Momentum-space Landau levels in driven-dissipative cavity arrays

Berceanu, A. C.; Price, Hannah M.; Ozawa, Tomoki; Carusotto, Iacopo

doi:10.1103/physreva.93.013827

Cited by 9 publications

(10 citation statements)

References 58 publications

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“…Looking to the future, our proposal can be naturally extended to include a confining external potential, leading to novel oscillation features associated with analogue momentum-space magnetism [60][61][62]. Beyond the small oscillation regime considered so far, systems of pendula also show nonlinear effects such as amplitude-dependent oscillation frequencies.…”

Section: Discussionmentioning

confidence: 94%

Floquet topological system based on frequency-modulated classical coupled harmonic oscillators

et al. 2016

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We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency-modulation of the different oscillators. We illustrate how the topologically-protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.

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Section: Discussionmentioning

confidence: 94%

Floquet topological system based on frequency-modulated classical coupled harmonic oscillators

et al. 2016

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“…In physics, there is a powerful duality between position and momentum, such that a physical system can be equivalently described in either position space or momentum space. If the roles of position and momentum are reversed, this can lead to momentum-space topological physics, ranging from momentum-space lattices 70,71 , to momentum-space Landau levels 72,73 , and momentumspace integer 74 and fractional 75 quantum Hall effects. In the context of synthetic dimensions, the positionmomentum duality is reflected in a re-interpretation of a discrete set of free-particle momentum states as the set of lattice sites 38,39,43 .…”

Section: B Momentum Statesmentioning

confidence: 99%

Topological quantum matter in synthetic dimensions

Ozawa¹,

2019

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In the field of quantum simulation of condensed matter phenomena by artificially engineering the Hamiltonian of an atomic, molecular or optical system, the concept of 'synthetic dimensions' has recently emerged as a powerful way to emulate phenomena such as topological phases of matter, which are now of great interest across many areas of physics. The main idea of a synthetic dimension is to couple together suitable degrees of freedom, such as a set of internal atomic states, in order to mimic the motion of a particle along an extra spatial dimension. This approach provides a way to engineer lattice Hamiltonians and enables the realisation of higher-dimensional topological models in platforms with lower dimensionality. We give an overview of the recent progress in studying topological matter in synthetic dimensions. After reviewing proposals and realizations in various setups, we discuss future prospects in many-body physics, applications, and topological effects in three or more spatial dimensions.

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“…Thus, ψ 1,p is the only nonzero component of the wave function. Its time evolution obeys i∂ t ψ 1,p (t) = H M ψ 1,p (t), with an effective Hamiltonian [16,17]…”

Section: Effective Momentum-space Hamiltonianmentioning

confidence: 99%

Quantum Hall effect in momentum space

Ozawa¹,

Price²,

Carusotto³

2016

Phys. Rev. B

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We theoretically discuss a momentum-space analog of the quantum Hall effect, which could be observed in topologically nontrivial lattice models subject to an external harmonic trapping potential. In our proposal, the Niu-Thouless-Wu formulation of the quantum Hall effect on a torus is realized in the toroidally shaped Brillouin zone. In this analogy, the position of the trap center in real space controls the magnetic fluxes that are inserted through the holes of the torus in momentum space. We illustrate the momentum-space quantum Hall effect with the noninteracting trapped Harper-Hofstadter model, for which we numerically demonstrate how this effect manifests itself in experimental observables. Extension to the interacting trapped Harper-Hofstadter model is also briefly considered. We finally discuss possible experimental platforms where our proposal for the momentum-space quantum Hall effect could be realized.Comment: 12 pages, 5 figure

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Momentum-space Landau levels in driven-dissipative cavity arrays

Cited by 9 publications

References 58 publications

Floquet topological system based on frequency-modulated classical coupled harmonic oscillators

Floquet topological system based on frequency-modulated classical coupled harmonic oscillators

Topological quantum matter in synthetic dimensions

Quantum Hall effect in momentum space

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