3.3 Strong Exciton–Photon Coupling and Polariton Bose–Einstein Condensation
83
3.3.1 Cavity–Polaritons Exposed to External Fields
When placing strongly-coupled light–matter systems in external electric or magnetic
fields, numerous interesting effects can be studied and the response of polaritons in
the linear and nonlinear regime (i.e. dynamical condensates of polaritons) explored.
A topical introduction into this subject is provided for instance in [243]. To start
with a practical example, one simple effect arising from the exposure to electric
bias in polariton diodes on the coupling regime can for instance allow one to switch
on ultrafast timescales between a polariton lasing and conventional lasing situation
[244], exploiting the quantum-confined Stark effect (QCSE) on the quantum-well
excitons. In the following, a few examples from the domain of magneto-optical and
transient-field studies are briefly summarised.
Polaritons in Magnetic Fields
Exposing polaritons to external magnetic fields (typically in Faraday configuration)
offers an important playground for the study of polariton interactions and degeneracylifted spinor condensates. On the one hand, with increasing magnetic flux, threshold
conditions are modified due to diamagnetic shifts [245], exciton Bohr-radius changes
[246], and altered polariton–polariton interactions [211, 247] when the spin-opposite
quasi-particles align oppositely in the external field (see [48, 49]). On the other
hand, the degeneracy lifting of spinor condensates due to Zeeman splitting offers
an important tool to identify the matter component of polariton modes, even when
quantisation spoils the typical dispersion, as shown by the works of the author and
co-workers (see [48, 248]).
In fact, the electronic g-factor and diamagnetic coefficient become effective ones
for hybrid light–matter modes in relation to the Hopfield coefficients (the understanding of which was developed through [212, 248–250]), that are the excitonic/photonic
fractions of the polariton mode. In addition, the spin-Meissner effect increasingly
suppresses (elliptically-polarised) superfluidity towards a critical magnetic field until
above the critical field spin degeneracy is lifted and the (circularly-polarised) superfluidity reappears for Zeeman-split spinor-polariton condensates [211]. This was
indicated in the circular-polarisation resolved electroluminescence from polariton
lasers at finite magnetic flux by Schneider and Rahimi-Iman et al. [48], and further
discussed in a later experimental demonstration of the non-equilibrium spin-Meissner
effect with optically-pumped spinor condensates by Fischer et al. [212], which similarly discussed modified polariton–polariton interactions.
Another experiment with spinor condensates (Fig. 3.10) revealed that one of
the two coexisting circularly-polarised condensates quickly approached a secondorder temporal autocorrelation function of G
(2)
(0) = 1 above condensation threshold for 5 T (for the lower-energetic condensate). This improved degree of coherence for one of the condensates corresponded to changes in the populations of the
spin-polarised Zeeman-split sublevels, whereas the counterpart (spin-opposite condensate) still exhibited noticeable intensity fluctuations [214]—indicating modified
polariton–polariton scattering rates and effective uncoupling of the spin-opposite
baths of polaritons. Chernenko et al. could also show with polarisation-sensitive pho-
83
3.3.1 Cavity–Polaritons Exposed to External Fields
When placing strongly-coupled light–matter systems in external electric or magnetic
fields, numerous interesting effects can be studied and the response of polaritons in
the linear and nonlinear regime (i.e. dynamical condensates of polaritons) explored.
A topical introduction into this subject is provided for instance in [243]. To start
with a practical example, one simple effect arising from the exposure to electric
bias in polariton diodes on the coupling regime can for instance allow one to switch
on ultrafast timescales between a polariton lasing and conventional lasing situation
[244], exploiting the quantum-confined Stark effect (QCSE) on the quantum-well
excitons. In the following, a few examples from the domain of magneto-optical and
transient-field studies are briefly summarised.
Polaritons in Magnetic Fields
Exposing polaritons to external magnetic fields (typically in Faraday configuration)
offers an important playground for the study of polariton interactions and degeneracylifted spinor condensates. On the one hand, with increasing magnetic flux, threshold
conditions are modified due to diamagnetic shifts [245], exciton Bohr-radius changes
[246], and altered polariton–polariton interactions [211, 247] when the spin-opposite
quasi-particles align oppositely in the external field (see [48, 49]). On the other
hand, the degeneracy lifting of spinor condensates due to Zeeman splitting offers
an important tool to identify the matter component of polariton modes, even when
quantisation spoils the typical dispersion, as shown by the works of the author and
co-workers (see [48, 248]).
In fact, the electronic g-factor and diamagnetic coefficient become effective ones
for hybrid light–matter modes in relation to the Hopfield coefficients (the understanding of which was developed through [212, 248–250]), that are the excitonic/photonic
fractions of the polariton mode. In addition, the spin-Meissner effect increasingly
suppresses (elliptically-polarised) superfluidity towards a critical magnetic field until
above the critical field spin degeneracy is lifted and the (circularly-polarised) superfluidity reappears for Zeeman-split spinor-polariton condensates [211]. This was
indicated in the circular-polarisation resolved electroluminescence from polariton
lasers at finite magnetic flux by Schneider and Rahimi-Iman et al. [48], and further
discussed in a later experimental demonstration of the non-equilibrium spin-Meissner
effect with optically-pumped spinor condensates by Fischer et al. [212], which similarly discussed modified polariton–polariton interactions.
Another experiment with spinor condensates (Fig. 3.10) revealed that one of
the two coexisting circularly-polarised condensates quickly approached a secondorder temporal autocorrelation function of G
(2)
(0) = 1 above condensation threshold for 5 T (for the lower-energetic condensate). This improved degree of coherence for one of the condensates corresponded to changes in the populations of the
spin-polarised Zeeman-split sublevels, whereas the counterpart (spin-opposite condensate) still exhibited noticeable intensity fluctuations [214]—indicating modified
polariton–polariton scattering rates and effective uncoupling of the spin-opposite
baths of polaritons. Chernenko et al. could also show with polarisation-sensitive pho-