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arXiv:1809.06836 · Physical Review A

Local manipulation of quantum magnetism in one-dimensional ultracold Fermi gases across narrow resonances

Lei Pan, Xiaoling Cui, Shu Chen

Published Jan 10, 2019• 2 citations
arXivHTMLPDF

Abstract

Effective range is a quantity to characterize the energy dependence in two-body scattering strength and is widely used in cold atomic systems, especially across narrow resonances. Here we show that the effective range can significantly modify the magnetic property of one-dimensional (1D) spin-$1/2$ fermions in the strongly repulsive regime. In particular, the effective range breaks the large spin degeneracy in the hard-core limit and induces a Heisenberg exchange term in the spin chain that is much more sensitive to the local density than that induced by the bare coupling. With an external harmonic trap, this leads to a very rich magnetic pattern where the antiferromagnetic and ferromagnetic correlations can coexist and distribute in highly tunable regions across the trap. Finally, we propose to detect the range-induced magnetic order in the tunneling experiment. Our results can be directly tested in 1D Fermi gases across narrow resonance and suggest a convenient route toward the local manipulation of quantum magnetism in cold atoms.

DOI
10.1103/physreva.99.013607

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Effective range is a quantity to characterize the energy dependence in two-body scattering strength and is widely used in cold atomic systems, especially across narrow resonances. Here we show that the effective range can significantly modify the magnetic property of one-dimensional (1D) spin-1/21/21/2 fermions in the strongly repulsive regime. In particular, the effective range breaks the large spin degeneracy in the hard-core limit and induces a Heisenberg exchange term in the spin chain that is much more sensitive to the local density than that induced by the bare coupling. With an external harmonic trap, this leads to a very rich magnetic pattern where the antiferromagnetic and ferromagnetic correlations can coexist and distribute in highly tunable regions across the trap. Finally, we propose to detect the range-induced magnetic order in the tunneling experiment. Our results can be directly tested in 1D Fermi gases across narrow resonance and suggest a convenient route toward the local manipulation of quantum magnetism in cold atoms.
The highly controllable ultracold atoms in a one-dimensional (1D) trap provide a new platform for the ultimate simulation of quantum magnetism. In this regard, the N\'eel antiferromagnetism and the itinerant ferromagnetism are of central importance and great interest. Here we show that these magnetic orders can be achieved in the strongly interacting spin-1/2 trapped Fermi gases with additional ppp-wave interactions. In this strong-coupling limit, the 1D trapped Fermi gas exhibits an effective Heisenberg spin XXZXXZXXZ chain in the anisotropic ppp-wave scattering channels. For a particular ppp-wave attraction or repulsion within the same species of fermionic atoms, the system displays ferromagnetic domains with full spin segregation or the antiferromagnetic spin configuration in the ground state. Such engineered magnetisms are likely to be probed in a quasi-1D trapped Fermi gas of 40K^{40}\mathrm{K}40K atoms with very close sss-wave and ppp-wave Feshbach resonances.
The nature of strongly interacting Fermi gases and magnetism is one of the most important and studied topics in condensed-matter physics. Still, there are many open questions. A central issue is under what circumstances strong short-range repulsive interactions are enough to drive magnetic correlations. Recent progress in the field of cold atomic gases allows one to address this question in very clean systems where both particle numbers, interactions and dimensionality can be tuned. Here we study fermionic few-body systems in a one dimensional harmonic trap using a new rapidly converging effective-interaction technique, plus a novel analytical approach. This allows us to calculate the properties of a single spin-down atom interacting with a number of spin-up particles, a case of much recent experimental interest. Our findings indicate that, in the strongly interacting limit, spin-up and spin-down particles want to separate in the trap, which we interpret as a microscopic precursor of one-dimensional ferromagnetism in imbalanced systems. Our predictions are directly addressable in current experiments on ultracold atomic few-body systems.
The nature of strongly interacting Fermi gases and magnetism is one of the most important and studied topics in condensed-matter physics. Still, there are many open questions. A central issue is under what circumstances strong short-range repulsive interactions are enough to drive magnetic correlations. Recent progress in the field of cold atomic gases allows one to address this question in very clean systems where both particle numbers, interactions and dimensionality can be tuned. Here we study fermionic few-body systems in a one dimensional harmonic trap using a new rapidly converging effective-interaction technique, plus a novel analytical approach. This allows us to calculate the properties of a single spin-down atom interacting with a number of spin-up particles, a case of much recent experimental interest. Our findings indicate that, in the strongly interacting limit, spin-up and spin-down particles want to separate in the trap, which we interpret as a microscopic precursor of one-dimensional ferromagnetism in imbalanced systems. Our predictions are directly addressable in current experiments on ultracold atomic few-body systems.
We study quasi-one-dimensional atomic gases across wide and narrow confinement-induced resonances (CIRs). We show using the virial expansion that, by tuning the magnetic field, the repulsive scattering branch initially prepared at low fields can continuously go across CIRs without decay; instead, the decay occurs when the noninteracting limit is approached. The interaction properties essentially rely on the resonance width of the CIR. Universal thermodynamics holds for the scattering branch right at a wide CIR, but is smeared out in a narrow CIR due to the strong energy dependence of the coupling strength. In wide and narrow CIRs, the interaction energy of the scattering branch shows different types of strong asymmetry when the decay is approached from opposite sides of the magnetic field. Finally, we discuss the stability of the repulsive branch for a repulsively interacting Fermi gas in different trapped geometries at low temperatures.
We study the effective one-dimensional (1D) scattering of two distinguishable atoms confined individually by separatedtransverse harmonic traps. With equal trapping frequency for two sss-wave interacting atoms, we find that by tuning the trap separations, the system can undergo double 1D scattering resonance, named as the separation-induced resonance (SIR), when the ratio between the confinement length and sss-wave scattering length is within (0.791,1.46](0.791,1.46](0.791,1.46]. Near SIR, the scattering property shows unique dependence on the resonance position. The universality of a many-body system on scattering branch near SIR is demonstrated by studying the interaction effect of a localized impurity coupled with a Fermi sea of light atoms in a quasi-1D trap.
We present a general form of the effective spin-chain model for strongly interacting atomic gases with an arbitrary spin in one-dimensional (1D) traps. In particular, for high-spin systems the atoms can collide in multiple scattering channels, and we find that the resulting form of spin-chain model generically follows the same structure as that of the interaction potentials. This is a unified form working for any spin, statistics (Bose or Fermi), and confinement potentials. We adopt the spin-chain model to reveal both the ferromagnetic (FM) and antiferromagnetic (AFM) magnetic orders for strongly interacting spin-1 bosons in 1D traps. We further show that by adding the spin-orbit coupling, the FM and AFM orders can be gradually destroyed and eventually the ground state exhibits universal spin structure and contacts that are independent of the strength of spin-orbit coupling.