Anyon Hubbard Model in One-Dimensional Optical Lattices

Abstract

Raman-assisted hopping may be used to realize the anyon Hubbard model in one-dimensional optical lattices. We propose a feasible scenario that significantly improves the proposal of T. Keilmann et al. [Nat. Commun. 2, 361 (2011)], allowing as well for an exact realization of the two-body hard-core constraint, and for controllable effective interactions without the need of Feshbach resonances. We show that the combination of anyonic statistics and two-body hard-core constraint leads to a rich ground-state physics, including Mott insulators with attractive interactions, pair superfluids, dimer phases, and multicritical points. Moreover, the anyonic statistics results in a novel two-component superfluid of holon and doublon dimers, characterized by a large but finite compressibility and a multipeaked momentum distribution, which may be easily revealed experimentally. DOI: 10.1103/PhysRevLett.115.053002 PACS numbers: 37.10.Jk, 67.85.-d, 05.30.Pr Particles are classified as bosons or fermions depending on whether their wave function is symmetric or antisymmetric under exchange. Other types of quantum statistics are, however, possible in lower dimensions. Remarkably, 2D systems allow for the existence of anyons, i.e., particles with fractional statistics interpolating between bosons and fermions [1][2][3]. Anyons play a fundamental role in key areas of modern physics, as fractional quantum Hall effect [4][5][6][7] and topological quantum computing [8]. Fractional statistics is, however, not exclusive of 2D systems [9]. In particular, 1D anyons have attracted a large deal of interest [10][11][12][13][14][15][16][17][18][19][20][21][22][23], although the experimental realization of a 1D anyon gas is still lacking.Ultracold atoms offer extraordinary possibilities for the analysis of interesting many-body systems [24]. In particular, several ideas have been proposed for the creation and manipulation of anyons in cold gases [25][26][27][28][29]. Particularly interesting is the recent proposal for the realization of the anyon Hubbard model (AHM) using Raman-assisted hopping in 1D optical lattices [30]. In this proposal, the anyonic statistics may be controlled at will, opening the possibility for the observation of statistically induced quantum phase transitions [30], asymmetric momentum distributions [21], and intriguing particle dynamics in the lattice [20,22,23].In this Letter, we first discuss a scheme for realizing the AHM that, although following Ref. [30], solves crucial drawbacks that would render the original proposal, in general, unfeasible. The scheme also allows for controllable effective interactions without the need of Feshbach resonances, and for an exact two-body hard-core constraint (2BHCC), contrary to the approximate realization of 2BHCC resulting from Zeno projection due to large three-body loss rates [31], where non-negligible losses are typically present. Neither the controllable interactions nor the inherent 2BHCC were considered in Ref. [30], which focused exclusively on statistically induced su...

One-body reduced density matrix of trapped impenetrable anyons in one dimension

“…In fact, in the cold atom framework a number of proposals have been formulated that indicate the realization of one-dimensional anyons as feasible within the current experimental techniques. Among those proposals, the one elaborated by Keilmann et al [19] and subsequently refined by Greschner and Santos [20] appears to be particularly promising. Their idea starts from ordinary bosonic or fermionic atoms and employs a Raman-assisted tunneling process to induce an effective occupation-dependent hopping; the system obtained in this way can be shown to be equivalent to the anyonic Hubbard model, in which the statistical parameter and the on-site interaction can be changed continuously.…”

Topological phases of lattice bosons with a dynamical gauge field

“…[27], namely, the maximum occupancy per site will be set to two bosons. To clarify our discussion we will compare our results to those obtained with an static field, that is,…”

“…[18][19][20][21][22]. An intermediate step might be the realization of simpler but nevertheless dynamical gauge fields, engineering an occupation number-dependent tunneling term [23][24][25][26][27][28][29][30].…”

Quasimomentum distribution and expansion of an anyonic gas

“…The one-dimensional (1D) version of anyons [18][19][20][21][22][23][24][25][26] has also aroused interest, especially in 1D optical lattices [23][24][25][26]. Such particles were proposed to emerge from occupation dependent hopping amplitudes, which could be realized with laser-assisted tunneling [23,25], or Floquet modulations [26]. Other proposals include lattices of polar molecules [27], photonics lattices [28] and circuit-QED systems [29].…”

“…Ultracold atoms with two hyperfine levels in non-Abelian potentials could yield ground states with non-Abelian anyonic excitations [16], while bosons in Floquet-driven optical lattices may effectively exhibit fermionic statistics [17]. The one-dimensional (1D) version of anyons [18][19][20][21][22][23][24][25][26] has also aroused interest, especially in 1D optical lattices [23][24][25][26]. Such particles were proposed to emerge from occupation dependent hopping amplitudes, which could be realized with laser-assisted tunneling [23,25], or Floquet modulations [26].…”