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.

Mathematical formulation

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

  (1)

where   is the vector potential of the electromagnetic field of the laser;   is periodic in time as  . The position and momentum of the  -th particle are denoted as   and  , respectively, while its mass and charge are symbolized as   and  , respectively.   is the speed of light. By virtue of this time-periodicity of the laser field, the total Hamiltonian is also periodic in time as

 

The Floquet theorem guarantees that any solution   of the Schrödinger equation with this type of Hamiltonian,

 

can be expressed in the form

 

where   has the same time-periodicity as the Hamiltonian,   Therefore, this part can be expanded in a Fourier series, obtaining

  (2)

where   is the frequency of the laser field. This expression (2) reveals that a quantum state of the system governed by the Hamiltonian (1) can be specified by a real number   and an integer  .

The integer   in eq. (2) can be regarded as the number of photons absorbed from (or emitted to) the laser field. In order to prove this statement, we clarify the correspondence between the solution (2), which is derived from the classical expression of the electromagnetic field where there is no concept of photons, and one which is derived from a quantized electromagnetic field (see quantum field theory). (It can be verified that   is equal to the expectation value of the absorbed photon number at the limit of  , where   is the initial number of total photons.)

References

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  • Shirley, Jon H. (1965). "Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time". Physical Review. 138 (4B): B979–B987. Bibcode:1965PhRv..138..979S. doi:10.1103/PhysRev.138.B979. ISSN 0031-899X.
  • Sambe, Hideo (1973). "Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field". Physical Review A. 7 (6): 2203–2213. Bibcode:1973PhRvA...7.2203S. doi:10.1103/PhysRevA.7.2203. ISSN 0556-2791.
  • Guérin, S; Monti, F; Dupont, J-M; Jauslin, H R (1997). "On the relation between cavity-dressed states, Floquet states, RWA and semiclassical models". Journal of Physics A: Mathematical and General. 30 (20): 7193–7215. Bibcode:1997JPhA...30.7193G. doi:10.1088/0305-4470/30/20/020. ISSN 0305-4470.
  • Cardoso, G.C.; Tabosa, J.W.R. (2000). "Four-wave mixing in dressed cold cesium atoms". Optics Communications. 185 (4–6): 353–358. Bibcode:2000OptCo.185..353C. doi:10.1016/S0030-4018(00)01033-6. ISSN 0030-4018.
  • Guérin, S.; Jauslin, H. R. (2003). "Control of Quantum Dynamics by Laser Pulses: Adiabatic Floquet Theory". Advances in Chemical Physics. pp. 147–267. doi:10.1002/0471428027.ch3. ISBN 9780471214526. ISSN 1934-4791.
  • F.H.M. Faisal, Theory of Multiphoton Processes, Plenum (New York) 1987 ISBN 0-306-42317-0.

See also

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