[Paper Review] Fermionic Superfluidity with Imbalanced Spin Populations and the Quantum Phase Transition to the Normal State

Martin W. Zwierlein, André Schirotzek+2 more|arXiv (Cornell University)|Nov 8, 2005

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper experimentally maps the superfluid phase transition in ultracold 6Li fermionic gases with imbalanced spin populations, demonstrating that superfluidity remains robust near unitarity despite population imbalance. Using vortex formation in rotating clouds and measuring the fraction of condensed pairs, the authors identify the quantum phase transition to the normal state at a critical population imbalance of δc ≈ 70(3)%, consistent with the Pauli limit and indicating breakdown when the chemical potential difference exceeds the pairing gap.

ABSTRACT

Whether it occurs in superconductors, helium-3 or inside a neutron star, fermionic superfluidity requires pairing of fermions, particles with half-integer spin. For an equal mixture of two states of fermions ("spin up" and "spin down"), pairing can be complete and the entire system will become superfluid. When the two populations of fermions are unequal, not every particle can find a partner. Will the system nevertheless stay superfluid? Here we study this intriguing question in an unequal mixture of strongly interacting ultracold fermionic atoms. The superfluid region vs population imbalance is mapped out by employing two complementary indicators: The presence or absence of vortices in a rotating mixture, as well as the fraction of condensed fermion pairs in the gas. Due to the strong interactions near a Feshbach resonance, the superfluid state is remarkably stable in response to population imbalance. The final breakdown of superfluidity marks a new quantum phase transition, the Pauli limit of superfluidity.

Motivation & Objective

• To investigate the stability of superfluidity in strongly interacting ultracold fermionic gases with unequal spin populations.
• To experimentally determine the critical population imbalance at which superfluidity collapses, marking a quantum phase transition.
• To probe the nature of the superfluid-to-normal transition in the unitary regime using two complementary indicators: vortex formation and pair condensate fraction.
• To test theoretical predictions of the Pauli limit in a clean, tunable system with no magnetic field complications.
• To explore the interplay between superfluidity, population imbalance, and interaction strength in a strongly correlated Fermi gas.

Proposed method

• Employed a rotating trap to induce vortex formation as a direct signature of superfluidity in imbalanced spin mixtures.
• Measured the fraction of condensed fermion pairs using time-of-flight expansion and momentum distribution analysis.
• Tuned the interaction strength via Feshbach resonances to explore the BEC-BCS crossover regime.
• Varied the population imbalance between spin-up and spin-down 6Li atoms in a harmonic trap to map the superfluid phase boundary.
• Used temperature-dependent measurements to confirm that the critical imbalance is weakly temperature-dependent, indicating near-zero-temperature quantum phase transition behavior.
• Compared experimental results with Monte Carlo simulations and theoretical models, particularly the prediction that δμ ≈ 2Δ marks the breakdown point.

Experimental results

Research questions

• RQ1 What is the maximum population imbalance for which superfluidity persists in a strongly interacting ultracold Fermi gas?
• RQ2 How does the superfluid phase boundary evolve across the BEC-BCS crossover regime under population imbalance?
• RQ3 What is the nature of the quantum phase transition from superfluid to normal state when spin populations are imbalanced?
• RQ4 Does the critical imbalance for superfluid breakdown align with the theoretical Pauli limit prediction δμ ≈ 2Δ?
• RQ5 How do vortex formation and pair condensate fraction serve as reliable indicators of superfluidity in imbalanced Fermi mixtures?

Key findings

• The critical population imbalance for superfluid breakdown was measured at δc ≈ 70(3)%, corresponding to a Fermi energy difference of δEF ≈ 0.53(3)EF in a harmonic trap.
• Superfluidity remains robust near unitarity, with the superfluid region extending to large population imbalances due to strong pairing correlations.
• Vortex formation strongly damped near the transition point, signaling the onset of the normal state and confirming the quantum phase transition.
• The condensate fraction decreased with increasing population imbalance and vanished at large asymmetries, indicating loss of Cooper pairing in the minority component.
• The critical imbalance showed weak temperature dependence, indicating the transition occurs at zero temperature and is dominated by quantum fluctuations.
• Experimental results are consistent with Monte Carlo predictions that superfluidity breaks down when δμ ≈ 2.0(1)Δ, supporting the Pauli limit as the correct theoretical description.