[Paper Review] Higgs-like Excitations of Cold Atom System with Spin-orbit Coupling

Fei-Jie Huang, Qi-Hui Chen+1 more|arXiv (Cornell University)|Jul 16, 2012

Cold Atom Physics and Bose-Einstein Condensates28 references3 citations

TL;DR

This paper proposes that Higgs-like excitations—single-particle modes arising from non-Abelian gauge potentials—emerge in ultracold atomic systems with spin-orbit coupling when an SU(2) gauge potential is reduced to U(1), where the non-Abelian part generates a massive gauge field. The induced mass suppresses spin Hall currents, offering a tunable platform to simulate mass generation in condensed matter and high-energy physics.

ABSTRACT

The Higgs-like excitations, which distinguish from the Higgs amplitude mode in many-body system, are single-particle excitations in system with non-Abelian gauge potential. We investigate the Higgs-like excitations of cold atom system in artificial non-Abelian gauge potential. We demonstrate that when a non-Abelian gauge potential is reduced to Abelian potential, its Abelian part constructs spin-orbit coupling, and its non-Abelian part emerges Higgs-like excitations. The Higgs-like excitations induce a mass of the non-Abelian gauge field, which offsets the defect of massless of the gauge theories. We show that the mass of gauge field can affect the spin Hall currents which are produced by the spin-orbit coupling. We also discuss the observation of these phenomena in real experiment.

Motivation & Objective

• To investigate Higgs-like excitations in ultracold atomic systems with engineered non-Abelian gauge potentials.
• To clarify the distinction between Higgs-like excitations (single-particle) and Higgs amplitude modes (collective excitations) in many-body systems.
• To demonstrate that the non-Abelian part of a reduced SU(2) gauge potential gives rise to massive gauge field excitations.
• To explore the interplay between these Higgs-like excitations and spin Hall currents induced by spin-orbit coupling.
• To propose experimental detection of these effects through spin Hall current measurements in trapped ultracold atoms.

Proposed method

• Engineered a three-level Λ-type configuration in ultracold atoms using two laser fields with Rabi frequencies Ω₁ and Ω₂ to simulate an effective SU(2) gauge potential.
• Derived the effective SU(2) gauge potential 𝒜₀ = [γ, A]₊ from the Berry phase of the adiabatic eigenstates, where A = (1/2)qσ_y + (1/4)δ²Qσ_z.
• Reduced the SU(2) gauge potential to a U(1) potential by decomposing it into Abelian (spin-orbit coupling) and non-Abelian (Higgs-like excitation) parts.
• Calculated the gauge field mass using the action expansion S = TrF₀ᵢF₀ᵢ + ½TrF₀₀F₀₀, identifying the mass term as M_B²Tr[ℬ·ℬ] with M_B = M₀ / [1 + (Q·p / 2q·p)²δ⁴]^½.
• Diagonalized the effective Hamiltonian H = p²/2m + g𝒜₀ + V, expanding in M_B to derive the energy spectrum H±(p,r) = p²/2m ± (q·p/2m + M_B) + ..., revealing mass-dependent spin splitting.
• Simulated time evolution of the system via ẋ = -i[x, H], yielding time-dependent Hamiltonians that include dynamical terms in y and z coordinates.

Experimental results

Research questions

• RQ1 How do Higgs-like excitations emerge in a single-particle system with non-Abelian gauge potentials, and how do they differ from Higgs amplitude modes in many-body systems?
• RQ2 What is the role of the non-Abelian part of a reduced SU(2) gauge potential in generating a massive gauge field?
• RQ3 How does the mass of the gauge field affect spin Hall currents generated by spin-orbit coupling in cold atoms?
• RQ4 Can Higgs-like excitations be experimentally detected through measurable signatures like spin Hall current modulation?
• RQ5 To what extent can this model be generalized to other systems involving Berry phases and artificial gauge potentials?

Key findings

• Higgs-like excitations arise from the breaking of parallel transport in non-Abelian gauge potentials and are distinct from collective Higgs amplitude modes in many-body systems.
• The non-Abelian part of the reduced SU(2) gauge potential generates a massive gauge field with mass M_B = M₀ / [1 + (Q·p / 2q·p)²δ⁴]^½, which depends on momentum and laser parameters.
• The mass of the gauge field suppresses the spin-down current while slightly enhancing the spin-up current, as shown in Fig. 5, indicating tunable spin Hall transport.
• The effective Hamiltonian H±(p,r) = p²/2m ± (q·p/2m + M_B) + ... reveals that the spin-orbit coupling term is modified by the Higgs-like mass term, altering the energy dispersion.
• The system’s spin Hall currents can be experimentally probed via time-of-flight or spin-resolved imaging, providing a direct signature of Higgs-like excitation effects.
• The results are applicable beyond cold atoms to any system with Berry phase and artificial gauge fields, suggesting broader relevance in condensed matter and high-energy physics.