Quantum decay and amplification in a non-Hermitian unstable continuum

Abstract

The decay of a bound state weakly-coupled to a non-Hermitian tight-binding unstable continuum, i.e. a continuum of states comprising energies with positive imaginary part, is theoretically investigated. As compared to quantum decay in an Hermitian continuum, in the non-Hermitian case a richer scenario can be found as a result of non-unitary dynamics. Different behaviors are observed depending on the kind of instability of the continuum. These include complete or fractional decay in convectively-unstable continua, the absence of quantum decay for a bound state with energy embedded in the continuum loop, and unstable (secular) growth with pseudo exponential amplification in the absolutely-unstable regime. Analytical results are presented for a nearest-neighboring tight-binding continuum with asymmetric hopping rates ${\kappa }_1$ and ${\kappa }_2$, which shows a transition from convective to absolute instability when the sign ${\kappa }_1{\kappa }_2$ changes from positive to negative. In the convectively unstable regime the model describes the decay of a bound state coupled to a tight-binding lattice with an imaginary gauge field, which shows a pseudo-Hermitian dynamics. In the absolutely-unstable regime, pseudo-Hermitian dynamics is broken and a pseudo exponential secular growth is observed.

11 pages, 5 figures

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• Phase Transitions and Virtual Exceptional Points in Quantum Emitters Coupled to Dissipative Baths
• Unconventional and robust light-matter interactions based on the non-Hermitian skin effect
• Non-Hermitian interaction of a discrete state with a continuum
• Dressed bound states and non-Markovian dynamics with a whispering-gallery-mode microcavity coupled to a two-level atom and a semi-infinite photonic waveguide
• Scattering States in One-Dimensional Non-Hermitian Baths
• Exact dynamics and bound states of a cavity coupled to a two-dimensional reservoir