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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Indistinguishable particles in non-Hermitian lattices and their correlations

Markus Gräfe, René Heilmann, Robert Keil, Toni Eichelkraut, Matthias Heinrich, Stefan Nolte, Alexander Szameit

Published May 1, 2013• 0 citations
Publisher

Abstract

Quantum random walks of identical particles are ubiquitous in various fields of physics [1]. They give rise to particle number correlations which have been explored in several discrete systems [2; 3]. However, an essential property of all these quantum systems is their Hermiticity. Recently parity-time(PT)-symmetric systems [4] attracted much attention. The Hamiltonians of such systems are not necessarily Hermitian, yet they still can exhibit purely real eigenvalue spectra.

DOI
10.1109/cleoe-iqec.2013.6801660

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Quantum random walks of identical particles are ubiquitous in various fields of physics [1]. They give rise to particle number correlations which have been explored in several discrete systems [2; 3]. However, an essential property of all these quantum systems is their Hermiticity. Recently parity-time(PT)-symmetric systems [4] attracted much attention. The Hamiltonians of such systems are not necessarily Hermitian, yet they still can exhibit purely real eigenvalue spectra.
A novel approach to investigate the dynamics of indistinguishable particles in non-Hermitian lattice systems is presented, allowing an efficient calculation of quantum correlations between these particles in the presence of losses. Particular attention is paid to quasi-parity-time-symmetric systems, for which we numerically analyze two-particle quantum random walks for a variety of input states. Our results show how in some scenarios coherence is lost, inducing classical random walks, while in others the characteristic signatures of bosonic and fermionic exchange symmetry prevail.
Non-Hermitian PT{\cal PT}PT-symmetric relativistic quantum theory in an intensive magnetic field
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of physical parameters. This condition not only guarantees the reality of the eigenvalues of Hamiltonian operators, but also implies the preservation of the probabilities of the considered quantum processes. However as it was shown relatively recently (Bender, Boettcher 1998), Hermiticity is a sufficient but it is not a necessary condition. It turned out that among non-Hermitian Hamiltonians it is possible to allocate a number of such which have real energy spectra and can ensure the development of systems over time with preserving unitarity. This type of Hamiltonians includes so-called parity-time (PT{\cal PT}PT) symmetric models which is already used in various fields of modern physics. The most developed in this respect are models, which used in the field of PT{\cal PT}PT-symmetric optics, where for several years produced not only theoretical but experimental studies.
Abstract A wide class of non-Hermitian Hamiltonians can possess entirely real eigenvalues when they have parity-time (PT) symmetric potentials. Recently, this family of non-Hermitian systems has attracted considerable attention in diverse areas of physics due to their extraordinary properties, especially in optical systems based on solid-state materials, such as coupled gain–loss waveguides and microcavities. Considering the desired refractive index can be effectively manipulated through atomic coherence, it is important to realize such non-Hermitian optical potentials and further investigate their distinct properties in atomic systems. In this paper, we review the recent theoretical and experimental progress of non-Hermitian optics with coherently prepared multi-level atomic configurations. The realizations of (anti-) PT symmetry with different schemes have extensively demonstrated the special optical properties of non-Hermitian optical systems with atomic coherence.