Recent experiments with Yb-173 and Sr-87 isotopes provide new possibilities to study high spin two-orbital systems. Within these experiments part of the atoms are excited to a higher energy metastable electronic state mimicking an additional internal (orbital) degree of freedom. The interaction between the atoms depends on the orbital states, therefore four different scattering channels can be identified in the system characterized by four independent couplings. When the system is confined into a one-dimensional chain the scattering lengths can be tuned by changing the transverse confinement, and driven through four resonances. Using the new available experimental data of the scattering lengths we analyze the phase diagram of the one-dimensional system as the couplings are tuned via transverse confinement, and the populations of the two orbital states are changed. We found that three orders compete showing power law decay: a state with dominant density wave fluctuations, another one with spin density fluctuations, and a third one characterized by exotic Fulde-Ferrell-Larkin-Ovchinnikov-like pairs consisting one atom in the electronic ground state and one in the excited state. We also show that sufficiently close to the resonances the compressibility of the system starts to diverge indicating that the emerging order is unstable and collapses to a phase separated state with a first order phase transition.
Recent experiments with Yb-173 and Sr-87 isotopes provide new possibilities to study high spin two-orbital systems. Within these experiments part of the atoms are excited to a higher energy metastable electronic state mimicking an additional internal (orbital) degree of freedom. The interaction between the atoms depends on the orbital states, therefore four different scattering channels can be identified in the system characterized by four independent couplings. When the system is confined into a one-dimensional chain the scattering lengths can be tuned by changing the transverse confinement, and driven through four resonances. Using the new available experimental data of the scattering lengths we analyze the phase diagram of the one-dimensional system as the couplings are tuned via transverse confinement, and the populations of the two orbital states are changed. We found that three orders compete showing power law decay: a state with dominant density wave fluctuations, another one with spin density fluctuations, and a third one characterized by exotic Fulde-Ferrell-Larkin-Ovchinnikov-like pairs consisting one atom in the electronic ground state and one in the excited state. We also show that sufficiently close to the resonances the compressibility of the system starts to diverge indicating that the emerging order is unstable and collapses to a phase separated state with a first order phase transition.
We study the effect of the coupling between the electronic ground state of high-spin alkaline-earth fermionic atoms and their metastable optically excited state, when the system is confined in a one-dimensional chain, and show that the system provides a possible realization of a finite momentum pairing (Fulde-Ferrell-Larkin-Ovchinnikov-like) state without spin- or bare mass imbalance. We determine the $\ensuremath{\beta}$-functions of the renormalization group trajectories for general spin and analyze the structure of the possible gapped and gapless states in the hydrodynamic limit. Due to the SU(N) symmetry in the spin space, complete mode separation can not be observed even in the fully gapless 2N-component Luttinger liquid state. Contrary, four velocities characterize the system. We solve the renormalization group equations for spin-9/2 strontium-87 isotope and analyze in detail its phase diagram. The fully gapless Luttinger liquid state does not stabilize in the two-orbital system of the 87Sr atoms, instead, different gapped non-Gaussian fixed points are identified either with dominant density or superconducting fluctuations. The superconducting states are stable in a nontrivial shaped region in the parameter space as a consequence of the coupling between the two electronic states.
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).
We examine the existence and characteristics of the exotic Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in a one-dimensional Fermi gas with attractive Hubbard interactions, in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that a robust FFLO phase can be created in the presence of attractive on-site interactions and Zeeman field, and that the addition of SOC suppresses the FFLO order and enhances the pair formation. In absence of SOC, the system shows four phases: Bardeen-Cooper-Schrieffer (BCS), FFLO, multi- mode pairing and fully polarized phases by tuning the Zeeman field h, and the quantum transition between these phases is discontinuous with respect to h. In the presence of SOC, the transition from the BCS to FFLO phase becomes continuous. We present a complete phase diagram of this model both in the presence and in the absence of SOC at quarter electron filling and also explore the effect of SOC on the FFLO phase.
We examine the existence and characteristics of the exotic Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in a one-dimensional Fermi gas with attractive Hubbard interactions in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that a robust FFLO phase can be created in the presence of attractive on-site interactions and Zeeman field, and that the addition of SOC suppresses the FFLO order and enhances the pair formation. In the absence of SOC, the system shows four phases: Bardeen-Cooper-Schrieffer (BCS), FFLO, multimode pairing, and fully polarized phases by tuning the Zeeman field h. The quantum transition between these phases is discontinuous with respect to h. In the presence of SOC, the transition from the BCS to FFLO phase becomes continuous. We present a complete phase diagram of this model both in the presence and in the absence of SOC at a quarter electron filling and also explore the effect of SOC on the FFLO phase.
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.
Motivated by recent experiments on ultracold fermions we study the effect of the spin-orbit interaction in an exactly solvable one-dimensional model with strong local attractive correlations between the fermions. We show that the asymptotes of correlation functions, calculated in the framework of the conformal field theory and finite size corrections of the Bethe ansatz exact solution, are strongly affected by the spin-orbit coupling. In the mixed phase, the correlation functions consist of terms that are the product of a power law of the distance and an oscillating function of the distance. We obtain the critical exponents for superfluidity and density waves. The leading exponents decrease as a function of spin-orbit coupling. In particular, the exponent for superfluidity is the smallest one signaling an instability to a phase where a weak interchain coupling can produce superfluidity of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type. The spatial oscillation of the order parameter is also modified by the spin-orbit parameter, i.e., its modulation is not just given by the spin imbalance.