Figure 1

Schematic diagram of the apparatus.Reuse & Permissions

Figure 2

(a) Simulated spatial distribution (projected onto the $xy$ plane) immediately following application of a 2.5-ns-long pump pulse of magnitude 346 mV/cm. The results are obtained by numerically solving the classical equations of motion for an initial ensemble comprising a restricted microcanonical ensemble modeling the extreme parabolic state with $n_i=150$, $k_x=-149$, and $m_x=0$. The corresponding average principal action $\langle n(x,y)\rangle$ evaluated locally at each position $(x,y)$ is shown in (b). (c) and (d) Results obtained, for the same conditions, by numerically solving the time-dependent Schrödinger equation. (e) and (f) Results of quantum mechanical calculations for an initial state comprising an ensemble of near extreme parabolic states $n_i=150$, $k_x=-117,-119,...,-133$ (each equally populated), and $m_x=0$ (see text). In all plots, the coordinates are in scaled units $x_0=x/n_i^2$ and $y_0=y/n_i^2$. $\langle n(x,y)\rangle$ is evaluated only at positions where the probability density $\tilde{\rho }(x,y)$ is larger than 0.01 (in scaled units) to avoid divergence with small denominators [see Eqs. (18) and (20)].Reuse & Permissions

Figure 3

(a) and (b) Survival probabilities Eq. (16) of the Bohr wave packet ($n_i=150$) as a function of time of application of the probe pulse calculated according to Eq. (15) with ${\phi }_{\mathrm{ion}}=2\pi /3$ and $\pi /2$, respectively. The results are obtained by numerically solving the Schrödinger equation. The pump pulse and initial state are the same as for Figs. 1e and 1f. The unit of the scaled time is the Kepler period $2\pi n_i^3$ ($\simeq$513 ps for $n=150$) and that of the length is $n_i^2$. The expectation values of the moments $\langle y_0\left(t\right)\rangle$ [Eq. (4)] and $\langle y_0^2\left(t\right)\rangle$ [Eq. (10)] are presented in panels (c) and (d).Reuse & Permissions

Figure 4

(a) to (d) Amplitudes of the Fourier transforms of the data in Fig. 3, shown in the same order. (e) and (f) Expanded views in the vicinity of the first and second harmonics. The dots indicate the phases of the complex Fourier coefficients for the dominant peaks (phase scale provided by the axes on the right). The conversion from frequency to the quantum number $n$ [dashed lines and top axes in panels (e) and (f)] is done using ${\omega }_n={(n-1/2)}^{-3}$ and ${\omega }_n=2n^{-3}$ for the first and second harmonics, respectively.Reuse & Permissions

Figure 5

Survival probabilities measured following sudden turn-off of a transverse 43-ns-long, 10 mV cm${}^{-1}$ pump pulse applied to a mix of quasi-1D $n_i=304$ and 306 atoms (see text). Probe pulses of 6 ns in duration and amplitudes of (a) 104 mV cm${}^{-1}$ and (b) 76 mV cm${}^{-1}$ are employed. The inset illustrates the data on a finer scale.Reuse & Permissions

Figure 6

(a) and (b) Fourier transform of the survival probabilities shown in Figs. 5a and 5b, respectively. The solid lines show the amplitudes of the Fourier expansion coefficients. The dots indicate the phases $\phi$ of the dominant peaks. Frequency is mapped to the quantum number $n$ (indicated by the dashed lines) by ${\omega }_n={(n-1/2)}^{-3}$ and ${\omega }_n=2n^{-3}$ for the first (a) and second (b) harmonics, respectively.Reuse & Permissions

Figure 7

(a) Survival probability measured following application of an 85-ns-long, 5 mV cm${}^{-1}$ pump pulse to a mix of quasi-1D $n_i\sim 305$ atoms and (d) its Fourier transform. The 6-ns-long probe pulse has an amplitude of 104 mV/cm. (b) and (c) Survival probabilities and (e) and (f) Fourier transforms obtained after application, following a delay of $\sim$1.1 ns, of an HCP delivering a kick of scaled strength $\Delta p_0\equiv n_i\Delta p=0.007$ in the $-y$ and $+y$ directions, respectively (see text).Reuse & Permissions