Effects of correlation between inhomogeneously broadened transitions on quantum beats in transient four-wave mixing

Abstract

The transient four-wave-mixing signal from a three-level system is calculated in the short-pulse limit including a general distribution function for the energies of the levels between which beating occurs. This allows an examination of the effects of correlation between the energetic splitting of the levels. As expected, the results demonstrate that the degree of correlation can significantly alter the four-wavemixing signal. However, the results also show that in the case where the level energies are completely correlated, in a rigorous sense, but that the correlation is not a simple offset, a strong modification of the beat amplitude occurs. This case describes the type of correlation expected in semiconductor quantum wells. Examination of several representative cases demonstrates that these effects can easily be incorrectly ascribed to dephasing. PACS number(s): 42.50.Md, 78.66.w Quantum beats arise due to the excitation of a quantum-mechanical coherent superposition of several discrete levels. Their presence has been observed in many optical experiments and they are considered a spectroscopic tool for the determination of energy splittings [1]. Early observations in atomic and molecular systems include resonance fluorescence [2] and photon-echo experiments [3,4]. These optical experiments were preceded by the observation of quantum beats (QB) in nuclear quadrupole resonance [5], which are theoretically very similar, although not so experimentally. With the recent advances in short-pulse laser technology, which have made subpicosecond pulses readily available, nonlinear optical techniques have been extensively applied to the study of electronic excitations in semiconductors and semiconductor heterostructures [6]. The picosecond time scale for dephasing in these materials necessitates the use of such short-pulse widths. The experiments that have been performed include the observations of QB between excitons confined to distinct regions in a quantum well [7,8], heavy-and light-hole excitons [9], free and bound excitons [10], Zeeman split excitons [ll], and excitons and biexcitons [12]. Related experiments include the observation of coherent oscillations between coupled quantum wells [13], a distinction between true QB and interference between the radiated field from two distinct transitions [known as polarization interference (PI)] [14], and interference between the different excitonic states [15].Inhomogeneous broadening is we11 known to strongly influence the effects of nonlinear optical experiments, and in the case of transient four-wave mixing (TFWM) is responsible for the free decay observed for a homogeneously broadened two-level system becoming a photon echo.The theoretical treatment presented in most of the recent work on quantum beats has largely ignored the presence of inhomogeneous broadening [13,16,17], although it was included in the case in which the beats were thought to arise from PI [7,16]. These treatments are generally p(3) b) k2 ! ! ! ! Time Time FIG. 1. (a) The origin of the four terms which...

Quantum beats due to excitonic ground-state splitting in colloidal quantum dots

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Heavy-Light Hole Quantum Beats in the Band-to-Band Continuum of GaAs Observed in 20 Femtosecond Pump-Probe Experiments

“…For an ensemble with different transition frequencies, e.g., heavy hole excitons of different binding energy in quasi-two-dimensional (2D) structures, the oscillatory overall polarization originates from the contributions from the individual two-level constituents [2,4]. A different situation exists if the transitions are coupled via a common state and quantum interference in three-level systems causes polarization beats for heavy hole (HH) and light hole (LH) excitons [3][4][5]. In 2D systems, studies of the coherent response are facilitated by the-relatively slow-picosecond phase relaxation of excitonic polarizations.…”

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

“…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][5][6] compared to that of excitons. 7 In four-wave mixing ͑FWM͒ 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.…”