Light dressed state

In the fields of atomic, molecular, and optical science, the term light dressed state refers to a quantum state of an atomic or molecular system interacting with a laser light in terms of the Floquet picture, i.e. roughly like an atom or a molecule plus a photon. The Floquet picture is based on the Floquet theorem in differential equations with periodic coefficients.

The Hamiltonian of a system of charged particles interacting with a laser light can be expressed as

where ${\displaystyle \mathbf {A} }$ is the vector potential of the electromagnetic field of the laser; ${\displaystyle \mathbf {A} }$ is periodic in time as ${\displaystyle \mathbf {A} (t+T)=\mathbf {A} (t)}$. The position and momentum of the ${\displaystyle i\,}$-th particle are denoted as ${\displaystyle \mathbf {r} _{i}\,}$ and ${\displaystyle \mathbf {p} _{i}\,}$, respectively, while its mass and charge are symbolized as ${\displaystyle m_{i}\,}$ and ${\displaystyle z_{i}\,}$, respectively. ${\displaystyle c\,}$ is the speed of light. By virtue of this time-periodicity of the laser field, the total Hamiltonian is also periodic in time as

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