Time-integrated Four-wave Mixing Signal Research Articles

Fifth-order nonlinear optical response of excitonic states in an InAs quantum dot ensemble measured with two-dimensional spectroscopy

Exciton, trion and biexciton dephasing rates are measured within the inhomogeneous distribution of an InAs quantum dot (QD) ensemble using two-dimensional Fourier-transform spectroscopy. The dephasing rate of each excitonic state is similar for all QDs in the ensemble and the rates are independent of excitation density. An additional spectral feature -- too weak to be observed in the time-integrated four-wave mixing signal -- appears at high excitation density and is attributed to the $\chi^{\textrm{(5)}}$ biexcitonic nonlinear response.

Effect of nanocrystal growth conditions on exciton decay and spin dephasing in an ensemble of CdSe nanocrystals grown in glass

The dynamics of exciton decay and spin dephasing in an ensemble of CdSe quantum dots grown in a glass matrix has been investigated by studying the polarized time-integrated four-wave mixing signal at $10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Quantum dots of equal size, but with different growth conditions, have been found to exhibit similar decay times but significantly (orders of magnitude) different spin depolarization times. We connect this effect to the difference in the quantum dot anisotropy. The anisotropy results in the splitting of bright $J=1$ exciton states that causes the oscillation of circularly excited excitons between the two linearly polarized split states. In a quantum dot ensemble with a random distribution in the exciton level splitting, that results in the depolarization of the four-wave mixing signal observed in the scattering of ${\ensuremath{\sigma}}^{\ensuremath{-}}$ and ${\ensuremath{\sigma}}^{+}$ polarized light on the population grating created by two ${\ensuremath{\sigma}}^{+}$ pulses. The dependence of the quantum dot anisotropy on the growth conditions is discussed in terms of thermophysics of nanoparticle growth in glass.

Effect of Static Electric Field on the Beat Structures in Four-Wave Mixing Signals from Semiconductor Microcavities

Beat structures in the time-integrated four-wave mixing signals in semiconductor microcavities under a static electric field were investigated experimentally. We observed a significant change in the phase of the oscillation in the upper polariton mode with the change of the electric field. Through comparison with results of a theoretical analysis based on modified optical Bloch equations, the experimental results were found to strongly suggest that the exciton–exciton interaction, represented by the electric field renormalization, is significantly modified by the static electric field.

Time-integrated four-wave mixing in GaN and ZnSe: Polarization-sensitive phase shift of the excitonic quantum beats

We report on the study of quantum beats in the time-integrated four-wave mixing signal in reflection geometry from a pair of excitons with different valence orbitals in GaN and ZnSe. We observe a \ensuremath{\pi}-phase shift between quantum beats in the co- and cross-linear polarization configuration, and nearly 100% modulation of the signal for both materials. In the co-circular polarization configuration, the observed phases of the quantum beats at the frequency of the A exciton in GaN and heavy-hole exciton in ZnSe are 0.2\ensuremath{\pi} and 0.1\ensuremath{\pi}, respectively. The phases of the quantum beats change sign for co- and counter-circular polarization configurations and also for A- (heavy-hole) and B-(light-hole) excitons in GaN(ZnSe). We describe the third-order coherent optical response of the exciton pair with different valence orbitals by taking into account the finite memory depth of the four-particle correlation. In particular, our experimental findings indicate that excitons with different valence orbitals and equal angular momentum attract each other similar to excitons with the same valence orbitals but opposite angular momentum. Excitons with different orbitals and opposite angular momenta repel one another. The comparison between experimental and theoretical results allows us to develop a quantitative analysis of the four-particle correlation in the presence of an exciton pair with different valence orbitals. We show that the observed \ensuremath{\pi}-phase shift and nearly 100% modulation of the signal in the co- and cross-linear polarization configuration impose restraints on the memory functions, which describe the exciton-exciton interaction. These restraints imply, in particular, that electron spins play a more important role in the exciton-exciton interaction in comparison to hole spins. We show that a striking similarity, which we observe in the quantum beat signal from GaN and ZnSe, originates from the strong four-particle correlation contribution to the third-order excitonic nonlinearity.

Ultrafast Coulomb-induced dynamics of quantum well magnetoexcitons

We study theoretically the ultrafast nonlinear optical response of quantum well excitons in a perpendicular magnetic field. We show that for magnetoexcitons confined to the lowest Landau levels, the third-order four-wave-mixing (FWM) polarization is dominated by the exciton-exciton interaction effects. For repulsive interactions, we identify two regimes in the time-evolution of the optical polarization characterized by exponential and {\em power law} decay of the FWM signal. We describe these regimes by deriving an analytical solution for the memory kernel of the two-exciton wave-function in strong magnetic field. For strong exciton-exciton interactions, the decay of the FWM signal is governed by an antibound resonance with an interaction-dependent decay rate. For weak interactions, the continuum of exciton-exciton scattering states leads to a long tail of the time-integrated FWM signal for negative time delays, which is described by the product of a power law and a logarithmic factor. By combining this analytic solution with numerical calculations, we study the crossover between the exponential and non-exponential regimes as a function of magnetic field. For attractive exciton-exciton interaction, we show that the time-evolution of the FWM signal is dominated by the biexcitonic effects.

Role of exciton–exciton interaction on resonant third-order nonlinear optical responses

Weakly interacting boson model with the account for the bound biexciton is employed to obtain the evolution equations for the macroscopic exciton polarization. The polarization-sensitive degenerate four-wave mixing measurements in frequency domain enable us to estimate the relative contribution of the bound biexciton state on the nonlinear optical response. In the time-domain measurements, we study the amplitude and phase of the beating in the time-integrated four-wave mixing signal. On the basis of the developed evolution equations, we show that the phase shift of the beating signal is polarization sensitive and is determined by the interplay between excitation-induced dephasing, exciton–exciton interaction and other mechanisms of the nonlinearity.

Effect of propagation on pulsed four-wave mixing

We examine the effect of propagation on the resonance Rabi sideband of the four-wave mixing (FWM) spectrum, obtained when short temporally displaced pump and probe pulses interact with an optically thick medium of two-level atoms. We find that the dependence of the time-integrated FWM signal on the pump-probe delay is considerably altered by propagation. In particular, the logarithm of the FWM signal, for the case where the probe precedes the pump, deviates from linearity and may even increase over a range of values. An explanation is given in terms of the overlap of the pump envelope with the coherent response of the atomic system to the probe, both of which are modified on propagation.

Coherent control of the dephasing time of a 2D magnetoplasma

We show theoretically that by changing the delay time between two phase-locked femtosecond laser pump pulses, the magnitude of quantum beats of time-integrated four-wave mixing signals and the effective dephasing time of magnetoplasma of a semiconductor quantum well can be manipulated.

Degenerate four-wave-mixing signals from a dc- and ac-driven semiconductor superlattice

Within the one-dimensional tight-binding model and $\ensuremath{\chi}\ensuremath{-}3$ approximation, we have calculated four-wave-mixing (FWM) signals for a semiconductor superlattice in the presence of both static and high-frequency electric fields. When the exciton effect is negligible, the time-periodic field dynamically delocalizes the otherwise localized Wannier-Stark states, and accordingly quasienergy band structures are formed, and manifest in the FWM spectra as a series of equally separated continua. The width of each continuum is proportional to the joint width of the valence and conduction minibands and is independent of the Wannier-Stark index. The realistic homogeneous broadening blurs the continua into broad peaks, whose line shapes, far from the Lorentzian, vary with the delay time in the FWM spectra. The swinging range of the peaks is just the quasienergy bandwidth. The dynamical delocalization (DDL) also induces significant FWM signals well beyond the excitation energy window. When the Coulomb interaction is taken into account, the unequal spacing between the excitonic Wannier-Stark levels weakens the DDL effect, and the FWM spectrum is transformed into groups of discrete lines. Strikingly, the groups are evenly spaced by the ac field frequency, reflecting the characteristic of the quasienergy states. The homogeneous broadening again smears out the line structures, leading to the excitonic FWM spectra quite similar to those without the exciton effect. However, all these features predicted by the dynamical theory do not appear in a recent experiment [Phys. Rev. Lett. 79, 301 (1997)], in which, by using the static approximation the observed Wannier-Stark ladder with delay-time-dependent spacing in the FWM spectra is attributed to a temporally periodic dipole field, produced by the Bloch oscillation of electrons in real space. The contradiction between the dynamical theory and the experiments is discussed. In addition, our calculation indicates that the dynamical localization coherently enhances the time-integrated FWM signals. The feasibility of using such a technique to study the dynamical localization phenomena is shown.

Magnetically enhanced exciton-exciton correlations in semiconductors

Recent experiments on fs time-resolved coherent wave mixing under a high magnetic field have revealed a new regime at low excitation densities which is not in accordance with the semiconductor Bloch equations. We present a theory of coherently driven biexcitons in a strong magnetic field, which — due to the restriction of excitonic degrees of freedom — results in a strong enhancement of Coulomb correlation effects. The theory describes most of the observed features. Especially, the slow rising time of the time-integrated four-wave mixing signal is shown to result from biexcitonic correlation. The same interaction effects yield a strong dependence of the oscillator strength of the heavy- (hh) and light-hole (lh) excitons on the time delay between the two pulses.

Ultrafast coherent spectroscopy of one-dimensional magnetoexcitons in semiconductors

Abstract We investigate the ultrashort coherent dynamics of one-dimensional Fano andvLorentzian magnetoexcitons in GaAs using temporally and spectrally resolved four-wave mixing (FWM). The dephasing time of a Fano resonance is intrinsically limited by the coupling between discrete states and continua which is responsible for Fano interference. In contrast, the coherent emission from Lorentzian magnetoexcitons dephases solely due to quasi-particle scattering, dominated by exciton-exciton scattering at low temperatures. We find a very fast decay of the time-integrated FWM signal from Fano magnetoexciton resonances. This decay is not due to dephasing. The quenching of the FWM signal for non-overlapping excitation pulses is the result of quantum interference. This destructive quantum interference is not observed for purely Lorentzian dynamics. For the simultaneous excitation of Lorentzian and Fano magnetoexciton resonances, destructive quantum interference also quenches the coherent emission from Lorentzian magnetoexcitons due to quantum mechanical coupling between the different resonances.

Strong instantaneous contribution in femtosecond degenerate four-wave mixing from 350 μm InP due to virtual excitation

We have observed strong four-wave mixing (FWM) signals from the third up to the seventh order for a 350 μm undoped InP at 10 K with an excitation at far below the band gap. The third order spectrally resolved FWM signal shifts continuously to blue as time delay moves away from positive to negative. The peak intensities of the third and fifth order time-integrated FWM signals decrease rapidly as the detuning increases, as (detuning)−2 and (detuning)−6, respectively. The FWM signal at far below the band gap is attributable to the strong instantaneous contribution of the excitation pulse.

Coherent dynamics of exciton wavepackets in semiconductor heterostructures

The coherent dynamics of exciton wavepackets in (GaIn)As/GaAs as well as (GaIn)As/Ga(PAs) multiple quantum well structures is studied by means of transient four-wave mixing (FWM) experiments. The wavepackets are generated by simultaneous excitation of several exciton transitions with laser pulses of about 100 fs duration. The time-integrated FWM signals exhibit a pronounced modulation superimposed on the overall decay which can be attributed to the quantum interference of the different eigenstates. In the time-resolved FWM signals this interference is not present, reflecting the interplay between many-body Coulomb effects and inhomogeneous broadening. This experimental technique is then employed to extract the exciton binding energies in pseudomorphic symmetrically strained (GaIn)As/GaIPAs) with various In contents.

Polariton effects in four-wave mixing.

We show that polariton effects lead to time-delayed components in the time-resolved four-wave-mixing (FWM) signal. Hence we find that recent observations in FWM experiments that have been ascribed to many-body Coulomb interactions can also be explained from the formation of exciton polaritons. In addition, we find that due to the formation of polaritons, the rate of decay of the time-integrated FWM signal strongly depends on the oscillator strength and the propagation length.