# Bichromatic dressing of Rydberg atoms and on the correctness of many-mode Floquet theory

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## Date

2020-01-20

## Authors

Poertner, Adam

## Advisor

Martin, James

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## Publisher

University of Waterloo

## Abstract

Many-mode Floquet theory [T.-S. Ho, S.-I. Chu, and J. V. Tietz, Chem. Phys. Lett.
96, 464 (1983)] was designed as an extension of Floquet theory suitable for solving the
time-dependent Schrodinger equation with multiple periodicities, however its limitations
are not well understood. I show that for two commensurate frequencies (integer multiples of
a common frequency), many-mode Floquet theory always produces an exact expression for
the time evolution of a system, despite only part of the eigenvalue spectrum being directly
relevant. I show that the rest of the spectrum corresponds to eigenvalues of the same
system but at other values of the relative phase between the bichromatic field components.
I show by using a Floquet perturbative analysis that dressing a Rydberg atom with a
bichromatic field with frequency components ω2 and ω1, such that ω2 = 2ω1, can induce a
permanent dipole moment (first order energy shift with dc electric field) without a dc bias
field. With frequency ω1 = 2π5.997GHz, ω2 = 2ω1 and field strengths of Eac1 = 0.1 V/cm
and Eac2 = 0.05 V/cm, a permanent dipole moment of magnitude 44.06 MHz/(V/cm) is
induced in the dressed 65s1/2 state of ⁸⁵Rb. The permanent dipole moment depends on the
relative phase between the fields and can be made to be zero at certain values of phase.