Shiue-Yuan Shiau

Electronic structure and absorption spectrum of biexciton obtained by using exciton basis

Abstract We approach the biexciton Schrodinger equation not through the free-carrier basis as usually done, but through the free-exciton basis, exciton–exciton interactions being treated according to the recently developed composite boson many-body formalism which allows an exact handling of carrier exchange between excitons, as induced by the Pauli exclusion principle. We numerically solve the resulting biexciton Schrodinger equation with the exciton levels restricted to the ground state and we derive the biexciton ground state as well as the bound and unbound excited states as a function of hole-to-electron mass ratio. The biexciton ground-state energy we find, agrees reasonably well with variational results. Next, we use the obtained biexciton wave functions to calculate optical absorption in the presence of a dilute exciton gas in quantum well. We find an asymmetric peak with a characteristic low-energy tail, identified with the biexciton ground state, and a set of Lorentzian-like peaks associated with biexciton unbound states, i.e., exciton–exciton scattering states. Last, we propose a pump–probe experiment to probe the momentum distribution of the exciton condensate.

Effect of Pauli blocking on coherent states of composite bosons

The quantum nature of elementary bosons can be completely erased by using coherent states known as Glauber states. Here, we consider composite bosons (cobosons) made of two fermions and look for the possibility to erase the bosonic quantum nature of the field and the fermionic quantum nature of its constituents, when the distribution of the coboson Schmidt decomposition is either flat like Frenkel excitons, or localized like Wannier excitons. We show that for Frenkel-like cobosons, complete erasure of the field quantum nature is possible up to a density which corresponds to a sizable fraction of the number of fermion-pair states making the coboson at hand. At higher density, the Pauli exclusion principle between fermionic constituents shows up dramatically. It induces: (i) the decrease of number-operator eigenvalues down to 1 and the increase of the number-state second-order correlation function up to 2; (ii) the disappearance of the usual sharp peak in the coherent-state distribution and the increase of the coherent-state second-order correlation function up to 2. It also is possible to construct number states and coherent states for Wannier-like cobosons, but their forms are far more complex. Finally, we show that Pauli blocking makes the coboson coherent states qualitatively different from the Andersons ansatz.

Scattering amplitudes for dark and bright excitons

Using the composite boson many-body formalism that takes single-exciton states rather than free carrier states as a basis, we derive the integral equation fulfilled by the exciton-exciton effective scattering from which the role of fermion exchanges can be unraveled. For excitons made of -spin electrons and -spin holes, as in GaAs heterostructures, one major result is that most spin configurations lead to brightness-conserving scatterings with equal amplitude Δ, despite differences in the carrier exchanges involved. A brightness-changing channel also exists when two opposite-spin excitons scatter: dark excitons can end either in the same dark states with an amplitude , or in opposite-spin bright states , with a different amplitude , the number of carrier exchanges involved in these scatterings being even or odd, respectively. Another major result is that these amplitudes are linked by a striking relation, , which has decisive consequence on exciton Bose-Einstein condensation. By using Born values, we show that the exciton condensate can be optically observed through a bright part when excitons have large dipole only, that is, when the electrons and holes are in two well-separated layers, as in current experiments.

Cancellation of the N -composite-boson correlation energy under a BCS-like potential: A dimensionality-dependent effect

We use Richardson-Gaudin exact equations to derive the ground-state energy of N composite bosons (cobosons) interacting via a potential which acts between fermion pairs having zero centerof-mass momentum, that is, a potential similar to the reduced BCS potential used in conventional superconductivity. Through a density expansion, we show that while, for 2D systems, the Ncoboson correlation energy undergoes a surprising cancellation which leaves the interaction part with a N(N − 1) dependence only, such a cancellation does not exist in 1D, 3D, and 4D systems — which corresponds to 2D parabolic traps — nor when the cobosons interact via a similar short-range potential but between pairs having an arbitrary center-of-mass momentum. This shows that the previously-found cancellation which exists for the Cooper-pair correlation energy results not only from the very peculiar form of the reduced BCS potential, but also from a quite mysterious dimensionality effect, the density of states for Cooper pairs feeling the BCS potential being essentially constant, as for 2D systems.

Correlated-pair approach to composite-boson scattering lengths

We derive the scattering length of composite bosons (cobosons) within the framework of the composite-boson many-body formalism that uses correlated-pair states as a basis instead of free-fermion states. The integral equation constructed from this physically relevant basis makes transparent the role of fermion exchange in the coboson-coboson effective scattering. Three potentials used for Cooper pairs, fermionic-atom dimers, and semiconductor excitons are considered. While the s-wave scattering length for the BCS-like potential is just equal to its Born value, the other two are substantially smaller. For fermionic-atom dimers and semiconductor excitons, our results, calculated within a restricted correlated-pair basis, are in good agreement with those obtained from procedures numerically more demanding. We also propose model coboson-coboson scatterings that are separable and thus easily workable and that produce scattering lengths which match quantitatively well with the numerically obtained values for all fermion mass ratios. These separable model scatterings can facilitate future works on many-body effects in coboson gases.

Coboson many-body formalism for cold-atom dimers with attraction between different fermion species only

Unlike the Coulomb potential that acts between all semiconductor carriers, the potential commonly used for BCS superconductors and cold-atom gases acts between different fermion species only, these species differing by their spin or hyperfine index. The coboson formalism we develop here evidences that such composite bosons interact through fermion exchange only, thus rendering the structure of the Shiva diagrams that visualize their many-body effects far simpler. A separable potential is used to obtain analytical results for the N-coboson normalization factor and the N-coboson ground-state energy within the Born approximation, in terms of the Born dimer-dimer scattering length. This formalism opens the route toward approaching complex many-body effects, such as Bose-Einstein condensation, through a different perspective.

Partition function of N composite bosons

Abstract The partition function of composite bosons (“cobosons” for short) is calculated in the canonical ensemble, with the Pauli exclusion principle between their fermionic components included in an exact way through the finite temperature many-body formalism for composite quantum particles we recently developed. To physically understand the very compact result we obtain, we first present a diagrammatic approach to the partition function of N elementary bosons. We then show how to extend this approach to cobosons with Pauli blocking and interaction between their fermions. These diagrams provide deep insights on the structure of a coboson condensate, paving the way toward the determination of the critical parameters for their quantum condensation.