Spin-Imbalance in a One-Dimensional Fermi Gas

📝 Abstract

Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs. Nearly forty years ago Fulde and Ferrell and Larkin and Ovchinnikov proposed an exotic pairing mechanism (FFLO) where magnetism is accommodated by formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarized superconductivity remains largely elusive. Here we report experimental measurements of density profiles of a two spin mixture of ultracold 6Li atoms trapped in an array of one dimensional (1D) tubes, a system analogous to electrons in 1D wires. At finite spin imbalance, the system phase separates with an inverted phase profile in comparison to the three-dimensional case. In 1D we find a partially polarized core surrounded by wings composed of either a completely paired BCS superfluid or a fully polarized Fermi gas, depending on the degree of polarization. Our observations are in quantitative agreement with theoretical calculations in which the partially polarized phase is found to be a 1D analogue of the FFLO state. This study demonstrates how ultracold atomic gases in 1D may be used to create non-trivial new phases of matter, and also paves the way for direct observation and further study of the FFLO phase.

💡 Analysis

Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs. Nearly forty years ago Fulde and Ferrell and Larkin and Ovchinnikov proposed an exotic pairing mechanism (FFLO) where magnetism is accommodated by formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarized superconductivity remains largely elusive. Here we report experimental measurements of density profiles of a two spin mixture of ultracold 6Li atoms trapped in an array of one dimensional (1D) tubes, a system analogous to electrons in 1D wires. At finite spin imbalance, the system phase separates with an inverted phase profile in comparison to the three-dimensional case. In 1D we find a partially polarized core surrounded by wings composed of either a completely paired BCS superfluid or a fully polarized Fermi gas, depending on the degree of polarization. Our observations are in quantitative agreement with theoretical calculations in which the partially polarized phase is found to be a 1D analogue of the FFLO state. This study demonstrates how ultracold atomic gases in 1D may be used to create non-trivial new phases of matter, and also paves the way for direct observation and further study of the FFLO phase.

📄 Content

1 Spin-imbalance in a one-dimensional Fermi gas Yean-an Liao1*, Ann Sophie C. Rittner1*, Tobias Paprotta1, Wenhui Li1,†, Guthrie B. Partridge1,‡, Randall G. Hulet1, Stefan K. Baur2 & Erich J. Mueller2 1Department of Physics and Astronomy and Rice Quantum Institute, Rice University, Houston, TX 77251, USA. 2Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853, USA.

• These authors contributed equally to this work.
  † Permanent address: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore, 117543. ‡ Present address: Laboratoire Charles Fabry de l’Institut d’Optique, UMR CNRS 8501, Palaiseau, France. Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs.
  Nearly forty years ago Fulde and Ferrell1 and Larkin and Ovchinnikov2 (FFLO) proposed an exotic pairing mechanism where magnetism is accommodated by formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarised superconductivity remains largely elusive3.
  Here we report experimental measurements of density profiles of a two spin mixture of ultracold 6Li atoms trapped in an array of one dimensional (1D) tubes, a system analogous to electrons in 1D wires. At finite spin imbalance, the system phase separates with an inverted phase profile as compared to the three-dimensional (3D) case. In 1D, we find a partially polarised core surrounded by wings composed of

2 either a completely paired or a fully polarised Fermi gas, depending on the degree of polarisation. At zero temperature, this system is predicted to be a 1D analogue of the FFLO state4-12. This study demonstrates how ultracold atomic gases in 1D may be used to create non-trivial new phases of matter, and also paves the way for direct observation and characterization of the FFLO phase.
The FFLO states are perhaps the most interesting of a number of exotic polarised superconducting phases proposed in the past 40 years. In the original concept of Fulde and Ferrell (FF), Cooper pairs form with finite centre of mass momentum1. Larkin and Ovchinnikov (LO) proposed a related model where the superconducting order parameter oscillates in space2. These two ideas are closely related, as the oscillating order parameter may be interpreted as an interference pattern between condensates with opposite centre of mass momenta. The spin density oscillates in the LO model, leading to a build-up of polarisation in the nodes of the superconducting order parameter. Thus the LO state can be considered a form of micro-scale phase separation with alternating superfluid and polarised normal regions. By including more and more momenta, subsequent theorists were able to evaluate the stability of ever more complicated spatial structures3. Previous studies of superfluidity in fermionic atoms show that ultracold atoms are a powerful tool for investigating the emergent properties of interacting systems of many particles. While largely analogous to an electronic superconductor, the atomic systems feature tunable interactions. This extra degree of control has lead to a number of unique experiments and conceptual advances. Furthermore, the absence of spin relaxation enables us to spin-polarise the atoms in order to explore the interplay between magnetism and superfluidity, with the potential to observe the FFLO phase. Recent calculations indicate that if a FFLO phase exists in three dimensional trapped gases, it will occupy a very small

3 volume in parameter space13,14. Experiments in 3D and in the strongly-interacting limit show that the gas phase separates with an unpolarised superfluid core surrounded by a polarised shell15-19, with no evidence for the FFLO phase. Here, we study a polarised Fermi gas in 1D, where theory predicts that a large fraction of the phase diagram is occupied by an FFLO-like phase (see Fig. 1a)4-12. In this 1D setting, the physics should be closest to that described by LO, where an oscillating superfluid order parameter coexists with a spin- density wave. Due to fluctuations, the order will be algebraic rather than long-ranged. The increased stability of FFLO-like phases in 1D can be understood as a “nesting” effect, where a single wavevector connects all points on the Fermi surface, allowing all atoms on the Fermi surface to participate in finite momentum pairing, while in 3D, only a small fraction of these atoms are able to do so. Similar enhancements are predicted for systems of lattice fermions and quasi-1D geometries10,20.
Our work complements studies of astrophysical objects3 and solid state systems. Like our current experiment, the solid state experiments typically involve highly anisotropic materials – made up either of weakly

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