The interaction of quantum radiation and a two-level atom is described in the context through the Jaynes-Cummings-Paul Hamiltonian which is obtained through Heisenberg's interaction picture of the Atom-Radiation Hamiltonian. We argue that such a transformation is not mathematically exact in case of ultrastrong coupling, where the coupling rate is comparable to the transition frequency, and leads to erroneous results. In addition, we introduce an exact mathematical solution to calculate optical spectrum of this system.The interaction of quantum radiation and a two-level atom is described in the context through the Jaynes-Cummings-Paul Hamiltonian which is obtained through Heisenberg's interaction picture of the Atom-Radiation Hamiltonian. We argue that such a transformation is not mathematically exact in case of ultrastrong coupling, where the coupling rate is comparable to the transition frequency, and leads to erroneous results. In addition, we introduce an exact mathematical solution to calculate optical spectrum of this system.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEFeb 4, 20116 citations

Hamiltonian vector fields in quantum mechanics

Renzo Cirelli, P. Lanzavecchia

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BFeb 1, 198445 citations

Quantum phases of Bose–Fermi mixtures in optical lattices

K Noda, Robert Peters, N. Kawakami +1 more

We consider a mixture of interacting bosons and fermions in optical lattices described by the Bose–Fermi Hubbard Hamiltonian. To treat bosonic degrees of freedom, we use a generalized dynamical mean field theory (GDMFT). By combining the GDMFT with the numerical renormalization group method, we revisit the zero-temperature phase diagram with particular emphasis on many-body effects in a supersolid state and discuss the origin of an anomalous peak structure emerging in the density of states for fermions.We consider a mixture of interacting bosons and fermions in optical lattices described by the Bose–Fermi Hubbard Hamiltonian. To treat bosonic degrees of freedom, we use a generalized dynamical mean field theory (GDMFT). By combining the GDMFT with the numerical renormalization group method, we revisit the zero-temperature phase diagram with particular emphasis on many-body effects in a supersolid state and discuss the origin of an anomalous peak structure emerging in the density of states for fermions.

Journal of Physics Conference SeriesJan 1, 20113 citations

Non-Hermitian interaction representation and its use in relativistic quantum mechanics

Miloslav Znojil

arXiv:1702.08493Annals of PhysicsAug 14, 201750 citations

Disordered complex systems using cold gases and trapped ions

Aditi Sen De, Ujjwal Sen, Maciej Lewenstein +3 more

We report our research on disordered complex systems using cold gases and trapped ions, and address the possibility of using complex systems for quantum information processing. Two simple paradigmatic models of disordered complex systems are revisited here. The first one corresponds to a short range disordered Ising Hamiltonian (spin glasses), which can be implemented with a Bose-Fermi (Bose-Bose) mixture in a disordered optical lattice. The second model we address here is a long range disordered Hamiltonian, characteristic of neural networks (Hopfield model), which can be implemented in a chain of trapped ions with appropriately designed interactions.We report our research on disordered complex systems using cold gases and trapped ions, and address the possibility of using complex systems for quantum information processing. Two simple paradigmatic models of disordered complex systems are revisited here. The first one corresponds to a short range disordered Ising Hamiltonian (spin glasses), which can be implemented with a Bose-Fermi (Bose-Bose) mixture in a disordered optical lattice. The second model we address here is a long range disordered Hamiltonian, characteristic of neural networks (Hopfield model), which can be implemented in a chain of trapped ions with appropriately designed interactions.

arXiv:quant-ph/0508018Aug 2, 20050 citations

QED of resonators in quantum optics

L. Knöll, D.‐G. Welsch

Progress in Quantum ElectronicsJan 1, 199234 citations

Interaction Hamiltonian in Quantum Optics Or:

\vec p \cdot \vec Avs.\vec E \cdot \vec r

Revisited