Exciton-biexciton System Research Articles

Exciton absorption properties of coherently coupled exciton-biexciton systems in quantum dots

Exciton-biexciton coherent coupling effects are examined in semiconductor quantum dots. The exciton absorption spectrum is measured with the microphotoluminescence excitation technique in a single InGaAs quantum dot. The spectrum changes from a Lorenztian-type line shape to an unusual dip-shaped line shape with increasing excitation intensities in a higher exciton state where there is a large oscillator strength between the exciton and biexciton states. The intensity dependence of the dip energy width clearly indicates that coherent Rabi oscillation occurs between the exciton and biexciton states. The absorption properties with excitation light of different polarizations show that the dip-shaped spectra only appear when there is a large biexciton state population with linear polarization. A theoretical analysis undertaken with the density matrix method agrees well with experimental results. This agreement reveals that exciton-biexciton coherent interactions lead to unusual absorption spectra and contribute crucially to the optical properties of quantum dots. The exciton-biexciton coherent effects provide a scheme for controlling four distinguishable states, which can be applied to a demonstration of quantum gate operations.

Biexciton formation induced by bright-dark exciton transitions in a diluted magnetic semiconductor asymmetric quantum well

We have investigated excitonic states in a (Cd,Mg)Te/CdTe/(Cd,Mn)Te asymmetric quantum well, during the photoluminescence decay processes. The intensity ratio of biexciton to exciton showed almost a linear dependence. The biexciton luminescence showed a longer decay time when compared with that of the exciton. The rate equations based on our model taking account of the dark exciton level ( J = ± 2 ) were used to analyze this anomalous exciton–biexciton system. Our analysis leads to a conclusion that the new channel from a dark exciton has an essential role when biexcitons are created in II–VI diluted magnetic semiconductor quantum wells.

Effects of exciton–biexciton coherent coupling on exciton absorption in quantum dots

We report unusual excitonic absorption spectra with dip-shaped structures caused by exciton–biexciton coherent interactions in quantum dots. The exciton absorption spectrum is measured with the micro-photoluminescence excitation technique in a single InGaAs quantum dot. The spectrum changes from Lorenztian-shaped to dip-shaped with increasing excitation intensity. A theoretical analysis with the density matrix method reveals that exciton–biexciton coherent interactions create dressed states in the exciton–biexciton system and lead to the unusual absorption spectra.

Renormalization Effects in the Spectrum of a Coherently Driven Exciton–Biexciton System

Starting from the total Hamiltonian of an excited exciton–biexciton system, nonresonant renormalizations in the electronic spectrum of a coherently driven direct semiconductor are considered. Stringent group-theoretical inclusion of the particle spin in the Hamiltonian allows one to account for the dependence of different renormalization effects on polarizations of the incident laser fields. On the example of circularly polarized driving and probing pulses it is shown that the kind of observed renormalization is defined by the pump-and-probe polarization geometry. Thus, the exciton optical Stark effect must appear in the case of co-circular pump-and-probe, whereas a mixing of the polariton and biexciton spectra is possible only in the case of counter-circular pump-and-probe. The polariton--biexciton dispersion renormalization may manifest itself as synchronous splittings of the exciton--polariton and biexciton spectra under resonant pumping at a frequency of the polariton--biexciton transition, or in their shifts in opposite directions under near-resonant pumping. The mechanisms of both kinds of renormalization effects are analyzed, and the dependence of their characteristics on the pump parameters and microscopic parameters of the exciton–biexciton–photon system is established. An evaluation of the characteristics shows that the effect of polariton–biexciton dispersion renormalization dominates in the spectra of semiconductors with stable biexciton formation. Results of the theoretical study provide an adequate explanation of available experimental data.

Polarization dependence of excitonic and biexcitonic contributions to FWM signals

The time-averaged polarization angles of excitonic and biexcitonic four-wave-mixing signals are investigated in spectrally resolved measurements for different angles between the linear excitation polarizations, delay times and pulse energies. For an angle close to 90° between the two incident polarizations the signal emitted at the spectral position of the excitonic resonance clearly shows different polarization angles as the delay is changed from negative to positive. Additionally, the polarization angles of the signals exhibit oscillations which are differently pronounced for negative and positive delay times. The experimental results are compared with numerical calculations based on a phenomenologically extended five-level model of the exciton-biexciton system.

Optical coherent control and phase shift of excitonic and biexcitonic four-wave-mixing polarization

The optical coherent control of the exciton–biexciton system is studied in four-wave-mixing (FWM) experiments on a ZnSe single-quantum well. Coherent control is achieved by applying a pair of phase-locked laser pulses which produce an FWM signal in combination with an additional third pulse. Oscillations as a function of the interpulse delay time are observed in the FWM signal at the energetic position of the exciton and biexciton resonance, respectively. A phase shift between these oscillations is found for certain orders of arrival of the excitation pulses at the sample. This clearly demonstrates that the coherent control acts in different ways: if the phase shift is observed the FWM polarization is coherently controlled. Otherwise, the coherent control just involves the polarization induced by the two phase-locked pulses.

Quantum-Statistics Behavior of the Exciton-Biexciton System In GaAs/AlAs Type-II Superlattices

We have investigated the quantum-statistics behavior of the exciton-biexciton system from the photoluminescence properties in (GaAs) m /(AlAs) m type-II superlattices with m = 12 and 13 monolayers, where the lowest-energy type-II exciton consists of the n = 1 X electron of AlAs and n = 1 o heavy hole of GaAs. The long exciton lifetime of the order of w s due to the indirect transition nature enables us to obtain precisely the density relation between the exciton and biexciton from the line-shape analysis of time-resolved photoluminescence spectra. In a relatively low exciton-density region, the biexciton density obeys a well-known square law. At an exciton density around 1 2 10 10 cm m 2 , the biexciton density suddenly increases with a threshold-like nature. This behavior, which is realized at a bath temperature up to 8 K under an excitation power of the order of 100 mW/cm 2 , results from the characteristics of Bose-Einstein statistics of the exciton-biexciton system.

Boson characteristics of the exciton–biexciton system in a GaAs/AlAs type-II superlattice

We report on the appearance of Bose–Einstein statistics of the exciton–biexciton system in a (GaAs) 12/(AlAs) 12 type-II superlattice. The density relation of the exciton and biexciton is estimated from time-resolved photoluminescence spectra at various excitation powers and bath temperatures. The long lifetime of the type-II exciton, e.g., 2 μs at 5 K, enables us to obtain the precise information of the density relation. In a relatively low exciton-density region, the biexciton density obeys a well-known square law. At an exciton density around 1×10 10 cm −2, the biexciton density suddenly increases with a threshold-like nature. This behavior, which is realized at temperatures up to 8 K, can be understood from Bose–Einstein statistics.

Evidence for quantum statistics of the exciton-biexciton system in a GaAs/AlAs type-II superlattice

We have investigated the decay processes of the photoluminescence from excitons and biexcitons in a $(\mathrm{GaAs}{)}_{12}/(\mathrm{AlAs}{)}_{12}$ type-II superlattice, where electrons and holes are confined in the X-valley potential of the AlAs layer and in the \ensuremath{\Gamma}-valley potential of the GaAs layer, respectively. The long lifetime of the type-II exciton, e.g., $\ensuremath{\sim}2\ensuremath{\mu}\mathrm{s}$ at a bath temperature of 5 K, enables us to obtain the precise information of the exciton-biexciton density relation estimated from the line-shape analysis of time-resolved photoluminescence spectra. In a relatively low-exciton-density region (a time region later than $\ensuremath{\sim}1\ensuremath{\mu}\mathrm{s}),$ the biexciton density obeys a well-known square law. At an exciton density around $1\ifmmode\times\else\texttimes\fi{}{10}^{10}{\mathrm{cm}}^{\ensuremath{-}2},$ the biexciton density suddenly increases with a thresholdlike nature. This behavior can be understood from Bose-Einstein statistics of the exciton-biexciton system. We have examined the quantum-statistics characteristics of the exciton-biexciton system at various excitation powers and bath temperatures. It is found that the quantum-statistics regime is realized at the bath temperature up to 8 K under a low excitation power of the order of 100 ${\mathrm{m}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ and that it continues in a long time range of the order of submicroseconds.

Influence of exciton-exciton interactions on frequency-mixing signals in a stable exciton-biexciton system

Transient nondegenerate four-wave mixing was performed in the femtosecond domain on a stable exciton-biexciton system. For excitation with two spectrally narrow pulses of frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ that have no spectral overlap with each other, only a frequency-mixing signal at $2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ was observed. The polarization dependence of the frequency-mixing signal intensity changed dramatically with increasing frequency difference between the incident pulses. Our results demonstrate that the frequency-mixing signal is strongly correlated with the exciton dynamics and the dramatic change of its polarization dependence is caused by the exciton-exciton interactions.

Biexcitons in CdMnTe/CdTe/CdMgTe single quantum well

We have performed two-pulse and three-pulse time-integrated as well as spectrally resolved four-wave-mixing measurements on a single CdMnTe/CdTe/CdMgTe quantum well. The polarization dependence of both four-wave-mixing measurements can be explained well by the five-level model of the exciton–biexciton system including two-biexciton states with parallel spin and anti-parallel spin orientations.

Dephasing in the quasi-two-dimensional exciton-biexciton system

The polarization decay in the exciton-biexciton system of a homogeneously broadened single quantum well is studied by transient four-wave mixing. All three decay rates in the exciton-biexciton three-level system are deduced. The relation between the rates unravels correlations between scattering processes of excitons and biexcitons. Density and temperature dependences show that the involved processes are mainly radiative decay and phonon scattering. The radiative decay rate of the biexcitons is found to be comparable to the one of the excitons, and the involved spontaneous photon emissions from excitons and biexcitons are mutually uncorrelated. In contrast, the biexciton phonon scattering is twice as fast and correlated to exciton-phonon scattering, indicating the interaction with similar phonon modes. The enhancement of the Coulomb interaction between electrons and holes in semiconductor nanostructures leads to pronounced excitonic effects. This gives a strong influence on the optical nonlinearity not only from excitons but also from biexcitons. The binding energy of the biexcitons has been investigated in great detail, 1‐3 while only little is known about the scattering processes of biexcitons 4‐6 compared to that of excitons. 7 In four-wave mixing ~FWM! spectroscopy, commonly used to measure scattering processes, the disorder present in nanostructures strongly modifies the FWM response, 8 especially the biexcitonic signal, 9,10 and the analysis of the biexciton scattering is intricate. 11 In a homogeneously broadened system instead, the dephasing rates of exciton and biexciton to ground-state transitions and also of the exciton-biexciton transition can be determined. This gives the opportunity to analyze not only the biexciton scattering processes but also their correlation with the exciton scattering processes, providing insight into the microscopic dynamics of the involved scattering events. A prominent example of a strong correlation of such scattering events is a slow dephasing of intraband coherences created by interband transitions of fast dephasing, like heavy-hole‐light-hole

Features of the optical bistability in an exciton-biexciton system

The role of exciton-exciton, exciton-biexciton, and biexciton-biexciton interactions in the nonlinear transmission function of a ring cavity is studied. It is shown that transmission functions both without hysteresis and with one or two hysteresis loops can be obtained by taking into account the elastic interparticle interactions in the exciton-biexciton system.

Four-Particle Condensate in Strongly Coupled Fermion Systems

Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of ``quartetting.'' Applying to symmetric nuclear matter, below a critical density, the four-particle condensation ( $\ensuremath{\alpha}$-like quartetting) is found to be favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the exciton-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.

Polarization choices in exciton-biexciton system of GaAs quantum wells

We study the induced absorption due to biexciton formation in absorption bleaching pump-probe signals and the quantum beats between exciton and biexciton in the four-wave-mixing signals. The origin is confirmed by the polarization dependence of the signals in both experiments. The definite discrimination between exciton-biexciton quantum beats and the others by the polarization choices is demonstrated clearly. We also show the well-width dependence of the biexciton binding energy that is determined by the period of the quantum beats in the range of well width 45--150 \AA{} of GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As (x=0.3--1.0) multiple quantum wells.

Optical Bistability Induced by Additive Colored Noise in the Exciton-Biexciton System

An increasing attention has been paid lately to the noise-induced transitions arising in nonlinear systems far from thermodynamic equilibrium [1-12]. It is known that the noise in nonlinear systems has not only disorganizing effects but under certain conditions leads also to the appearance of nonequilibrium phase transitions that have no deterministic analogues [9]. The Optical bistable system with a medium of two-level atoms is one of the systems in which the noise-induced transitions have been predicted; the external multiplicative white noise can induce optical bistability (OB) [7-9] and multistability for high values of noise intensity [10]. For the same system the colored noise influence on the OB has also been studied, revealing that optical bimodality can arise from the multiplicative colored noise, as well as due to the additive colored noise [11]. The theoretical study and experimental observation of the OB phenomenon in semiconductors present a large interest owing to its possibility of practical applications. Many experimental results have demonstrated the existence of OB in different types of semiconductors [13-15]. Theoretically, the OB in semiconductors has also been investigated in a series of works [7, 16-18].

Biexcitons in short-pulse optical experiments in strong magnetic fields in GaAs quantum wells.

We present time-resolved differential-absorption data for GaAs quantum wells, in which temporal oscillations originating in a biexcitonic pairing appear. We interpret the oscillations within a four-level model of the exciton-biexciton system, and discuss the cases of homogeneously and inhomogeneously broadened exciton absorption lines. Our differential absorption measurements in high magnetic fields normal to the quantum wells' layers show that both the oscillations' frequency and phase depend on the strength and direction of the magnetic field. The frequency change corresponds to the exciton Zeeman splitting in our samples. These findings are in excellent agreement with the predictions of the model, and thus verify its validity.

Coherent excitonic molecules

A model which allows to consider self-consistently many-body exciton effects, including biexciton formation, is proposed for the theoretical description of an excitonic polarization induced by intense electromagnetic field. In the presence of a pump the normal electromagnetic wave spectrum in the vicinity of the nonlinear biexciton resonance is shown to be composed by four polariton branches, each being as a matter of fact the superposition of two photons and two excitons. In the self-consistent field approximation the structure of the interconnected strongly nonlinear exciton and biexciton resonances is studied, including optical Stark shift, multistable behaviour, etc. For a certain range of the exciton interaction parameters at strong enough pump wave the system of excitons and excitonic molecules transforms abruptly to a dense coherent electron-hole “liquid”. Appearance and temporary evolution of an exciton-biexciton system after the switching on of a pump is also considered.

Excitonic Molecules in Nonlinear Optical Response

AbstractA model which allows to treat self‐consistently many‐body exciton effects, including biexciton formation, is proposed for the theoretical description of an excitonic polarization induced by an intense electromagnetic field. In the presence of a pump field the normal spectrum of electromagnetic waves in the vicinity of the nonlinear biexciton resonance is shown to be composed of four polariton branches, where each is the superposition of two photons and two excitons. In the self‐consistent field approximation, the structure of the interconnected, strongly nonlinear exciton and biexciton resonances is studied, including optical Stark shift, multistable behaviour, etc. For a certain range of the exciton interaction parameters at sufficiently strong pump wave the system of excitons and excitonic molecules transforms abruptly to a dense coherent electron–hole “liquid”. Appearance and temporary evolution of an exciton–biexciton system after switching on a pump is also considered.

Dynamical Stark effect in an exciton-biexciton system

A coherently excited exciton-biexciton system under the action of a non-resonant pump field is analysed within the framework of the Hartree-Fock-Bogolyubov theory. The excitation spectra, which consist of optical absorption and gain, are determined. It is pointed out that the optical gain is greatly enhanced through the giant oscillator strength effect of biexcitonic molecules. Numerical examples for CuCl are also presented.