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QI: Fachverband Quanteninformation

QI 31: Decoherence and Open Quantum Systems

QI 31.6: Talk

Friday, March 22, 2024, 10:45–11:00, HFT-FT 101

Schrieffer-Wolff transformation for non-Hermitian systems — •Grigory A. Starkov¹, Mikhail V. Fistul², and Ilya M. Eremin² — ¹Theoretische Physik IV, Universität Würzburg, Würzburg, Germany — ²Institut für Theoretische Physik III, Ruhr-Universität Bochum, Bochum, Germany

Non-Hermitian Hamiltonians arise ubiquitously as the effective description of dissipative systems. Their important feature is the presence of the special type of degeneracies called Exceptional Points (EP), where not only the eigenvalues but the corresponding eigenvectors coalesce. The properties of EPs have interesting applications, e.g., for increasing the sensitivity of quantum sensors or for adiabatic state switching.

The structure of EPs of order n is typically studied by employing the effective local n x n Hamiltonian without specifying the means to obtain it. Here, we establish the Schrieffer-Wolff transformation for non-Hermitian systems as a way to systematically derive such effective Hamiltonians in a perturbative manner. We show that under certain conditions the transformation preserves the PT-symmetry or the pseudo-Hermitian symmetry of the original Hamiltonian. Finally, we briefly mention the PT-symmetric circuit QED with two qubits as an example of the application of the approach.

[1] G. A. Starkov, M. V. Fistul, and I. M. Eremin, arXiv:2309.09829 (2023).

[2] G. A. Starkov, M. V. Fistul, and I. M. Eremin, Phys. Rev. A 108, 022206 (2023).

Keywords: non-Hermitian physics; Schrieffer-Wolff transformation; Exceptional Points; non-Hermitian symmetries