The effect of a combined static and microwave field on an excited hydrogen atom

The authors examine the behaviour of extremal Stark states of excited hydrogen under the influence of parallel static and microwave electric fields in order to assess when the system can be approximated by a Hamiltonian with one degree of freedom. The authors show that without a static field the Runge-Lenz vector precesses, so that only for short times does the electron remain approximately aligned along the field direction. In this case they provide estimates of the time during which the motion is nearly one-dimensional; this has a complicated dependence upon the microwave frequency. The amplitude of the Runge-Lenz oscillations decreases with increasing static field strength F s ; there is a critical static field, depending upon the microwave field frequency Omega and amplitude F m , at which these oscillations are small enough for the electron motion to be considered one-dimensional. The authors provide estimates of this critical field for various microwave frequencies and show that it is largest when the microwave field is in resonance with the electron motion, in which case it is necessary that F s 0.22F m .