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Physical Review A

Population of Stark wave-packet states by cw laser excitation

Jonathan Baugh, W. P. Garver, Charles E. Burkhardt, Jacob J. Leventhal

Published Aug 1, 1998• 1 citation
Publisher

Abstract

Using a unique method, we create coherent states in an atom by periodically (\ensuremath{\sim}100--200 MHz) applying a low-amplitude, \ensuremath{\sim}5-V/cm, ns electric-field pulse that drives the atoms to a realm where many stationary states lie within a very narrow energy range. Using a cw laser we excite a coherent superposition of these coherent states and probe the attributes of such a state in the frequency domain (rather than in the time domain). We show that such coherent superpositions exhibit localized electronic probability densities and, therefore, qualify as wave packets.

DOI
10.1103/physreva.58.r785

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Using a unique method, we create coherent states in an atom by periodically (\ensuremath{\sim}100--200 MHz) applying a low-amplitude, \ensuremath{\sim}5-V/cm, ns electric-field pulse that drives the atoms to a realm where many stationary states lie within a very narrow energy range. Using a cw laser we excite a coherent superposition of these coherent states and probe the attributes of such a state in the frequency domain (rather than in the time domain). We show that such coherent superpositions exhibit localized electronic probability densities and, therefore, qualify as wave packets.
Using techniques of ultrafast coherent control, we propose a method to produce high-purity high-l\mathcal{l}l (angular momentum) states in Rydberg Stark wave packets. Two time-delayed phase-locked laser pulses excite the atom from a low-lying ``launch state'' into a low-l\mathcal{l}l Rydberg wave packet, in the presence of a static electric field. By choosing the time delays between the pulses, and the static electric field, we find that a high-l\mathcal{l}l state with high purity can be created at the target time.
It is well known that for the nonrelativistic hydrogen atom it is possible to separate the Schrödinger equation in parabolic as well as spherical coordinates. The eigenfunctions obtained in these coordinate systems are each a suitable basis set in the absence of an electric field, but only the parabolic states, the Stark eigenfunctions, retain their character in the presence of a weak field. The properties of coherent superpositions of these Stark states are investigated and the motion of the resulting wave packet described. It is shown that a properly constituted superposition will mimic classical motion. It is also shown that the constant energy separation between adjacent Stark states of a given principal quantum number leads to periodic motion. In general, they split into distinct “clumps” of probability, but revive to form a single packet after each period. It is, however, possible to construct a packet that maintains its shape for all time.
High angular momentum Rydberg wave packets are studied. Application of carefully tailored electric fields to low angular momentum, high- n ( n ∼ 300) Rydberg atoms creates coherent superpositions of Stark states with near extreme values of angular momentum, [cursive l]. Wave packet components orbit the parent nucleus at rates that depend on their energy, leading to periods of localization and delocalization as the components come into and go out of phase with each other. Monitoring survival probability signals in the presence of position dependent probing leads to observation of characteristic oscillations based on the composition of the wave packet. The discrete nature of electron energy levels is observed through the measurement of quantum revivals in the wave packet localization signal. Time-domain spectroscopy of these signals allows determination of both the population and phase of individual superposition components. Precise manipulation of wave packets is achieved through further application of pulsed electric fields. Decoherence effects due to background gas collisions and electrical noise are also detailed. Quantized classical trajectory Monte-Carlo simulations are introduced and agree remarkably well with experimental results.
Ultrashort, nearly unipolar electric field pulses are used to produce novel dynamic states in Rydberg atoms. A single 500 fsec field pulse redistributes essentially all of the population from a single stationary Rydberg state to hundreds of different final states. The dynamic evolution of the nonstationary wave packet is monitored using a second, time-delayed pulse. The time-dependent momentum-space probability distribution of the wave packet can be retrieved experimentally using a classical impulse approximation.
Rabi oscillations of quantum population are known to occur in two-level systems driven by spectrally narrow laser fields. In this work we study Rabi oscillations induced by shaped broadband femtosecond laser pulses. Due to the broad spectral width of the driving field, the oscillations are initiated between a ground state and a coherent superposition of excited states, or a ``wave packet,'' rather than a single excited state. Our experiments reveal an intricate dependence of the wave-packet phase on the intensity of the laser field. We confirm numerically that the effect is associated with the strong-field nature of the interaction and provide a qualitative picture by invoking a simple theoretical model.