Abstract
The interaction between atoms and molecules and intense laser pulses is typically described in either the velocity gauge, length gauge or in the Kramers–Henneberger frame. Here, certain relations between these forms are discussed. In particular expansions of the solution to the time-dependent Schrödinger equation in adiabatic states are considered. Such expansions in adiabatic states could be expected to be attractive for intense long-wavelength infrared laser pulses, where the external field changes on a slow timescale compared with the electron motion. It is shown that an expansion in velocity gauge adiabatic states gives the equations of motions that follow from an expansion in field-free states and by expressing the interaction operator in the length gauge. Likewise, it is shown that an expansion in the Kramers–Henneberger frame adiabatic states gives the equations of motion following an expansion in field-free states and using the velocity gauge interaction operator. Finally, an alternative form for the laser–matter interaction operator is considered, which is similar to the velocity gauge, but shifts the canonical momentum operator by the impulse associated with the Kramers–Henneberger interaction operator, rather than that of the electric field as is the case in the velocity gauge.
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Acknowledgements
The author thanks Simon Vendelbo Bylling Jensen for useful discussions. This work was supported by the Danish Council for Independent Research (Grant nos. 7014-00092B, 9040-00001B).
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The author conceived the idea regarding elucidation of the relations between the equations of motion after expansion in adiabatic states with equations of motion following the expansion in field-free states. The author derived the presented relations and formulas. The author wrote the manuscript.
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Madsen, L.B. Different forms of laser–matter interaction operators and expansion in adiabatic states. Eur. Phys. J. Spec. Top. 230, 4141–4150 (2021). https://doi.org/10.1140/epjs/s11734-021-00026-y
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DOI: https://doi.org/10.1140/epjs/s11734-021-00026-y