Exact eigenstates for a class of models describing two-mode multiphoton processes.

Area of Science:

• Quantum optics
• Nonlinear dynamics
• Spectroscopy

Background:

• Multiphoton processes are fundamental in quantum optics.
• Studying spectra and eigenstates of nonlinear models is computationally challenging.
• Existing methods often lack exact analytical solutions.

Purpose of the Study:

• To present an efficient, analytical approach for studying nonlinear multiphoton processes.
• To derive exact expressions for energy spectra and eigenstates.
• To investigate two-mode multiphoton systems.

Main Methods:

• Development of an efficient analytical technique.
• Derivation of exact explicit expressions for energy spectra.
• Identification of a parameter determined by polynomial roots.

Main Results:

• Obtained exact analytical expressions for energy spectra and eigenstates.
• Demonstrated the method's applicability to two-mode multiphoton processes.
• Showed the parameter is linked to simple polynomial roots.

Conclusions:

• The presented approach offers an efficient way to solve complex multiphoton models.
• This method provides exact analytical insights into quantum system dynamics.
• The findings simplify the analysis of nonlinear optical phenomena.