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Journal of Physics B Atomic Molecular and Optical Physics

Bound-state interferometry using incoherent light

R. R. Jones, Douglass W. Schumacher, Thomas F. Gallagher, P. H. Bucksbaum

Published Jul 14, 1995• 54 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/28/13/001

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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.
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.
Pulsed dye lasers are used to excite sodium atoms into a coherent superposition of high Rydberg nd(2D32,2D52)\mathrm{nd} (^{2}\mathrm{D}_{\frac{3}{2}},^{2}D_{\frac{5}{2}})nd(2D23​​,2D25​​) states. Analysis of the field ionization behavior of these atoms reveals the time evolution of the superposition state. Rapid application of a weak electric field projects different components of the superposition state onto states having identifiably different field ionization behavior. Analysis of the signal from subsequent field ionization as a function of the time of weak-field application reveals fine-structure quantum beats. These beats result from the time development of the original superposition state. Measurements of the fine-structure quantum beat frequency are presented for the principal quantum numbers n=32,34,35,36,38,and40n=32, 34, 35, 36, 38, \mathrm{and} 40n=32,34,35,36,38,and40.
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.
Matter-wave interferometry has many possible uses, ranging from tests of funda- mental physics to applications in sensing. In order to achieve this interferometry, quantum superpositions of spatially-separated components need to be generated. There are several possible methods to accomplish this using Rydberg atoms; this thesis presents the experimental investigation of two of these. Both of these methods use inhomogeneous electric fields to spatially split beams of Rydberg atoms. In the first method, field distributions were generated above two-dimensional electrode structures and used to transversely split beams of helium Rydberg atoms into pairs of components spatially separated by up to 15.6 mm. Effects of amplitude modulation of the electric fields of this beam splitter were shown to cause particle losses through transitions into unconfined Rydberg-Stark states. This led to further studies of the depolarisation of Rydberg-Stark states in radio-frequency electric fields. Through this work it is shown that both ‘resonant’ and ‘non-resonant’ broadband modulation with amplitudes on the order of 10 mV·cm⁻¹ are sufficient to cause significant depolarisation of initially prepared quantum states on a timescale of 5 μs in a static offset electric field of 0.43 V·cm⁻¹. In a second class of experiments, matter-wave interferometry has been per- formed with helium atoms in high Rydberg states. In this work a series of mi- crowave and electric field gradient pulses were used to create a spatial separation between two components of a coherent superposition of states, while ensuring that the momenta of these components were equal at the end of the process to enable matter-wave interference to be observed. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ∼ 320 nm and displacements of up to 150 pm were observed between the pairs of matter-wave components at the end of the interferometry sequences.
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.
An experiment on Ramsey interferometry of the 37S 1/2 → 37P 1/2 microwave transition in sodium Rydberg atoms has been performed. Interaction of Rydberg atoms with a cw microwave radiation was effectively controlled by a pulse of weak (<1 V cm −1 ) electric field, that manipulated the transition frequency near 70 050 MHz. The pulse detuned the microwave radiation from exact resonance, and induced additional phases to the wavefunctions of Rydberg states due to the quadratic Stark shifts. As a result, the Ramsey fringes were observable both on scanning the frequency of the microwave field and on scanning the strength of the electric field pulse. The experiment confirmed that this Stark-switching technique provides a fast and effective control of the atom–light interactions, and preserves the atomic coherence. Possible applications of this technique to experiments on quantum computers are discussed.