# Optical Absorption in Incoherent and Coherent States of a Quantum Hall System

### Abstract

In connection with recent studies of extremely long-living spin-cyclotron excitations (actually magneto-excitons) in a quantum Hall electron gas, we discuss contribution to the light-absorption related to the presence of a magneto-exciton ensemble in this purely electronic system. Since the weakly interacting excitations have to obey the Bose-Einstein statistics, one can expect appearance of a coherent state in the ensemble. A comparative analysis of both incoherent and coherent cases is done. Conditions for a phase transition from the incoherent state to the coherent one are discussed.

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### References

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This feature is due to the symmetry of the purely electronic system considered. Formally, as applied to the case of a common two-particle magnetoexciton [7], this symmetry would correspond to electron and hole masses satisfying the me = ?mh equivalence and thus results in vanishing of the ? E 2 term in the magnetoexciton energy.

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Norm RN was first calculated for the q = 0 case in the work of A.B. Dzyubenko and Yu.E. Lozovik, J. Phys. A, 24, 415 (1991). The calculation was based on certain commutation rules for Q†0-exciton operators. It can also be performed in a similar way based on commutation rules for the Q†q operators at arbitrary q (see, e.g., Ref. [8])

but results in the same formula.

Eq. (22) corresponds to effect of absorption amplified by factor N (and thereby also an amplified radiation in the resonance-reflection optical measurements) typical for systems of coherent quantum oscilators [cf. spontaneous radiation by a dense molecular gas: R.H. Dicke, Phys. Rev. 93, 99 (1953)].

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