[Paper Review] Observation of a dynamical topological phase transition

Nick Fläschner, Dominik Vogel+8 more|arXiv (Cornell University)|Aug 19, 2016

Quantum many-body systems31 references149 citations

TL;DR

The paper reports the first observation of a dynamical phase transition in a fermionic many-body state after a quench between two lattice Hamiltonians, using time-resolved state tomography in ultracold atoms to track vortices in reciprocal space as a dynamical topological order parameter.

ABSTRACT

Phase transitions are a fundamental concept in science describing diverse phenomena ranging from, e.g., the freezing of water to Bose-Einstein condensation. While the concept is well-established in equilibrium, similarly fundamental concepts for systems far from equilibrium are just being explored, such as the recently introduced dynamical phase transition (DPT). Here we report on the first observation of a DPT in the dynamics of a fermionic many-body state after a quench between two lattice Hamiltonians. With time-resolved state tomography in a system of ultracold atoms in optical lattices, we obtain full access to the evolution of the wave function. We observe the appearance, movement, and annihilation of vortices in reciprocal space. We identify their number as a dynamical topological order parameter, which suddenly changes its value at the critical times of the DPT. Our observation of a DPT is an important step towards a more comprehensive understanding of non-equilibrium dynamics in general.

Motivation & Objective

• Motivate the study of non-equilibrium dynamics beyond equilibrium phase transitions.
• Demonstrate experimental observation of a dynamical phase transition (DPT) in a fermionic many-body system.
• Show that the number and motion of vortices in reciprocal space serve as a dynamical topological order parameter.
• Provide full access to the wave-function evolution through state tomography in an optical lattice setup.

Proposed method

• Quench a fermionic many-body system between two lattice Hamiltonians.
• Perform time-resolved state tomography to obtain the evolution of the wave function.
• Identify and count vortices in momentum (reciprocal) space as a dynamical topological feature.
• Track appearance, movement, and annihilation of vortices to locate critical times of the DPT.

Experimental results

Research questions

• RQ1 Can a dynamical phase transition be observed in the non-equilibrium dynamics of a fermionic many-body state?
• RQ2 Do vortices in reciprocal space act as a dynamical topological order parameter that changes at critical times during the DPT?
• RQ3 How does the evolution of the wave function reflect topology during non-equilibrium dynamics?

Key findings

• Vortices in reciprocal space appear, move, and annihilate during the dynamics following the quench.
• The number of these vortices acts as a dynamical topological order parameter that changes at critical times.
• This provides experimental evidence for a dynamical phase transition in a non-equilibrium quantum system.