2017/09/30 by Adam Stokes, Ahsan Nazir · 23 citations
Computer Science · Physics and Astronomy · #Atomic and Subatomic Physics Research #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Coulomb #Dipole #Gauge boson #Gauge fixing #Gauge theory #Hamiltonian (control theory) #Interaction energy #Master equation #Physics #Quantum #Quantum Information and Cryptography #Quantum electrodynamics #Quantum mechanics #quant-ph
paper · pdf · doi:10.1088/1367-2630/aab29d
published in New Journal of Physics 20(4), 043022 (IOP Publishing) · 18 pages including appendix, 8 figures
openalex publication_date 2018/02/27 · arxiv created 2018/04/16 · arxiv updated 2018/04/17 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
We consider a pair of dipoles such as Rydberg atoms for which direct electrostatic dipole–dipole interactions may be significantly larger than the coupling to transverse radiation. We derive a master equation using the Coulomb gauge, which naturally enables us to include the inter-dipole Coulomb energy within the system Hamiltonian rather than the interaction. In contrast, the standard master equation for a two-dipole system, which depends entirely on well-known gauge-invariant S -matrix elements, is usually derived using the multipolar gauge, wherein there is no explicit inter-dipole Coulomb interaction. We show using a generalised arbitrary-gauge light-matter Hamiltonian that this master equation is obtained in other gauges only if the inter-dipole Coulomb interaction is kept within the interaction Hamiltonian rather than the unperturbed part as in our derivation. Thus, our master equation depends on different S -matrix elements, which give separation-dependent corrections to the standard matrix elements describing resonant energy transfer and collective decay. The two master equations coincide in the large separation limit where static couplings are negligible. We provide an application of our master equation by finding separation-dependent corrections to the natural emission spectrum of the two-dipole system.