Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate

Chisholm, C. S.; Frölian, A.; Neri, Elettra; Ramos, Ramón; Tarruell, Leticia; Celi, Alessio

doi:10.1103/physrevresearch.4.043088

Cited by 13 publications

(11 citation statements)

References 138 publications

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“…Moreover, the continuum limit of the traid-anyon Hubbard model is found to be Galilean invariant. This is in clear contrast to the continuum limit of the braid-anyon-Hubbard model, which breaks Galilean invariance by a Hamiltonian that, like the Kundu model [42][43][44][45][46][47] and chiral BF model [48][49][50][51][52], depends on the current-density operator [15]. We attribute this difference to the fact that traid anyons are naturally defined also in the continuum in 1D using the intrinsic approach to topological exchange statistics.…”

Section: Discussionmentioning

confidence: 88%

“…In the presence of non-quadratic trapping potentials or additional interactions between the particles, the above reasoning remains valid, except that separability is lost and the wave functions do not have a simple form like (51). We can also generalize Eqs.…”

Section: Mapping Between Bosonic and Traid Anyon Wave Functionsmentioning

confidence: 95%

“…Fractional exchange statistics emerge for quasiparticle excitations in certain quantum liquid and quantum spin liquid models like the fractional quantum Hall effect [8] or the Haldane-Shastry spin-chain model [34,35]. In addition to motivating the braid-anyon-Hubbard model [11], implementing fractional exchange statistics in one-dimensional systems provided the original motivation for several continuum models, including the recently experimentally-realized chiral BF model [48][49][50][51][52], the closely-related Kundu model (also called Lieb-Liniger anyons) [42][43][44][45][46][47], the Calogero-Sutherland anyon model [25,68,69], and hard-core anyon models [70][71][72]. Note that we have only discussed abelian braid anyons; non-abelian representations of B N are carried by multi-component, multi-valued wave functions, c.f.…”

Section: B Braid Group and Fractional Exchange Statisticsmentioning

confidence: 99%

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Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Nagies,

Wang,

Knapp

et al. 2024

SciPost Phys.

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Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be associated to non-trivial geometric phases for abelian anyons. Braid-anyon exchange statistics can also be found in one dimension (1D), but this requires broken Galilean invariance to distinguish different ways for two anyons to exchange. However, recently it was shown that an alternative form of exchange statistics can occur in 1D because hard-core three-body constraints also make the configuration space not simply-connected. Instead of the braid group, the topology of exchange paths and their associated non-trivial geometric phases are described by the traid group. In this article we propose a first concrete model realizing this alternative form of anyonic exchange statistics. Starting from a bosonic lattice model that implements the desired geometric phases with number-dependent Peierls phases, we then define anyonic operators so that the kinetic energy term in the Hamiltonian becomes local and quadratic with respect to them. The ground-state of this traid-anyon-Hubbard model exhibits several indications of exchange statistics intermediate between bosons and fermions, as well as signs of emergent approximate Haldane exclusion statistics. The continuum limit results in a Galilean invariant Hamiltonian with eigenstates that correspond to previously constructed continuum wave functions for traid anyons. This provides not only an a-posteriori justification of our lattice model, but also shows that our construction serves as an intuitive approach to traid anyons, i.e. anyons intrinsic to 1D.

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Section: Discussionmentioning

confidence: 88%

Section: Mapping Between Bosonic and Traid Anyon Wave Functionsmentioning

confidence: 95%

Section: B Braid Group and Fractional Exchange Statisticsmentioning

confidence: 99%

See 1 more Smart Citation

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Nagies,

Wang,

Knapp

et al. 2024

SciPost Phys.

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“…Secondly, a gauge potential which depends on the position of the other particle allows us to draw parallels with density dependent gauge potentials in the many particle mean field limit [8] which are encountered in Chern Simons theory in the context of flux attachment [9]. This is further emphasised by the recent experimental realisation and emulation of a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate [10] together with a comprehensive theoretical investigation of the mappings required to connect the experimental platform with the chiral BF theory [11].…”

Section: Introductionmentioning

confidence: 99%

The gauge coupled two-body problem in a ring

Priestley

Valentí-Rojas²,

Wright³

et al. 2023

J. Phys. A: Math. Theor.

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We study the properties of two quantum particles which are conﬁned in a ring. The particles interact via a long-range gauge potential proportional to the distance between the particles. It is found that the two-body ground state corresponds to a state with non-zero angular momentum provided that the interaction between the particles is strong enough. In addition, the particles are correlated in the sense that depending on the interaction strength there is a propensity to be found close together or separated in the ring. We discuss the eﬀect of measuring the position of one of the particles and thereby removing the particle from the ring, where we show that the remaining particle can be prepared in a non-dispersive state with non-zero angular momentum.

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“…Key proposals in this direction have recently been experimentally realized [31,43,44]. In particular, signatures of the chiral BF model, connected to 1D Kundu anyons, have been observed [43,45] by generating a magnetic-like vector potential proportional to matter density. On the other hand, the magnetic gauge picture of 2D anyons corresponds to a magnetic-like field proportional to matter density.…”

mentioning

confidence: 99%

Anyons in a tight wave-guide and the Tonks-Girardeau gas

Rougerie,

Yang

2023

SciPost Phys. Core

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We consider a many-body system of 2D anyons, free quantum particles with general statistics parameter \alpha ∈ ]0,2[α∈]0,2[. In the magnetic gauge picture they are described as bosons attached to Aharonov-Bohm fluxes of intensity 2\pi \alpha2πα, generating long-range magnetic forces. A dimensional reduction to 1D is obtained by imposing a strongly anisotropic trapping potential. This freezes the motion in the direction of strong trapping, leading to 1D physics along the weak direction. The latter is governed to leading order by the Tonks-Girardeau model of impenetrable bosons, independently of \alphaα.

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Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate

Cited by 13 publications

References 138 publications

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

The gauge coupled two-body problem in a ring

Anyons in a tight wave-guide and the Tonks-Girardeau gas

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