Quantum critical behavior of ultracold atoms in two-dimensional optical lattices

TL;DR

This paper reports the experimental observation of quantum critical behavior in a two-dimensional ultracold Bose gas near a quantum phase transition, demonstrating universal scaling laws and critical exponents in a controlled setting.

Contribution

It provides the first direct measurement of quantum critical scaling and critical exponents in a 2D ultracold atomic system, validating theoretical predictions.

Findings

Universal scaling of the equation of state observed at low temperatures

Identification of the quantum critical point in the system

Finite entropy per particle in the critical regime

Abstract

As the temperature of a many-body system approaches absolute zero, thermal fluctuations of observables cease and quantum fluctuations dominate. Competition between different energies, such as kinetic energy, interactions or thermodynamic potentials, can induce a quantum phase transition between distinct ground states. Near a continuous quantum phase transition, the many-body system is quantum critical, exhibiting scale invariant and universal collective behavior \cite{Coleman05Nat, Sachdev99QPT}. Quantum criticality has been actively pursued in the study of a broad range of novel materials \cite{vdMarel03Nat, Lohneysen07rmp, G08NatPhys, Sachdev08NatPhys}, and can invoke new insights beyond the Landau-Ginzburg-Wilson paradigm of critical phenomena \cite{Senthil04prb}. It remains a challenging task, however, to directly and quantitatively verify predictions of quantum criticality in a clean and controlled system. Here we report the observation of quantum critical behavior in a two-dimensional Bose gas in optical lattices near the vacuum-to-superfluid quantum phase transition. Based on \textit{in situ} density measurements, we observe universal scaling of the equation of state at sufficiently low temperatures, locate the quantum critical point, and determine the critical exponents. The universal scaling laws also allow determination of thermodynamic observables. In particular, we observe a finite entropy per particle in the critical regime, which only weakly depends on the atomic interaction. Our experiment provides a prototypical method to study quantum criticality with ultracold atoms, and prepares the essential tools for further study on quantum critical dynamics.