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AIP conference proceedings

Femtosecond Ramsey fringes in strongly-driven Rydberg systems

R. R. Jones, Chandra Raman, Douglass W. Schumacher, P. H. Bucksbaum

Published Jan 1, 1993• 2 citations
Publisher

Abstract

The evolution of atomic systems under the influence of two coherent, temporally separated 100 fs laser pulses has been studied. Ramsey interference fringes are observed in the populations of various energy levels as a function of delay between the two pulses. At high intensities the temporal interferograms are quite complicated and yield information on the couplings between all of the states in the atomic system. A simple three‐level system as well as localized and dark radial Rydberg wavepackets have been studied.

DOI
10.1063/1.45066

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Following the experiment of Jones et al. [Phys. Rev. Lett. 71, 2575 (1993)], we present a theory of coherent redistribution of population in a model Rydberg atom exposed to a sequence of two identical laser pulses separated in time and shorter in duration than the Rydberg-electron Kepler period. For different initial-population conditions, we solve the problem of redistribution in a fully analytical and rigorously nonperturbative way, thus obtaining discrete-state population amplitudes, dependent on laser intensity, and a time delay between the pulses. Using this solution, we study the population in a given state versus pulse delay (Ramsey fringes), as well as the corresponding Fourier spectrum, for both low and high laser intensities. From the number of frequency components and their positions in the Fourier spectrum, we deduce the redistribution of the initial-state population over a number of states by the first pulse. Within our model calculations we achieve qualitative agreement with the experimental observation of Jones et al. that an increase in laser intensity results in a general increase in the number of frequency components in the Fourier spectrum. Our theoretical results are also consistent with the experimental finding of Noordam et al. [Phys. Rev. Lett. 68, 1496 (1992)] that Raman transitions via the continuum between different Rydberg states are essential for population redistribution. We suggest new experiments to measure the effect of the initial-state depletion on the Fourier spectrum. As follows from our model calculations, some frequency components (both low and optical) present in the low-intensity Fourier spectrum should vanish in the high-intensity spectrum due to complete depletion of the initial state by the first pulse.

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Physical Review A•Jul 1, 1994•1 citation
The evolution of atomic systems under the influence of two coherent, temporally separated 100 fs laser pulses has been studied. Ramsey interference fringes are observed in the populations of various energy levels as a function of delay between the two pulses. At high intensities the temporal interferograms are quite complicated and yield information on the couplings between all of the states in the atomic system. A simple three‐level system as well as localized and dark radial Rydberg wavepackets have been studied.
We have studied the evolution of regular and ``dark'' radial wave packets under the influence of two coherent, temporally separated 100 fs laser pulses. The atomic states are probed by ramped-field ionization. The final state populations exhibit Ramsey oscillations with periods ranging from 2.6--1000 fs as a function of the delay between the two pulses. This time-domain bound-state interferometry reveals several new aspects of the dynamic evolution of wave packets in the presence of strong laser fields. Lowest order perturbation theory is inadequate to describe wave packet formations, even at the lowest intensities studied.
Following the experiment of Jones et al. [Phys. Rev. Lett. 71, 2575 (1993)], we present a theory of coherent redistribution of population in a model Rydberg atom exposed to a sequence of two identical laser pulses separated in time and shorter in duration than the Rydberg-electron Kepler period. For different initial-population conditions, we solve the problem of redistribution in a fully analytical and rigorously nonperturbative way, thus obtaining discrete-state population amplitudes, dependent on laser intensity, and a time delay between the pulses. Using this solution, we study the population in a given state versus pulse delay (Ramsey fringes), as well as the corresponding Fourier spectrum, for both low and high laser intensities. From the number of frequency components and their positions in the Fourier spectrum, we deduce the redistribution of the initial-state population over a number of states by the first pulse. Within our model calculations we achieve qualitative agreement with the experimental observation of Jones et al. that an increase in laser intensity results in a general increase in the number of frequency components in the Fourier spectrum. Our theoretical results are also consistent with the experimental finding of Noordam et al. [Phys. Rev. Lett. 68, 1496 (1992)] that Raman transitions via the continuum between different Rydberg states are essential for population redistribution. We suggest new experiments to measure the effect of the initial-state depletion on the Fourier spectrum. As follows from our model calculations, some frequency components (both low and optical) present in the low-intensity Fourier spectrum should vanish in the high-intensity spectrum due to complete depletion of the initial state by the first pulse.
Molecular or atomic coherence generated with the irradiation of ultrashort optical pulses should make a significant role for realizing the control of quantum states in a matter. By virtue of the advancement of the ultrashort light sources towards the short wavelength region, the energy range of the quantum states that could be coherently generated reached much more than 15 eV at the present [1] . In particular, Ramsey-type interference fringes observed by scanning the delay between a pair of phase-locked XUV femtosecond pulses unveiled spectral information of the atomic states [2] - [4] . The time ranges of the delay scans in such preceding studies were long enough to finely resolve the spectral features, while the XUV pulse pairs could not temporally overlap because the light sources were split into two before generating the XUV pulses. The near 0 delay control of the XUV pulse pair is important for investigating the dynamics of a cationic system entangled with an ionized continuum electron [5] . In this paper, we performed the delay scan of the XUV pulse pair starting from the complete temporal overlap to show that the optical interference seamlessly continued to the Ramsey-type atomic interference as a prototype of such study.
Rydberg states in sodium are excited using two identical broadband, dye laser pulses. Each 8 ns pulse has a bandwidth of approximately 45 cm -1 , and Rydberg states with several different principal quantum numbers are simultaneously excited. The number of Rydberg atoms created by each pulse pair is detected as a function of the delay between the two pulses. Strong modulations in the population in each Rydberg level and in the total Rydberg signal are observed. The oscillations are identical to those which would be expected if two transform-limited, 300 fs laser pulses had been used. We show explicitly, in the limit of weak pulses, that these 'bound-state interferograms' acquired using the time-domain, Ramsey separated-oscillatory fields method are only dependent on the excitation cross section and pulse frequency spectrum. Therefore, weak-field interferograms do not in themselves give information on the spatial-distribution of the electron wavefunction. In addition, the benefits of using strong or weak pulses for bound-state interferometry are discussed.
The AC Stark shift of electronic levels is ubiquitous in the interaction of intense light fields with atoms and molecules. As the light intensity changes on the rising and falling edges of a femtosecond laser pulse, it shifts the Rydberg states in and out of multiphoton resonances with the ground state. The two resonant pathways for transient excitation arising at the leading and the trailing edges of the pulse generate Young's type interference, generally referred to as the St\"uckelberg oscillations. Here we report the observation of the St\"uckelberg oscillations in the intensity of the coherent free-induction decay following resonant multiphoton excitation. Moreover, combining the experimental results with accurate numerical simulations and a simple model, we use the St\"uckelberg oscillations to recover the population dynamics of strongly driven Rydberg states inside the laser pulse by all-optical measurements after the end of the pulse. We demonstrate the potential of this spectroscopy to characterize lifetimes of Rydberg states dressed by laser fields with strengths far exceeding the Coulomb field between the Rydberg electron and the core.
It is shown theoretically that Ramsey fringes can be produced when a laser-assisted reaction of the form A2{\mathrm{A}}_{2}A2​+${\mathrm{A}}_{1}^{\ensuremath{'}}$+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}A1{\mathrm{A}}_{1}A1​+${\mathrm{A}}_{2}^{\ensuremath{'}}$ is driven by a pair of ultrafast radiation pulses, each of whose temporal widths is less than the duration ${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$ of a collision between the A and A\ensuremath{'} atoms. The excitation profile of the laser-assisted collision is calculated as a function of detuning of the laser field frequency from the initial- to final-state transition frequency. For radiation pulses separated by time T, Ramsey fringes appear separated in frequency by ${\mathrm{T}}^{\mathrm{\ensuremath{-}}1}$. The modulation depth and shift of the central Ramsey fringe as a function of (T/${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$) provide information about the collisional interaction. Both the weak- and strong-field regions are considered and comparison with laser-assisted collisions using excitation pulses having temporal widths greater than ${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$ is made.