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AIP conference proceedings

Efficient wave function simulations in nonlinear quantum optics using an adaptive coherent state basis

Sebastian Krämer, Helmut Ritsch

Published Jan 1, 2012• 0 citations
Publisher
DOI
10.1063/1.4750121

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Recently we introduced the von Neumann representation as a joint time-frequency description for femtosecond laser pulses. Here we show that the von Neumann basis can be implemented into an evolutionary algorithm for adaptive optimization in coherent control. We perform simulations that demonstrate the efficiency compared to other parametrizations in the frequency domain. We also illustrate pulse-shape simplification by basis-function reduction. Essential structures using the von Neumann basis are retained without losing control performance significantly. In an optical demonstration experiment we show the practicality by producing double pulses with a given time separation. Adaptive control in time-frequency space will be especially valuable for quantum systems requiring specific transition frequencies at definite times.
We introduce a discretized coherent state representation (DCSR) for quantum dynamics. Expansion of a wave function in the nonorthogonal slightly overcomplete set is made with an identity operator computed using an iterative refinement method. Calculating the inverse of the overlap matrix is not necessary. The result is an accurate and efficient representation, where you only put basis functions in the region of phase space where the wave function is nonvanishing. Compared to traditional spatial grid methods, fewer grid points are needed. The DCSR can be viewed as an application of the Weyl–Heisenberg frame and extends it into a useful computational method. A scheme for fully quantum mechanical propagation is constructed and applied to the realistic problem of highly excited vibration in the heavy diatomic molecule Rb2. Compared to split-operator propagation in a conventional spatial grid, an order of magnitude longer time steps can be taken and fewer grid points are needed. The computational effort scales linearly with the number of basis functions. Nonreflecting boundary conditions are a natural property of the representation and is illustrated in a model of predissociation.