temporal profiles, amplitudes, and greatly reduced group velocities, and one mode can grow and take on features of the other mode. When only one mode of probe field is injected, the generation and growth of the second mode has the characteristics of four-wave mixing, resulting in a tunable, ultraslow four-wave mixing field with nearly 100% photon flux conversion efficiency. We further show a type of induced transparency resulting from an efficient one- and three-photon destructive interference. This is to be contrasted with the conventional one-mode, three-level electromagnetically induced transparency where the interference involves two one-photon pathways.
We show that in a two-mode, three-level, double-$\ensuremath{\Lambda}$ system an efficient multiphoton destructive interference involving one- and three-photon pumping pathways occurs, leading to a unique type of induced transparency. Unlike the conventional electromagnetically induced transparency achieved with a three-state $\ensuremath{\Lambda}$ system, the induced transparency is critically dependent upon two distinctive relaxation processes involving the production and propagation of an internally generated field. When a two-mode probe field is injected under suitable conditions, we show that the two probe pulses, after a characteristic propagation distance, evolve into a pair of temporal, amplitude, and group velocity matched pulse, traveling loss free in a highly dispersive medium.
We present a fully time dependent, adiabatic solution, and steady-state analysis for the ultraslow propagation of the nondegenerate four-wave mixing (NDFWM) signal and the weak probe beam in a closely-cycled double-ladder system. Under appropriate (especially power balance) conditions, the two-mode probe and phase-matched NDFWM pulses, after a characteristic propagation length, evolve into a pair of amplitude and group velocity matched pulses. Double transparency for the probe and NDFWM beams can be achieved owing to an efficient one- and three-photon destructive interference involving the NDFWM beam and its back reaction to the probe beam. The forward and backward configurations are investigated in this double-ladder system, and their efficiencies are calculated and compared.
We investigate the simultaneous formation and stable propagation of ultraslow optical soliton pairs in a lifetime broadened four-state atomic system under double-Lambda excitation with large one- and two-photon detunings. We show that detrimental probe field distortions due to strong dispersion effects under weak driving conditions can be well balanced by self- and cross-phase modulation effects, leading to a pair of temporal, group velocity, and amplitude matched ultraslow optical solitons of different frequencies.
We investigate a four-state system interacting with long and short laser pulses in a weak probe beam approximation. We show that when all lasers are tuned to the exact unperturbed resonances, part of the four-wave mixing (FWM) field is strongly absorbed. The part that is not absorbed has the exact intensity required to destructively interfere with the excitation pathway involved in producing the FWM state. We show that with this three-photon destructive interference, the conversion efficiency can still be as high as 25%. Contrary to common belief, our calculation shows that this process, where an ideal one-photon electromagnetically induced transparency is established, is not most suitable for high-efficiency conversion. With appropriate phase matching and propagation distance, and when the three-photon destructive interference does not occur, we show that the photon flux conversion efficiency is independent of probe intensity and can be close to 100%. In addition, we show clearly that the conversion efficiency is not determined by the maximum atomic coherence between two lower excited states, as commonly believed. It is the combination of phase matching and constructive interference involving the two terms arising in producing the mixing wave that is the key element for the optimized FWM generation. Indeed, in this scheme no appreciable excited state is produced, so that the atomic coherence between states |0〉 and |2〉 is always very small.
We propose a dual electromagnetically induced transparency (EIT) based multiwave mixing scheme that retains the significantly enhanced conversion efficiency enabled by ultraslow propagation of pump waves, yet is also capable of inhibiting and delaying the onset of the detrimental three-photon destructive interference that limits the further growth of the four-wave mixing (FWM) field. We show that the new scheme exhibits a wave-matching condition that is fundamentally different from the conventional FWM without EIT, and the efficient generation of the mixing wave is not critically dependent upon the FWM detuning to achieve constructive interference as required in the conventional FWM. These are significant steps forward in enabling applications of ultraslow wave nonlinear optics.
We theoretically study the coherent interaction of a tripod-type atomic system with three laser fields, i.e., one probe and two coupling, or two probe and one coupling field. Our analytical and numerical results show that, when all three fields are on two-photon resonance, in addition to the Rabi frequencies of the coupling fields, the probe group velocities also depend on the spontaneous decay rates and the initial population distribution. So we can manipulate the probe pulses to achieve controllable ultraslow group velocities by preparing different initial atomic states. With an incoherent pump field applied, a narrow transparent window accompanied by abnormal dispersion may occur in the probe absorption spectrum, which then allows us to switch a probe pulse from ultraslow to superluminal propagation.