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Register a new userReconfiguration of quantum states in $mathcal PT$-symmetric quasi-one dimensional lattices
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We demonstrate mesoscopic transport through quantum states in quasi-1D lattices maintaining the combination of parity and time-reversal symmetries by controlling energy gain and loss. We investigate the phase diagram of the non-Hermitian system where transitions take place between unbroken and broken $mathcal{PT}$-symmetric phases via exceptional points. Quantum transport in the lattice is measured only in the unbroken phases in the energy band-but not in the broken phases. The broken phase allows for spontaneous symmetry-broken states where the cross-stitch lattice is separated into two identical single lattices corresponding to conditionally degenerate eigenstates. These degeneracies show a lift-up in the complex energy plane, caused by the non-Hermiticity with $mathcal{PT}$-symmetry.
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A series of geometric concepts are formulated for $mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a Berry curvature whereas the real part induces a metric tensor on systems parameter manifold. This results in a unified conceptual framework to understand and explore physical properties of $mathcal{PT}$-symmetric systems from a geometric perspective. To illustrate the usefulness of the extended QGT, we show how its real part, i.e., the metric tensor, can be exploited as a tool to detect quantum phase transitions as well as spontaneous $mathcal{PT}$-symmetry breaking in $mathcal{PT}$-symmetric systems.
We theoretically study the dynamics of typical optomechanical systems, consisting of a passive optical mode and an active mechanical mode, in the $mathcal{PT}$- and broken-$mathcal{PT}$-symmetric regimes. By fully analytical treatments for the dynamics of the average displacement and particle numbers, we reveal the phase diagram under different conditions and the various regimes of both $mathcal{PT}$-symmetry and stability of the system. We find that by appropriately tuning either mechanical gain or optomechanical coupling, both phase transitions of the $mathcal{PT}$-symmetry and stability of the system can be flexibly controlled. As a result, the dynamical behaviors of the average displacement, photons, and phonons are radically changed in different regimes. Our study shows that $mathcal{PT}$-symmetric optomechanical devices can serve as a powerful tool for the manipulation of mechanical motion, photons, and phonons.
Time-dependent $mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of time-dependent $mathcal{PT}$-symmetric quantum mechanics. We not only find a geometric phase factor emerging naturally from cyclic evolutions of $mathcal{PT}$-symmetric systems, but also formulate a series of differential geometry concepts, including connection, curvature, parallel transport, metric tensor, and quantum geometric tensor. Our findings constitute a useful, perhaps indispensible, tool to tackle physical problems involving $mathcal{PT}$-symmetric systems with time-varying systems parameters. To exemplify the application of our findings, we show that the unconventional geometrical phase [Phys. Rev. Lett. 91, 187902 (2003)], consisting of a geometric phase and a dynamical phase proportional to the geometric phase, can be expressed as a single geometric phase identified in this work.
Over the past decade, non-Hermitian, $mathcal{PT}$-symmetric Hamiltonians have been investigated as candidates for both, a fundamental, unitary, quantum theory, and open systems with a non-unitary time evolution. In this paper, we investigate the implications of the former approach in the context of the latter. Motivated by the invariance of the $mathcal{PT}$ (inner) product under time evolution, we discuss the dynamics of wave-function phases in a wide range of $mathcal{PT}$-symmetric lattice models. In particular, we numerically show that, starting with a random initial state, a universal, gain-site location dependent locking between wave function phases at adjacent sites occurs in the $mathcal{PT}$-symmetry broken region. Our results pave the way towards understanding the physically observable implications of time-invariants in the non-unitary dynamics produced by $mathcal{PT}$-symmetric Hamiltonians.
Parity-time($mathcal{PT}$)-symmetric systems, featuring real eigenvalues despite its non-Hermitian nature, have been widely utilized to achieve exotic functionalities in the classical realm, such as loss-induced transparency or lasing revival. By approaching the exceptional point (EP) or the coalescences of both eigenvalues and eigenstates, unconventional effects are also expected to emerge in pure quantum $mathcal{PT}$ devices. Here, we report experimental evidences of spontaneous $mathcal{PT}$ symmetry breaking in a single cold $^{40}mathrm{Ca}^{+}$ ion, and more importantly, a counterintuitive effect of perfect quantum coherence occurring at the EP. Excellent agreement between experimental results and theoretical predictions is identified. In view of the versatile role of cold ions in building quantum memory or processor, our experiment provides a new platform to explore and utilize pure quantum EP effects, with diverse applications in quantum engineering of trapped ions.
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