Vacuum-Induced Abelian and Non-Abelian Gauge Potentials in Cavity Quantum Electrodynamics

Gediminas Juzeliūnas

Hailong Zhang, Qifeng Liang, Lixian Yu +1 more

Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems. In this paper, we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics. It is shown that a non-Abelian gauge potential is achieved only for a single atom, whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble. More importantly, two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted. The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes, which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.

Farokh Mivehvar

Abelian and non-Abelian gauge potentials and quantum gauge theories play central roles in our understanding of Nature. Gauge potentials are also of great significance in condensed matter physics. In fact, minimal coupling of electrons to an Abelian or non-Abelian gauge potential is the essential ingredient for the realization of topological states of matter. Due to the high controllability of ultracold atoms, they are commonly exploited to test fundamental theories of physics, simulate intractable systems, and realize exotic many-body states. Nonetheless, the charge neutrality of atoms places severe constraints on ultracold atomic systems, since neutral particles do not couple to gauge potentials the way charged particles do. That said, coupling a multi-component quantum gas to laser light can lead to the emergence of artificial Abelian and non-Abelian gauge potentials minimally coupled to the center-of-mass momenta of ultracold neutral atoms, paving the way for realizing topological states of matter and simulating gauge theories in quantum gases. All previous proposals for inducing gauge potentials have been developed in the semiclassical regime, where the radiation field is treated classically. I have developed a two-photon Raman scheme in the strong atom-photon coupling (i.e., quantum) regime, based on two counter-propagating modes of a ring cavity, to induce both synthetic magnetic field and spin-orbit coupling for a single neutral atom inside the cavity. The spin-orbit interaction is only weakly dependent on the occupation of the cavity modes, whereas the strength of the magnetic field is proportional to the square of the total number of photons in the cavity and can be made arbitrarily large, which is desirable for realizing the quantum Hall phase. I have then extended this single-atom cavity quantum-electrodynamics scheme to many bosons in the weak atom-photon coupling regime. In addition to inducing spin-orbit coupling for the individual atoms, the cavity fields also mediate infinite-ranged interactions between atoms, whose strengths and signs can readily be tuned experimentally. The interplay between these cavity-mediated interactions and the intrinsic two-body interactions determines the many-body ground state and its elementary excitations, with novel consequences such as the stabilization of an attractive Bose-Einstein condensate which otherwise is unstable.

J. M. Raimond

Lucia Valor, Jacquelin Luneau, Klaus Liegener +2 more

In quantum optics and related fields, cavity quantum electrodynamics provides a powerful framework for modeling the low-energy properties of bound charges coupled to electromagnetic fields, using a minimal set of atomic levels and isolated photonic modes. Here, we develop a similar framework for non-Abelian gauge theories, focusing on the pure-gauge dynamics of SU(2) fields as the conceptually simplest example. Starting from the corresponding Yang-Mills Lagrangian, we derive an SU(2) cavity Hamiltonian in the Coulomb gauge, represented in terms of only three localized bosonic modes. Unlike its non-interacting electromagnetic counterpart, this model exhibits a nontrivial excitation spectrum featuring bound composite gauge particles ('glueballs') as the lowest-energy configurations. We extend this framework to one-dimensional arrays of coupled SU(2) cavities and discuss the driven excitation of a glueball condensate and the clustering of multi-glueball states as two elementary interaction-induced processes in these models. These examples offer a glimpse into the multitude of novel many-body phenomena that arise within this cavity SU(2) framework and we show how this physics at the interface between particle physics and quantum optics can be experimentally explored using state-of-the-art superconducting quantum circuits.