Visualizing the Coupling between Red and Blue Stark States Using Photoionization Microscopy

In nonhydrogenic atoms in a dc electric field, the finite size of the ionic core introduces a coupling between quasibound Stark states that leads to avoided crossings between states that would otherwise cross. Near an avoided crossing, the interacting states may have decay amplitudes that cancel each other, decoupling one of the states from the ionization continuum. This well-known interference narrowing effect, observed as a strongly electric field-dependent decrease in the ionization rate, was previously observed in several atoms. Here we use photoionization microscopy to visualize interference narrowing in helium atoms, thereby explicitly revealing the mechanism by which Stark states decay. The interference narrowing allows measurements of the nodal patterns of red Stark states, which are otherwise not observable due to their intrinsic short lifetime.

Figure 1

Schematic representation of the experimental setup. Metastable $2{}^1\mathrm{S}$ helium atoms are created by means of a dc electric discharge maintained between a Tantalum needle (a), surrounded by a quartz tube (b) and filled with He gas provided by a gas inlet (c), and a grounded skimmer (d). The ignition starts at $-2\mathrm{kV}$ and is sustained at $-0.7\mathrm{kV}$ and 20 mA. The ${\mathrm{He}}^{*}$ beam, formed by the skimmer ($\varphi =1\mathrm{mm}$), crosses a tunable UV laser inside a velocity map imaging (VMI) spectrometer, permitting the excitation of quasibound Stark states that subsequently ionize. By applying a voltage difference across the repeller (e) and extractor (f) plates the photoelectrons are accelerated towards a position-sensitive detector (g) comprising 4-cm diameter MCP plates, a phosphor screen and a CCD camera. Halfway towards the detector, the photoelectrons pass through an Einzel lens (h), enabling magnification of the recorded photoelectron images by one order of magnitude.

Figure 2

Photoelectron images recorded for Stark states that decay via core-induced coupling to fast-ionizing red states. The examples shown in (a)–(d) are the (28, 22, 5, 0), (28, 25, 2, 0), (29, 21, 7, 0) and (21, 23, 5, 0) states, acquired at energies of $-126.59{\mathrm{cm}}^{-1}$, $-121.46{\mathrm{cm}}^{-1}$, $-119.42{\mathrm{cm}}^{-1}$ and $-115.87{\mathrm{cm}}^{-1}$, respectively, in the presence of a $468\mathrm{V}/\mathrm{cm}$ dc electric field. In all images, the intensities are normalized to the maximum occurring intensity. The main observation is that the number of interference minima increases smoothly as a function of energy. The interferences can be explained by considering the phase difference between different trajectories by which electrons can move from the ion to the detector. This is further illustrated in (e), where the positions of experimentally observed interference minima ($+$) are compared with semiclassically calculated positions (solid lines, using the method described in [19]).

Figure 3

(a)–(c) Three electron images recorded at energies of $-130.95{\mathrm{cm}}^{-1}$, $-130.43{\mathrm{cm}}^{-1}$, and $-130.19{\mathrm{cm}}^{-1}$ corresponding to adjacent Stark states identified as $(n,n_1,n_2,m)=(31,7,23,0)$, (34, 1, 32, 0) and (27, 26, 0, 0), respectively. (d)–(f) Comparison between the experimental radial distributions (solid line), and calculated radial distributions (dashed lines) obtained by means of TDSE calculations. Please note that, since $\mathrm{P}(\mathrm{R})=\int \mathrm{P}(\mathrm{R},\alpha )\mathrm{R}\mathrm{d}\alpha$, the radial probability distributions P(R) have a zero at $\mathrm{R}=0$, even if the two-dimensional images described in polar coordinates by $\mathrm{P}(\mathrm{R},\alpha )$ do not. The main result is the appearance of a minimum in the radial distribution for the (34, 1, 32, 0) state, which corresponds to the value of $n_1$ and directly reveals the nodal structure of the ${\chi }_1(\xi )$ wave function. N.B. The computational results shown here and in Fig. 4 were scaled to the dimensions of the experiment in order that the best fit is achieved for the (34, 1, 32, 0) state. (g) Stark map for helium obtained from calculated photoabsorption cross sections (squares); superimposed dashed lines schematically indicate the field dependence of the related diabatic, uncoupled Stark states. The gray bar indicating the experimental field strength illustrates that the photoelectron image for the (34, 1, 32, 0) state was recorded near an avoided crossing of this red state with the blue (27, 26, 0, 0) state. (h) Field-dependent reduction in the linewidth of the (34, 1, 32, 0) state, extracted from the calculated photo-absorption spectra and confirming the occurrence of the interference narrowing effect.

Figure 4

(a) Raw photoelectron image for the (35, 5, 29, 0) state measured near an avoided crossing, showing five minima in the radial distribution, (b) comparison between the experimental (solid line) and theoretical radial distributions (dashed line, obtained from the TDSE calculations), showing an excellent agreement in the position of the nodes. A calculated Stark map (c) indicates that the measurement was taken for a dc electric field of approximately $467.4\mathrm{V}/\mathrm{cm}$, where the (35, 5, 29, 0) state has an avoided crossing with the (31, 13, 17, 0) and (28, 26, 1, 0) states. Note that the absence of black squares implies a disappearance of the oscillator strength in the photoabsorption spectra for a given state. The calculated ionization rate of the (35, 5, 29, 0) state, shown in (d), decreases by three orders of magnitude within a field range of $0.5\mathrm{V}/\mathrm{cm}$, due to the occurrence of interference narrowing.