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arXiv:quant-ph/9608040 · Physical Review A

Revival structure of Stark wave packets

Robert Bluhm, V. Alan Kostelecký, Bogdan Tudose

Published Jan 1, 1997• 36 citations
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Abstract

The revival structure of Stark wave packets is considered. These wave packets have energies depending on two quantum numbers and are characterized by two sets of classical periods and revival times. The additional time scales result in revival structures different from those of free Rydberg wave packets. We show that Stark wave packets can exhibit fractional revivals. We also show that these wave packets exhibit particular features unique to the Stark effect. For instance, the wave functions can be separated into distinct sums over even and odd values of the principal quantum number. These even and odd superpositions interfere in different ways, resulting in unexpected periodicities in the interferograms of Stark wave packets.

DOI
10.1103/physreva.55.819

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Fractional Revival of Rydberg Wave Packets in Twice-Kicked One-Dimensional Atoms

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We study revival and fractional revival phenomena of wave packets in a one-dimensional Rydberg atom irradiated by two time-delayed half-cycle pulses using an autocorrelation function characterized by electronic transition probabilities as weighting factors rather than modeling them by a Gaussian or Lorentzian distribution.If the momentum (q2) delivered to the atom by the second kick is much smaller than that (q1) imparted by the first one, the times of revival and fractional revival coincide with those of the single kicked atom.For q2 ≥ q 1 4 appearance of revival and fractional revival depends on both the values of q2 and time delay t1 between the pulses but more sensitively on t1.The number of fractional revivals tends to become numerous as the value of t1 increases.

Acta Physica Polonica A•Sep 1, 2011•2 citations
The revival structure of Stark wave packets is considered. These wave packets have energies depending on two quantum numbers and are characterized by two sets of classical periods and revival times. The additional time scales result in revival structures different from those of free Rydberg wave packets. We show that Stark wave packets can exhibit fractional revivals. We also show that these wave packets exhibit particular features unique to the Stark effect. For instance, the wave functions can be separated into distinct sums over even and odd values of the principal quantum number. These even and odd superpositions interfere in different ways, resulting in unexpected periodicities in the interferograms of Stark wave packets.
We examine the revival structure of Rydberg wave packets. These wave packets exhibit initial classical periodic motion followed by a sequence of collapse, fractional/full revivals, and fractional/full superrevivals. The effects of quantum defects on wave packets in alkali-metal atoms and a squeezed-state description of the initial wave packets are also described. We then examine the revival structure of Rydberg wave packets in the presence of an external electric field, i.e., the revival structure of Stark wave packets. These wave packets have energies that depend on two quantum numbers and exhibit new types of interference behavior.
After a Rydberg wave packet forms, it is known to undergo a series of collapses and revivals within a time period called the revival time trevt_{\rm rev}trev​, at the end of which it resembles its original shape. We study the behavior of Rydberg wave packets on time scales much greater than trevt_{\rm rev}trev​. We find that after a few revival cycles the wave packet ceases to reform at multiples of the revival time. Instead, a new series of collapses and revivals commences, culminating after a time period tsr≫trevt_{\rm sr} \gg t_{\rm rev}tsr​≫trev​ with the formation of a wave packet that more closely resembles the initial packet than does the full revival at time trevt_{\rm rev}trev​. Furthermore, at times that are rational fractions of tsrt_{\rm sr}tsr​, we show that the motion of the wave packet is periodic with periodicities that can be expressed as fractions of the revival time trevt_{\rm rev}trev​. These periodicities indicate a new type of fractional revival, occurring for times much greater than trevt_{\rm rev}trev​. We also examine the effects of quantum defects and laser detunings on the revival structure of Rydberg wave packets for alkali-metal atoms.
The revival structure and evolution of Rydberg wave packets are studied on a time scale much greater than the revival time trevt_{\rm rev}trev​. We find a new level of revival structure and periodic motion different from that of the known fractional revivals. The new sequence of revivals culminates with the formation of a wave packet that more closely resembles the initial packet than does the full revival at time trevt_{\rm rev}trev​. We refer to such a revival as a superrevival. We also show that an initial radial wave packet may be described as a type of squeezed state known as a radial squeezed state. Our results apply not only for hydrogenic wave packets, but for wave packets in alkali-metal atoms as well in the context of quantum defect theory.
This paper begins with an examination of the revival structure and long-term evolution of Rydberg wave packets for hydrogen. We show that after the initial cycle of collapse and fractional or full revival, which occurs on the time scale trev{\mathit{t}}_{\mathrm{rev}}trev​, a new sequence of revivals begins. We find that the structure of the new revivals is different from that of the fractional revivals. The new revivals are characterized by periodicities in the motion of the wave packet with periods that are fractions of the revival time scale trev{\mathit{t}}_{\mathrm{rev}}trev​. These long-term periodicities result in the autocorrelation function at times greater than trev{\mathit{t}}_{\mathrm{rev}}trev​ having a self-similar resemblance to its structure for times less than trev{\mathit{t}}_{\mathrm{rev}}trev​. The new sequence of revivals culminates with the formation of a single wave packet that more closely resembles the initial wave packet than does the full revival at time trev{\mathit{t}}_{\mathrm{rev}}trev​, i.e., a superrevival forms. Explicit examples of the superrevival structure for both circular and radial wave packets are given. We then study wave packets in alkali-metal atoms, which are typically used in experiments. The behavior of these packets is affected by the presence of quantum defects that modify the hydrogenic revival time scales and periodicities. Their behavior can be treated analytically using supersymmetry-based quantum-defect theory. We illustrate our results for alkali-metal atoms with explicit examples of the revival structure for radial wave packets in rubidium.
In this paper, a coherent superposition of angular-momentum states created by absorption of polarized light by molecules is analyzed. Attention is paid to the time evolution of wave packets representing the spatial orientation of the internuclear axis of a diatomic molecule. Two examples are considered in detail. Molecules absorbing light in a permanent magnetic field experiencing the Zeeman effect and molecules absorbing light in a permanent electric field experiencing the quadratic Stark effect. In a magnetic field, we have a wave packet that evolves in time exactly as a classical dipole oscillator in a permanent magnetic field (classical-physics picture of the Zeeman effect). In the second case, we have a wave packet that goes through periodical changes of shape of the packet with revivals of the initial shape. This is pure quantum behavior. The classical motion of angular momentum in an electric field in the case of a quadratic Stark effect is known to be a periodic. Solutions obtained for wave packet evolution are briefly compared with Rydberg-state coherent wave packets and harmonic-oscillator wave packets. Zeeman and Stark effects in small molecules continuously attract the attention of researchers, theoreticians, as well as experimentalists. These investigations allow us to obtain a deeper understanding of the interaction of molecules with stationary external fields and also can be used as a practical tool to measure different molecular characteristics, such as permanent electric or magnetic dipole moments, intramolecular perturbations, etc. It is worthwhile analyzing these effects as an evolution of wave packets. All this motivates a comparison of the quantum and classical picture of Zeeman and Stark effects in molecules.PACS No.: 33.55.Be
We study revival and fractional revival phenomena of wave packets in a one-dimensional Rydberg atom irradiated by two time-delayed half-cycle pulses using an autocorrelation function characterized by electronic transition probabilities as weighting factors rather than modeling them by a Gaussian or Lorentzian distribution.If the momentum (q2) delivered to the atom by the second kick is much smaller than that (q1) imparted by the first one, the times of revival and fractional revival coincide with those of the single kicked atom.For q2 ≥ q 1 4 appearance of revival and fractional revival depends on both the values of q2 and time delay t1 between the pulses but more sensitively on t1.The number of fractional revivals tends to become numerous as the value of t1 increases.