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The case of a condensate in a trap can be derived in the same fashion. Applying such solutions to interferometers in traps is the focus of ongoing work.
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The case of a condensate in a trap can be derived in the same fashion. Applying such solutions to interferometers in traps is the focus of ongoing work.
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26
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In full simulations all time evolution was performed in momentum space using fourth-order, adaptive Runge-Kutta and fast Fourier transforms. Initial in-trap states were found by imaginary-time evolution to find the lowest energy steady state. All numerical results were performed with multiple grid sizes to check convergence of numerical solutions. Grid sizes were increased until the differences between results of simulations run on different grids were negligible on the scale of the results presented.
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The use closest in application to the present case comes in modeling wavelength division multiplexing systems. See Ref.
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The use closest in application to the present case comes in modeling wavelength division multiplexing systems. See Ref.
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j and so on.
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Accurate simulation of the physics during laser interactions requires keeping track of a number of initially unpopulated condensate branches. We have found that for both Kapitza-Dirac and Bragg pulses it is sufficient to consider two extra accessible branches on each side of the range you expect to populate (for better than percent-level accuracy of all final wave functions). For instance, a Bragg pulse that takes rec to -rec will also require keeping track of the 0 momentum branch, two more states above rec and two more states below -rec. However, once a laser interaction is complete, the branches that are no longer populated can be removed from the simulation, keeping the number of states tracked from growing during simulation of an experiment with many light gratings.
-
Accurate simulation of the physics during laser interactions requires keeping track of a number of initially unpopulated condensate branches. We have found that for both Kapitza-Dirac and Bragg pulses it is sufficient to consider two extra accessible branches on each side of the range you expect to populate (for better than percent-level accuracy of all final wave functions). For instance, a Bragg pulse that takes k rec to - rec will also require keeping track of the 0 momentum branch, two more states above k rec and two more states below - k rec. However, once a laser interaction is complete, the branches that are no longer populated can be removed from the simulation, keeping the number of states tracked from growing during simulation of an experiment with many light gratings.
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We believe the small differences in signal envelope arise from spurious gratings created by higher momentum states, which we remove from the SVEA simulations.
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We believe the small differences in signal envelope arise from spurious gratings created by higher momentum states, which we remove from the SVEA simulations.
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We have ignored the branches with higher magnitude momentum because SVEA simulations show that they contribute only small effects for the splitting parameters we have considered.
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We have ignored the branches with higher magnitude momentum because SVEA simulations show that they contribute only small effects for the splitting parameters we have considered.
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