Effective Abelian and Non-Abelian Gauge Potentials in Cavity QED

Abstract

Cavity QED models are analyzed in terms of field quadrature operators. We demonstrate that in such representation, the problem can be formulated in terms of effective gauge potentials. In this respect, it presents a completely new system in which gauge fields arise, possessing the advantages of purity, high control of system parameters as well as preparation and detection methods. Studying three well known models, it is shown that either Abelian or non-Abelian gauge potentials can be constructed. The non-Abelian characteristics are evidenced via numerical simulations utilizing experimental parameters.

Force sensors with precision beyond the standard quantum limit

“…In the symmetric case δ x = δ y and g x = g y the model (1) describes the U(1) invariant Jahn-Teller spin-boson interaction. In the limit of N = 1 the model reduces to E ⊗ e symmetrical Jahn-Teller model which has been shown to possesses an effective gauge potential description [18]. On the other hand in the semiclassical limit N ≫ 1 the model exhibits a magnetic structural phase transition [19].…”

“…Let us assume that the system is initially prepared in the spin state | j, − j . The corresponding bosonic Hamiltonian becomeŝ Note that the model (18) has been studied in the context of a quantum phase transition [38,39] without the force symmetry breaking termĤ F . The unitary propagator corresponding to the Hamiltonian (18) can be written asÛ(t) =Û x (t)Û y (t), whereÛ…”

Travelling to exotic places with cavity QED systems

“…That is, they transform appropriately under unitary transformations [20]. For any atomic basis, these gauge potentials are matrices and they are said to be Abelian if [ k , l ] = 0 ∀ k and l and non-Abelian for non-commuting operators.…”

“…In Ref. [20], the time evolution of an initial state consisting of one empty mode and the other with a coherent state was numerically simulated. By properly choosing the phase of the coherent state, it will either set off clockwise or anti-clockwise around the conical intersection.…”

Synthetic Spin-Orbit Coupling in Two-Level Cold Atoms

“…Examples include trapped-ion systems [1,2], band electrons in graphene [3], cavity electrodynamics [4], macroscopic sonic crystals and photonic superlattices [5], as well as the more controllable ultracold atoms in designed laser fields [6][7][8][9]. In particular, one intensively studied model for implementing SOC in cold atoms is the so-called "tripod" scheme, where three levels with different magnetic quantum numbers are coupled with a common excited state by three laser beams [6][7][8][9].…”