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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Origin of the Reaction of Probe Spectra on the Coupling Pump Laser Absorption

Harry Friedmann, T. Zigdon, A. D. Wilson‐Gordon

Published Jun 1, 2007• 0 citations
Publisher

Abstract

In this paper it is shown that the effect of the probe spectrum on the pump absorption results from a probe-frequency-dependent modulation of the populations of the states involved in the transitions interacting with the radiation. We distinguish between two elementary situations: 1. simple two-level systems and V-tvpe three-level systems and 2. Lambda-tvpe three-level systems. In a four-level V-type configuration, where the two vertical legs represent the transitions that interact with the pump(s), and the diagonal leg represents the transition that interacts with the probe. There are two contributions to the pump spectrum. The left-hand transition corresponds to a Lambda-tvpe situation and the right-hand transition to a V-type situation.

DOI
10.1109/cleoe-iqec.2007.4386811

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Physical Review A•Feb 20, 2002•31 citations
In this paper it is shown that the effect of the probe spectrum on the pump absorption results from a probe-frequency-dependent modulation of the populations of the states involved in the transitions interacting with the radiation. We distinguish between two elementary situations: 1. simple two-level systems and V-tvpe three-level systems and 2. Lambda-tvpe three-level systems. In a four-level V-type configuration, where the two vertical legs represent the transitions that interact with the pump(s), and the diagonal leg represents the transition that interacts with the probe. There are two contributions to the pump spectrum. The left-hand transition corresponds to a Lambda-tvpe situation and the right-hand transition to a V-type situation.
We calculate the absorption spectrum of a weak probe interacting with a \ensuremath{\Lambda}-shaped three-level system driven by a single pump. We find that there are four types of terms that contribute to the probe absorption: population-difference and two-photon coherence terms which derive solely from interaction with the pump (dc terms) and population-difference and two-photon coherence terms that pulsate at the pump-probe frequency offset. We find that the main features of the probe spectrum derive from the pulsating terms whereas the dc terms either interfere destructively with each other or with the pulsating terms. This is a clear extension to the three-level system of the concept of light amplification by coherence. We calculate the spectrum for three cases: (i) a degenerate population-trapped system, (ii) a degenerate system in which both transitions are population inverted, and (iii) a nondegenerate population-trapped system. The results of case (i) are similar to those for the two-level system but the population-trapped system has the advantage of avoiding pump absorption. We show that the Rabi frequency of the nonabsorbed pump can be found by determining the probe frequencies at which probe nonabsorption occurs. In (ii), the results are compared with the case where two pumps interact resonantly with a nondegenerate system. In (iii), we find that the populations in the lower states behave dispersively as a function of the pump detuning. For Rabi frequencies that are small compared to the separation between the lower levels, the lower level nearer to resonance is less populated than the other level. However, at higher Rabi frequencies, the situation is reversed. The probe spectrum contains two absorption peaks when the pump Rabi frequency is small and two emission peaks when it is large.
Pump–probe spectroscopy of a four-level system (FLS) consisting of a Λ system with an additional close lying excited level is investigated. The level configuration gives rise to two simultaneously excited Λ resonances driven by the same pump and probe laser beams. Two such four-level configurations, 5s1/2F=1,2→5p1/2F′=1,2 (FLS1) and 5s1/2F=1,2→5p3/2F′=1,2 (FLS2) respectively in the D1 and D2 transitions of 87Rb, are used as model systems to study theoretically the probe absorption spectrum. It is observed that the signature of the quantum interference is dependent on the nature of the FLS; FLS1 exhibits probe amplification as against probe absorption in FLS2. This contrasting behaviour is further corroborated by analytical results, which highlight the importance of transition dipole moments, atom–field interaction parameters and incoherent decays associated with the FLS. The discussion is further augmented using quantum jump formalism, which provides useful insight into the underlying mechanism responsible for probe amplification versus absorption.
The response of a coherently prepared four-level λ-type system, interacting with two electromagnetic fields in a Doppler-free pump–probe configuration is analytically formulated. Under density matrix formalism the probe coherence (field-dependent phase) and atomic coherence (field-independent phase) are introduced through the off-diagonal matrix elements. The coherent effects on probe response is investigated for probe coherence, as well as for the driving contribution (coherence) of the pump field. We show how probe coherence can modify the Rabi splitting and two-photon absorption, through shifting and broadening of spectral lines for on- and off-resonance pumping, respectively. In addition, we report on the enhancement of absorptionless dispersion (i.e. refractive index for on and around probe resonance) and two-photon absorption, via coherent control of the driving contribution of the pump field.
When a two-level system interacts resonantly with a saturating pump laser, the absorption profile of a probe wave in the Rabi sidebands resembles two separate dispersion profiles. At sufficiently high probe intensity this effect is accompanied by a dispersive profile in the pump-wave absorption, considered as a function of the probe-wave frequency, and also by a dip in the population of the upper state of the two-level system. The relative stabilization of the ground state is interpreted in terms of two-laser-photon processes where absorption of a pump (probe) photon is followed by stimulated emission of a probe (pump) photon. The dispersive absorption profile is attributed to the competition between three- and four-photon scattering processes.
Abstract The quantum dynamics of a system of Rb atoms, modeled by a V -type three-level system interacting with intense probe and pump pulses, are studied. The time-delay-dependent transient-absorption spectrum of an intense probe pulse is thus predicted, simulating pump-probe experiments in which this is preceded or followed by a strong pump pulse. Numerical results are interpreted in terms of an analytical model based on interaction operators , which quantify the transformation undergone by the system under the action of an intense pulse. The oscillating features of the resulting transient-absorption spectra, due to the coupling of several excited states, are thus interpreted in terms of the atomic population and phase changes imposed by the pump and probe pulses. Strong-field-induced phases and their influence on the resulting transient-absorption spectra are thereby investigated for different values of pump and probe intensities and frequencies, focusing on the atomic properties which are encoded in the absorption line shapes for positive and negative time delays.
We examine the absorption of a weak probe beam by a laser driven V-type atom with a pair of closely lying excited levels, where both the driving and probe lasers interact simultaneously with the two transitions. The effects of quantum interference among decay channels on the absorption spectra are also investigated. We introduce dipole moments in the dressed-state representation and the Hamiltonian in terms of the dressed states describing the interaction between the probe and the atom. In the degenerate case, features similar to that of a driven two-level atomic system are found due to some dark transitions in the spontaneous emission and the fact that the probe beam only detects certain transitions. In the nondegenerate case, the absorption spectrum is strongly influenced by the degree of quantum interference, resulting in different line shapes for emission peaks, absorption peaks, and dispersionlike profiles. The effect of probe polarization on the absorption spectrum is also investigated.