Collective ground states in small lattices of coupled quantum dots

TL;DR

This paper theoretically investigates the ground states of small, coupled quantum dot systems, revealing a crossover from Wigner crystal to Mott insulator phases driven by system parameters, with implications for quantum emulation experiments.

Contribution

It introduces a detailed numerical analysis of the Wigner-Mott crossover in finite quantum dot systems, connecting theoretical predictions with experimental feasibility.

Findings

Identification of a Wigner crystal phase at low electron density

Observation of a Mott insulator phase with localized electrons

Demonstration of a smooth crossover between these phases via parameter tuning

Abstract

Motivated by recent developments on the fabrication and control of semiconductor-based quantum dot qubits, we theoretically study a finite system of tunnel-coupled quantum dots with the electrons interacting through the long-range Coulomb interaction. When the inter-electron separation is large and the quantum dot confinement potential is weak, the system behaves as an effective Wigner crystal with a period determined by the electron average density with considerable electron hopping throughout the system. For stronger periodic confinement potentials, however, the system makes a crossover to a Mott-type strongly correlated ground state where the electrons are completely localized at the individual dots with little inter-dot tunneling. In between these two phases, the system is essentially a strongly correlated electron liquid with inter-site electron hopping constrained by strong Coulomb interaction. We characterize this Wigner-Mott-liquid quantum crossover with detailed numerical finite-size diagonalization calculations of the coupled interacting qubit system, showing that these phases can be smoothly connected by tuning the system parameters. Experimental feasibility of observing such a hopping-tuned Wigner-Mott-liquid crossover in currently available semiconductor quantum dot qubits is discussed. In particular, we connect our theoretical results to recent quantum-dot-based quantum emulation experiments where collective Coulomb blockade was demonstrated. One conclusion of our theory is that currently available realistic quantum dot arrays are unable to explore the low-density Wigner phase with only the Mott-liquid crossover being accessible experimentally.