TY - JOUR

T1 - A master equation for strongly interacting dipoles

AU - Stokes, Adam

AU - Nazir, Ahsan

N1 - Funding Information:
This work was supported by the Engineering and Physical Sciences Research Council grant number EP/ N008154/1. We thank Jake Iles-Smith and Victor Jouffrey for useful discussions.
Publisher Copyright:
© 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft.

PY - 2018/4

Y1 - 2018/4

N2 - 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.

AB - 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.

KW - Rydberg atoms

KW - dipole-dipole interactions

KW - master equation

KW - strong coupling

UR - http://www.scopus.com/inward/record.url?scp=85046687645&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/master-equation-strongly-interacting-dipoles

U2 - 10.1088/1367-2630/aab29d

DO - 10.1088/1367-2630/aab29d

M3 - Article

SN - 1367-2630

VL - 20

JO - New Journal of Physics

JF - New Journal of Physics

IS - 4

M1 - 043022

ER -