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

We present an accurate, efficient, and flexible method for propagating spat ially distributed density matrices in anharmonic potentials interacting wit h solvent and strong fields. The method is based on the Nakajima-Zwanzig pr ojection operator formalism with a correlated reference state of the bath t hat takes memory effects and initial/final correlations to second order in the system-bath interaction into account. A key feature of the method propo sed is a special parametrization of the bath spectral density leading to a set of coupled equations for primary and N auxiliary density matrices. Thes e coupled master equations can be solved numerically by representing the de nsity operator in eigenrepresentation or on a coordinate space grid, using the Fourier method to calculate the action of the kinetic and potential ene rgy operators, and a combination of split operator and Cayley implicit meth od to compute the time evolution. The key advantages of the method are: (1) The system potential may consist of any number of electronic states, eithe r bound or dissociative. (2) The cost for arbitrarily long solvent memories is equal to only N + 1 times that of propagating a Markovian density matri x. (3) The method can treat explicitly time-dependent system Hamiltonians n onperturbatively, 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. Cho osing as an illustrative example the asymmetric two-level system, we compar e our numerical results with full path-integral results and we show the imp ortance of initial correlations and the effects of strong fields onto the r elaxation. Contrary to a Markovian theory, our method incorporates memory e ffects, correlations in the initial and final state, and effects of strong fields onto the relaxation; and is yet much more effective than path integr al calculations. It is thus well-suited to study chemical systems interacti ng with femtosecond short laser pulses, where the conditions for a Markovia n theory are often violated. (C) 1999 American Institute of Physics. [S0021 -9606(99)01631-1].