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Europhysics Letters (EPL)

Dipolar interaction driven phase transitions in a one-dimensional optical lattice with a synthetic dimension

Yu-Hang Li, Hua Chen, Xiaoming Xie

Published Feb 1, 2017• 2 citations
Publisher

Abstract

Extensive research interest has been attracted by the fact that recent experiments in cold atoms simulate the chiral edge states of (1 + 1)-dimensional quantum Hall systems with laser-assisted transitions between different atomic nuclear spin states in a one-dimensional optical lattice. Within such an optical lattice, we study the phase diagrams of ν = 1 / 3 filling hard-core fermions and ν = 1 / 2 hard-core bosons with internal spin states in the presence of dipole-dipolar interactions. Our results show that the interaction drives the fermionic (bosonic) systems from the normal (superfluid) phase into the fractional topological phase with possible crystalline orderings. The topological nature of the latter phase is identified by the numerical evaluation of the many-body Chern number. Remarkably, we find that a considerable spectrum gap stabilizes the fractional topological phase with a moderate interaction strength, while, for the normal/superfluid phase, the Thouless charge pumping fluctuates strongly for small spin systems but approaches its universal value 1/3 for fermionic and 1/2 for bosonic systems with large spins.

DOI
10.1209/0295-5075/117/43001

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•Jan 1, 2025•0 citations
Extensive research interest has been attracted by the fact that recent experiments in cold atoms simulate the chiral edge states of (1 + 1)-dimensional quantum Hall systems with laser-assisted transitions between different atomic nuclear spin states in a one-dimensional optical lattice. Within such an optical lattice, we study the phase diagrams of ν = 1 / 3 filling hard-core fermions and ν = 1 / 2 hard-core bosons with internal spin states in the presence of dipole-dipolar interactions. Our results show that the interaction drives the fermionic (bosonic) systems from the normal (superfluid) phase into the fractional topological phase with possible crystalline orderings. The topological nature of the latter phase is identified by the numerical evaluation of the many-body Chern number. Remarkably, we find that a considerable spectrum gap stabilizes the fractional topological phase with a moderate interaction strength, while, for the normal/superfluid phase, the Thouless charge pumping fluctuates strongly for small spin systems but approaches its universal value 1/3 for fermionic and 1/2 for bosonic systems with large spins.
We study the properties of dipolar fermions trapped in one-dimensional bichromatic optical lattices and show the existence of fractional topological states in the presence of strong dipole-dipole interactions. We find some interesting connections between fractional topological states in one-dimensional superlattices and the fractional quantum Hall states: (i) the one-dimensional fractional topological states for systems at filling factor ν=1/p have p-fold degeneracy, (ii) the quasihole excitations fulfill the same counting rule as that of fractional quantum Hall states, and (iii) the total Chern number of p-fold degenerate states is a nonzero integer. The existence of crystalline order in our system is also consistent with the thin-torus limit of the fractional quantum Hall state on a torus. The possible experimental realization in cold atomic systems offers a new platform for the study of fractional topological phases in one-dimensional superlattice systems.
We study fermions and hard-core bosons with long-range dipolar interactions at fractional fillings in a topological checkerboard lattice with short-range hoppings up to next-next-nearest neighbors [T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys. Rev. Lett. 106, 236804 (2011)]. We consider the case that the dipoles are aligned in the perpendicular direction by an external field without the complication of anisotropic interaction. Using exact diagonalization, we find clear signatures of fractional quantum Hall (FQH) states at filling factors 1/3 and 1/5 for fermions (1/2 and 1/4 for bosons) in the lowest Chern band with a robust spectrum gap at moderate dipolar interaction strength. The robustness of these FQH states against a long-range interaction tail and band flatness is investigated. When the dipolar interaction decreases, the fermionic FQH states turn into normal states, and the bosonic 1/4 FQH state turns into a superfluid state. The bosonic 1/2 FQH state survives even in the absence of the dipolar interaction, but vanishes when the hard core becomes a soft core with a critical on-site repulsion. In the thin torus limit, the static density structure factors indicate that the FQH state turns into a commensurate charge density wave state.
In this research, we study the bosonic fractional quantum Hall (FQH) states in a system of ultracold bosons in a two-dimensional optical lattice in the presence of a synthetic magnetic field, described by the bosonic Harper–Hofstadter Hamiltonian. We use the cluster Gutzwiller mean-field and exact diagonalization techniques in our work. We obtain incompressible states as ground states at various filling factors similar to those of the FQH states. We focus in particular on the ν = 1/2 FQH state, and it is characterized by the two-point correlation function and the many-body Chern number. We further investigate the effect of dipolar interaction on the ν = 1/2 FQH state. We find that the dipolar interaction stabilizes the FQH state against the competing superfluid state.
We study the hard-core bosons in one-dimensional (1D) interacting topological bands at different filling factors using exact diagonalization. At the filling factor $\ensuremath{\nu}=1$ and in the presence of the on-site Hubbard interaction, we find no sign of the existence of the bosonic topological phase, which is in contrast to the fermionic case. Instead by studying the momentum distribution and the condensate fraction we find a superfluid to Mott-insulator transition driven by the Hubbard interaction. At the filling factor $\ensuremath{\nu}=1/3$ and in the presence of longer-ranged interactions, we identify the bosonic fractional topological phase whose ground states are characterized by a threefold degeneracy and a quantized total Berry phase, which is very similar to the fermionic case. Finally we discuss the reason for the different behaviors of hard-core bosons at different filling factors by mapping them to spinless fermions. Our results can be realized in cold-atom experiments.
Using the example of dysprosium atoms in an optical lattice, we show how dipolar interactions between magnetic dipoles can be used to obtain fractional quantum Hall states. In our approach, dysprosium atoms are trapped one atom per site in a deep optical lattice with negligible tunneling. Microwave and spatially dependent optical dressing fields are used to define an effective spin-12\frac{1}{2}21​ or spin-1 degree of freedom in each atom. Thinking of spin-12\frac{1}{2}21​ particles as hard-core bosons, dipole-dipole interactions give rise to boson hopping, topological flat bands with Chern number 1, and the $\ensuremath{\nu}=\frac{1}{2}$ Laughlin state. Thinking of spin-1 particles as two-component hard-core bosons, dipole-dipole interactions again give rise to boson hopping, topological flat bands with Chern number 2, and the bilayer Halperin (2,2,1) state. By adjusting the optical fields, we find a phase diagram, in which the (2,2,1) state competes with superfluidity. Generalizations to solid-state magnetic dipoles are discussed.
This thesis is devoted to the study of dipolar lattice gases, i.e. many-body quantum systems of particles with a strong magnetic or electric dipole moment in optical lattices. Such systems are adequately described by the extended Hubbard model, which accounts for inter-site dipole-dipole interactions (DDI). These interactions, due to their long-range and anisotropic character, result in rich groundstate physics and intriguing dynamics as we illustrate in this thesis for the particular case of bosons in one- and quasi-one-dimensional lattices. We start by focusing on the non-trivial role played by the transversal confinement in one-dimensional dipolar lattice gases. We show that weakening the transversal confinement enhances beyond-nearest-neighbor interactions. Then, we analyze how this affects the ground-state physics of hard-core bosons with repulsive dipolar interactions and reveal quantitative differences to the standard case of the DDI falling off as 1/r^3 where r is the inter-particle distance. With attractive interactions, a new quantum liquid phase of self-bound lattice droplets emerges without the need for super-exchange processes. In the soft-core regime, proper consideration of the transversal confinement not only quantitatively shifts phase boundaries, but introduces novel phases with peculiar correlations in the site occupancies that may be either topological or topologically trivial. Furthermore, we study the effect of the transversal confinement on the dynamical properties of one-dimensional hard-core bosons at half-filling. We show in particular that the localization-to-delocalization transition induced by Hilbert space fragmentation resembles that of a system with an effective power-law decay different from 1/r^3 which can be controlled by the transversal confinement. To conclude this thesis, we analyze ground-state properties of hard-core dipolar bosons in a square ladder at unit rung filling with an energy bias between the two legs. We show that the interplay between the energy bias and the dipolar tail results in a peculiar topological quantum floating phase.