2000 character limit reached
Quantum nonlinear optics on the edge of a few-particle fractional quantum Hall fluid in a small lattice
Published 15 Mar 2024 in cond-mat.mes-hall, quant-ph, and cond-mat.quant-gas | (2403.10598v3)
Abstract: We study the quantum dynamics in response to time-dependent external potentials of the edge modes of a small fractional quantum Hall fluid composed of few particles on a lattice in a bosonic Laughlin-like state at filling {\nu} = 1/2. We show that the nonlinear chiral Luttinger liquid theory provides a quantitatively accurate description even for the small lattices that are available in state-of-the-art experiments, away from the continuum limit. Experimentally-accessible data related to the quantized value of the bulk transverse Hall conductivity are identified both in the linear and the non-linear response to an external excitation. The strong nonlinearity induced by the open boundaries is responsible for sizable quantum blockade effects, leading to the generation of nonclassical states of the edge modes.
- R. B. Laughlin, Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations, Phys. Rev. Lett. 50, 1395 (1983) .
- X. G. Wen, Electrodynamical properties of gapless edge excitations in the fractional quantum Hall states, Phys. Rev. Lett. 64, 2206 (1990a) .
- X. G. Wen, Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states, Phys. Rev. B 41, 12838 (1990b) .
- X. G. Wen, Gapless boundary excitations in the quantum Hall states and in the chiral spin states, Phys. Rev. B 43, 11025 (1991a) .
- X.-G. Wen, Edge transport properties of the fractional quantum Hall states and weak-impurity scattering of a one-dimensional charge-density wave, Phys. Rev. B 44, 5708 (1991b) .
- X.-G. Wen, Topological orders and edge excitations in fractional quantum Hall states, Adv. Phys. 44, 405 (1995) .
- X.-G. Wen, Theory of the Edge States in Fractional Quantum Hall Effects, International Journal of Modern Physics B 06, 1711 (1992) .
- A. M. Chang, Chiral Luttinger liquids at the fractional quantum Hall edge, Rev. Mod. Phys. 75, 1449 (2003) .
- X.-G. Wen, Choreographed entanglement dances: Topological states of quantum matter, Science 363, eaal3099 (2019) .
- N. Cooper, Rapidly rotating atomic gases, Advances in Physics 57, 539 (2008) .
- I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013) .
- D. T. Tran, A. Dauphin, A. G. Grushin, P. Zoller, and N. Goldman, Probing topology by “heating”: Quantized circular dichroism in ultracold atoms, Science Advances 3 (2017), 10.1126/sciadv.1701207 .
- C. Repellin and N. Goldman, Detecting Fractional Chern Insulators through Circular Dichroism, Phys. Rev. Lett. 122, 166801 (2019) .
- R. O. Umucalılar, Bulk density signatures of a lattice quasihole with very few particles, Phys. Rev. A 108, L061302 (2023) .
- J. A. Kjäll and J. E. Moore, Edge excitations of bosonic fractional quantum Hall phases in optical lattices, Phys. Rev. B 85, 235137 (2012) .
- R. Fern and S. H. Simon, Quantum Hall edges with hard confinement: Exact solution beyond Luttinger liquid, Phys. Rev. B 95, 201108 (2017) .
- E. Macaluso and I. Carusotto, Hard-wall confinement of a fractional quantum Hall liquid, Phys. Rev. A 96, 043607 (2017) .
- E. Macaluso and I. Carusotto, Ring-shaped fractional quantum Hall liquids with hard-wall potentials, Phys. Rev. A 98, 013605 (2018) .
- A. Nardin and I. Carusotto, Linear and nonlinear edge dynamics of trapped fractional quantum Hall droplets, Phys. Rev. A 107, 033320 (2023a) .
- A. Nardin and I. Carusotto, Refermionized theory of the edge modes of a fractional quantum Hall cloud, arXiv:2305.00291 [cond-mat.str-el] (2023b).
- M. A. Kastner, The single-electron transistor, Rev. Mod. Phys. 64, 849 (1992) .
- P. Rabl, Photon Blockade Effect in Optomechanical Systems, Phys. Rev. Lett. 107, 063601 (2011) .
- D. R. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B 14, 2239 (1976) .
- G. Möller and N. R. Cooper, Composite Fermion Theory for Bosonic Quantum Hall States on Lattices, Phys. Rev. Lett. 103, 105303 (2009) .
- G. Möller and N. R. Cooper, Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number, Phys. Rev. Lett. 115, 126401 (2015) .
- M. A. Cazalilla, Surface modes of ultracold atomic clouds with a very large number of vortices, Phys. Rev. A 67, 063613 (2003) .
- P. Wiegmann, Nonlinear Hydrodynamics and Fractionally Quantized Solitons at the Fractional Quantum Hall Edge, Phys. Rev. Lett. 108, 206810 (2012) .
- W. Kohn, Cyclotron Resonance and de Haas-van Alphen Oscillations of an Interacting Electron Gas, Phys. Rev. 123, 1242 (1961) .
- B. I. Halperin and J. K. Jain, Fractional Quantum Hall Effects (WORLD SCIENTIFIC, 2020).
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