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We present a program to simulate the dynamics of a wave packet interacting with a time-dependent potential. The time-dependent Schrodinger equation is solved on a one-, two-, or three-dimensional spatial grid using the split operator method. The program can be compiled for execution either on a single processor or on a distributed-memory parallel computer.
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We develop an approach to solving numerically the time-dependent Schrodinger equation when it includes source terms and time-dependent potentials. The approach is based on the generalized Crank-Nicolson method supplemented with an Euler-MacLaurin expansion for the time-integrated nonhomogeneous term. By comparing the numerical results with exact solutions of analytically solvable models, we find that the method leads to precision comparable to that of the generalized Crank-Nicolson method applied to homogeneous equations. Furthermore, the systematic increase in precision generally permits making estimates of the error.
We demonstrate an efficient algorithm for inverse problems in time-dependent quantum dynamics based on feedback loops between Hamiltonian parameters and the solutions of the Schr{o}dinger equation. Our approach formulates the inverse problem as a target vector estimation problem and uses Bayesian surrogate models of the Schr{o}dinger equation solutions to direct the optimization of feedback loops. For the surrogate models, we use Gaussian processes with vector outputs and composite kernels built by an iterative algorithm with Bayesian information criterion (BIC) as a kernel selection metric. The outputs of the Gaussian processes are designed to model an observable simultaneously at different time instances. We show that the use of Gaussian processes with vector outputs and the BIC-directed kernel construction reduce the number of iterations in the feedback loops by, at least, a factor of 3. We also demonstrate an application of Bayesian optimization for inverse problems with noisy data. To demonstrate the algorithm, we consider the orientation and alignment of polyatomic molecules SO$_2$ and chiral propylene oxide (PPO) induced by strong laser pulses. We use simulated time evolutions of the orientation or alignment signals to determine the relevant components of the molecular polarizability tensors to within 1% accuracy. We show that, for the five independent components of the polarizability tensor of PPO, this can be achieved with as few as 30 quantum dynamics calculations.
We present a method to extract the phase shift of a scattering process using the real-time evolution in the early and intermediate stages of the collision in order to estimate the time delay of a wave packet. This procedure is convenient when using noisy quantum computers for which the asymptotic out-state behavior is unreachable. We demonstrate that the challenging Fourier transforms involved in the state preparation and measurements can be implemented in $1+1$ dimensions with current trapped ion devices and IBM quantum computers. We compare quantum computation of the time delays obtained in the one-particle quantum mechanics limit and the scalable quantum field theory formulation with accurate numerical results. We discuss the finite volume effects in the Wigner formula connecting time delays to phase shifts. The results reported involve two- and four-qubit calculations, and we discuss the possibility of larger scale computations in the near future.
A new method for the study of resonant behavior - using wave-packet dynamics - is presented, based on the powerful window operator technique. The method is illustrated and quantified by application to the astrophysically-important example of low-energy $^{12}$C + $^{12}$C collisions. For this selected, potential model test case, the technique is shown to provide both resonance energies and widths in agreement with alternative methods, such as complex-energy scattering-matrix pole searches and scattering phase-shift analyses. The method has a more general capability to study resonance phenomena across disciplines, that involve particles temporarily trapped by potential pockets.
We study wave equations with energy dependent potentials. Simple analytical models are found useful to illustrate difficulties encountered with the calculation and interpretation of observables. A formal analysis shows under which conditions such equations can be handled as evolution equation of quantum theory with an energy dependent potential. Once these conditions are met, such theory can be transformed into ordinary quantum theory.
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