[Paper Review] First order phase transitions in optical lattices with tunable three-body onsite interaction

Arghavan Safavi-Naini, Javier von Stecher+2 more|DSpace@MIT (Massachusetts Institute of Technology)|Feb 14, 2012

Climate Change and Environmental Impact1 references4 citations

TL;DR

This paper proposes a tunable three-body onsite interaction in two-dimensional ultracold bosonic atoms in optical lattices via an rf field coupling triply occupied sites to a universal three-body bound state. Using mean-field theory and quantum Monte Carlo simulations, it demonstrates that for sufficiently attractive three-body interactions ($|U_3| > U$), the $n=2$ Mott lobe vanishes and first-order phase transitions emerge between $n=1$ and $n=3$ Mott insulators and between these insulators and the superfluid phase, even at finite temperatures up to $T \sim J$. The transitions remain first order at $T \sim J$, with hysteretic density responses as a key experimental signature.

ABSTRACT

We study the two-dimensional Bose-Hubbard model in the presence of a three-body interaction term, both at a mean field level and via quantum Monte Carlo simulations. The three-body term is tuned by coupling the triply occupied states to a trapped universal trimer. We find that, for sufficiently attractive three-body interaction the n = 2 Mott lobe disappears and the system displays first order phase transitions separating the n = 1 from the n = 3 lobes, and the n = 1 and n = 3 Mott insulator from the superfluid. We have also analyzed the effect of finite temperature and found that transitions are still of first order at temperatures T\simJ where J is the hopping matrix element.

Motivation & Objective

• To investigate the effects of tunable, attractive three-body onsite interactions on the phase diagram of the two-dimensional Bose-Hubbard model.
• To propose a physically realizable mechanism for engineering such interactions using rf coupling to a universal three-body bound state in an excited hyperfine state.
• To determine how three-body interactions alter the order of Mott-insulator to superfluid transitions and whether first-order transitions emerge between $n=1$ and $n=3$ Mott lobes.
• To analyze the persistence of first-order transitions at finite temperatures, relevant for experimental observation.

Proposed method

• A modified Bose-Hubbard Hamiltonian is introduced with a tunable three-body onsite interaction term $U_3$ that only acts on triply occupied sites, given by $H = -J\sum_{\langle i,j\rangle}a_i^\dagger a_j + \sum_i\left[\frac{U}{2}n_i(n_i-1) + \delta_{n_i,3}U_3 - \mu n_i\right]$.
• A mean-field Gutzwiller approach is used to study the phase diagram, particularly in the regime $U_3 < 0$ and $|U_3| > U$, where the $n=2$ Mott lobe is expected to disappear.
• Quantum Monte Carlo (QMC) simulations on square lattices up to $L=30$ are performed at $\beta = L/J$ to simulate zero-temperature behavior and validate mean-field predictions.
• Hysteresis analysis is conducted by sweeping the chemical potential $\mu$ back and forth to identify first-order transitions via discontinuous density jumps.
• Finite-temperature effects are studied via QMC at $T \sim J$, with the stability of first-order transitions assessed by monitoring density profiles and transition character.
• The experimental feasibility is discussed, highlighting hysteretic density responses and loss of adiabaticity as detectable signatures of first-order transitions.

Experimental results

Research questions

• RQ1 Can a tunable, attractive three-body onsite interaction be engineered in ultracold atomic systems using rf fields and universal three-body bound states?
• RQ2 How does the inclusion of a three-body interaction term $U_3$ alter the phase diagram of the two-dimensional Bose-Hubbard model, particularly the structure of Mott lobes?
• RQ3 Does a first-order phase transition emerge directly between the $n=1$ and $n=3$ Mott insulator phases when the $n=2$ lobe is suppressed?
• RQ4 What is the effect of finite temperature on the order of the Mott-insulator to superfluid transition in the presence of strong three-body attraction?
• RQ5 Can experimentally accessible observables such as density hysteresis or adiabaticity loss be used to detect first-order transitions in this system?

Key findings

• For $|U_3| > U$, the $n=2$ Mott lobe disappears, enabling a direct first-order phase transition between the $n=1$ and $n=3$ Mott insulator phases at finite hopping.
• Quantum Monte Carlo simulations confirm the existence of a first-order transition between the $n=1$ and $n=3$ Mott insulators, with a phase boundary indicated by a dotted line in the phase diagram.
• First-order transitions between the $n=1$ and $n=3$ Mott insulators and the superfluid phase are observed, with hysteretic behavior in particle density during chemical potential sweeps.
• The triple point, where $n=1$, $n=3$, and superfluid phases coexist, is estimated at $J/U = 0.05$ for $U_3 = -1.5U$ and $z=4$ using mean-field theory.
• First-order transitions persist at finite temperatures up to $T \sim J$, with QMC results showing that the transition order remains first order even at $T \sim J$, where Mott features are still well defined.
• The $n=1$ and $n=3$ Mott-insulator to superfluid transitions become second order at $zJ/U \approx 0.20 \pm 0.02$ and $0.133 \pm 0.02$, respectively, as hopping increases.