Exceptional points in bichromatic Wannier–Stark systems

Elsen, Christoffer; Rapedius, Kevin; Witthaut, Dirk; Korsch, Hans Jürgen

doi:10.1088/0953-4075/44/22/225301

Cited by 11 publications

(10 citation statements)

References 63 publications

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“…[14]. Topological properties have also been of interest in other recent investigations with cold atoms concerning, e.g., quantum Hall effects [15,16], Berry phases [17,18], or dissipative quantum wires [19]. We will demonstrate an interactioninduced decoherence, i.e., a quantum-to-classical transition for a conceptually simple model system.…”

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confidence: 77%

“…In this brief report, we analyze the mechanism of decoherence in the nonequilibrium dynamics of an interacting Bose gas by means of a topological quantity introduced in [14]. Topological properties have also been of interest in other recent investigations with cold atoms concerning, e.g., quantum Hall effects [15,16], Berry phases [17,18] or dissipative quantum wires [19]. We will demonstrate an interaction induced decoherence, i.e.…”

mentioning

confidence: 93%

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Interaction-induced decoherence in non-Hermitian quantum walks of ultracold bosons

Rapedius

Korsch

2012

Phys. Rev. A

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We study the decoherence caused by particle interaction for a conceptually simple model, a quantum walk on a bipartite one-dimensional lattice with decay from every second site. The corresponding noninteracting (linear) system has been shown to have a topological transition described by the average displacement before decay. Here, we use this topological quantity to distinguish coherent quantum dynamics from incoherent classical dynamics caused by a breaking of the translational symmetry. Furthermore, we analyze the behavior by means of a rate equation providing a quantitative description of the incoherent nonlinear dynamics.

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confidence: 77%

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confidence: 93%

Interaction-induced decoherence in non-Hermitian quantum walks of ultracold bosons

Rapedius

Korsch

2012

Phys. Rev. A

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“…On the other hand much theoretical work has been done on PT -symmetric BECs, including the proof of existence of stable states of interacting systems [10], a microscopic treatment based on the Bose-Hubbard model [11], and a thorough investigation on dynamics of stable and unstable regimes [12]. In contrast to injecting and removing particles from a double-well potential, one could think of a double-well included in a tilted optical lattice, with an incoming and outgoing transport of particles, so called Wannier-Stark systems [13,14]. These incoming and outgoing particle currents could in principle serve as the necessary currents for realizing a PT -symmetric system.…”

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confidence: 99%

RealizingPT-symmetric non-Hermiticity with ultracold atoms and Hermitian multiwell potentials

et al. 2014

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We discuss the possibility of realizing a non-Hermitian, i. e. an open two-well system of ultra-cold atoms by enclosing it with additional time-dependent wells that serve as particle reservoirs. With the appropriate design of the additional wells PT -symmetric currents can be induced to and from the inner wells, which support stable solutions. We show that interaction in the mean-field limit does not destroy this property. As a first method we use a simplified variational ansatz leading to a discrete nonlinear Schrödinger equation. A more accurate and more general variational ansatz is then used to confirm the results.

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“…While in the Hermitian case such an accidental coalescence yields exact wave packet revivals at time intervals multiplies than t B = 2π/F [80,81], in the non-Hermitian lattice the coalescence of energy ladders can correspond to the simultaneous coalescence of the localized WS eigenstates, i.e. to a WS EP [82]. This occurs when the eigenvectors u 1,2 of the matrix U [Eq.…”

Section: Chiral Zener Tunneling Between Dispersive Bloch Bandsmentioning

confidence: 99%

Non-Bloch-Band Collapse and Chiral Zener Tunneling

Longhi¹

2020

Phys. Rev. Lett.

150

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Non-Bloch band theory describes bulk energy spectra and topological invariants in non-Hermitian crystals with open boundaries, where the bulk eigenstates are squeezed toward the edges (skin effect). However, the interplay of non-Bloch band theory, skin effect and coherent Bloch dynamics is so far unexplored. In two-band non-Hermitian lattices, it is shown here that collapse of non-Bloch bands and skin modes deeply changes the Bloch dynamics under an external force. In particular, for resonance forcing non-Bloch band collapse results in Wannier-Stark ladder coalescence and chiral Zener tunneling between the two dispersive Bloch bands.Introduction. Bloch band theory is the fundamental tool to describe electronic states in crystals [1]. Under the action of a weak dc electric field, Bloch theory predicts that electrons undergo an oscillatory motion, the famous Bloch oscillations (BOs) [1], which can be explained from the formation of a Wannier-Stark (WS) ladder energy spectrum [2]. Transitions among different bands occur for stronger fields because of Zener tunneling (ZT) [3]. BOs and ZT are ubiquitous phenomena of coherent wave transport in periodic media and have been observed in a wide variety of physical systems [4][5][6][7][8][9][10][11][12][13][14]. It is remarkable that, after one century from the seminal paper by Felix Bloch [1], there are still treasures to be uncovered within Bloch band theory. For example, Bloch band theory is central in the understanding of topological insulators [15][16][17] and in the description of flat band systems showing unconventional localization, anomalous phases, and strongly correlated states of matter [18][19][20][21][22][23][24][25][26][27][28]. Recently, a great interest is devoted to extend Bloch band theory and topological order to non-Hermitian lattices . In Bloch band theory, an electronic state is defined by the quasi-momentum k, which spans the first Brillouin zone, and is delocalized all along the crystal, regardless periodic boundary conditions (PBC) or open boundary conditions (OBC) are assumed. However, in non-Hermitian crystals something strange happens: energy bands in crystals with OBC are described by non-Bloch bands that deviate from ordinary Bloch bands; bulk eigenstates cease to be delocalized and get squeezed toward the edges (non-Hermitian skin effect); and the bulk-boundary correspondence based on Bloch topological invariants generally fails to correctly predict the existence of topological zero-energy modes [29, 33-39, 45, 56, 59]. Recent seminal works [35,37,45] showed that to correctly describe energy spectra and topological invariants in crystals with OBC one needs to extend Bloch band theory so as the quasi-momentum k becomes complex and varies on a generalized Brillouin zone. Bloch and non-Bloch bands can show different symmetry breaking phase transitions and, interestingly, band flat-

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Exceptional points in bichromatic Wannier–Stark systems

Cited by 11 publications

References 63 publications

Interaction-induced decoherence in non-Hermitian quantum walks of ultracold bosons

Interaction-induced decoherence in non-Hermitian quantum walks of ultracold bosons

RealizingPT-symmetric non-Hermiticity with ultracold atoms and Hermitian multiwell potentials

Non-Bloch-Band Collapse and Chiral Zener Tunneling

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