Photoassociation of cold atoms with chirped laser pulses: Time-dependent calculations and analysis of the adiabatic transfer within a two-state model

Abstract

This theoretical paper presents numerical calculations for photoassociation of ultracold cesium atoms with a chirped laser pulse and detailed analysis of the results. In contrast with earlier work, the initial state is represented by a stationary continuum wavefunction. In the chosen example, it is shown that an important population transfer is achieved to ≈ 15 vibrational levels in the vicinity of the v=98 bound level in the external well of the 0 − g (6s + 6p 3/2 ) potential. Such levels lie in the energy range swept by the instantaneous frequency of the pulse, thus defining a "photoassociation window". Levels outside this window may be significantly excited during the pulse, but no population remains there after the pulse. Finally, the population transfer to the last vibrational levels of the ground a 3 Σ + u (6s + 6s) is significant, making stable molecules. The results are interpreted in the framework of a two state model as an adiabatic inversion mechanism, efficient only within the photoassociation window. The large value found for the photoassociation rate suggests promising applications. The present chirp has been designed in view of creating a vibrational wavepacket in the excited state which is focussing at the barrier of the double well potential.

Short-pulse photoassociation in rubidium below theD1line

“…This allows to employ a fairly extended grid (R max ≈ 18500 a 0 ) with a comparatively small number of grid points (N grid = 1027). Such a large grid is needed to faithfully represent the scattering continuum above the singlet ground and lowest triplet state potentials by box states [14,15,27]. Diagonalization of the Hamiltonians, Eqs.…”

“…The continuum of scattering states is represented by a finite number of box states [14,15,27]. These box states are normalized to one.…”

“…In previous work on cesium, only excitation of the 0 − g (P 3/2 ) excited state and molecule formation in the lowest triplet state a 3 Σ + u were considered [27]. In order to analyze short pulse PA from the point of view of a prospective experiment, the present study goes beyond the two-state description [13,14,15,16,27]. Formation of molecules in both the singlet ground state X 1 Σ + g and the lowest triplet state a 3 Σ + u can then be tested.…”

“…Photoassociation with short laser pulses on cold systems has sparked interest from both experiment [8,16,19,20] and theory [13,14,15,25,26,27]. Specifically, a pump-dump scheme has been suggested with the idea to create a wavepacket on the excited state and make use of its timedependence for efficient stabilization [14,15,27]. In order to obtain an overall high efficiency, both excitation (photoassociation) and deexcitation (stabilization) steps must be efficient.…”

“…Two time-delayed pulses can be employed to realize pumpprobe experiments: The first or pump pulse creates a wavepacket whose dynamics is monitored by a second probe pulse, varying the time delay [11,12]. The shape of the pulse can be manipulated, for example by introducing a controlled frequency chirp which enforces adiabatic following conditions [13,14,15,16]. More elaborate coherent control which shapes amplitude and phase can also be employed.…”