Biexciton Wave Functions Research Articles

Accurate modeling of electron-hole binding in CuCl. II. Biexciton wavefunction

We present an approach to calculate the biexciton ground state including the electron-longitudinal-optical-phonon coupling and an accurate variational function to describe the Coulomb correlations in the biexciton. We apply this method to the long-standing problem of biexciton binding energy in CuCl and obtain a binding energy of 32.6 meV. We also discuss the effect of electron-hole ($e$-h) exchange interaction on the biexciton binding energy. Including correction due to $e$-h exchange, the theoretical binding energy is 28.8 meV, in good agreement with the experimental value of 32 meV. Details of the biexciton wavefunction are presented in the form of correlation functions with respect to two-particle separations, which show how the particles in the biexciton are distributed.

Cavity effect on a biexciton in a CuCl microcavity

We studied the population and coherence dynamics of a biexciton in a planar CuCl microcavity. We developed a time-resolved two-photon polarization spectroscopy technique, by which we extracted the population dynamics of the biexciton even when the biexciton was spectrally overlapped with the lower cavity polariton. The observed lifetime of the cavity biexciton in the weak-coupling regime was much shorter than that of a bare CuCl thin film without a cavity, which directly demonstrates cavity enhancement of the radiative decay rate of the biexciton. The cavity enhancement originates from the hybridization of the unbound two-cavity-polariton state to the biexciton wave function by the biexciton-cavity coupling. By comparing the population and coherence decay curves of the biexciton, we found that the coherence of the cavity biexciton was limited by the radiative population decay.

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

We approach the biexciton Schrödinger 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 Schrödinger 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.

Optical recombination of biexcitons in semiconductors

We calculate the photoluminescence spectrum and lifetime of a biexciton in a semiconductor using Fermi's golden rule. Our biexciton wavefunction is obtained using a Quantum Monte Carlo calculation. We consider a recombination process where one of the excitons within the biexciton annihilates. For hole masses greater than or equal to the electron mass, we find that the surviving exciton is most likely to populate the ground state. We also investigate how the confinement of excitons in a quantum dot would modify the lifetime in the limit of a large quantum dot where confinement principally affects the centre of mass wavefunction. The lifetimes we obtain are in reasonable agreement with experimental values. Our calculation can be used as a benchmark for comparison with approximate methods.

Dissecting biexciton wave functions of self-assembled quantum dots by double-quantum-coherence optical spectroscopy

Biexcitons feature prominently in various scenarios for utilization of quantum dots (QDs) for enhancing the efficiencies of solar cells, and for the generation of entangled photon pairs in single QD sources. Two-dimensional double quantum coherence (2D-DQC) nonlinear optical spectra provide novel spectroscopic signatures of such states beyond global intensity and lifetime characteristics which are available by more conventional techniques. We report the simulation of a prototype 2D-DQC optical experiment of a self-assembled InAs/GaAs dot. The simulations consider the QD in different charged states and are based on a state-of-the-art atomistic many-body pseudopotential method for the calculation of the electronic structure and transition dipole matrix elements. Comparison of the spectra of negatively charged, neutral, and positively charged QD reveals optical signatures of their electronic excitations. This technique directly accesses the biexciton ($XX$) energies as well as the projections of their wave functions on the single-exciton manifold. These signals also provide a unique tool for probing the charged state of the QD and thus the occupation of the quantum state. Signatures of Pauli blockade of the creation of certain single and two excitons due to charges on the particles are observed. For all quantum states of the QD, the spectra reveal a strong multiconfiguration character of the biexciton wave functions. Peak intensities can be explained by interference of the contributing Liouville space pathways.

Biexciton oscillator strength

Our goal is to provide a physical understanding of the elementary coupling between photon and biexciton and to derive the physical characteristics of the biexciton oscillator strength, following the procedure we used for trion. Instead of the more standard two-photon absorption, this work concentrates on molecular biexciton created by photon absorption in an exciton gas. We first determine the appropriate set of coordinates in real and momentum spaces to describe one biexciton as two interacting excitons. We then turn to second quantization and introduce the "Fourier transform in the exciton sense" of the biexciton wave function which is the relevant quantity for oscillator strength. We find that, like for trion, the oscillator strength for the formation of one biexciton out of one photon plus a \emph{single} exciton is extremely small: it is one biexciton volume divided by one sample volume smaller than the exciton oscillator strength. However, due to their quantum nature, trion and biexciton have absorption lines which behave quite differently. Electrons and trions are fermionic particles impossible to pile up all at the same energy. This would make the weak trion line spread with electron density, the peak structure only coming from singular many-body effects. By contrast, the bosonic nature of exciton and biexciton makes the biexciton peak mainly rise with exciton density, this rise being simply linear if we forget many-body effects between the photocreated exciton and the excitons present in the sample.

Impacts of structural asymmetry on the magnetic response of excitons and biexcitons in single self-assembled In(Ga)As quantum rings

The diamagnetic shifts of neutral excitons and biexcitons confined in single self-assembled In(Ga)As/GaAs quantum rings are investigated. Unlike quantum dots, quantum rings reveal a considerably large biexciton diamagnetic shift, about two times larger than that of single excitons. Based on model calculations, we found that the inherent structural asymmetry and imperfection, combined with the interparticle Coulomb interactions, is the fundamental cause of the more extended biexciton wave function in the quantum rings. The exciton wave function tends to be localized in one of the potential valleys induced by structural imperfections of the quantum ring due to the strong localization of hole and the electron-hole Coulomb attraction, resembling the behavior in single dots. Our results suggest that the phase coherence of neutral excitons in quantum rings will be smeared out by such wave function localizations.

Near-field wave-function spectroscopy of excitons and biexcitons

Improvements in spatial resolution of near-field spectroscopy have recently allowed for wave-function imaging of single excitons and biexcitons localized in semiconductor quantum wells. Surprisingly, the apparent extent of the biexciton wave function was found to be considerably reduced compared to a single exciton. We analyze theoretically the image contrast in general near-field wave-function mapping, taking into account the finite spatial resolution of the experiment. In particular, we show that due to the nonlinear nature of biexciton spectroscopy, a smaller biexciton image size is expected even if the spatial resolution is insufficient to resolve the wave functions.

Biexcitons inInxGa1−xAs/GaAsquantum wells subject to high magnetic fields

The biexciton states in ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum wells of varying widths have been studied by spectrally resolved and time-integrated four-wave mixing in magnetic fields up to $B=8 \mathrm{T}.$ Surprisingly, the biexciton binding energy is found to be independent of the field strength. These results challenge theoretical descriptions of the biexciton wave function. Furthermore, the polarization selection rules for the biexcitonic contributions to the four-wave mixing are left unchanged by B, in contrast to the excitonic signal.

Biexciton Wavefunction in Bulk CuCl Probed by Inverse Polariton Series

Biexciton Wavefunction in Bulk CuCl Probed by Inverse Polariton Series

Weak localization of biexcitons in quantum wells

Recent experimental studies have demonstrated localization of biexcitons in quantum wells, providing even optical gain up to elevated temperatures. We present a theoretical treatment of exciton and biexciton states in the weak localization limit using a center-of-mass separation ansatz. An advanced approach based on an extensive numerical solution is compared with a more simple model for the quantum well biexciton wave function. Our explicit results, derived for parameters of the ternary quantum well material (Zn,Cd)Se, yield that the localization of the biexciton is---despite its larger spatial extension---stronger than that of the single exciton state.

Biexciton-biexciton interaction in semiconductors

For a semiconductor with single isotropic conduction and valence bands, the effective biexciton-biexciton interaction is derived starting from the second-quantization representation for the Hamiltonian of the system of interacting excitons and for the biexciton wave function within the framework of the adiabatic approximation. The interaction is found to be an average of the sum of effective interactions between excitons forming interacting biexcitons over the envelope functions of these biexcitons. Depending on the momentum transfer and on the difference between the momenta of interacting biexcitons, the interaction admits an analytical study when the first vanishes. In this case, the interaction has in the r space the form of a function of the interbiexciton distance consisting of a strong repulsive and a weak attractive part. At low temperatures the function describes main features in the behavior of the interaction among biexcitons, in which repulsion predominates over attraction. It is shown that while biexcitons remain stable quasiparticles they weakly attract each other for any value of the distance. A quantitative analysis of obtained results for the CuCl crystal shows that the biexciton system in this model substance is a weakly nonideal Bose gas with positive scattering length ${\mathrm{a}}_{\mathrm{s}}$\ensuremath{\simeq}${3\mathrm{a}}_{\mathrm{x}}$, which closely approaches the ideal one at excitation densities n\ensuremath{\leqslant}${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.

Strongly confined semiconductor quantum dots: Pair excitations and optical properties

This paper reviews a microscopic model of basic electron-hole pair excitation processes in strongly confined semiconductor quantum dots (QD) and their influence on the optical QD properties. The effects of valence band mixing, Coulomb interaction, and surface polarization are taken into account. The exciton and biexciton wave functions and energies are obtained using a numerical diagonalization method. The computed optical spectra, such as absorption, gain, pump-probe, and two-photon absorption, agree well with experiments.

Radiative lifetime of CuCl biexcitons in wide wave-number region

The biexciton radiative lifetime in CuCl is measured in a wide wave-number region ( k = 0.89 to 7.6 × 10 6cm −1) via non-degenerate two-photon resonant excitation of biexcitons. The radiative lifetime increases with wave number by 1.6 times, possibly indicating the spread of the biexciton wave function or the instability of bipolaritons.