Analytical investigation of one-dimensional Rydberg atoms interacting with half-cycle pulses

Bersons, I.; Veilande, Rita

doi:10.1103/physreva.69.043408

Cited by 23 publications

(34 citation statements)

References 11 publications

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“…We have chosen to work with three different values of q, 0.0010, 0.0016 and 0.0020 a.u., and used dotted, solid and dashed lines to represent the corresponding curves for |T n n |. Note that q = 0.0016 a.u., corresponds to qn 2 = 1, a relation often used in the weak electric field limit [6] when only a few neighbouring states are populated. From this figure we see that the curves for |T n n | becomes more and more peaked at the centre (n = 25) and flat on the wings as the value of q decreases.…”

Section: Evolution Of Wave Packets and Related Observablesmentioning

confidence: 99%

“…In particular, x ii calculated using (5) exhibits an awkward singularity although i|x|i represents a well-defined function. We note that the expression for T n n evaluated in the semiclassical approximation by the method of stationary phase is free from this problem and has been used by Bersons and Veilande [6] to reproduce experimental results of Wetzels et al [9] on the interaction of Rydberg atoms with half-cycle pulses. It is quite straightforward however to derive an exact expression for the transition matrix element that can be used to evaluate the limit in (5) unambiguously for both f = i and f = i.…”

Section: Introductionmentioning

confidence: 96%

“…Consequently, we can use the form factors [6] T n n (q) = n |e iqx |n (1) for the weight factors in superposing energy eigenstates to construct the wave packet for a 1D atom. In terms of these transition amplitudes the Rydberg wave packet ψ(x, t) can be written as…”

Section: Introductionmentioning

confidence: 99%

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Electron Rydberg wave packets in one-dimensional atoms

et al. 2010

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An expression for the transition probability or form factor in one-dimensional Rydberg atom irradiated by short half-cycle pulse was constructed. In applicative contexts, our expression was found to be more useful than the corresponding result given by Landau and Lifshitz. Using the new expression for the form factor, the motion of a localized quantum wave packet was studied with particular emphasis on its revival and super-revival properties. Closed form analytical expressions were derived for expectation values of the position and momentum operators that characterized the widths of the position and momentum distributions. Transient phase-space localization of the wave packet produced by the application of a single impulsive kick was explicitly demonstrated. The undulation of the uncertainty product as a function of time was studied in order to visualize how the motion of the wave packet in its classical trajectory spreads throughout the orbit and the system becomes nonclassical. The process, however, repeats itself such that the atom undergoes a free evolution from a classical, to a nonclassical, and back to a classical state.

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Section: Evolution Of Wave Packets and Related Observablesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

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Electron Rydberg wave packets in one-dimensional atoms

et al. 2010

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“…transferred to the atom from HCP. For the 1D case, it was derived by Bersons and Veilande [5], although their formula needs to be multiplied by nn :…”

Section: Rydberg Wave Packet Dynamicsmentioning

confidence: 99%

One-Dimensional versus Three-Dimensional Approaches to the Rydberg Wave Packet Dynamics

Kopyciuk

Parzyński

2006

Acta Phys. Pol. A

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“…The one-dimensional atomic model is an excellent approximation for the Rydberg atom in the extreme Stark states and can faithfully mimic many properties of three--dimensional atoms [5]. Moreover, in this case one can construct an exact analytical expression for the wave packet irrespective of whether it is formed by the impact of a single HCP or two time delayed HCPs [6,7].…”

Section: Introductionmentioning

confidence: 99%

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

Chatterjee¹,

Saha

Talukdar

2011

Acta Phys. Pol. A

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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.

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Analytical investigation of one-dimensional Rydberg atoms interacting with half-cycle pulses

Cited by 23 publications

References 11 publications

Electron Rydberg wave packets in one-dimensional atoms

Electron Rydberg wave packets in one-dimensional atoms

One-Dimensional versus Three-Dimensional Approaches to the Rydberg Wave Packet Dynamics

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

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