1. Kenji Kamide* and Tetsuo Ogawa
Advanced Photons and Science Evolution 2010 (APSE2010)
June 14-18, 2010, Osaka Japan
Laser-like behaviors in a polariton condensate: the thermodynamic regime
Kenji Kamide* and Tetsuo Ogawa
Department of Physics, Osaka University, Toyonaka, Osaka, Japan *
[1] K. Kamide and T. Ogawa, ArXiv:
[2] K. Kamide and T. Ogawa, J. Phys.: Conf. Ser. 210, (2010).
This work is supported by and
Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST).

2. Observation of the BEC 1.67Pth 1.14Pth 0.55Pth P=Pth
[3] J. Kasprzak et al, Nature 443, 409 (2006).
condition: non-resonant pumping + 16 CdTe Q-Wells
detection: angle resolved emission spectrum (Far-field)
strong light-matter coupling
Bose narrowing in the momentum and energy space
0.55Pth
1.14Pth
Emission Spectrum
Angular distribution
1.67Pth
Q-Wells
photon
Pumping Laser
Excitons
Bragg Mirror
P=Pth
pump power
energy
Ground state occupancy
linewidth
momentum
Polariton BEC is similar to Bose-Einstein Condensation of atomic gases in a thermal equilibrium!

3. Thermodynamic BEC Polariton Laser Conventional Laser
What is the relationship among three type of the coherent light sources? :
Thermodynamic BEC
Polariton Laser
Conventional Laser
Crossover between Polariton Laser and Polariton BEC was investigated theoretically using the Bosonic description in:
[6] A. Imamoglu et al., Phys. Rev. A 53, 4250 (1996).
Crossover behavior among them was already reported in :
[5] H. Deng et al., PNAS 100, (2003).
The detuning effects are also seen.

4. Our recent results by a variational theory
[1] K. Kamide and T. Ogawa, ArXiv:
[2] K. Kamide and T. Ogawa, J. Phys.: Conf. Ser.
210, (2010).

5. Phase Diagram Conventional Laser (threshold-ful ) Polariton laser
results for 2D systems (variational calculation)
Phase Diagram
Conventional Laser
(threshold-ful )
Polariton laser
(threshold-less)
High density
Low density
Different ground states are expected to occur depending on the detuning and the pump power (total excitation density ntot).

6. Laser-like Behaviors: the detuning effect
results for 2D systems (variational calculation)
Laser-like Behaviors: the detuning effect
Dependencies of the photon and carrier densities on the excitation density change from thresholdless-type to thresholdful-type as the detuning increases.
threshold-less
threshold-ful
=RS
=RS
Photon density
Carrier density
In the strong coupling regime with small detuning, nph and ncar increase with pumping power (ntot) altogether. Thus, the threshold of lasing is unclear.
In the weak coupling regime with large detuning, the threshold is clear.

7. Momentum Distribution of Carriers
results for 2D systems (variational calculation)
Momentum Distribution of Carriers
The laser-like behaviors depend on whether or not the population inversion exists (fe(k)>0.5 or not) near the threshold density.
threshold-less
threshold-ful
fe(k)
RS=
RS values near the threshold.
There is “No population inversion”.
There is “population inversion”.

8. Conclusions
We determined the coherent ground states of microcavity polaritons by using interpolating variational theory, assuming the thermal equilibrium.
It is shown that, even in an equilibrium situation, the photonic fraction and inversion density of carriers have characteristic dependencies on the pumping power.
Lasing-like behaviors are found: the laser-like threshold in the input-output curve together with the saturation of the inversion density above the threshold are found, although their physical origin is quite different from the conventional laser in a kinetic regime.
Laser-like behaviors depend on detuning parameters; for large detuning, the threshold is clearly defined where there exists population inversion; for small detuning, the threshold is unclear where there is no population inversion.

9. First report of the Stimulated Emission ・・・ [4] Le Si Dang et al
First report of the Stimulated Emission ・・・ [4] Le Si Dang et al., Phys. Rev. Lett. 81, 3920 (1998).
condition: non-resonant pumping + 16 CdTe Q-Wells
detection: angle integrated intensity
Lower Polariton
Upper Polariton
Absorption Spectrum
Emission Spectrum
Excitation density
(Pumping Power)
Cavity mode A B
Polariton Laser
Conventional
Laser
Polariton BEC
density
See also [5] H. Deng et al., PNAS 100, (2003).