Calculations of coherent two-dimensional electronic spectra using forward and backward stochastic wavefunctions

Abstract

Within the well-established optical response function formalism, a new strategy with the central idea of employing the forward-backward stochastic Schrödinger equations in a segmented way to accurately obtain the two-dimensional (2D) electronic spectrum is presented in this paper. Based on the simple excitonically coupled dimer model system, the validity and efficiency of the proposed schemes are demonstrated in detail, along with the comparison against the deterministic hierarchy equations of motion and perturbative second-order time-convolutionless quantum master equations. In addition, an important insight is provided in this paper that the characteristic frequency of the overdamped environment is an extremely crucial factor to regulate the lifetimes of the oscillating signals in 2D electronic spectra and of quantum coherence features of system dynamics. It is worth noting that the proposed scheme benefiting from its stochastic nature and wavefunction framework and many other advantages of substantially reducing the numerical cost has a great potential to systematically investigate various quantum effects observed in realistic large-scale natural and artificial photosynthetic systems.

Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (HEOM)

“…This makes the scalability of the system size very low, in particular when the system is described in Wigner space. Therefore, wave-function-based HEOM approaches whose scalabilities are similar to that of the Schrödinger equation have been developed [166][167][168][169][170][171][172][173][174][175][176][177] (see Sec. VC).…”

“…As shown in the derivation of the influence functional with a correlated initial condition, the Feynman-Vernon influence functional can also be defined on the basis of the wave function using complex time counter integrals. 43 This indicates that we can derive HEOM for a wave function: such approaches include the stochastic hierarchy of pure states (HOPS), [166][167][168][169] the stochastic Schrödinger equation (SSE), 170 the hierarchy of stochastic Schrödinger equations (HSSE), [171][172][173][174][175][176] and the hierarchical Schrödinger equations of motion (HSEOM), 177 all of whose scalabilities are similar to that of the Schrödinger equation. These equations are advantageous not only because the scale of the memory required becomes N for an N -level system, but also because various numerical techniques developed for the Schrödinger equation can be employed for configuration space or energy eigenstate representations or a mixture of these.…”

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

“…Combined with the third-order NRF formalism, the forward−backward SSE method has been applied to simulate 2D electronic spectra of molecular aggregates. 408 The stochastic wave function formalism can be efficient especially for the calculation of multidimensional spectra of large systems. In addition, it is trivial to account for static disorder by sampling excitonic parameters from a suitable distribution for each stochastic trajectory.…”

Open quantum dynamics theory for a complex subenvironment system with a quantum thermostat: Application to a spin heat bath

“…Such wavefunction-based approaches have also been developed based on an explicit treatment of noise, including the stochastic hierarchy of pure states, [58][59][60][61][62] the stochastic Schrödinger equation, 63 the stochastic Schrödinger equation with a diagonalized influence functional along the contour in the complex time plane, 64 and a hierarchy of stochastic Schrödinger equations. [65][66][67][68][69][70] Although the formulation of the stochastic approaches is considerably simpler than the HSEOM approach, it is not suitable for studying a system with slow relaxation or a system subjected to a slowly varying time-dependent external force, because the convergence of the trajectories is slow in the stochastic approaches. For this reason, here we use the HSEOM approach.…”