Field-ionization processes in high Rydberg states of Rb under a rotating electric field

Field ionization of high Rydberg manifold states $(n=112\text{–}137)$ of rubidium-85 under a rotating electric field has been investigated experimentally and theoretically. Applying a rapidly reversed electric field with a small static perpendicular field to rotate the total electric field around zero, we have observed substantial increase of the fraction of the tunneling field-ionization process and a profound broadening of its ionization peak over a wide range of field strengths with increasing transverse electric field. The observed tunneling field-ionization fraction is almost independent of the slew rate of the applied electric field, and also on the principal quantum number $n$ over the range investigated. To compare with these experimental results, theoretical calculations have been performed with a successive two-step regime. As the first step we calculated the redistributions of magnetic quantum number $m_{\ell }$ and parabolic quantum number $n_1-n_2$ of the states under the rotating electric field. Then the following time evolution of the manifold states with $\mid m_{\ell }\mid ⩽3$ was traced on the Stark map in a coherent as well as an incoherent model. The calculated results are generally in good agreement with the experimental ones. The increase of the tunneling field-ionization fraction under a rotating electric field plays an essential role in achieving the high efficiency in the recently proposed selective-field-ionization scheme for high Rydberg atoms.

Figure 1

Calculated results of incoherent and coherent time evolution under a ramped electric field. The results of incoherent time evolution are shown for $\mid m_{\ell }\mid =$ (a) 0, (b) 1, (c) 2, and (d) 3. Those of coherent time evolution are shown for $\mid m_{\ell }\mid =$ (e) 0, (f) 1, (g) 2, and (h) 3. The initial manifold state is at $W_r=-0.52$ of $n=112$ and the slew rate of the ramped electric field is $5.9\mathrm{V}∕\mathrm{cm}\mu \mathrm{s}$. Only the reddest and bluest states in each manifold are drawn in the figures to make the Stark map more transparent. Dashed arrows show the diabatic paths. In (d) and (h), the drawing scale of the magnitude for the population is reduced to five times smaller than the other cases.

Figure 2

Schematic view of the present experimental setup. The coordinate system used in this paper is also shown.

Figure 3

Typical excitation spectra of the $n=112$ manifold states of ${}^{85}\mathrm{Rb}$ (a) with the applied electric field of 80 mV/cm, and (b) without field.

Figure 4

Dependence of the fraction of the tunneling field-ionization process on the transverse electric field $F_y^{\mathrm{app}}$. The initial value of $W_r$ is 0.30 with a quantization axis along the direction of the initial electric field, and the slew rate $F_z$ adopted is $5.9\mathrm{V}∕\mathrm{cm}\mu \mathrm{s}$. (a) Solid circles show the experimental data and the three lines are calculated results with the following values of $F_x^{\mathrm{cal}}$ and magnetic field: $F_x^{\mathrm{cal}}$ and $\mid \mathbf{B}\mid ∕\mid {\mathbf{B}}^{\mathrm{geo}}\mid$ $0\mathrm{mV}∕\mathrm{cm}$ and $1∕2$ (dash-dotted line), $0\mathrm{mV}∕\mathrm{cm}$ and 1.0 (solid line), and $5\mathrm{mV}∕\mathrm{cm}$ and 1.0 (dotted line), respectively. Taking into account the existence of the stray field of $1.3\mathrm{mV}∕\mathrm{cm}$ strength in the $y$ direction, the calculated lines are shifted by $\Delta F_y^{\mathrm{cal}}=-1.3\mathrm{mV}∕\mathrm{cm}$ such that the minimum of the calculated fraction matches that of the experimental one. In the inset are shown typical ionization spectra at $F_y^{\mathrm{app}}=$ (b) $-21.7$ and (c) $-1.3\mathrm{mV}∕\mathrm{cm}$. (d) Solid and open circles show the experimental data with and without the geomagnetic field canceled out, respectively. Solid line is a theoretical prediction without the external magnetic field. Assumed values of $F_x^{\mathrm{cal}}$ and magnetic field adopted: $F_x^{\mathrm{cal}}$ and $\mid \mathbf{B}\mid ∕\mid {\mathbf{B}}^{\mathrm{geo}}\mid$ $0\mathrm{mV}∕\mathrm{cm}$ and $1∕2$ (dash-dotted line), $0\mathrm{mV}∕\mathrm{cm}$ and 1.0 (solid line), and $5\mathrm{mV}∕\mathrm{cm}$ and 1.0 (dotted line), respectively. For simplicity, the effect of the stray electric field was included in the values of the transverse electric field of the abscissa so that the ionization fraction takes a minimum at zero transverse electric field $F_y^{\mathrm{app}}$.

Figure 5

Slew-rate dependence of the fraction of the tunneling field-ionization process for the initial $n=112$ manifold state of ${}^{85}\mathrm{Rb}$. Solid circles show the experimental results. Two lines are the calculated results where $F_x^{\mathrm{cal}}$ and $\mid \mathbf{B}\mid ∕\mid {\mathbf{B}}^{\mathrm{geo}}\mid$ are $0\mathrm{mV}∕\mathrm{cm}$ and $1∕2$ (solid line), and $5\mathrm{mV}∕\mathrm{cm}$ and 1.0 (dotted line), respectively. The initial value of $W_r$ is 0.52 and $F_y=-21.3\mathrm{mV}∕\mathrm{cm}$.

Figure 6

Principal-quantum-number $n$ dependence of the fraction of the tunneling field-ionization process. Solid circles show the experimental results. Two lines show calculated results: $F_x^{\mathrm{cal}}$ and $\mid \mathbf{B}\mid ∕\mid {\mathbf{B}}^{\mathrm{geo}}\mid$ are $0\mathrm{mV}∕\mathrm{cm}$ and $1∕2$ (solid line), and $5\mathrm{mV}∕\mathrm{cm}$ and 1.0 (dotted line), respectively. The initial value of $W_r$ is 0.52. The slew rate of the applied pulsed electric field $F_z$ is $5.9\mathrm{V}∕\mathrm{cm}\mu \mathrm{s}$. The values of $F_y$ applied for the six $n$ data points are $-21.6$, $-17.7$, $-14.6$, $-11.7$, $-9.2$, and $-7.8\mathrm{mV}∕\mathrm{cm}$, respectively, from lowest to highest $n$.