80
3 Light–Matter Interactions for Photonic Applications
3.3 Strong Exciton–Photon Coupling and Polariton
Bose–Einstein Condensation
Strong quantum coupling of excitons and photons in semiconductors results in
coherent superpositions of the two components, or quasi-particles called exciton–
polaritons [1, 188]. In recent years, quantum-well exciton–polaritons in optical
microresonator structures (cf. Fig. 3.9a, b), also referred to as cavity–polaritons
[189–194], attracted considerable interest beyond the quantum optics community
[8, 15, 42, 51, 81, 102]. Quantum wells—the more wells (emitters in resonance),
the more robust the strong coupling—placed at anti-node positions of a microcavity mode’s standing wave electric field deliver the matter component, which gets
dressed with the cavity field in the strong coupling regime [1, 38, 169, 190, 195].
The appropriate description of the hybridised quantum system, i.e. the eigen-states of
the coupled-oscillator system, is based on composite quasi-particles, the polaritons,
with their appealing bosonic character and ultralight effective masses [2, 3, 7, 42].
Thus, the hybrid modes are part light (bosonic) and part matter excitation (composite
boson made of two fermions), with the Rabi frequency characterizing the interaction strength between the two components. A typical in-plane-momentum-dependent
diagram for such hybrid system is shown with Hopfield coefficients as well as lower
and upper polariton dispersions with Rabi splitting in the case of zero detuning at
k = 0 in Fig. 3.9c.
Favourable Properties of Polaritons
The effective mass of polaritons is heavily influenced by the photon dispersion in
the microcavity, which is quadratic close to the zero transverse momentum point
(the effective mass concept applies), and is typically four to five orders of magnitude
smaller than the mass of a bare electron. The appearance of such mixed modes is
interesting from both the point of view of fundamental and applied research. Strong
interparticle interactions result from the exciton component, whereas the extremely
low effective mass and the high mobility originate from the photonic component.
Thus, polaritons with their much more delocalised wave-function are less prone
to trapping, dephasing and non-radiative recombination due to inhomogeneities in
semiconductor structures than quantum-well excitons.
BEC-Like Phase Transition for Exciton–Polaritons
The field of Bose–Einstein-like condensation of exciton–polaritons opened in 2006,
when the first fully convincing report of BEC-like condensation of exciton–polaritons
was published which included the demonstration of a spontaneous symmetry breaking with extended spatial correlations (as a signature of off-diagonal long-range
order) [37]. However, previous experiments dating back to 2002 clearly showed
condensation effects for polaritons in microcavities [38], later amended by various
studies including spatial coherence studies [39, 198, 199]. It was demonstrated that
exciton–polaritons can exhibit behaviour analogous to Bose–Einstein condensation
[37, 39, 40], which is a phase transition to an exquisite quantum state of bosonic
particles (see polariton-related [41–45, 59, 200–203] and BEC-related [128, 131]).
3 Light–Matter Interactions for Photonic Applications
3.3 Strong Exciton–Photon Coupling and Polariton
Bose–Einstein Condensation
Strong quantum coupling of excitons and photons in semiconductors results in
coherent superpositions of the two components, or quasi-particles called exciton–
polaritons [1, 188]. In recent years, quantum-well exciton–polaritons in optical
microresonator structures (cf. Fig. 3.9a, b), also referred to as cavity–polaritons
[189–194], attracted considerable interest beyond the quantum optics community
[8, 15, 42, 51, 81, 102]. Quantum wells—the more wells (emitters in resonance),
the more robust the strong coupling—placed at anti-node positions of a microcavity mode’s standing wave electric field deliver the matter component, which gets
dressed with the cavity field in the strong coupling regime [1, 38, 169, 190, 195].
The appropriate description of the hybridised quantum system, i.e. the eigen-states of
the coupled-oscillator system, is based on composite quasi-particles, the polaritons,
with their appealing bosonic character and ultralight effective masses [2, 3, 7, 42].
Thus, the hybrid modes are part light (bosonic) and part matter excitation (composite
boson made of two fermions), with the Rabi frequency characterizing the interaction strength between the two components. A typical in-plane-momentum-dependent
diagram for such hybrid system is shown with Hopfield coefficients as well as lower
and upper polariton dispersions with Rabi splitting in the case of zero detuning at
k = 0 in Fig. 3.9c.
Favourable Properties of Polaritons
The effective mass of polaritons is heavily influenced by the photon dispersion in
the microcavity, which is quadratic close to the zero transverse momentum point
(the effective mass concept applies), and is typically four to five orders of magnitude
smaller than the mass of a bare electron. The appearance of such mixed modes is
interesting from both the point of view of fundamental and applied research. Strong
interparticle interactions result from the exciton component, whereas the extremely
low effective mass and the high mobility originate from the photonic component.
Thus, polaritons with their much more delocalised wave-function are less prone
to trapping, dephasing and non-radiative recombination due to inhomogeneities in
semiconductor structures than quantum-well excitons.
BEC-Like Phase Transition for Exciton–Polaritons
The field of Bose–Einstein-like condensation of exciton–polaritons opened in 2006,
when the first fully convincing report of BEC-like condensation of exciton–polaritons
was published which included the demonstration of a spontaneous symmetry breaking with extended spatial correlations (as a signature of off-diagonal long-range
order) [37]. However, previous experiments dating back to 2002 clearly showed
condensation effects for polaritons in microcavities [38], later amended by various
studies including spatial coherence studies [39, 198, 199]. It was demonstrated that
exciton–polaritons can exhibit behaviour analogous to Bose–Einstein condensation
[37, 39, 40], which is a phase transition to an exquisite quantum state of bosonic
particles (see polariton-related [41–45, 59, 200–203] and BEC-related [128, 131]).