Quantum phase transition in space in a ferromagnetic spin-1 Bose-Einstein condensate

TL;DR

This paper investigates a spatial quantum phase transition in a ferromagnetic spin-1 Bose-Einstein condensate, revealing how the transition's critical region scales with the control parameter gradient and proposing a method to measure the critical exponent.

Contribution

It introduces the concept of a space-induced quantum phase transition in spinor BECs and analyzes the scaling behavior near the critical point, providing a new approach to measure critical exponents.

Findings

Identifies a quantum phase transition in space within a spin-1 BEC.

Shows the critical region exhibits specific scaling laws.

Proposes a method to measure the critical exponent nu.

Abstract

A quantum phase transition between the symmetric (polar) phase and the phase with broken symmetry can be induced in a ferromagnetic spin-1 Bose-Einstein condensate in space (rather than in time). We consider such a phase transition and show that the transition region in the vicinity of the critical point exhibits scalings that reflect a compromise between the rate at which the transition is imposed (i.e., the gradient of the control parameter) and the scaling of the divergent healing length in the critical region. Our results suggest a method for the direct measurement of the scaling exponent nu.