Quantum graphs: Self-adjoint, and yet exhibiting a nontrivial PT-symmetry

AbstractWe identify and investigate isoscattering strings of concatenating quantum graphs possessing n units and 2n infinite external leads. We give an insight into the principles of designing large graphs and networks for which the isoscattering properties are preserved for $$n \rightarrow \infty $$ n → ∞ . The theoretical predictions are confirmed experimentally using $$n=2$$ n = 2 units, four-leads microwave networks. In an experimental and mathematical approach our work goes beyond prior results by demonstrating that using a trace function one can address the unsettled until now problem of whether scattering properties of open complex graphs and networks with many external leads are uniquely connected to their shapes. The application of the trace function reduces the number of required entries to the $$2n \times 2n $$ 2 n × 2 n scattering matrices $${\hat{S}}$$ S ^ of the systems to 2n diagonal elements, while the old measures of isoscattering require all $$(2n)^2$$ ( 2 n ) 2 entries. The studied problem generalizes a famous question of Mark Kac “Can one hear the shape of a drum?”, originally posed in the case of isospectral dissipationless systems, to the case of infinite strings of open graphs and networks.

Download Full-text

Driven-dissipative phase transition in a Kerr oscillator: From semiclassical PT symmetry to quantum fluctuations

Physical Review A ◽

10.1103/physreva.103.033711 ◽

2021 ◽

Vol 103 (3) ◽

Author(s):

Xin H. H. Zhang ◽

Harold U. Baranger

Keyword(s):

Phase Transition ◽

Quantum Fluctuations ◽

Pt Symmetry

Download Full-text

Quantum Zeno effects across a parity-time symmetry breaking transition in atomic momentum space

npj Quantum Information ◽

10.1038/s41534-021-00417-y ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Tao Chen ◽

Wei Gou ◽

Dizhou Xie ◽

Teng Xiao ◽

Wei Yi ◽

...

Keyword(s):

Symmetry Breaking ◽

State Of The Art ◽

Cold Atom ◽

Pt Symmetry ◽

Level System ◽

Flexible Control ◽

Time Symmetry ◽

Symmetry Phase ◽

Lattice Quantum ◽

Atomic Momentum

AbstractWe experimentally study quantum Zeno effects in a parity-time (PT) symmetric cold atom gas periodically coupled to a reservoir. Based on the state-of-the-art control of inter-site couplings of atoms in a momentum lattice, we implement a synthetic two-level system with passive PT symmetry over two lattice sites, where an effective dissipation is introduced through repeated couplings to the rest of the lattice. Quantum Zeno (anti-Zeno) effects manifest in our experiment as the overall dissipation of the two-level system becoming suppressed (enhanced) with increasing coupling intensity or frequency. We demonstrate that quantum Zeno regimes exist in the broken PT symmetry phase, and are bounded by exceptional points separating the PT symmetric and PT broken phases, as well as by a discrete set of critical coupling frequencies. Our experiment establishes the connection between PT-symmetry-breaking transitions and quantum Zeno effects, and is extendable to higher dimensions or to interacting regimes, thanks to the flexible control with atoms in a momentum lattice.

Download Full-text