A master equation for strongly interacting dipoles

Adam Stokes, Ahsan Nazir

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number043022
Number of pages21
JournalNew Journal of Physics
Issue number4
Early online date27 Feb 2018
Publication statusPublished - Apr 2018


  • Rydberg atoms
  • dipole-dipole interactions
  • master equation
  • strong coupling


Dive into the research topics of 'A master equation for strongly interacting dipoles'. Together they form a unique fingerprint.

Cite this