Energy spectra of fractional quantum Hall systems in the presence of a valence hole

The energy spectrum of a two-dimensional electron gas (2DEG) in the fractional quantum Hall regime interacting with an optically injected valence band hole is studied as a function of the filling factor $\nu$ and the separation $d$ between the electron and hole layers. The response of the 2DEG to the hole changes abruptly at $d$ of the order of the magnetic length $\lambda$. At $d<\lambda$, the hole binds electrons to form neutral ($X$) or charged ($X^{-}$) excitons, and the photoluminescence (PL) spectrum probes the lifetimes and binding energies of these states rather than the original correlations of the 2DEG. The dressed exciton'' picture (in which the interaction between an exciton and the 2DEG was proposed to merely enhance the exciton mass) is questioned. Instead, the low energy states are explained in terms of Laughlin correlations between the constituent fermions (electrons and $X^-$'s) and the formation of two-component incompressible fluid states in the electron--hole plasma. At $d>2\lambda$, the hole binds up to two Laughlin quasielectrons (QE) of the 2DEG to form fractionally charged excitons $h$QE$_n$. The previously found anyon exciton’’ $h$QE${}_3$ is shown to be unstable at any value of $d$. The critical dependence of the stability of different $h$QE${}_n$ complexes on the presence of QE’s in the 2DEG leads to the observed discontinuity of the PL spectrum at $\nu =\frac{1}{3}$ or $\frac{2}{3}$.