Abstract
In this chapter, we study macroscopically occupied condensates, which can be observed in semiconductor microcavities under conditions of resonant or non-resonant excitation. In the case of resonant excitation, polariton condensates form due to optical parametric oscillation (OPO) and are strongly non-equilibrium states. In case of non-resonantly incoherently pumped system, the distribution of the higher energy polaritons shows some thermalisation, but the resultant polariton condensates are also far from thermodynamic equilibrium due to finite polariton lifetime. In this chapter, we show that both systems have very similar properties. We reveal the effects of polariton–polariton interactions and non-equilibrium character on the condensate properties. Above threshold condensation into several polariton levels with different energies and k-vectors is observed, which arises from the non-equilibrium character of the polariton system. The specific k-vectors at which condensation is triggered are determined by the local disorder potential landscape. We also investigate the coherence of a single condensed mode by measuring the first (g (1))- and second (g (2))-order correlation functions. We find that the decay times of these functions are \(\sim 100\mbox{ \textendash }150\,\mathrm{ps}\), much longer than the 1.5 ps polariton lifetime. Even though the polariton condensate is a non-equilibrium system, the strong slowing down of the decay allows coherence decay processes characteristic of an equilibrium, interacting BEC to be observed. The signature of the interactions is a Gaussian form for the g (1)-function and a saturation of coherence time with increasing number of particles in the condensate, as observed experimentally and confirmed theoretically. Although predicted, these effects have not been observed for atom BECs.
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- 1.
During the power dependence measurements of τ c , the g (1)(τ) is measured at the delay times τ of \(5 --150\,\)ps and τ c is extracted as .
- 2.
The reservoir consists of all the occupied modes in the system, predominantly exciton states at high wavevector.
- 3.
The factor of 4 is a counting factor which arises when the interaction is between two different modes.
- 4.
Due to the small spatial overlap ( ∼ 10%) between the pump mode and emitting spots, the relevant value of N r may be a factor of 10 smaller than the total reservoir population, thus increasing the estimated coherence time due to interactions with the reservoir by up to a factor of ∼ 3, further decreasing any contribution from thermal reservoir fluctuations.
- 5.
The idler intensity is too weak to permit study of its coherence close to threshold.
- 6.
VCSEL Design, Fabrication, Characterization and Applications (Cambridge University Press, 1999), p. 240.
References
J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J.M.J. Keeling, F.M. Marchetti, M.H. Szymanska, R. Andre, J.L. Staehli, V. Savona, P.B. Littlewood, B. Deveaud, Le Si Dang, Nature 443, 409–414 (2006)
M. Richard, J. Kasprzak, R. Andr, R. Romestain, G. Le Si Dang Malpuech, A. Kavokin, Phys. Rev. B 72, 201301 (2005)
R. Balili, V. Hartwell, D. Snoke, L. Pfei_er, K. West, Science 316, 1007–1010 (2007)
D.N. Krizhanovskii, A.P. Love, D. Sanvitto, D.M. Whittaker, M.S. Skolnick, J.S. Roberts, Phys. Rev. B 75, 233307 (2007)
S. Christopoulos, G. Baldassarri von Hogersthal, A.J. Grundy, P.G. Lagoudakis, A.V. Kavokin, J.J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, N. Grandjean, Phys. Rev. Lett. 98, 126405 (2007).
G. Christmann, R. Butte, E. Feltin, J.F. Carlin, N. Grandjean, Appl. Phys. Lett. 93, 051102 (2008)
H. Deng et al., Phys. Rev. Lett. 97, 146402 (2006)
R.M. Stevenson, V.N. Astratov, M.S. Skolnick, D.M. Whittaker, M. Emam-Ismail, A.I. Tartakovskii, P.G. Savvidis, J.J. Baumberg, J.S. Roberts, Phys. Rev. Lett. 85, 3680 (2000)
M. Wouters, I. Carussoto, Phys. Rev. Lett. 99, 140402 (2007)
D.N. Krizhanovskii, D.M. Whittaker, R.A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Vina, E. Cerda, P. Santos, K. Biermann, R. Hey, M.S. Skolnick, Phys. Rev. Lett. 104, 126402 (2010)
M.H. Szymanska, J. Keeling, P.B. Littlewood, Phys. Rev. Lett. 96, 230602 (2006)
J. Keeling, N.G. Berlo, Phys. Rev. Lett. 100, 250401 (2008)
D. Sarchi, V. Savona, Phys. Rev. B 75, 115326 (2007)
D. Sanvitto, D.N. Krizhanovskii, D.M. Whittaker, S. Ceccarelli, M.S. Skolnick, J.S. Roberts, Phys. Rev. B 73, 241308 (2006)
D.N. Krizhanovskii, D. Sanvitto, A.P. Love, M.S. Skolnick, D.M. Whittaker, J.S. Roberts, Phys. Rev. Lett. 97, 097402 (2006)
A.P.D. Love, D.N. Krizhanovskii, D.M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M.S. Skolnick, P.R. Eastham, R. André, Le Si Dang, Phys. Rev. Lett. 101, 067404 (2008)
K.G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. Andre, B. Le Si Dang Deveaud-Pledran, Nat. Phys. 4, 706 (2008)
D.N. Krizhanovskii, K.G. Lagoudakis, M. Wouters, B. Pietka, R.A. Bradley, K. Guda, D.M. Whittaker, M.S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, Le Si Dang, Phys. Rev. B 80, 045317 (2009)
F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, P. Schwendimann, Phys. Rev. B 56, 7554 (1997)
A.I. Tartakovskii, M. Emam-Ismail, R.M. Stevenson, M.S. Skolnick, V.N. Astratov, D.M. Whittaker, J.J. Baumberg, J.S. Roberts, Phys. Rev. B 62, R2283 (2000)
M. Wouters, I. Carusotto, C. Ciuti, Phys. Rev. B 77, 115340 (2008)
P.R. Eastham, Phys. Rev. B 78, 035319 (2008)
R. Loudon, The Quantum Theory of Light (Oxford University Press, Oxford, 2000)
L.K. Thomsen, H.M. Wiseman, Phys. Rev. A 65, 063607 and reference there in (2002)
M. Kohl, T.W. Hansch, T. Esslinger, Phys. Rev. Lett. 87, 160404, (2001)
A. Ottl, S. Ritter, T. Esslinger, Phys. Rev. Lett. 95, 090404, (2005)
D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, A. Lemaître, J. Bloch, Phys. Rev. Lett. 100, 047401 (2008)
M. Wouters, I. Carusotto, Phys. Rev. A 76, 043807 (2007)
E.A. Cerda-Méndez, D.N. Krizhanovskii, M. Wouters, R. Bradley, K. Biermann, K. Guda, R. Hey, P.V. Santos, D. Sarkar, M.S. Skolnick, Phys. Rev. Lett. 105, 116402 (2010)
M. Gurioli et al., Phys. Rev. Lett. 94, 183901 (2005)
D. Porras, C. Tejedor, Phys. Rev. B 67, 161310 (R) (2003)
D.M. Whittaker, Phys. Rev. B 71, 115301 (2005)
Acknowledgements
The work was supported by the EU ITN Clermont 2 and Clermont 4 projects and EPSRC grants GR/S09838/01, GR/S76076/01. D. Krizhanovskii is an EPSRC Advanced Fellow (grant EP/E051448/1).
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Krizhanovskii, D.N., Whittaker, D.M., Skolnick, M.S., Lagoudakis, K.G., Wouters, M. (2012). Coexisting Polariton Condensates and Their Temporal Coherence in Semiconductor Microcavities. In: Timofeev, V., Sanvitto, D. (eds) Exciton Polaritons in Microcavities. Springer Series in Solid-State Sciences, vol 172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24186-4_5
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