Observation of the Wannier–Stark ladder in plasmonic waveguide arrays

Lindén, Stefan; Wetter, Helene; Fedorova, Zlata

doi:10.1364/ol.458954

Cited by 7 publications

(3 citation statements)

References 26 publications

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“…In contrast, we have shown that the state shift in a dynamically modulated Wannier-Stark ladder is also strictly quantized during one adiabatic cycle and at the same time, the dispersion of the distribution is bounded by one unit cell. The protocol can be implemented, for example, in arrays of evanescently coupled dielectric waveguides [32]. Finally, it should be mentioned that similar ideas can be applied to many-particle systems to study topological phenomena.…”

Section: Discussionmentioning

confidence: 99%

“…Tight-binding lattice Hamiltonians subject to a constant force parallel to the lattice are called Wannier-Stark ladders [31] and their spectral properties and dynamics has extensively been studied in the past. The Wannier-Stark ladder has recently been implemented in arrays of evanescently coupled dielectric waveguides for surface plasmon-polaritons [32].…”

Section: Introductionmentioning

confidence: 99%

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Controlled quantized adiabatic transport in a superlattice Wannier-Stark ladder

Unanyan

Vitanov

Fleischhauer

2023

J. Phys. B: At. Mol. Opt. Phys.

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The Born-Fock theorem is one of the most fundamental theorems of quantum mechanics and forms the basis for reliable and eﬃcient navigation in the Hilbert space of a quantum system with a time-dependent Hamiltonian by adiabatic evolution. In the absence of level crossings, i.e. without degeneracies, and under adiabatic time evolution all eigenstates of the Hamiltonian keep their energetic order, labelled by a conserved integer quantum number. Thus controlling the eigenstates of the Hamiltonian and their energetic order in asymptotic limits allows to engineer a perfect adiabatic transfer between a large number of initial and target states. The ﬁdelity of the state transfer is only limited by adiabaticity and the selection of target states is controlled by the integer invariant labelling the order of eigenstates. We here show for the example of a ﬁnite superlattice Wannier-Stark ladder, i.e. a one-dimensional lattice with alternating hopping amplitudes and constant potential gradient, that such an adiabatic control of eigenstates can be used to induce perfectly quantized single-particle transport across a pre-determined number of lattice sites. We dedicate this paper to the memory of our late friend and colleague Bruce Shore, who was an expert in adiabatic processes and taught us much about this ﬁeld.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Controlled quantized adiabatic transport in a superlattice Wannier-Stark ladder

Unanyan

Vitanov

Fleischhauer

2023

J. Phys. B: At. Mol. Opt. Phys.

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show abstract

“…A comprehensive review on optical Bloch oscillations, Zener tunneling and related effects can be found in [21]. It is important to acknowledge that Bloch oscillations are a very generic effect and occur in a large number of physical systems such as atomic systems [22][23][24][25][26][27], lasers [28], coupled LC circuits [29], mechanical systems [30][31][32][33], plasmonic [34][35][36][37][38][39] or exciton-polariton systems [40][41][42].…”

Section: Introductionmentioning

confidence: 99%