Stark effect in low-dimensional hydrogen

Studies of atomic systems in electric fields are challenging because of the diverging perturbation series. However, physically meaningful Stark shifts and ionization rates can be found by analytical continuation of the series using appropriate branch cut functions. We apply this approach to low-dimensional hydrogen atoms to study the effects of reduced dimensionality. We find that modifications by the electric field are strongly suppressed in reduced dimensions. This finding is explained from a Landau-type Wentzel–Kramers–Brillouin analysis of the ionization process.

Figure 1

Stark energy (red curve and dots, left axis) and decay rate (blue curve and dots, right axis) of three-dimensional hydrogen in the present approach and in comparison to exact values from Ref. [8].

Figure 2

Energy (red curves, left axes) and decay rate (blue curves, right axes) as a function of field strength for a range of integer and noninteger dimensions. Note the different field scales. The dashed lines are linear fits to the high-field decay rates.

Figure 3

Field dependence of the decay rate for various dimensions. The solid red lines are the hypergeometric resummation results and the dashed black lines are Landau-type expressions.