Excitation of high angular momentum Rydberg states

We describe and analyse an RF-optical technique for exciting alkali atoms in an atomic beam to a specific high angular momentum Rydberg state. In the procedure the Rydberg states are dressed by an RF field and two optical photons are used to excite the dressed state that goes adiabatically into the desired Rydberg state as the RF field is turned off. We describe in detail the excitation of the aligned-circular-orbit states. These states have the maximum angular momentum quantum numbers for a given principal quantum number, and thus are the most nearly classical of all eigenstates. It is shown that in excess of 90% of the excited state population can be put into the aligned-circular-orbit state. Rydberg atomic states have a number of striking properties, including nearly macroscopic dimensions, large polarisabilities, long radiative lifetimes and nearly classical behaviour (Haroche and Raimond 1985, Gallas et al 1985). Within this class of states exists a set with unique properties, the aligned-circular-orbit states. These states have maximum angular momentum ( 1 ) and Zeeman ( m ) quantum numbers for a given principal quantum number (n). Their properties include the largest magnetic moments, the smallest sensitivity to static electric fields, the greatest collisional anisotropy and the longest radiative lifetimes of all states within a given n manifold. Several papers have suggested that these states are ideally suited to the study of various phenomena; for example, the modified spectra of a two-level atom in a cavity (Kleppner 1981) and the role of orientation in the collision process (de Prunele 1985). There are two difficulties in efficient preparation of aligned-circular-orbit states. Firstly, the atom must be supplied with many units of angular momentum. It is not practical to supply approximately 20 units of angular momentum by means of an optical field, so it must be done with an RF or microwave field. Secondly, the high angular momentum Rydberg states are almost exactly degenerate so that it is difficult to populate selectively only one state. The production of high angular momentum Rydberg states was discussed by Richards (1984). Hulet and Kleppner (1983; see also Hulet et al 1985) have developed a method of exciting the high angular momentum Stark states of an atom using optical and microwave fields and a linearly ramped DC field. In particular, they have populated ‘circular states’ which are the Stark states with the parabolic quantum numbers n, and n, equal to zero and / m / = n 1. We propose here a method that excites the aligned-circular-orbit state selectively. The method uses RF and optical fields. The RF field interacts strongly with the states in the Rydberg manifold, preparing or ‘dressing’ the atom for the optical excitation. The resulting dressed states are linear combinations of many different angular momentum states, but each dressed state will go continuously into a particular angular t Present address: Lawrence Livermore National Laboratories, Mail Stop L447, Livermore, CA 94550, USA, 0022-3700/86/ 120461 + 05$02.50 @ 1986 The Institute of Physics L46 1 L462 Letter to the Editor momentum state as the RF field is turned off adiabatically. While the atom is dressed, the dressed state that is connected to the aligned-circular-orbit state is excited optically. The method allows either pulsed or cw optical excitation of the dressed state. An adiabatic turn-off of the RF field leaves the population in the aligned-circular-orbit state. We first examine the dressed-state analysis which describes this method and then present the results of a numerical model of a system in which it is implemented. The Hamiltonian for the atom-field system is H = Ha+ Hf+ HI (1) where Ha is the atomic Hamiltonian in which the atom’s ionic core has been characterised by a dipole and a quadrupole polarisability, Hf is the field Hamiltonian and the interaction Hamiltonian, H,, is -d E ( t ) . A few assumptions can simplify the representation of this Hamiltonian and make it more applicable to our problem. Firstly, assume that the ground state is in an s state and that the optical excitation is by two-photon absorption of a circularly polarised field (figure l(a)) , which will populate a d state with m =2. Also the RF field that supplies the necessary n -3 units of angular momentum (figure l (b ) ) is circularly polarised. The frequency of the RF field is chosen near the n 3 multiphoton resonance between the d state and the aligned-circular-orbit state so that the mixing of these states is strong. These assumptions reduce the number of states that need to be included in our analysis. The s and p Rydberg states may be ignored since their energies are quite different from the other states of the n manifold. This energy difference is sufficiently large to keep the RF field from mixing these states with the rest of the manifold. The circular polarisation of the fields eliminates the need to consider states that would be excited by Am = 0 transitions. The transitions between aligned states are favoured over those from aligned to unaligned states. The squares of the dipole