Transferring Rydberg wave packets between islands across the chaotic sea

S. Yoshida, C. O. Reinhold, J. Burgdörfer, J. J. Mestayer, J. C. Lancaster, and F. B. Dunning

Phys. Rev. A 77, 013411 – Published 25 January 2008

Abstract

A protocol to take a Rydberg wave packet that is trapped in a period-1 island, i.e., that is synchronized with the period of the driving field, and transfer it to a period-2 island such that the wave packet evolves with twice the period is theoretically analyzed and experimentally demonstrated. Such period-doubling transitions are realized using two superposed trains of half-cycle pulses whose relative time delay is varied adiabatically. It is shown that this protocol provides a tool to manipulate the angle variable of a Rydberg wave packet while its conjugate principal action is maintained constant.

Received 22 October 2007

DOI:https://doi.org/10.1103/PhysRevA.77.013411

Authors & Affiliations

S. Yoshida¹, C. O. Reinhold^2,3, J. Burgdörfer^1,3, J. J. Mestayer⁴, J. C. Lancaster⁴, and F. B. Dunning⁴

¹Institute for Theoretical Physics, Vienna University of Technology, Vienna, Austria
²Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6372, USA
³Department of Physics, University of Tennessee, Knoxville, Tennessee 37996, USA
⁴Department of Physics and Astronomy and the Rice Quantum Institute, Rice University, Houston, Texas 77005-1892, USA

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Vol. 77, Iss. 1 — January 2008

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Images

Figure 1
(a)–(d) Poincaré surfaces of section of the periodically kicked Rydberg atom. (a) A single train is applied with a scaled kick strength of $Δ p_{0} = n_{i} Δ p = - 0.1$ and period $T = 6 ns$ . The stroboscopic snapshots are taken immediately before each kick using a cut at $(ρ, p_{ρ}) = (0, 0)$ . (b), (c) Two identical HCP trains with $Δ p_{0} = - 0.1$ and period $T^{'} = 12 ns$ and a relative time delay $τ = 3 ns$ are applied. The stroboscopic snapshots are taken immediately before each kick in the first (b) and second (c) train. (d) Same as (a) but for a period $T^{'} = 12 ns$ . The phase space coordinates are scaled to $n_{i} = 350$ , i.e., $z_{0} = z ∕ n_{i}^{2}$ and $p_{z 0} = p_{z} n_{i}$ . The upper panels show the associated pulse profiles and each HCP is approximated by a $δ$ function. The gray dashed lines in (a) show Kepler orbits with principal actions of $n_{A_{1}} ≃ 435$ and $n_{A_{2}} ≃ 465$ . In (b) the Kepler orbit with $n = n_{A_{2}}$ and in (c) and (d) that with $n = n_{A_{1}}$ is drawn. In (e), the steps involved in the protocol for transporting phase space density from island $A$ to $A_{1}$ or $A_{2}$ via $D$ are schematically indicated.Reuse & Permissions
Figure 2
(Color online) Calculated evolution of the phase space distribution of the wave packet for an initial mix of maximally polarized Stark states (see text). The phase space distributions are projected on the $(z, p_{z})$ plane and are taken at the times when the 1st, 10th, 21st, 31st, and 32nd HCPs reach their peak values. The shaded areas represent the stable islands associated with the transient train of pulses in which the wave packet is evolving. The colored line shows the profile of the applied HCP sequence.Reuse & Permissions
Figure 3
Power spectrum of the pulse train $F_{s}$ [Eq. (7)] as a function of the time delay $τ$ separating the two trains of HCPs. Each HCP has a pulse duration of $600 ps$ at full width at half maximum, $Δ p_{0} = - 0.1$ , and period $T^{'} = 2 T = 12 ns$ .Reuse & Permissions
Figure 4
Dependence of the calculated survival probabilities on (a) the strength and direction of the probe kicks, (b) the number of kicks $N$ in the HCP train, and (c) the delay time $τ_{delay}$ between the end of the HCP train and application of the probe kick. In (a) the probe HCP is applied $6 ns$ after the 31st (solid) and the 32nd (dashed) kicks. In (b) the train of HCPs is turned off after $N$ kicks and the probe HCP with strength $Δ p_{probe, 0} = - 0.8$ is applied $6 ns$ later. In (c) the probe HCP $Δ p_{probe, 0} = 0.5$ is applied after the 31st (solid) and 32nd (dashed) kicks. The initial wave packet is taken to be a mix of the 18 extreme redshifted Stark states in the $n_{i} = 350$ , $m = 0$ manifold and is oriented along the same axis as the applied HCPs.Reuse & Permissions
Figure 5
(Color online) Calculated evolution of the distributions of (a) the principal action $n$ and (b) and (c) its conjugate angle $θ$ , during the HCP sequence (see text). A positive (negative) chirp in the time shift $τ$ is used to steer the wave packet toward island $A_{1}$ (b) [island $A_{2}$ (c)]. The stroboscopic values in (b) and (c) are displayed for every other pulse in the superposed train $F_{s}$ [Eq. (4)].Reuse & Permissions
Figure 6
Dependence of the measured and calculated survival probabilities on (a) the strength and direction of the probe kicks, (b) the number of kicks $N$ in the HCP train, and (c) the delay time $τ_{delay}$ between the end of the HCP train and application of a probe pulse. The parameters are the same as in Fig. 4. The open triangles show survival probabilities measured after the 30th kick, filled squares the 31st kick. Calculated survival probabilities after the 30th and 31st kicks are shown in (a) and (c) by dashed and solid lines, respectively. The initial wave packet used in the CTMC simulations is a mix of 36 Stark states with $n_{i} = 350$ , $m = 0$ centered around $k = - 175$ oriented along the same axis as the applied HCPs (see text).Reuse & Permissions

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