2 topics in PTQM: I. Tachistochrones in PT−symmetric LRC circuits; II. PT−symmetric Jaynes-Cummings models via gauged Hamiltonians


2 topics in PTQM: I. Tachistochrones in PT−symmetric LRC circuits; II. PT−symmetric Jaynes-Cummings models via gauged Hamiltonians

Günther, U.

The presentation consists of two parts. In the first part, recent results on PT-symmetric LRC circuits are reported, including the hidden special representations of the linear parity involution P and the antilinear time reversal operation T. Analytical formulae for the evolution time contraction (so called tachistochrone solutions) and dilation are presented. The simple underlying phase-shift-versus-amplitude-enhancement mechanism is explained. (Partially based on common work with Hamid Ramezani, Joseph Schindler, Fred Ellis, and Tsampikos Kottos published in Phys. Rev. A 85, (2012), 062122.)

In the second part of the talk, it is shown that the mathematical investigation of the symmetry structures hidden in gauged PT-symmetric systems indicates on possible realizations of such setups as Jaynes-Cummings type models. The latter ones are used e.g. to describe multilevel artificial atoms in cavity QED. A question that naturally arises is whether PT-symmetric extensions of cavity QED might become feasible experimentally and how to possibly realize them. (Partially based on common work with Sergii Kuzhel published in J. Phys. A 43, (2010), 392002.)

Keywords: PT quantum mechanics; PT brachistochrone; tachistochrone; ultra-fast evolution; time contraction; time dilation; LRC circuit; Jaynes-Cummings model; cavity QED; multilevel artificial atoms; gauged PT-symmetry; Lie triple systems; Cartan decomposition of Lie algebras

  • Invited lecture (Conferences)
    Non-Hermitian degeneracies: new directions of research and applications., 21.-24.04.2012, Haifa, Israel

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Publ.-Id: 17584