Exciton correlations and input–output relations in non-equilibrium exciton superfluids
Tài liệu tham khảo
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Here we assume Σ(−k→,−iωn)=−Σ(k→,iωn). This is indeed justified under the Markov approximation Eq. (69). the crucial point here is the existence of the large optical characteristic frequency μ. However, in the dissipative exciton superfluids in BLQH [7–9], there is gapless electron–hole excitations instaed of such a large characteristic frequency, so the Markov approximation never holds in this kind of system. This is also the cruucial differences between the dissipations in quantum optical systems and in condesed matter systems.
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For the derivation of this input–output relation. See supplementary material at: http://link.aps.org/supplemental/10.1103/PhysRevLett.103.177401.
In order to be consistent with the conventional notations in the Green functions in condensed matter system [22], compared to the notations used in [14,15], we made a change Gn→iGn,Ga→−iGa.
In the following, we negelct the ̃ on top of the exciton opertaor.
In order to show clearly the different structures of various correlation functions, we choose different values than those used in [14,15].
When drawing Figs. 5–9, for given nVd(k→)=5μeV,γk→/2=1μeV and various E(k→), we use uk→2=E2(k→)+(n̄Vd(k→))22E(k→)+12,vk→2=E2(k→)+(n̄Vd(k→))22E(k→)−12 to determine ρn in Eq. (52) in Fig. 5, ρa in Eq. (54) in Fig. 7 and Eq. (59) in Fig. 10.
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F.D. Sun, et al. (in prepararion).