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Journal of Physics B Atomic Molecular and Optical Physics

Time-resolved spectroscopy of the dynamic Stark effect

Timothy W. Schmidt, Rodrigo López-Martens, Gareth O. Roberts

Published Feb 23, 2004• 7 citations
Publisher

Abstract

This study reports on the ac Stark effect of nitric oxide electron-vibration (vibronic) levels dressed by an intense, bichromatic laser field. The aims of the work are to make quantitative measurements of the magnitude of the ac Stark shift of vibrational levels connected by the A 2 Σ + ← X 2 Π 1/2 transition and to map out the cycle-averaged level separation during the Stark field. In pump–probe experiments at intensities up to 30 TW cm −2 , the ac Stark shift of the A 2 Σ + v A = 2 ← X 2 Π 1/2 v X = 0 transition is found to be Δ ( S ) 2←0 (800 nm) = 0.34 ± 0.05 U p , where U p is the ponderomotive energy. By varying the time delay between component fields, the time dependence of the population in the A 2 Σ + v A = 2 state is mapped out under different intensity conditions. Fluorescence monitoring of the upper level serves to identify the Stark-shifted transition and reveals that real population remains in the upper level after interacting with the short-pulse laser fields. Semiclassical calculations of NO irradiated by a bichromatic field indicate the direction of the A 2 Σ + and X 2 Π 1/2 level shifts and show that the population promoted to and retained in the A 2 Σ + state is determined predominantly by intra-Rydberg state interactions rather than by multiphoton loss processes. The calculations also indicate that the magnitude of the ac Stark effect of the A 2 Σ + ← X 2 Π 1/2 transition depends on the spatial orientation of the molecule with respect to the linear polarization sense of the applied laser field.

DOI
10.1088/0953-4075/37/5/015

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This study reports on the ac Stark effect of nitric oxide electron-vibration (vibronic) levels dressed by an intense, bichromatic laser field. The aims of the work are to make quantitative measurements of the magnitude of the ac Stark shift of vibrational levels connected by the A 2 Σ + ← X 2 Π 1/2 transition and to map out the cycle-averaged level separation during the Stark field. In pump–probe experiments at intensities up to 30 TW cm −2 , the ac Stark shift of the A 2 Σ + v A = 2 ← X 2 Π 1/2 v X = 0 transition is found to be Δ ( S ) 2←0 (800 nm) = 0.34 ± 0.05 U p , where U p is the ponderomotive energy. By varying the time delay between component fields, the time dependence of the population in the A 2 Σ + v A = 2 state is mapped out under different intensity conditions. Fluorescence monitoring of the upper level serves to identify the Stark-shifted transition and reveals that real population remains in the upper level after interacting with the short-pulse laser fields. Semiclassical calculations of NO irradiated by a bichromatic field indicate the direction of the A 2 Σ + and X 2 Π 1/2 level shifts and show that the population promoted to and retained in the A 2 Σ + state is determined predominantly by intra-Rydberg state interactions rather than by multiphoton loss processes. The calculations also indicate that the magnitude of the ac Stark effect of the A 2 Σ + ← X 2 Π 1/2 transition depends on the spatial orientation of the molecule with respect to the linear polarization sense of the applied laser field.
In this paper we demonstrate, through numerical calculations, the possibility of determining the field dependence of the ac Stark effect through the interaction of an atom (or molecule) with a bichromatic ultrafast laser field. The time-dependent Schrödinger equation is solved for a single active electron confined to move in a square-well potential distorted by an intense Stark field in combination with a perturbative probe field which connects a pair of levels through photon absorption. The aim is to determine the field parameters that allow the dependence of the dynamic shift of the optically connected levels on the Stark field to be mapped out in real time. The calculations show that this can be achieved when the duration of the probe field is at least as short as the half-cycle period of the Stark field. An experimental realization of the proposed measurement scheme and its limitations are discussed. It is also possible, in principle, to adopt the ac Stark effect to determine the absolute phase of the carrier wave of an ultrafast laser pulse.
We have measured the ac Stark effect in a two-zone stimulated Raman interaction in a sodium atomic beam. In addition, we have derived simple theoretical expressions for the ac Stark shift, based on a closed three-level system, in the Λ configuration, and have achieved qualitative agreement with the data. In particular, the magnitude and sense of the ac Stark shifts are found to depend on laser intensities as well as on the initial populations of the two low-lying levels of the Λ configuration. Specifically, the observed ac Stark shifts are smaller for larger laser intensities and also for smaller initial population differences between the two low-lying levels. The ac Stark effect must be considered for many potential applications of the Raman effect, such as a Raman clock. In this connection, we have identified conditions for the reduction of the ac Stark shift in our sodium Raman clock.
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.
Nonresonant ac Stark shifts of Rydberg states in Xe have been investigated by probing an atomic transition with a weak UV light in the presence of an intense YAG-laser pulse. Rydberg atoms produced through two-photon excitation, 5p → np (n = 15–48) and 5p → nf (n = 12–49), are subsequently ionized. IR-laser-induced shifts of the resonant ionization profiles are then measured. The measured shift, 3.9 ± 0.3 cm−1 at 1010 W cm−2, is more than a factor of 2 smaller than that expected from the basis of ponderomotive term, 8.5 cm−1 at 1010 W cm−2. In addition, the shift varies linearly as a function of the IR-laser intensity and does not depend on the principal quantum number of the np and nf series investigated here.
We investigate AC Stark-shifted resonances in argon with ultrashort near-infrared pulses. Using 30 fs pulses, we observe periodic enhancements of the excitation yield in the intensity regions corresponding to the absorption of 13 and 14 photons. By reducing the pulse duration to 6 fs with only a few optical cycles, we also demonstrate that the enhancements are significantly reduced beyond what is measurable in the experiment. Comparing these to numerical predictions, which are in quantitative agreement with experimental results, we find that even though the quantum state distribution can be broad, the enhancements are largely due to the efficient population of a select few AC Stark-shifted resonant states rather than the closing of an ionization channel. Because these resonances are dependent on the frequency and intensity of the laser field, the broad bandwidth of the 6 fs pulses means that the resonance condition is fulfilled across a large range of intensities. This is further exaggerated by volume-averaging effects, resulting in excitation of the 5g5g5g state at almost all intensities and reducing the apparent magnitude of the enhancements. For 30 fs pulses, volume averaging also broadens the quantum state distribution, but the enhancements are still large enough to survive. In this case, selectivity of excitation to a single state is reduced below 25% of the relative population. However, an analysis of time-dependent Schr\"odinger equation simulations indicates that excitation of up to 60% into a single state is possible if volume averaging can be eliminated and the intensity can be precisely controlled.
We present results from a time-dependent two-level-plus-continuum model of multiphoton ionization in order to better understand the short-pulse photoelectron spectrum resulting from multiphoton ionization and the role of intermediate states. Both resonant and nonresonant population transfer to the upper state are found to play an important role in the multiphonon ionization process. The dynamic modeling reveals the potential for broadening and shifting peaks in the photoelectron spectrum. However, we conclude that despite the complex dynamics of the excitation, short-pulse photoelectron spectra can be used to measure ac Stark shifts of both ponderomotively and nonponderomotively shifted states in strong laser fields.