Recently counterintuitive effect in lasing and amplification without inversion (LWI) was studied [1]. Here we present time dependent study of pulsed probe and drive fields in the Λ-scheme of three level system in the bare representation.
Introducing a short pulse probe field prior to the drive field exhibits an essential enhancement of the expected gain without inversion in a CW scheme. This is counterintuitive to what would be expected. A few diverse physical phenomena exist where such counterintuitive behavior was observed both theoretically and experimentally. Counterintuitive coherent control studies have recently shown the importance of the scheme in a number of subjects including population transfer [2-6], quantum computation [7-9], and others. Here we show the advantage of such a process in the Λ scheme for LWI. This is also expected in other schemes of LWI and in electromagnetically induced transparency (EIT).

Advanced preparation of the quantum state of the probe transition by advanced turn on of the probe field in three level system, results in an enhancement of the probe related effects. This is the so called counterintuitive sequence of applying the probe and drive fields. We demonstrate this concept, by observing that the probe related effects are not obtained when the probe field is turned on alone, namely without the drive field. Undoubtedly, the drive field is an essential one in generating the gain on the probe transition. Turning on the drive field alone without the probe field actually results in Rabi oscillation of the populations and coherences on the drive transition. Intuitively one expects that the effect of the probe field requires the existence and turn on of the drive field initially. However, quantum mechanically, initial turn on of the probe field prepares the quantum coherence on the probe transition. This counterintuitive sequencing results in enhancement of the probe effect, which is efficient transfer of population in the stimulated Raman adiabatic passage (STIRAP) case and in enhanced probe gain in the LWI case.

We found that the counterintuitive enhancement of the gain and dispersion of the probe field depend quite strongly on the time elapse between turning on the drive field and the advanced turn on of the probe field.

Similar behavior is encountered in STIRAP [2]. Although STIRAP is a different effect, the basic behavior is similar: quantum preparation of the probe transition by the initial turn on of the probe field, which by itself actuates no effect, exhibits
stronger effect in counterintuitive application of the probe and drive lasers. In this sense this is a universal behavior in three (or more) level systems with such sequencing of the probe-drive fields.

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