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.
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.
The Fulde-Ferrell Larkin-Ovchinnikov (FFLO) type superconductor is an exotic form of matter known as a supersolid because it simultaneously supports superfluid and magnetic order. In both condensed matter and ultracold atomic gases, this phase has yet to be conclusively observed despite long interest in both theory and experiment. In one-dimension (1D), unlike expectations for higher dimensions, the FFLO phase is found in a large region of the phase diagram [1]. The effect of quantum and thermal fluctuations, however, are expected to be reduced in higher dimensions. These considerations motivated the proposal to search for FFLO near the 1D-3D dimensional crossover [2], which we have identified and characterized [3]. We confine a spin-imbalanced Fermi gas of lithium 6 to an array of 1D tubes using a 2D optical lattice. We bring the system into the dimensional crossover by increasing the inter-tube tunneling rate and using a Feshbach resonance to tune interactions. The periodicity of these domain walls, which depends on the magnitude of the polarization, is a definitive signature of the FFLO phase. In this work, we develop new experimental and analytical methods to extract periodic signals that, if they indeed are domain walls, lay the foundation for full confirmation of the FFLO phase. [1] Y. A. Liao, A. S. C. Rittner, T. Paprotta, W. Li, G. B. Partridge, R. G. Hulet, S. K. Baur, and E. J. Mueller, “Spin-imbalance in a one-dimensional Fermi gas,” Nature 467, 567 (2010). [2] M. M. Parish, S. K. Baur, E. J. Mueller, and D. A. Huse, “Quasi-One- Dimensional Polarized Fermi Superfluids,” Phys. Rev. Lett. 99, 250403 (2007). [3] M. C. Revelle, J. A. Fry, B. A. Olsen, and R. G. Hulet, “1D to 3D Crossover of a Spin-Imbalanced Fermi Gas,” Physical Review Letters 117 (2016).
The FFLO modulated superconductor state was independently proposed by Fulde and Ferrell, and Larkin and Ovchinnikov, as a way of accommodating the excess spin in a spin-polarized superconductor. The pairs in the FFLO state have non-zero center-of-mass momentum, which can produce a periodic structure with a spatially-modulated order parameter. Although there is some evidence for FFLO pairing in certain heavy fermion compounds that are able to accommodate both magnetic and superconducting order, conclusive experimental proof remains elusive. Motivated by the search for exotic paired states, we have performed experiments with spin-imbalanced ultracold atomic Fermi gases in both 3D and 1D. We use two hyperfine levels of 6Li to emulate the spin-up and down states. The s-wave pairing interactions are controlled via a magnetically-tuned collisional (Feshbach) resonance. In 3D, we find that the gas phase separates into an evenly paired BCS-like core, surrounded by the excess spin-up atoms [1]. For the 1D experiment, a two-dimensional optical lattice was used to create an array of 1D tubes that are each filled with ∼200 atoms. The weak axial confinement again produces a phase separation, but in contrast to 3D we find a partially-polarized central core surrounded by either fully-paired or fully-polarized wings, depending on the degree of overall spin-polarization [2]. Theory predicts that the partially-polarized phase is an FFLO superfluid. We are currently trying to obtain direct evidence for FFLO pairing, which may be revealed in the pair momentum distribution found by releasing the atoms axially and allowing them to expand in time-of-flight. We are also exploring the 1D-3D dimensional crossover that occurs when the coupling between tubes is reduced.
The recent development of experimental techniques in ultracold atomic Fermi gases is extremely helpful in the progress of the realization of the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase in quasi-one dimensional systems (Liao et al 2010 Nature 467 567). Due to a Fermi surface nesting, which is enhanced in 1D, the low-dimensional systems are particularly good candidates to find the FFLO phase stable. We investigate the influence of a dimensional crossover (from one dimension (1D) to two dimensions (2D) or three dimensions (3D)) on the stability of the FFLO state in the spin-imbalanced attractive Hubbard model.
Abstract Atomic Fermi gases have been an ideal platform for simulating conventional and engineering exotic physical systems owing to their multiple tunable control parameters. Here we investigate the effects of mixed dimensionality on the superfluid and pairing phenomena of a two-component ultracold atomic Fermi gas with a short-range pairing interaction, while one component is confined on a one-dimensional (1D) optical lattice whereas the other is in a homogeneous 3D continuum. We study the phase diagram and the pseudogap phenomena throughout the entire BCS-BEC crossover, using a pairing fluctuation theory. We find that the effective dimensionality of the non-interacting lattice component can evolve from quasi-3D to quasi-1D, leading to strong Fermi surface mismatch. Upon pairing, the system becomes effectively quasi-two dimensional in the BEC regime. The behavior of T c bears similarity to that of a regular 3D population imbalanced Fermi gas, but with a more drastic departure from the regular 3D balanced case, featuring both intermediate temperature superfluidity and possible pair density wave ground state. Unlike a simple 1D optical lattice case, T c in the mixed dimensions has a constant BEC asymptote.
We calculate the zero-temperature (T=0) phase diagram of a polarized two-component Fermi gas in an array of weakly coupled parallel one-dimensional (1D) "tubes" produced by a two-dimensional optical lattice. Increasing the lattice strength drives a crossover from three-dimensional (3D) to 1D behavior, stabilizing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulated superfluid phase. We argue that the most promising regime for observing the FFLO phase is in the quasi-1D regime, where the atomic motion is largely 1D but there is weak tunneling in the other directions that stabilizes long-range order. In the FFLO phase, we describe a phase transition where the quasiparticle spectrum changes from gapless near the 3D regime to gapped in quasi-1D.
The pairing of fermionic particles is an essential ingredient of superconductivity and of the superfluidity of 3He. While such phenomena are accurately described by BCS theory in the limit of weak pairing strength, a complete understanding remains elusive when pairing strength is increased, such as in high temperature superconductors. We create ultracold gases of trapped fermionic 6Li atoms, through which we directly observe fermionic pairing. In our system, there are no impurities whatsoever, and parameters such as the number and temperature of the trapped atoms are precisely and independently controlled. In addition, a Feshbach resonance enables the continuous tuning of interaction strength and sign between the paired atoms. This control allows us to observe the smooth crossover of a molecular Bose Einstein condensate (MBEC) to a superfluid of weakly interacting Cooper pairs. With these tools, we have performed several fundamental measurements of pairing in fermionic systems.\nWe use optical molecular spectroscopy to precisely measure the closed-channel contribution to the many body state of paired 6Li atoms within a broad Feshbach resonance. The magnitude of this contribution is small, and supports the concept of universality for the description of broad Feshbach resonances. Moreover, the dynamics of the excitation provide clear evidence for pairing across the BEC-BCS crossover, and for the first time, into the weakly interacting BCS regime.\nWe also prepare a polarized Fermi gas with unequal numbers of two spin states of 6Li atoms. The real-space densities of the polarized, strongly-interacting, two-component Fermi gas reveal two low temperature regimes. At the lowest temperatures, the gas separates into a phase with a uniformly paired superfluid core surrounded by a shell of normal, unpaired atoms. This phase separation is accompanied by a spatial deformation of the core. At higher temperatures, the uniformly paired core persists, though it does not deform. This temperature dependence is consistent with a tri-critical point in the phase diagram. These measurements of pairing in a polarized Fermi gas are relevant to predictions of exotic phases of quark matter and magnetized superconductors.