Multiphoton Processes

Multiphoton processes - the processes of emission or absorption of electromagnetic radiation by atoms, molecules or electrons, which as a result of any elementary act of interaction gain (or lose) energy due to the simultaneous absorption (or emission) of several photons. According to the law of conservation of energy , in a multiphoton transition between quantum states, the difference in their energies is always equal to the total energy of the absorbed (or radiated) photons. The probability of multiphoton processes decreases with a unit increase in the number of photons participating in them in${\displaystyle <span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">(</span></span>\frac{\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">E</span></span>}}{{\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">E</span></span>}}_{\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">a</span></span>}}}{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">)</span></span>}^{\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">2</span></span>}}}$ {\ displaystyle ({\ frac {E} {E_ {a}}}) ^ {2}} times where${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">E</span></span>}}$ {\ displaystyle E} - the amplitude of the electric field radiation${\displaystyle {\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">E</span></span>}}_{\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">a</span></span>}}}$ {\ displaystyle E_ {a}} - the average electric field inside the atom ^[1] Therefore, multiphoton processes with a number of photons greater than two, manifest themselves noticeably only in electromagnetic fields created by laser radiation, comparable in intensity with intraatomic fields${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">E</span></span>}<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">\sim </span></span>\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">E</span></span>}\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">a</span></span>}}$ {\ displaystyle E \ sim E {a}} . Examples of multiphoton processes are: multiphoton transitions between quantum states, multiphoton ionization ^[2] , multiphoton photoelectric effect , Raman scattering. Multiphoton processes are used in nonlinear spectroscopy , optical frequency converters, parametric light generators.