The tunneling contributions to optical coherence in femtosecond pump–probe spectroscopy of a three level system

Abstract

We present theory and observations to show that the proper description of the interaction of femtosecond light pulses resonant with both transitions of a three level system must consider additional excitation pathways which do not include population creation on the intermediate electronic level. This leads to the extra tunneling contributions to the pump–probe signal around zero delay time when the light pulse is centered close to the isosbestic point, i.e., the wavelength where the absorption from the lower and higher transitions are equal. We use the density matrix approach in the perturbative limit to simulate the pump–probe signal under various conditions. In the conventional calculation of transient anisotropy as measured by pump–probe spectroscopy, the assumption is made that the system is excited by the pump pulse only. However, this is not the case at zero delay time when pump and probe pulses overlap. The mutual coherence of pump and probe pulses derived from the same laser source makes it necessary to include nonsequential contributions to the signal. We show that some of these terms can have distinct anisotropic properties and lead to noticeable deviations of the zero delay anisotropy from the long time value. Effects of the pulse wavelength and the relative orientation of the transition dipole moments on the transient anisotropy are examined in detail. Application is made to our earlier femtosecond pump–probe experiments on the light harvesting pigment proteins of Rhodobacter sphaeroides, whereby we present a more elaborate explanation of the short lived induced absorption signal at negative delay times.