Generation of quasiclassical Bohr-like wave packets using half-cycle pulses

We demonstrate the experimental realization of Bohr-like atoms by applying a pulsed unidirectional field, termed a half-cycle pulse (HCP), to atoms in quasi-two-dimensional near-circular states. This leads to creation of localized wave packets that travel in near-circular orbits and mimic the dynamics of an electron in the original Bohr model of the hydrogen atom. This motion can be followed for several orbital periods before the localization of the wave packet is lost due to dephasing. We show, however, that localization can be recovered by application of further HCPs.

Figure 1

(Color online) CTMC simulations showing the electron probability density projected on the $xz$ plane: (a) Immediately before application of the field step; (b) $150\mathrm{ns}$ after turn-off of a $-10\mathrm{mV}{\mathrm{cm}}^{-1}$ pump field of duration $43\mathrm{ns}$ (see text); [(c), (d), (e), and (f)] after application (at $t_D=150\mathrm{ns}$) of a HCP delivering a scaled impulse $\Delta p_{z0}=n\Delta p_z=-0.035$ and additional time delays of 10.3, 11.3, 12.3, and $13.3\mathrm{ns}$; [(g) and (h)] optimum localization achieved after a third and fifth localization kick applied $350\mathrm{ns}$ and $550\mathrm{ns}$ after the pump field. The localization kicks alternate in sign and are spaced at $100\mathrm{ns}$ intervals. The axes are expressed in scaled units $x_0=x∕n^2$, $z_0=z∕n^2$.

Figure 2

(Color online) CTMC calculations of the time dependence of (a) the angular and (b) the radial distributions of the wave packet following application of a HCP of scaled strength $\Delta p_{z0}=-0.035$ at $t_D=150\mathrm{ns}$ to a near circular $n\sim 306$ state. The radius is expressed in scaled units $(r∕n^2)$.

Figure 3

(Color online) Dependence of $\varphi ({\varphi }_i,t)$ on ${\varphi }_i$ at various times following application of a kick of scaled strength $\Delta p_{z0}=-0.035$ to a perfectly circular $n=306$ initial state (see text). The shaded horizontal areas denote a focusing width of $\sim 1\mathrm{rad}$. The inset shows the assumed geometry.

Figure 4

(Color online) Experimental (●, ○) and calculated (—,- - -) survival probabilities following application of HCPs with scaled strengths $\Delta p_{z0}$ of (a) $-0.018$, (b) $-0.035$, and (d) $-0.10$ $150\mathrm{ns}$ after turn-off of $F_z^{\text{pump}}$ (see text). The probe pulses used were of $6\mathrm{ns}$ duration and amplitude $100\mathrm{mV}{\mathrm{cm}}^{-1}$ and directed along the $x$ (○) and $z$ (●) axes. The blow-up in (c) demonstrates the 90° phase shift between measurements along the $x$ and $z$ axes. (e) Relocalization induced by a second HCP of strength $\Delta p_{z0}=-0.035$ applied $100\mathrm{ns}$ after an initial localizing HCP of the same strength.