[Paper Review] Comment on "Pairing and Phase Separation in a Polarized Fermi Gas" by G. B. Partridge, W. Li, R. I. Kamar, Y. Liao, R. G. Hulet, Science 311, 503 (2006)

Martin W. Zwierlein, Wolfgang Ketterle|arXiv (Cornell University)|Mar 20, 2006

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This comment challenges the interpretation of experimental data in a 2006 Science paper claiming a quantum phase transition and phase separation in a polarized ultracold Fermi gas. The authors argue that the observed double-peak density profiles cannot reliably distinguish between phase-separated and non-phase-separated states due to limitations in the local density approximation and potential anharmonicities, undermining claims of superfluidity and a quantum phase transition.

ABSTRACT

We argue that it is not possible to infer from the results of Partridge et al. (Reports, 27 January 2006, p. 503) which of their data was taken in the superfluid or normal regime, and which of their clouds are phase-separated and which are not. Some of the conclusions in this paper are inconsistent with recent experiments.

Motivation & Objective

• To challenge the interpretation of double-peak density profiles in a polarized Fermi gas experiment as evidence of phase separation.
• To argue that the local density approximation (LDA) breaks down in the experimental data, invalidating the inference of superfluid-core/normal-shell structure.
• To demonstrate that double-peak structures in integrated density profiles are expected even for non-phase-separated states, including normal or superfluid phases.
• To show that the absence of abrupt changes in density profiles with temperature undermines claims of a superfluid-to-normal phase transition.
• To emphasize that cloud size agreement with theory does not confirm superfluidity, as size is insensitive to the superfluid transition.

Proposed method

• Analyzing the mathematical inversion of doubly integrated density profiles to reconstruct 3D density distributions.
• Applying the local density approximation (LDA) to model spin population distributions in a harmonic trap.
• Demonstrating that a thin hollow sphere (phase-separated state) produces a flat-top-hat profile after double integration, not double peaks.
• Comparing experimental profiles with simulated profiles under LDA and non-LDA conditions to assess validity.
• Using tomographic reconstruction and direct 3D density comparison as superior methods to infer phase separation.
• Evaluating the role of anharmonicities and finite-size effects in distorting density profiles and invalidating LDA-based interpretations.

Experimental results

Research questions

• RQ1 Can double-peak structures in doubly integrated density profiles reliably distinguish phase-separated from non-phase-separated Fermi gas clouds?
• RQ2 Is the observed transition from single-peak to double-peak profiles indicative of a quantum phase transition or LDA breakdown?
• RQ3 Can the local density approximation be trusted in strongly interacting Fermi gases with significant population imbalances?
• RQ4 What evidence is required to confirm the presence of a superfluid core surrounded by a shell of excess spin-up atoms?
• RQ5 Why do some experiments observe phase separation while others do not, and is this discrepancy due to interpretation or experimental conditions?

Key findings

• Double-peak structures in doubly integrated density profiles are expected for any state, including non-phase-separated states, and thus cannot be used as evidence of phase separation.
• The local density approximation (LDA) breaks down in the experimental data, making it mathematically impossible to reconstruct 3D density distributions unambiguously.
• The observed double-peak profiles are more consistent with LDA violation or anharmonicities than with phase separation, especially since anharmonicities were not controlled in the original experiment.
• The absence of abrupt changes in density profiles with temperature contradicts claims of a superfluid-to-normal phase transition.
• The cloud size agreement with theoretical predictions does not support superfluidity, as the beta factor is insensitive to the superfluid transition temperature.
• More recent experiments have observed shell structures at small imbalances and failed to confirm the claimed quantum phase transition, indicating the original interpretation is inconsistent with updated data.