The hidden symmetry of the asymmetric quantum Rabi model
Vladimir V. Mangazeev, Murray T. Batchelor, Vladimir V. Bazhanov
Abstract
Abstract The asymmetric quantum Rabi model (AQRM) exhibits level crossings in the eigenspectrum for the values <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>ϵ</mml:mi> <mml:mo>∈</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfrac> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:math> of the bias parameter ϵ . Such level crossings are expected to be associated with some hidden symmetry of the model. The origin of this hidden symmetry is established by finding the operators which commute with the AQRM Hamiltonian at these special values. The construction is given explicitly for the first several cases <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>ϵ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfrac> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:math> and can be applied to other related light–matter interaction models for which similar level crossings have been observed in the presence of a bias term.