3.3 Strong Exciton–Photon Coupling and Polariton Bose–Einstein Condensation
81
Fig. 3.9 a Emitter–cavity system with coupling strength g between resonant light field and quantum
emitter. b Planar Fabry–Pérot resonator with multiple quantum wells as active region, displaying
momentum conservation for emitted photons from an in-plane 2D exciton gas with centre-of-mass
momentum k . In the wells, excitons can only couple to cavity photons of total photon momentum k
when their in-plane momentum projection k matches. Correspondingly, the photon momentum of
the angle (θ) dependent emission can be decomposed into an in-plane component k and an out-ofplane component |k C,0 | = 2π/λ C,0 (with resonance wavelength in vacuum at zero incidence angle
λ C,0 ). c For the hybrid cavity–polaritons, the Hopfield coefficients can be given for any detuning and
momentum configuration, here displayed for resonance conditions at zero momentum (top) with
the corresponding polariton dispersions (bottom) in a planar quantum-well microresonator system.
The characteristic normal mode splitting between upper and lower polariton branch (LP/UP) of
2 (the Rabi splitting) is displayed at resonance conditions for the cavity C and exciton mode X.
a–c Drawn after the author’s schematics in [196], based on [197]
First Realisation of Bose–Einstein Condensation
Originally, condensation was predicted from statistical properties of a system of
bosons at low temperatures by S. Bose and A. Einstein, in the mid-twenties of the
20th century. The first true Bose–Einstein condensate (BEC) of dilute atomic gases
was observed in 1995 (by three groups working on this subject) [204–206], opening
a new chapter in the field of atomic and molecular physics and quantum optics.
The historic evolution of condensate experiments and the path towards polariton
quasi-BEC is highlighted in [81].
The Super Flow of Condensation Studies
Condensation of polaritons was a major breakthrough in this field from both fundamental and applied point of view. In the past two decades, polaritons in microcavities
evolved to a unique, easily-accessible and versatile testbed for condensation studies in
solids, owing to the remarkable properties of exciton–polaritons (see aforementioned
literature on these hybrid quasi-particles, also cf. [196, 207] for an overview of the
fundamentals of cavity–polaritons). Condensates of polaritons were achieved away
from ideal thermal equilibrium, in a gas of particles with only picoseconds lifetime
[42, 199, 208–210], and exhibited interesting properties such as superfluidity (up to
room temperature) [60, 66], a spin-Meissner effect (spin analogue of the Meissner
81
Fig. 3.9 a Emitter–cavity system with coupling strength g between resonant light field and quantum
emitter. b Planar Fabry–Pérot resonator with multiple quantum wells as active region, displaying
momentum conservation for emitted photons from an in-plane 2D exciton gas with centre-of-mass
momentum k . In the wells, excitons can only couple to cavity photons of total photon momentum k
when their in-plane momentum projection k matches. Correspondingly, the photon momentum of
the angle (θ) dependent emission can be decomposed into an in-plane component k and an out-ofplane component |k C,0 | = 2π/λ C,0 (with resonance wavelength in vacuum at zero incidence angle
λ C,0 ). c For the hybrid cavity–polaritons, the Hopfield coefficients can be given for any detuning and
momentum configuration, here displayed for resonance conditions at zero momentum (top) with
the corresponding polariton dispersions (bottom) in a planar quantum-well microresonator system.
The characteristic normal mode splitting between upper and lower polariton branch (LP/UP) of
2 (the Rabi splitting) is displayed at resonance conditions for the cavity C and exciton mode X.
a–c Drawn after the author’s schematics in [196], based on [197]
First Realisation of Bose–Einstein Condensation
Originally, condensation was predicted from statistical properties of a system of
bosons at low temperatures by S. Bose and A. Einstein, in the mid-twenties of the
20th century. The first true Bose–Einstein condensate (BEC) of dilute atomic gases
was observed in 1995 (by three groups working on this subject) [204–206], opening
a new chapter in the field of atomic and molecular physics and quantum optics.
The historic evolution of condensate experiments and the path towards polariton
quasi-BEC is highlighted in [81].
The Super Flow of Condensation Studies
Condensation of polaritons was a major breakthrough in this field from both fundamental and applied point of view. In the past two decades, polaritons in microcavities
evolved to a unique, easily-accessible and versatile testbed for condensation studies in
solids, owing to the remarkable properties of exciton–polaritons (see aforementioned
literature on these hybrid quasi-particles, also cf. [196, 207] for an overview of the
fundamentals of cavity–polaritons). Condensates of polaritons were achieved away
from ideal thermal equilibrium, in a gas of particles with only picoseconds lifetime
[42, 199, 208–210], and exhibited interesting properties such as superfluidity (up to
room temperature) [60, 66], a spin-Meissner effect (spin analogue of the Meissner