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arXiv:1605.06986 · Physical Review Letters

1D to 3D Crossover of a Spin-Imbalanced Fermi Gas

Melissa Revelle, Jacob A. Fry, Ben A. Olsen, Randall G. Hulet

Published Nov 30, 2016• 61 citations
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Abstract

We have characterized the one-dimensional (1D) to three-dimensional (3D) crossover of a two-component spin-imbalanced Fermi gas of ^{6}Li atoms in a 2D optical lattice by varying the lattice tunneling and the interactions. The gas phase separates, and we detect the phase boundaries using in situ imaging of the inhomogeneous density profiles. The locations of the phases are inverted in 1D as compared to 3D, thus providing a clear signature of the crossover. By scaling the tunneling rate t with respect to the pair binding energy ε_{B}, we observe a collapse of the data to a universal crossover point at a scaled tunneling value of t[over ˜]_{c}=0.025(7).

DOI
10.1103/physrevlett.117.235301

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We have characterized the one-dimensional (1D) to three-dimensional (3D) crossover of a two-component spin-imbalanced Fermi gas of ^{6}Li atoms in a 2D optical lattice by varying the lattice tunneling and the interactions. The gas phase separates, and we detect the phase boundaries using in situ imaging of the inhomogeneous density profiles. The locations of the phases are inverted in 1D as compared to 3D, thus providing a clear signature of the crossover. By scaling the tunneling rate t with respect to the pair binding energy ε_{B}, we observe a collapse of the data to a universal crossover point at a scaled tunneling value of t[over ˜]_{c}=0.025(7).
Ultracold atoms have become an essential tool in studying condensed matter phenomena. The advantage of atomic physics experiments is that they provide an easily tunable system. This experiment uses the lowest two ground state hyperfine levels of fermionic lithium. Having two different states creates a pseudo-spin-1/2 system and allows us to emulate electronic systems, such as superconductors and crystal lattices. In our experiment, we can control the ratio between these two states resulting in either a spin-balanced or a spin-imbalanced gas. Imposing an imbalance is analogous to applying a magnetic field to a superconductor which causes the electrons in the material to align to the field (thus breaking the electron pairs which cause superconductivity). This motivates us to understand the phases created when a spin-imbalance is created and the effect of changing the atomic interactions. In a 3D system, we find where superfluidity is suppressed throughout the BEC to BCS crossover. Using phase separation as a guide, we probe the dimensional crossover between 1D and 3D. The phase separation in 1D is inverted from that in 3D, which provides a unique characteristic to distinguish between the dimensions. By varying the tunneling between tubes and the atomic interactions in a 2D optical lattice, we control whether the system is 1D, 3D, or in between. Using the properties of a 3D gas as a guide, we directly observe when the gas has crossed over from being dominated by 1D-like behavior to 3D. In this way, we have found a universal value for the dimensional crossover. The 1D-3D crossover paves the way to search for the exotic FFLO (Fulde-Ferrell-Larkin-Ovchinnikov) superconductor. While most superconductors do not coexist with magnetism, the FFLO phase requires large magnetic fields to support its pairing mechanism. Additionally, this phase is more likely to be found in lower dimensional systems. However, at low dimensions, the effect of temperature fluctuations on the phase is destabilizing, but these temperature effects are reduced with higher dimensionality. Thus, the quasi-1D regime is the optimal region of parameter space to find this phase. The search for direct evidence of FFLO continues in this regime.
Motivated by a recent experiment Revelle et al., [Phys. Rev. Lett. 117, 235301 (2016)] that characterized the one- to three-dimensional crossover in a spin-imbalanced ultracold gas of 6Li^{6}\mathrm{Li}6Li atoms trapped in a two-dimensional array of tunnel-coupled tubes, we calculate the phase diagram for this system by using Hartree-Fock Bogoliubov-de Gennes mean-field theory and compare the results with experimental data. Mean-field theory predicts fully-spin-polarized normal, partially-spin-polarized normal, spin-polarized superfluid, and spin-balanced superfluid phases in a homogeneous system. We use the local density approximation to obtain density profiles of the gas in a harmonic trap. We compare these calculations with experimental measurements in Revelle et al. as well as previously unpublished data. Our calculations qualitatively agree with experimentally measured densities and coordinates of the phase boundaries in the trap and quantitatively agree with experimental measurements at moderate-to-large polarizations. Our calculations also reproduce the experimentally observed universal scaling of the phase boundaries for different scattering lengths at a fixed value of scaled intertube tunneling. However, our calculations have quantitative differences with experimental measurements at low polarization and fail to capture important features of the one- to three-dimensional crossover observed in experiments. These suggest the important role of physics beyond mean-field theory in the experiments. We expect that our numerical results will aid future experiments in narrowing the search for the Fulde-Ferrell-Larkin-Ovchinnikov phase.
We have observed phase separation between the superfluid and the normal component in a strongly interacting Fermi gas with imbalanced spin populations. The in situ distribution of the density difference between two trapped spin components is obtained using phase-contrast imaging and 3D image reconstruction. A shell structure is clearly identified where the superfluid region of equal densities is surrounded by a normal gas of unequal densities. The phase transition induces a dramatic change in the density profiles as excess fermions are expelled from the superfluid.
We model the one-dimensional (1D) to three-dimensional (3D) crossover in a cylindrically trapped Fermi gas with attractive interactions and spin imbalance. We calculate the mean-field phase diagram and study the relative stability of exotic superfluid phases as a function of interaction strength and temperature. For weak interactions and low density, we find 1D-like behavior, which repeats as a function of the chemical potential as new channels open. For strong interactions, mixing of single-particle levels gives 3D-like behavior at all densities. Furthermore, we map the system to an effective 1D model, finding significant density dependence of the effective 1D scattering length.
We calculate the superfluid transition temperature for a two-component 3D Fermi gas in a 1D tight optical lattice and discuss a dimensional crossover from the 3D to quasi-2D regime. For the geometry of finite size discs in the 1D lattice, we find that even for a large number of atoms per disc the critical effective tunneling rate for a quantum transition to the Mott insulator state can be large compared to the loss rate caused by three-body recombination. This allows the observation of the Mott transition, in contrast to the case of Bose-condensed gases in the same geometry.
This thesis presents the experimental study on the two-spin component, strongly interacting 6 Li Fermi gases in 3D and 1D traps. The interaction strength is tuned from the molecular BEC regime to the BCS regime using a Feshbach resonance. The trap dimension can be tuned from 3D to 1D with the implementation of optical lattice. The evaporation of imbalanced Fermi gases in 3D trap is studied. The anisotropic and fast evaporation is the cause of the deformation observed in the 2006 Rice experiment. In a balanced Fermi system, the fraction of correlated states is measured as a function of interaction and temperature. At unitarity, the fraction of correlated states is ∼85% and exists above T c . The one-body-like photoexcitation rate can be related to the contact quantity. Lastly, the spin-imbalance in a one-dimensional Fermi gas is studied. The 1D phase diagram is mapped out. The result agrees well with the 1D theory, in which the partially polarized regime is predicted to be a FFLO phase, an exotic superfluid with pairs carrying finite center-of-mass momentum proposed almost 50 years ago.