Non-Markovian evolution of the density operator in the presence of strong laser fields

We present an accurate, efficient, and flexible method for propagating spatially distributed density matrices in anharmonic potentials interacting with solvent and strong fields. The method is based on the Nakajima–Zwanzig projection operator formalism with a correlated reference state of the bath that takes memory effects and initial/final correlations to second order in the system–bath interaction into account. A key feature of the method proposed is a special parametrization of the bath spectral density leading to a set of coupled equations for primary and N auxiliary density matrices. These coupled master equations can be solved numerically by representing the density operator in eigenrepresentation or on a coordinate space grid, using the Fourier method to calculate the action of the kinetic and potential energy operators, and a combination of split operator and Cayley implicit method to compute the time evolution. The key advantages of the method are: (1) The system potential may consist of any number of electronic states, either bound or dissociative. (2) The cost for arbitrarily long solvent memories is equal to only N+1 times that of propagating a Markovian density matrix. (3) The method can treat explicitly time-dependent system Hamiltonians nonperturbatively, making the method applicable to strong field spectroscopy, photodissociation, and coherent control in a solvent surrounding. (4) The method is not restricted to special forms of system–bath interactions. Choosing as an illustrative example the asymmetric two-level system, we compare our numerical results with full path-integral results and we show the importance of initial correlations and the effects of strong fields onto the relaxation. Contrary to a Markovian theory, our method incorporates memory effects, correlations in the initial and final state, and effects of strong fields onto the relaxation; and is yet much more effective than path integral calculations. It is thus well-suited to study chemical systems interacting with femtosecond short laser pulses, where the conditions for a Markovian theory are often violated.