Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms (0905.2610v2)

Abstract: Fermionic alkaline-earth atoms have unique properties that make them attractive candidates for the realization of novel atomic clocks and degenerate quantum gases. At the same time, they are attracting considerable theoretical attention in the context of quantum information processing. Here we demonstrate that when such atoms are loaded in optical lattices, they can be used as quantum simulators of unique many-body phenomena. In particular, we show that the decoupling of the nuclear spin from the electronic angular momentum can be used to implement many-body systems with an unprecedented degree of symmetry, characterized by the SU(N) group with N as large as 10. Moreover, the interplay of the nuclear spin with the electronic degree of freedom provided by a stable optically excited state allows for the study of spin-orbital physics. Such systems may provide valuable insights into strongly correlated physics of transition metal oxides, heavy fermion materials, and spin liquid phases.

• The paper introduces a two-orbital SU(N) Hubbard model that leverages decoupled nuclear spin to uncover novel quantum magnetism.
• It employs models like Kugel-Khomskii and Kondo lattice to illustrate precise control of spin and orbital interactions in optical lattices.
• The study paves the way for simulating exotic quantum phases, informing high-temperature superconductivity and heavy fermion research.

Overview of "Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms"

The paper in question investigates the unique many-body phenomena that can be realized using fermionic alkaline-earth atoms loaded in optical lattices. The primary focus is on the theoretical demonstration of these atoms as quantum simulators, exploring the implementation of systems characterized by exceptional symmetry properties, specifically those governed by the SU(N) group where N can be as large as 10. Key to this exploration is the decoupling of nuclear spin from electronic angular momentum in these atoms.

Key Concepts and Models

Alkaline-earth atoms, unlike alkali atoms, possess two useful metastable electronic states ($^1S_0$ and $^3P_0$) that decouple the nuclear spin from the electronic state. The remarkable feature is that the s-wave scattering lengths in interactions involving these states are independent of nuclear spin due to this decoupling. This paper leverages this symmetry to propose the development of a generalized SU(N) Hubbard model for ultracold gases in optical lattices.

The paper introduces the two-orbital SU(N)-symmetric Hubbard model, focusing on the physics of $^1S_0$ and $^3P_0$ states. Strong interactions and resultant many-body dynamics are explored through effective spin Hamiltonians that decouple or intertwine spin and orbital degrees of freedom through terms such as the Kugel-Khomskii model, known for its role in describing transition metal oxides.

Computational and Theoretical Insights

The authors derive several situations of interest from the innovative two-orbital SU(N) Hubbard model:

1. Kugel-Khomskii model: Fundamental to studying transition metal oxides, this model is implemented using one atom per site in an optical lattice. It showcases intricate interactions between spins and orbitals, predicted to aid in the understanding of complex orders found in magnetic solids.
2. SU(N) antiferromagnet: By utilizing nuclear spin in one specific ground state (only g-atoms), the authors explore the properties of systems whose interaction symmetry—SU(N)—surpasses the traditional SU(2), promising insights into exotic quantum states like spin liquids and valence bond solids.
3. Kondo lattice model: This model explores the heavy fermion behavior prevalent in materials such as rare-earth metals and manganites by considering a system with localized and delocalized spins.

Implications and Future Directions

The model presents a comprehensive framework for exploring symmetry-based exotic phases in quantum simulations using alkaline-earth atoms. These proposals are complemented by promising experimental possibilities wherein the microscopic parameters of these models can be precisely controlled within optical lattices.

Practically, the proposed methodologies show promise for deeper explorations into the quantum phases of matter and simulate complex models pertinent to high-temperature superconductivity and many-body physics. Theoretical explorations indicate the potential to address questions related to quantum criticality and non-Fermi liquid behaviors, which remain challenging in condensed matter physics.

Furthermore, the paper suggests the flexibility of alkaline-earths in realizing SU(N) magnetism opens new pathways in quantum information processing, suggesting potential applications in quantum computing architectures where spin and orbital manipulations are crucial.

Final Remarks

While this research paves the way for exciting explorations in ultracold atomic physics, continued empirical advancements are necessary to fully realize the theoretical propositions—namely, the detailed studies of transition metal oxides and heavy fermion systems through controlled atomic simulations.

Overall, this paper offers substantial groundwork for retuning our understanding of many-body physics, supported by the symmetries accessible in alkaline-earth atomic systems.