Probing coordinates of Rydberg wave packets B. E. Tannian, 1 C. L. Stokely, 1 F. B. Dunning, 1 C. O. Reinhold, 2,3 and J. Burgdo ¨ rfer 2,3.4 1 Department of Physics and Astronomy and the Rice Quantum Institute, Rice University, MS 61, 6100 Main Street, Houston, Texas 77005-1892 2 Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6373 3 Department of Physics, University of Tennessee, Knoxville, Tennessee 37996-1200 4 Institute for Theoretical Physics, Vienna University of Technology, A-1040 Vienna, Austria Received 2 May 2001; published 17 July 2001 We propose a method for determining the time development of the position coordinates of a Rydberg wave packet using the sudden turn-on of a strong field a ‘‘field step’’. The feasibility of the technique is investi- gated using wave packets created by a half cycle pulse HCP that comprise a superposition of very-high-lying Rydberg states. The time evolution of the wave packet is measured using probe pulses that are applied following a variable time delay. The probe pulse ionizes a fraction of the atoms and the survival probability exhibits pronounced oscillations that are associated with the quasiperiodic evolution of the wave packet. Good agreement is found between the experimental data and the results of classical trajectory Monte Carlo simula- tions. Extraction of classical phase space coordinates from the data is discussed. DOI: 10.1103/PhysRevA.64.021404 PACS numbers: 32.80.Rm, 42.50.Hz In recent years there has been increasing interest in the control and manipulation of atomic wave functions. It has been demonstrated that specific targeted Rydberg wave pack- ets can be engineered and probed by means of carefully tai- lored electromagnetic pulses 1–5. Rydberg wave packets provide a bridge between quantum and classical physics be- cause they display dynamical behaviors that mimic the clas- sical motion of the excited electron. One important question that arises concerning such wave packets is how to probe the evolution of their phase-space coordinates. Previous work has shown that the momentum of a wave packet can be monitored using a short unidirectional electric-field pulse, termed a half cycle pulse HCP6,7. Since photon absorp- tion occurs when the electron is close to the core ion, the radial position coordinate of a wave packet can be monitored using an ultrafast laser pulse 8,9. Here we propose an al- ternative approach to monitoring the time evolution of the position coordinates of the wave packet, namely the rapid application of a dc field. Key to producing and probing wave packets are electro- magnetic pulses whose time variations are much shorter than the classical electron orbital period T n =2  n 3 , where n is the principal quantum number and atomic units are used throughout. This condition can be satisfied by working with atoms in which one electron is excited to a state of very large principal quantum number n. For example, for n 400, T n 10 ns and the short pulse regime can be accessed using electric-field pulses produced by applying voltage pulses to a nearby electrode from a fast pulse generator. For HCPs with pulse duration T p T n , a single electric-field pulse F  HCP ( t ) simply delivers an impulsive momentum transfer or ‘‘kick’’  p  =- dtF  HCP ( t ) to the excited electron 10. Here we use such a kick to create a Rydberg wave packet. Its subse- quent evolution is then probed either by using a second HCP or by application of a strong dc field with a rise time T R T n , to be referred to as a field step. The present pump- probe schemes are described by the Hamiltonian H t  =H at +V PUMP  t  +V PROBE  t  =H at +zF  t  , 1 H at = p 2 2 +V at  r   p 2 2 - 1 r , 2 where r and p denote the position and momentum of the electron, respectively. In the atomic Hamiltonian, H at , the interaction between the excited electron and core ion is ap- proximated by a simple -1/r Coulomb potential. The elec- tric fields applied along the z axis used to create and probe the wave packets are described by V PUMP and V PROBE , re- spectively, where V PUMP +V PROBE =zF ( t ). The insets in Fig. 1 show typical experimental pulse profiles Ft used in the present experiments. For initial discussions, the pump pulse that creates the wave packet is approximated by a  -function impulse, V PUMP =zF PUMP  t  -z  p PUMP   t  . 3 The probe consists of another HCP or a sudden field step that is applied after a variable time delay t D , i.e., V PROBE =zF PROBE  t -t D  -z  p PROBE   t -t D  4 or V PROBE =zF PROBE  t -t D  zF DC   t -t D  - t -t D -T dc  , 5 where  denotes the unit step function and T dc ( T n ) speci- fies the duration of the quasi dc field. The basic ideas that underlie the present pump-probe schemes can be illustrated most easily by considering Ryd- berg atoms in high-l , high-m states. Figure 1 shows the results of classical trajectory Monte Carlo CTMC simula- tions for a hydrogen atom initially in a stationary Rydberg state with quantum numbers n =390, l =m =389 the quan- tization axis is parallel to the z axis along which the pump RAPID COMMUNICATIONS PHYSICAL REVIEW A, VOLUME 64, 021404R 1050-2947/2001/642/0214044/$20.00 ©2001 The American Physical Society 64 021404-1