Manipulating emission rates and interactions of quantum emitters beyond electric dipole approximation
DIPC Seminars
 Speaker

Karolina Slowik, Nicolaus Copernicus University, Torun, Poland
 When

2019/01/24
13:00  Place
 Donostia International Physics Center
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Interaction of a quantum emitter with the surrounding photonic bath in its
ground state yields a correction to the emitterâ€™s transition energy,
referred to as Lamb shift, and gives rise to the process of spontaneous
emission. If multiple emitters are present, shared photonic bath acts as a
carrier of interactions between them and is responsible for collective
emission. An example is the phenomenon of Dicke superradiance. The spatial and
spectral structure of photonic bath of a quantum emitter can be tailored, e.g.
with traditional cavities or with nanostructured materials. The most extreme
illustration of impact of nanostructured surroundings on optical properties of
emitters is enhancement by many orders of magnitude of spontaneous emission
rates of molecules adjacent to plasmonic nanoparticles. The reason for such a
remarkable influence of plasmonic nanoparticles is their capability, upon
illumination, of strong electromagnetic field confinement to subwavelength
regions of space. There, the density of photonic states, which the quantum
emitter can couple to, is locally increased. Subwavelength confinement
suggests, however, that the paradigmatic approach to lightmatter interaction
within the electric dipole approximation may not be sufficient, and steps
beyond may be required [1,2]. These steps include influence of higherorder
multipoles such as magnetic dipole or electric quadrupole, which scale
proportionally to spatial modulations of
electric field. To evaluate the impact of nanoparticles on properties of
emitters we use the dyadic Greenâ€™s tensor formalism following Refs. [3,4]
and generalize it beyond the electric dipole approximation. For this purpose
we consider quantum emittersâ€™ transitions characterized simultaneously by
multiple moments: the electric dipole, magnetic dipole, and electric
quadrupole. Remarkably, the optical properties of the photonic bath are
described by a classical quantity: the electromagnetic Green's tensor. In
particular, it accounts for the geometry and material properties of the
nanoparticle which the quantum emitter is adjacent to. In this framework we
solve Heisenberg equations for field and emittersâ€™ operators dynamics
combined with the Markovian approximation, to arrive at the desired
expressions for transition rates and interaction strengths. To provide
examples, we apply the formalism to simple geometries like a planar interface
between two different media or a nanoparticle, and identify scenarios where a
step beyond the electric dipole approximation is necessary for accurate
description of emittersâ€™ dynamics.
References:
[1] Rivera, N., Kaminer, I., Zhen, B., Joannopoulos, J. D., & SoljaÄiÄ‡, M.,
Shrinking light to allow forbidden transitions on the atomicscale. Science,
353(6296), 263269 (2016).
[2] Kosik M., Spontaneous emission enhancement beyond dipole approximation: a
Greenâ€™s functions approach (Masterâ€™s thesis), 2017.
[3] Dung, H. T., KnÃ¶ll L., Welsch D.G., Threedimensional quantization of
the electromagnetic field in dispersive and absorbing inhomogeneous
dielectrics, Phys. Rev. A 57, 3931 (1998).
[4] Dzsotjan D., SÃ¸rensen A.S., Fleischhauer M., Quantum emitters coupled to
surface plasmons of a nanowire: A Greenâ€™sfunction approach, Phys. Rev. B 82,
075427 (2010).
Host: Andres Ayuela and Marta Pelc