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The Journal of Chemical Physics

Can stimulated Raman pumping cause large population transfers in isolated molecules?

Nandini Mukherjee, Richard N. Zare

Published Nov 9, 2011• 13 citations
Publisher

Abstract

When stimulated Raman pumping (SRP) is applied to a stream of isolated molecules, such as found in a supersonic molecular beam expansion, we show that SRP can neither saturate nor power broaden a molecular transition connecting two metastable levels that is resonant with the energy difference between the pump and Stokes laser pulses. Using the optical Bloch-Feynman equations, we discuss the pumping of the hydrogen molecule from H(2) (v = 0, J = 0, M = 0) to H(2) (v = 1, J = 2, M = 0) as an illustration of how coherent population return severely reduces the SRP pumping efficiency unless the pump and Stokes laser pulses are applied with an appropriate relative delay and ratio of intensities.

DOI
10.1063/1.3657832

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When stimulated Raman pumping (SRP) is applied to a stream of isolated molecules, such as found in a supersonic molecular beam expansion, we show that SRP can neither saturate nor power broaden a molecular transition connecting two metastable levels that is resonant with the energy difference between the pump and Stokes laser pulses. Using the optical Bloch-Feynman equations, we discuss the pumping of the hydrogen molecule from H(2) (v = 0, J = 0, M = 0) to H(2) (v = 1, J = 2, M = 0) as an illustration of how coherent population return severely reduces the SRP pumping efficiency unless the pump and Stokes laser pulses are applied with an appropriate relative delay and ratio of intensities.
The feasibility of a novel technique for efficient and selective population transfer from a thermally populated level 1 via an intermediate state 2 to level 3 is experimentally demonstrated. It is shown for sodium dimers that the process of on- or near-resonance stimulated Raman scattering with only partially overlapping laser beams is, in particular, useful for the selective population of high vibrational levels of particles in a molecular beam. This is achieved when the interaction with the Stokes laser, coupling levels 2 and 3, begins earlier than the interaction with the pump laser. The phenomenon, which is closely related to the formation of ‘‘trapped states,’’ is quantitatively explained using the basis of eigenstates of molecules strongly coupled to the radiation fields. The similarity and difference to related techniques such as rapid adiabatic passage phenomena in two-level systems, off-resonant stimulated Raman scattering, or stimulated emission pumping is briefly discussed.
Abstract The population transfer of a NaH molecule from the ground state X 1 Σ + to the target state A 1 Σ + via stimulated Raman adiabatic passage (STIRAP) is investigated. The results show that the intensity, delay time and detuning have a significant effect on population transfer. A large population transfer is observed with increased pump and Stokes intensity, especially when the pump and Stokes intensity match. Population transfer also depends on the delay time between the pump laser pulse and the Stokes laser pulse. The detuning of the two pulses influences the population transfer. Efficient population transfer can be realized under the resonant or two-photon resonant condition.
The nonlinear regime of stimulated Raman scattering (SRS) may be reached in two ways. The best known is that of depletion of the pump laser as a large number of photons are scattered into the Stokes field. There is, however, another way in which gain saturation can occur, that is, by depletion of the atomic population while the laser remains undepleted. The equations which describe SRS, including damping and population inversion,1 are remarkably similar to those of well-known theories of two-level superfluorescence, and it is possible by analogy to define a delay time τ D for cooperative Raman scattering (CRS). This delay time is inversely proportional to the spontaneous scattering rate, which depends on the pump laser intensity. A sufficient condition for CRS is that the spontaneous Stokes linewidth Γ is very much greater than τ D − 1 . The only other requirement is that there be more laser photons than scatterers, so that τ D is independent of the number of scatterers. The S(1) transition in molecular hydrogen, when excited by a short (≅ 100-ps) laser pulse, provides a possible system for observing pure CRS. Similar studies have been carried out previously2 for Γ ≅ τ D − 1 .
By using Stark-induced adiabatic Raman passage (SARP) with partially overlapping nanosecond pump (532 nm) and Stokes (683 nm) laser pulses, 73% ± 6% of the initial ground vibrational state population of H(2) (v = 0, J = 0) is transferred to the single vibrationally excited eigenstate (v = 1, J = 0). In contrast to other Stark chirped Raman adiabatic passage techniques, SARP transfers population from the initial ground state to a vibrationally excited target state of the ground electronic surface without using an intermediate vibronic resonance within an upper electronic state. Parallel linearly polarized, co-propagating pump and Stokes laser pulses of respective durations 6 ns and 4.5 ns, are combined with a relative delay of ~4 ns before orthogonally intersecting the molecular beam of H(2). The pump and Stokes laser pulses have fluences of ~10 J/mm(2) and ~1 J/mm(2), respectively. The intense pump pulse generates the necessary sweeping of the Raman resonance frequency by ac (second-order) Stark shifting the rovibrational levels. As the frequency of the v = 0 → v = 1 Raman transition is swept through resonance in the presence of the strong pump and the weaker delayed Stokes pulses, the population of (v = 0, J = 0) is coherently transferred via an adiabatic passage to (v = 1, J = 0). A quantitative measure of the population transferred to the target state is obtained from the depletion of the ground-state population using 2 + 1 resonance enhanced multiphoton ionization (REMPI) in a time-of-flight mass spectrometer. The depletion is measured by comparing the REMPI signal of (v = 0, J = 0) at Raman resonance with that obtained when the Stokes pulse is detuned from the Stark-shifted Raman resonance. No depletion is observed with either the pump or the Stokes pulses alone, confirming that the measured depletion is indeed caused by the SARP-induced population transfer from the ground to the target state and not by the loss of molecules from photoionization or photodissociation. The two-photon resonant UV pulse used for REMPI detection is delayed by 20 ns with respect to the pump pulse to avoid the ac Stark shift originating from the pump and Stokes laser pulses. This experiment demonstrates the feasibility of preparing a large ensemble of isolated molecules in a preselected single quantum state without requiring an intermediate vibronic resonance.
We report the experimental realization of coherent population transfer from the 23S2{}^{3}S23S state to 23P2{}^{3}P23P fine-structure levels of helium, using the technique of hyper-Raman adiabatic passage, in which the pump-laser coupling involves a two-photon transition. We discuss the dependence of population transfer upon pump and Stokes detunings, and show that by suitably setting the detunings one can transfer population efficiently as either a two-step process to final states or as a single-step two-photon transition to an intermediate state. We use an adiabatic-state picture to interpret these experimental results. Since the optimum detuning depends on the pump laser intensity the transfer efficiency is compromised by the variation of the intensity across the spatial profile of the laser beam. Our experimental data agree well with numerical simulation based on density-matrix equations, including all 15 magnetic sublevels.
We undertake a theoretical investigation of the coherent optical propagation of Stokes light in a collisionally broadened three-level Raman amplifier. The Stokes light consists of two distinct spectral components: off-resonance stimulated Raman scattering and on-resonance stimulated fluorescence, induced by collisional transfer of population to a near-resonant intermediate state of the atomic system. Our model is based on the semiclassical Maxwell-Bloch formalism where the separation of the Stokes light into two components results in an expansion from the usual 9 to 13 atomic variables. We investigate the model both analytically and numerically. We point out the physical contributions to the simultaneous evolution of pump, fluorescence, and Raman light. We discuss the development during propagation of these separate pulses, emphasizing the nonlinear effects that lead to saturation.