110
4 In the Field of Quantum Technologies
Magnetic field strength (B/B c )
Sound velocities (v
± /v
0 )
0
1
0
1
B c
E ±
μ 0
0
B
Fig. 4.5 Diagram of the magnetic-field dependent superfluidic behaviour of a polariton condensate, freely sketched after [140]. For interacting massive bosons, Bogoliubov modes describe the
energy spectrum of excitations of the Bose condensed quantum fluid (experimentally demonstrated
for polaritons in [141]), with quasi-linear k dependence around the final state’s zero momentum.
According to theoretical considerations by Rubo et al., the long-wavelength sound velocities v ±
for the spinor polariton condensate with E ± in an external magnetic field deviate increasingly for
small fields towards reaching a critical field strength B c [140], at which superfluidity is suppressed.
Correspondingly, the Zeeman splitting at k = 0 (sketched as inset) exhibits a quenching up to B c
in order to keep the chemical potential μ 0 of the condensate constant. This effect has been referred
to as spin analogue of the Meissner effect, which is phenomenologically understood as a redistribution of polaritons between two Zeeman levels, caused by polariton–polariton interactions within
the condensate that compensate the effect of the field B at k = 0. It is represented by an elliptically
polarised superfluid below and circularly polarised one above B c (see [140]). Above B c , the Zeeman
splitting occurs ∝ B eff = B − B c (effective field). The non-equilibrium spin Meissner effect (with
quasi-equilibrium model assuming thermal equilibrium within each spinor population of opposite
polarisation) had been studied both experimentally and theoretically and delivered an additional
tool to distinguish polariton condensation from conventional weak-coupling lasing from polariton
microcavities [142]. This phenomenon motivated the investigation of photon statistics for spinor
condensates [143] and further studies on the superfluidic system’s response perturbed by transient
electromagnetic fields
Weak and Strong Light–Matter Coupling
Weak coupling simply specifies the scenario, in which decay rates exceed the coupling strength and, thus, reversible exchange of energy is inhibited through the loss
of excitation before one cycle of a Rabi oscillation can be completed. In this Purcell
regime, the mere presence of a vacuum field (empty optical mode) is enough for the
resonant emitter to couple to it and to release its energy radiatively. An optical cavity
with no photon inside, but a defined resonance, can indeed also couple strongly with
a single quantum emitter, provided that the coupling strength is high enough and
spatial and spectral resonance are established.
Such strong-coupling experiments in the quantum regime between a single twolevel matter system and a confined state of the vacuum field have been achieved
with quantum dots embedded in high-quality photonic microresonators [154–156],
resulting in a vacuum Rabi splitting of the “anticrossing” (coupled-oscillator) modes.
4 In the Field of Quantum Technologies
Magnetic field strength (B/B c )
Sound velocities (v
± /v
0 )
0
1
0
1
B c
E ±
μ 0
0
B
Fig. 4.5 Diagram of the magnetic-field dependent superfluidic behaviour of a polariton condensate, freely sketched after [140]. For interacting massive bosons, Bogoliubov modes describe the
energy spectrum of excitations of the Bose condensed quantum fluid (experimentally demonstrated
for polaritons in [141]), with quasi-linear k dependence around the final state’s zero momentum.
According to theoretical considerations by Rubo et al., the long-wavelength sound velocities v ±
for the spinor polariton condensate with E ± in an external magnetic field deviate increasingly for
small fields towards reaching a critical field strength B c [140], at which superfluidity is suppressed.
Correspondingly, the Zeeman splitting at k = 0 (sketched as inset) exhibits a quenching up to B c
in order to keep the chemical potential μ 0 of the condensate constant. This effect has been referred
to as spin analogue of the Meissner effect, which is phenomenologically understood as a redistribution of polaritons between two Zeeman levels, caused by polariton–polariton interactions within
the condensate that compensate the effect of the field B at k = 0. It is represented by an elliptically
polarised superfluid below and circularly polarised one above B c (see [140]). Above B c , the Zeeman
splitting occurs ∝ B eff = B − B c (effective field). The non-equilibrium spin Meissner effect (with
quasi-equilibrium model assuming thermal equilibrium within each spinor population of opposite
polarisation) had been studied both experimentally and theoretically and delivered an additional
tool to distinguish polariton condensation from conventional weak-coupling lasing from polariton
microcavities [142]. This phenomenon motivated the investigation of photon statistics for spinor
condensates [143] and further studies on the superfluidic system’s response perturbed by transient
electromagnetic fields
Weak and Strong Light–Matter Coupling
Weak coupling simply specifies the scenario, in which decay rates exceed the coupling strength and, thus, reversible exchange of energy is inhibited through the loss
of excitation before one cycle of a Rabi oscillation can be completed. In this Purcell
regime, the mere presence of a vacuum field (empty optical mode) is enough for the
resonant emitter to couple to it and to release its energy radiatively. An optical cavity
with no photon inside, but a defined resonance, can indeed also couple strongly with
a single quantum emitter, provided that the coupling strength is high enough and
spatial and spectral resonance are established.
Such strong-coupling experiments in the quantum regime between a single twolevel matter system and a confined state of the vacuum field have been achieved
with quantum dots embedded in high-quality photonic microresonators [154–156],
resulting in a vacuum Rabi splitting of the “anticrossing” (coupled-oscillator) modes.