[Paper Review] Quantum phases of hard-core dipolar bosons in coupled 1D optical lattices

Arghavan Safavi-Naini, Barbara Capogrosso-Sansone+1 more|arXiv (Cornell University)|May 16, 2014

Cold Atom Physics and Bose-Einstein Condensates41 references16 citations

TL;DR

This paper investigates quantum phases of hard-core dipolar bosons in stacked 1D optical lattices using ab initio continuous-time quantum Monte Carlo simulations and bosonization. It demonstrates that arbitrarily weak dipolar interactions induce threshold-less superfluid and insulating phases—such as chain superfluids and super-counterfluids—controlled solely by filling factors, with correlation lengths diverging exponentially as ∼exp(1/|Vd|).

ABSTRACT

Hard-core dipolar bosons trapped in a parallel stack of N>=2 1D optical lattices (tubes) can develop several phases made of composites of particles from different tubes: superfluids, supercounterfluids and insulators as well as mixtures of those. Bosonization analysis shows that these phases are threshold-less with respect to the dipolar interaction, with the key "control knob" being filling factors in each tube, provided the inter-tube tunneling is suppressed. The effective ab-initio quantum Monte Carlo algorithm capturing these phases is introduced and some results are presented.

Motivation & Objective

• To identify and characterize quantum phases in hard-core dipolar bosons confined to a stack of 1D optical lattices with suppressed inter-tube tunneling.
• To determine whether dipolar interactions can induce superfluidity and insulating order without a threshold, even at infinitesimally small interaction strength.
• To establish the role of filling factors as the primary control parameter for phase transitions in the absence of inter-tube tunneling.
• To develop and apply an ab initio continuous-time quantum Monte Carlo algorithm with a multi-worm update scheme to simulate these strongly correlated phases.
• To analyze the emergence of composite phases such as chain superfluids and super-counterfluids via generalized superfluid stiffness and winding number response.

Proposed method

• Employing a single-band tight-binding Hamiltonian with nearest-neighbor tunneling (J), on-site chemical potentials (µz), and long-range dipolar interactions V(x,z) = Vd(x²−2z²)/(x²+z²)^5/² along the tube stack.
• Using continuous-time path integral quantum Monte Carlo with a multi-worm algorithm to simulate the grand canonical ensemble, enabling accurate sampling of topological winding numbers.
• Applying bosonization techniques to derive the renormalization group flow equations for the Luttinger liquid parameters, identifying fixed points and correlation length divergences.
• Defining generalized superfluid stiffness Rzz′ and compressibility Czz′ via Thouless phase twists to probe topological order and response in the system.
• Measuring winding numbers Wx(z), Wτ(z) of particle worldlines to extract Rzz′ and Czz′ from second moments of the partition function under gauge fluxes.
• Analyzing the RG flow of the Luttinger parameter K and backward scattering amplitude u, with critical behavior determined by the initial value ξ(0) ∼|Vd| and correlation length l0 ∼exp(1/|Vd|).

Experimental results

Research questions

• RQ1 Can arbitrarily weak dipolar interactions induce superfluidity in a stack of 1D hard-core bosonic tubes without a threshold?
• RQ2 How do filling factors νz in individual tubes control the emergence of composite quantum phases such as chain superfluids and super-counterfluids?
• RQ3 What is the nature of the correlation length in the paired superfluid phase, and how does it scale with the dipolar interaction strength Vd?
• RQ4 Can the generalized superfluid stiffness and winding number response distinguish between different insulating and superfluid phases in the absence of inter-tube tunneling?
• RQ5 What is the role of the inter-tube dipolar interaction in stabilizing exotic insulating orders such as 1D checkerboard phases at νz = 1/2?

Key findings

• Arbitrarily weak dipolar interactions induce threshold-less superfluidity in the system, with the pairing of bosons across tubes forming chain superfluids (CSF) even at infinitesimal Vd.
• The correlation length of the paired superfluid diverges exponentially as l0 ∼ exp(κ′ / |Vd|), indicating a Berezinskii-Kosterlitz-Thouless-like behavior with a non-analytic dependence on Vd.
• At filling factor νz = 1/2 in each tube, an insulating phase with 1D checkerboard order emerges in the limit Vd → 0, even without explicit intra-layer repulsion.
• For perpendicular dipole alignment, the system supports super-counterfluid (SCF) phases that are also threshold-less with respect to Vd, driven by repulsive inter-tube interactions.
• The generalized superfluid stiffness Rzz′ and compressibility Czz′ are directly measurable via winding number correlations and serve as robust indicators of topological order and phase transitions.
• The RG flow analysis shows that initial values ξ(0) ∼ |Vd| and η ∼ |Vd| lead to algebraic order (gapless superfluid) if |η| < 1, while larger |η| leads to gapped, insulating states.