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arXiv:1706.00994 · Physical Review A

Protocol to engineer Fulde-Ferrell-Larkin-Ovchinnikov states in a cold Fermi gas

Shovan Dutta, Erich J. Mueller

Published Aug 14, 2017• 6 citations
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Abstract

We propose a two-step experimental protocol to directly engineer Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a cold two-component Fermi gas loaded into a quasi-one-dimensional trap. First, one uses phase imprinting to create a train of domain walls in a superfluid with equal number of $\ensuremath{\uparrow}$- and $\ensuremath{\downarrow}$-spins. Second, one applies a radio-frequency sweep to selectively break Cooper pairs near the domain walls and transfer the $\ensuremath{\uparrow}$-spins to a third spin state, which does not interact with the $\ensuremath{\uparrow}$- and $\ensuremath{\downarrow}$-spins. The resulting FFLO state has exactly one unpaired $\ensuremath{\downarrow}$-spin in each domain wall and is stable for all values of domain-wall separation and interaction strength. We show that the protocol can be implemented with high fidelity at sufficiently strong interactions for a wide range of parameters available in present-day experimental conditions.

DOI
10.1103/physreva.96.023612

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arXiv:1111.2407•Physical Review A•Dec 5, 2011•14 citations
We propose a two-step experimental protocol to directly engineer Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a cold two-component Fermi gas loaded into a quasi-one-dimensional trap. First, one uses phase imprinting to create a train of domain walls in a superfluid with equal number of \ensuremath↑\ensuremath{\uparrow}\ensuremath↑- and \ensuremath↓\ensuremath{\downarrow}\ensuremath↓-spins. Second, one applies a radio-frequency sweep to selectively break Cooper pairs near the domain walls and transfer the \ensuremath↑\ensuremath{\uparrow}\ensuremath↑-spins to a third spin state, which does not interact with the \ensuremath↑\ensuremath{\uparrow}\ensuremath↑- and \ensuremath↓\ensuremath{\downarrow}\ensuremath↓-spins. The resulting FFLO state has exactly one unpaired \ensuremath↓\ensuremath{\downarrow}\ensuremath↓-spin in each domain wall and is stable for all values of domain-wall separation and interaction strength. We show that the protocol can be implemented with high fidelity at sufficiently strong interactions for a wide range of parameters available in present-day experimental conditions.
We theoretically explore a promising route to achieve the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a spin-imbalanced ultracold Fermi gas. In the current stage of cold atom physics, search for this exotic Fermi superfluid is facing two serious difficulties: One is the desperate destruction of the FFLO long-range order by FFLO pairing fluctuations, which precludes entering the phase through a second-order transition, even in three dimension. The other is the fierce competition with the phase separation into the BCS (Bardeen-Cooper-Schrieffer) state and the spin-polarized normal state. By including strong FFLO pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that the anisotropy of Fermi surface introduced by an optical lattice makes the FFLO state stable against the paring fluctuations. This stabilized FFLO state is also found to be able to overcome the competition with the phase separation under a certain condition. Since the realization of unconventional Fermi superfluids is one of the most exciting challenges in cold atom physics, our results would contribute to the further development of this field.
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 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.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase was first predicted in two-dimensional superconductors about 50 years ago, but so far unambiguous experimental evidence is still lacking. The recently experimentally realized spin-imbalanced Fermi gases may potentially unveil this elusive state, but they require very stringent experimental conditions. In this Rapid Communication, we show that FFLO phases may be observed even in a three-dimensional (3D) degenerate Fermi gas with spin-orbit coupling and an in-plane Zeeman field. The FFLO phase is driven by the interplay between the asymmetry of the Fermi surface and the superfluid order, instead of the interplay between magnetic and superconducting order in solid materials. The predicted FFLO phase exists in a giant parameter region, possesses a stable long-range superfluid order due to the 3D geometry, and can be observed with an experimentally already achieved temperature ($T\ensuremath{\sim}0.05{E}_{F}$), thus opening a fascinating avenue for exploring FFLO physics.
We show that the combination of spin-orbit coupling and in-plane Zeeman field in a two-dimensional degenerate Fermi gas can lead to a larger parameter region for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases than that using spin-imbalanced Fermi gases. The resulting FFLO superfluids are also more stable due to the enhanced energy difference between FFLO and conventional Bardeen-Cooper-Schrieffer (BCS) excited states. We clarify the crucial role of the symmetry of Fermi surface on the formation of finite momentum pairing. The phase diagram for FFLO superfluids is obtained in the BCS-BEC crossover region and possible experimental observations of FFLO phases are discussed.
We study an effect of rotation on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of two-component Fermi superfluid gases in a toroidal trap. We investigate the stability of the FFLO states in the quasi-one-dimensional regime on the basis of the Bogoliubov--de Gennes equation. We find that two FFLO phases, i.e., the half-quantum-vortex state and the intermediate state of the Fulde-Ferrell (FF) state and the Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half-quantum-vortex state is shown in both the TTT-PPP plane and the TTT-hhh plane. We demonstrate characteristic features of these states, such as the order parameter, flux quantization, and local polarization. Several related works are discussed, and the advantages of cold Fermi gases are indicated.