Composite boson signature in the interference pattern of atomic dimer condensates

We predict the existence of high frequency modes in the interference pattern of two condensates made of fermionic-atom dimers. These modes, which result from fermion exchanges between condensates, constitute a striking signature of the dimer composite nature. From the 2-coboson spatial correlation function, that we derive analytically, and the Shiva diagrams that visualize many-body effects specific to composite bosons, we identify the physical origin of these high frequency modes and determine the conditions to see them experimentally by using bound fermionic-atom pairs trapped on optical lattice sites. The dimer granularity which appears in these modes comes from Pauli blocking that prevents two dimers to be located at the same lattice site.Comment: 10+7 pp, 3 figures. v2: version accepted for publication in New J. Phy

Way to observe the implausible "trion-polariton"

Using the composite boson (coboson) many-body formalism, we determine under which conditions "trion-polariton" can exist. Dipolar attraction can bind an exciton and an electron into a trion having an energy well separated from the exciton energy. Yet, the existence of long-lived "trion-polariton" is a priori implausible not only because the photon-trion coupling, which scales as the inverse of the sample volume, is vanishingly small, but mostly because this coupling is intrinsically "weak". Here, we show that a moderately dense Fermi sea renders its observation possible: on the pro side, the Fermi sea overcomes the weak coupling by pinning the photon to its momentum through Pauli blocking, it also overcomes the dramatically poor photon-trion coupling by providing a volume-linear trion subspace to which the photon is coherently coupled. On the con side, the Fermi sea broadens the photon-trion resonance due to the fermionic nature of trions and electrons, it also weakens the trion binding by blocking electronic states relevant for trion formation. As a result, the proper way to observe this novel polariton is to use doped semiconductor having long-lived electronic states, highly-bound trion and Fermi energy as large as a fraction of the trion binding energy.Comment: 6 pages, 3 figure

Cross-over from trion-hole to exciton-polaron in n-doped semiconductor quantum wells

We present a theoretical study of photo-absorption in n-doped two-dimensional (2D) and quasi-2D semiconductors that takes into account the interaction of the photocreated exciton with Fermi-sea (FS) electrons through (i) Pauli blocking, (ii) Coulomb screening, and (iii) excitation of FS electron-hole pairs---that we here restrict to one. The system we tackle is thus made of one exciton plus zero or one FS electron-hole pair. At low doping, the system ground state is predominantly made of a "trion-hole"---a trion (two opposite-spin electrons plus a valence hole) weakly bound to a FS hole---with a small exciton component. As the trion is poorly coupled to photon, the intensity of the lowest absorption peak is weak; it increases with doping, thanks to the growing exciton component, due to a larger coupling between 2-particle and 4-particle states. Under a further doping increase, the trion-hole complex is less bound because of Pauli blocking by FS electrons, and its energy increases. The lower peak then becomes predominantly due to an exciton dressed by FS electron-hole pairs, that is, an exciton-polaron. As a result, the absorption spectra of $n$-doped semiconductor quantum wells show two prominent peaks, the nature of the lowest peak turning from trion-hole to exciton-polaron under a doping increase. Our work also nails down the physical mechanism behind the increase with doping of the energy separation between the trion-hole peak and the exciton-polaron peak, even before the anti-crossing, as experimentally observed.Comment: 20 pages, 10 figure

Exciton ground-state energy with full hole warping structure

Most semiconductors, in particular III-V compounds, have a complex valence band structure near the band edge, due to degeneracy at the zone center. One peculiar feature is the warping of the electronic dispersion relations, which are not isotropic even in the vicinity of the band edge. When the exciton, all important for the semiconductor optical properties, is considered, this problem is usually handled by using some kind of angular averaging procedure, that would restore the isotropy of the hole effective dispersion relations. In the present paper, we consider the problem of the exciton ground-state energy for semiconductors with zinc-blende crystal structure, and we solve it exactly by a numerical treatment, taking fully into account the warping of the valence band. In the resulting four-dimensional problem, we first show exactly that the exciton ground state is fourfold degenerate. We then explore the ground-state energy across the full range of allowed Luttinger parameters. We find that the correction due to warping may in principle be quite large. However, for the semiconductors with available data for the band structure we have considered, the correction turns out to be in the $10\% - 15\%$ range.Comment: 10 pages, 1 figur

A fresh view on Frenkel excitons: Electron-hole pair exchange and many-body formalism

We here present a fresh approach to Frenkel excitons in cubic semiconductor crystals, with a special focus on the spin and spatial degeneracies of the electronic states. This approach uses a second quantization formulation of the problem in terms of creation operators for electronic states on all lattice sites -- their creation operators being true fermion operators in the tight-binding limit valid for semiconductors hosting Frenkel excitons. This operator formalism avoids using cumbersome ($6N_s$ x $6N_s$) Slater determinants -- 2 for spin, 3 for spatial degeneracy and $N_s$ for the number of lattice sites -- to represent state wave functions out of which the Frenkel exciton eigenstates are derived. A deep understanding of the tricky Coulomb physics that takes place in the Frenkel exciton problem, is a prerequisite for possibly diagonalizing this very large matrix analytically. This is done in three steps: (i) the first diagonalization, with respect to lattice sites, follows from transforming excitations on the $N_s$ lattice sites $\mathbf{R}_\ell$ into $N_s$ exciton waves $\mathbf{K}_n$, by using appropriate phase prefactors; (ii) the second diagonalization, with respect to spin, follows from the introduction of spin-singlet and spin-triplet electron-hole pair states, through the commonly missed sign change when transforming electron-absence operators into hole operators; (iii) the third diagonalization, with respect to threefold spatial degeneracy, leads to the splitting of the exciton level into one longitudinal and two transverse modes, that result from the singular interlevel Coulomb scattering in the small $\mathbf{K}_n$ limit.Comment: 80 pages, 21 figure