[Paper Review] Bad-Metal Relaxation Dynamics in a Fermi Lattice Gas

Wenchao Xu, William McGehee+2 more|arXiv (Cornell University)|Jun 21, 2016

Quantum and electron transport phenomena29 references4 citations

TL;DR

This study observes bad-metal relaxation dynamics in a strongly correlated ultracold Fermi gas realized in an optical lattice, using Raman-induced mass current decay to infer resistivity. It demonstrates T-linear resistivity scaling and violation of weak-scattering theory, confirming key signatures of bad metals consistent with dynamic mean-field theory predictions.

ABSTRACT

We report the discovery of phenomena consistent with bad-metal relaxation dynamics in the metallic regime of an optical-lattice Hubbard model. The transport lifetime induced by inter-particle scattering for a mass current of atoms excited by stimulated Raman transitions is measured, and the corresponding analog of resistivity is inferred. By exploring a range of temperature, we demonstrate incompatibility with weak-scattering theory and a key characteristic of bad metals: anomalous resistivity scaling consistent with $T$-linear behavior. We also observe the onset of two behaviors---incoherent transport and the approach to the Mott-Ioffe-Regel limit---associated with bad metals. The interaction and temperature scaling of resistivity are verified to be consistent with dynamic mean-field theory (DMFT) predictions of a bad metal, which is associated with the reduction of quasiparticle weight by strong interactions.

Motivation & Objective

• To investigate the emergence of bad-metal behavior in a strongly correlated Fermi system without disorder or phonons.
• To measure transport lifetime and infer resistivity in a clean, tunable optical lattice Hubbard model.
• To test whether the system exhibits anomalous resistivity scaling consistent with strong correlation effects.
• To compare experimental results with dynamic mean-field theory (DMFT) predictions for bad metals.
• To verify the breakdown of weak-scattering theory and the onset of incoherent transport near the Mott-Ioffe-Regel limit.

Proposed method

• Use of stimulated Raman transitions to create a coherent mass current by transferring spin-polarized 40K atoms between spin states with a momentum offset.
• Measurement of the decay dynamics of the Raman-induced current to extract the transport lifetime τt via time-of-flight imaging of quasimomentum distributions.
• Application of a density-weighted average correction to account for inhomogeneous atomic density in the trap, enabling comparison with uniform DMFT simulations.
• Definition of a dimensionless resistivity ϱ = (τt / (ħ/t) · n_dwd · d³)⁻¹ to normalize for effective mass and density effects.
• Classical trajectory simulations of dephasing dynamics in 1D to benchmark experimental dephasing effects and confirm that dephasing is not the dominant mechanism.
• Assumption of temperature-independent thermally averaged relative velocity to isolate the role of correlation effects in resistivity scaling.

Experimental results

Research questions

• RQ1 Does the resistivity in a strongly correlated Fermi gas scale linearly with temperature, as predicted for bad metals?
• RQ2 To what extent does the system violate weak-scattering theory in the metallic regime?
• RQ3 Are the observed transport properties consistent with dynamic mean-field theory predictions for a bad metal?
• RQ4 What is the role of quasiparticle breakdown and incoherent transport in the resistivity behavior?
• RQ5 How do the system's transport properties approach the Mott-Ioffe-Regel limit under strong correlations?

Key findings

• The measured resistivity exhibits T-linear scaling, a hallmark of bad-metal behavior, inconsistent with weak-scattering Fermi liquid theory.
• The transport lifetime τt decreases with increasing temperature, and the resistivity scaling deviates significantly from T² behavior.
• The system shows clear signs of incoherent transport and approaches the Mott-Ioffe-Regel limit, where the mean free path becomes comparable to the lattice spacing.
• The measured resistivity scaling is quantitatively consistent with dynamic mean-field theory (DMFT) predictions for a bad metal with reduced quasiparticle weight.
• Classical simulations confirm that dephasing effects are minor, with simulated dephasing times at least four times longer than measured transport lifetimes.
• The dimensionless resistivity ϱ is extracted with a correction for inhomogeneous density, enabling direct comparison with uniform DMFT simulations, and shows robust agreement with theoretical expectations.