Exactly solvable non-Hermitian Jaynes–Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry

Pijush K Ghosh
2005 Journal of Physics A: Mathematical and General  
It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is alwayas a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-hermitian Hamiltonians are constructed algebraically for certain shape-invariant potentials, including a non-hermitian version of the standard Jaynes-Cummings model for
more » ... -Cummings model for which the parent supersymmetric Hamiltonian is the superoscillator. The positive-definite metric operator in the Hilbert space is constructed explicitly along with the introduction of a new inner product structure, so that the eigenstates form a complete set of orthonormal vectors and the time-evolution is unitary.
doi:10.1088/0305-4470/38/33/007 fatcat:6ev2mf35s5gg7a6ol7rfwhcuzq