Devil's staircases in synthetic dimensions and gauge fields

Saito, Takeshi; Furukawa, Shunsuke

doi:10.1103/physreva.95.043613

Cited by 21 publications

(14 citation statements)

References 71 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above discussion allows us to follow the relation between the emerging devil's staircase of fractional CDW phases for the M-leg cylinder at ϕ ¼ 2π=M, realized for 1=M ≤ ρ ≤ 1 with the similar incompressible states of a quantum Hall system in the thin-cylinder limit [54][55][56][57][58] realized for the filling 1=M ≤ ν ≤ 1 [32]. Recent works [15][16][17] indicate that CDW states of M-leg ladders approach corresponding fractional quantum Hall states also in topological properties with increasing M.…”

Section: Weak Coupling (Jj)mentioning

confidence: 95%

“…In particular, a devil's staircaselike structure of CDW states emerges at π flux without the need for long-range (e.g., dipolar) interactions between the particles, which can be related to the fractional quantum Hall states in the thin-cylinder limit [15,16,58]. Hence, two cornerstone condensed matter systems (both defined on two-leg ladder lattices)-the classical Josephson-junctions array and the quantum Hall system-can be related to each other through the vortex-hole duality [62].…”

Section: Weak Coupling (Jj)mentioning

confidence: 99%

See 1 more Smart Citation

Vortex-Hole Duality: A Unified Picture of Weak- and Strong-Coupling Regimes of Bosonic Ladders with Flux

Greschner

Vekua

2017

Phys. Rev. Lett.

View full text Add to dashboard Cite

Two-leg bosonic ladders with flux harbor a remarkable vortex-hole duality between the weak-coupling vortex lattice superfluids and strong-coupling charge-density-wave crystals. The strong-coupling crystalline states, which are realized in the vicinity of π flux, are independent of particle statistics, and are related to the incompressible fractional quantum Hall states in the thin-cylinder limit. These fully gapped ground states, away from π flux, develop nonzero chiral (spin) currents. Contact-interacting quantum gases permit exploration of this vortex-hole duality in experiments. DOI: 10.1103/PhysRevLett.119.073401 Dualities encode important nonperturbative information in statistical, condensed matter and high-energy physics, by mapping weak and strong coupling regimes and providing a way for their unified description [1].A quantum system, depending on conditions, can manifest one of its dual natures profoundly. In a weakly coupled gas or liquid, where positions of particles are not fixed, at sufficiently low temperatures quantum effects set in, and, as a result, Bose particles can develop phase coherence and superfluidity. For strong repulsive interparticle interactions, crystals can form, where each particle is localized to a certain position in space to get as far as possible from the others. Phases of particles, being conjugate variables of densities, fluctuate strongly in crystals. Fluids can develop eddy currents, or vortices when excited. In superfluids with global phase coherence, vortices get topological protection by quantization. Crystals also harbour excitations of topological nature-e.g., point defects such as vacancies (holes).The purpose of this Letter is to demonstrate a spectacular correspondence between the topological defects of superfluids and crystals, referred in the following as a vortexhole duality, realized between weak and strong-coupling regimes of bosonic ladders with flux. Figure 1 shows the microscopic configurations of local particle currents (arrows) and densities (filled circles) of a few dual weak and strong-coupling ground states of bosonic ladders with flux. In the weak-coupling limit the phases of particles are the relevant degrees of freedom, whereas in strong-coupling particle densities they play a dominant role. Vortices are indicated by the letter V in those plaquettes of Fig. 1, wherewhere Θ is local phase and integration is along the boundary l of the plaquette □. Holes, defects of the local particle density distribution, are localized on rungs, indicated by the letter H. Vortices (elementary loop currents), topological excitations of a weak-coupling regime, repel each other [2] (like same pole magnets) and vortex lattices (VLs) at a commensurate vortex density ρ V are dual to hole crystals of chargedensity-wave (CDW) states at ρ H ¼ ρ V realized in a strong-coupling regime, as we will show. Table I summarizes the weak and strong-coupling duality relations. In the weak coupling regime of bosonic ladders few VL superfluids were observed [3,4] to survive quantum fluc...

show abstract

Section: Weak Coupling (Jj)mentioning

confidence: 95%

Section: Weak Coupling (Jj)mentioning

confidence: 99%

Vortex-Hole Duality: A Unified Picture of Weak- and Strong-Coupling Regimes of Bosonic Ladders with Flux

Greschner

Vekua

2017

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…Going beyond ladder geometries to longer synthetic dimensions, a crucial open question with no consensus being reached as yet is whether this unique form of interactions can give rise to familiar two-dimensional phenomena, such as two-dimensional fractional quantum Hall phases [113][114][115] . However, as mentioned above, a synthetic dimension based on the angular coordinate of a photonic ring resonator has been proposed, and in this scheme, local interactions in the resonator would also lead to local interactions along the synthetic dimension 56 .…”

Section: A Interparticle Interactions and Many-body Physicsmentioning

confidence: 99%

Topological quantum matter in synthetic dimensions

Ozawa¹,

2019

View full text Add to dashboard Cite

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.

show abstract

“…In recent years, controllable quantum systems have emerged as platforms for exploring phenomena in condensedmatter and high-energy physics 17 . This includes trapped ions 18,19 , cold polar molecules [20][21][22][23][24] and strongly interacting Rydberg atoms [25][26][27][28][29][30] , ultracold atoms in bichromatic lattices 31 , synthetic dimensions and gauge fields 32 , photons with engineered long-range interactions 33 and optomechanical cavity systems 34 . These platforms allow not only to control singlebody quantities (e.g.…”

Section: Introductionmentioning

confidence: 99%

Devil's staircases without particle-hole symmetry

Lan

Lesanovsky

2018

Phys. Rev. B

View full text Add to dashboard Cite

We present and analyze spin models with long-range interactions whose ground state features a so-called devil's staircase and where plateaus of the staircase are accessed by varying two-body interactions. This is in contrast to the canonical devil's staircase, for example, occurring in the one-dimensional Ising model with long-range interactions, where typically a single-body chemical potential is varied to scan through the plateaus. These systems, moreover, typically feature a particle-hole symmetry which trivially connects the hole part of the staircase (filling fraction f 1/2) to its particle part (f 1/2). Such symmetry is absent in our models and hence the particle sector and the hole sector can be separately controlled, resulting in exotic hybrid staircases.

show abstract

Devil's staircases in synthetic dimensions and gauge fields

Cited by 21 publications

References 71 publications

Vortex-Hole Duality: A Unified Picture of Weak- and Strong-Coupling Regimes of Bosonic Ladders with Flux

Vortex-Hole Duality: A Unified Picture of Weak- and Strong-Coupling Regimes of Bosonic Ladders with Flux

Topological quantum matter in synthetic dimensions

Devil's staircases without particle-hole symmetry

Contact Info

Product

Resources

About