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The Journal of Chemical Physics

Stark-induced adiabatic Raman passage examined through the preparation of D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0)

William E. Perreault, Nandini Mukherjee, Richard N. Zare

Published Jun 18, 2019• 14 citations
Publisher

Abstract

We study the conditions that must be met for successful preparation of a large ensemble in a specific target quantum state using Stark-induced adiabatic Raman passage (SARP). In particular, we show that the threshold condition depends on the relative magnitudes of the Raman polarizability (r0v) and the difference of the optical polarizabilities (Δα00→vj) of the initial (v = 0, j = 0) and the target (v, j) rovibrational levels. Here, v and j are the vibrational and rotational quantum numbers, respectively. To illustrate how the operation of SARP is controlled by these two parameters, we experimentally prepared D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0) in a beam of D2 (v = 0, j = 0) molecules using a sequence of partially overlapping pump and Stokes laser pulses. By comparing theory and experiment, we were able to determine the Raman polarizability r02 ≈ 0.3 × 10−41 Cm/(V/m) and the difference polarizabilities Δα00→20 ≈ 1.4 × 10−41 Cm/(V/m) and Δα00→22 ≈ 3.4 × 10−41 Cm/(V/m) for the two Raman transitions. Our experimental data and theoretical calculations show that because the ratio r/Δα is larger for the (0,0) → (2,0) transition than the (0,0) → (2,2) transition, much less optical power is required to transfer a large population to the (v = 2, j = 0) level. Nonetheless, our experiment demonstrates that substantial population transfer to both the D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0) is achieved using appropriate laser fluences. Our derived threshold condition demonstrates that with increasing vibrational quantum number, it becomes more difficult to achieve large amounts of population transfer.

DOI
10.1063/1.5109261

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We study the conditions that must be met for successful preparation of a large ensemble in a specific target quantum state using Stark-induced adiabatic Raman passage (SARP). In particular, we show that the threshold condition depends on the relative magnitudes of the Raman polarizability (r0v) and the difference of the optical polarizabilities (Δα00→vj) of the initial (v = 0, j = 0) and the target (v, j) rovibrational levels. Here, v and j are the vibrational and rotational quantum numbers, respectively. To illustrate how the operation of SARP is controlled by these two parameters, we experimentally prepared D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0) in a beam of D2 (v = 0, j = 0) molecules using a sequence of partially overlapping pump and Stokes laser pulses. By comparing theory and experiment, we were able to determine the Raman polarizability r02 ≈ 0.3 × 10−41 Cm/(V/m) and the difference polarizabilities Δα00→20 ≈ 1.4 × 10−41 Cm/(V/m) and Δα00→22 ≈ 3.4 × 10−41 Cm/(V/m) for the two Raman transitions. Our experimental data and theoretical calculations show that because the ratio r/Δα is larger for the (0,0) → (2,0) transition than the (0,0) → (2,2) transition, much less optical power is required to transfer a large population to the (v = 2, j = 0) level. Nonetheless, our experiment demonstrates that substantial population transfer to both the D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0) is achieved using appropriate laser fluences. Our derived threshold condition demonstrates that with increasing vibrational quantum number, it becomes more difficult to achieve large amounts of population transfer.
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 discuss various theoretical issues that arise when one extends the conventional stimulated Raman adiabatic passage, involving a pump pulse preceded by a Stokes pulse, to situations in which the pump interaction involves a two-photon transition. As in the simpler cases, it is possible to obtain complete population transfer between an initial state and a targeted final state, if certain general conditions on the pulses are met. We point out important considerations, associated with dynamic Stark shifts and multiphoton ionization, which make successful population transfer more difficult in the multiphoton extension. We illustrate these problems and requirements by considering specific examples of excitation in metastable helium.
We prepare an ensemble of isolated rovibrationally excited (v = 1, J = 2) H2 molecules in a phase-locked superposition of magnetic sublevels M using Stark-induced adiabatic Raman passage with linearly polarized single-mode pump (at 532 nm, ∼6 ns pulse duration, 200 mJ/pulse) and Stokes (699 nm, ∼4 ns pulse duration, 20 mJ/pulse) laser excitation. A biaxial superposition state, given by [line]ψ(t)⟩ = 1/√(2)[[line]ν = 1, J = 2, M = -2⟩ - [line]ν = 1, J = 2, M = +2⟩], is prepared with linearly but cross-polarized pump and Stokes laser pulses copropagating along the quantization z-axis. The degree of phase coherence is measured by using the O(2) line of the H2 E,F-X (0,1) band via 2 + 1 resonance enhanced multiphoton ionization (REMPI) at 210.8 nm by recording interference fringes in the REMPI signal in a time-of-flight mass spectrometer as the direction of the UV laser polarization is rotated using a half-wave plate. Nearly 60% population transfer from H2 (v = 0, J = 0) ground state to the superposition state in H2 (v = 1, J = 2) is measured from the depletion of the Q(0) line of the E,F-X (0,0) band as the Stokes frequency is tuned across the (v = 0, J = 0) → (v = 1, J = 2) Raman resonance.
We suggest that infrared stimulated Raman adiabatic passage, a coherent multiple excitation process, can be used to create a superposition of (2J+1) highly correlated M-state sublevels of a rigid rotor molecule with vibrational level v and rotational level J. This method employs the (v=0,J-2) to (v=2,J) S-branch transition, which is carried out in a counterintuitive manner in which the v=1 to v=2 transition is pumped prior to the v=0 to v=1 transition, causing nearly complete population transfer to the v=2 final level. We use perpendicular and parallel linearly polarized infrared excitation (biaxial excitation). Specifically, the perpendicular polarization connects the v=1 intermediate level to the final vibrational level v=2, and the parallel polarization connects the initial level v=0 to the intermediate level v=1. By this means we break the cylindrical symmetry for an ensemble of vibrationally excited molecules in a rovibrational eigenstate (v=2,J). The angular momentum polarization is determined by the relative phases rather than by the populations of the magnetic M-sublevels. For the phase correlated ensemble, the angular momentum polarization can be considered as a purely quantum mechanical effect. Using a fully general density matrix treatment, we illustrate this approach by considering a beam of carbon monoxide (CO) molecules. We find that significant polarization for J=2, 5, and 10 can be achieved with a cw infrared laser source having modest power (∼100 mW/mm(2)). We believe that this technique is a general one and may offer an experimentally accessible new platform for different applications, from scattering studies with M-state entangled ensembles of molecules to logic gate operations of a quantum computer.
We explore theoretically the rovibrational dynamics of stimulated Raman adiabatic passage (STIRAP) in molecular electronic states including both the rotational and the vibrational degrees of freedom, with the LiH molecule as an example. By using a pure rovibrational state as initial state, we find that, under the condition of two-photon resonance, an efficient rovibrational population transfer can be achieved via STIRAP in molecular electronic states and the desired target state can be selected by adjusting laser-pulse parameters. Besides the interested rovibrational states, however, some unwanted rovibrational states may affect population transfer process, especially while the two-photon detuning is taken into account. By inspecting the evolution process of wave packet, we can easily search these unwanted rovibrational states and study their influences. Moreover, the effect of rotational temperature on the population transfer process is discussed using thermal mixed state as initial state.
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.