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arXiv:0712.2263 · Physical Review Letters

Two-Dimensional Correlation Spectroscopy of Two-Exciton Resonances in Semiconductor Quantum Wells

Lijun Yang, Shaul Mukamel

Published Feb 4, 2008• 88 citations
arXivHTMLPDF

Abstract

We propose a three-pulse coherent ultrafast optical technique that is particularly sensitive to two-exciton correlations. Two Liouville-space pathways for the density matrix contribute to this signal which reveals double quantum coherences when displayed as a two-dimensional correlation plot. Two-exciton couplings spread the cross peaks along both axes, creating a characteristic highly resolved pattern. This level of detail is not available from conventional one-dimensional four-wave mixing or other two-dimensional correlation spectroscopy signals such as the photo echo, in which two-exciton couplings show up along a single axis and are highly congested.

DOI
10.1103/physrevlett.100.057402

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We propose a three-pulse coherent ultrafast optical technique that is particularly sensitive to two-exciton correlations. Two Liouville-space pathways for the density matrix contribute to this signal which reveals double quantum coherences when displayed as a two-dimensional correlation plot. Two-exciton couplings spread the cross peaks along both axes, creating a characteristic highly resolved pattern. This level of detail is not available from conventional one-dimensional four-wave mixing or other two-dimensional correlation spectroscopy signals such as the photo echo, in which two-exciton couplings show up along a single axis and are highly congested.
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We propose to employ multi-color narrow-bandwidth pulses to dissect the quantum pathways in two-dimensional correlation spectroscopy (2DCS) optical signals generated along the phase-matching directions k I = − k 1 + k 2 + k 3 (photon echo) and k III = k 1 + k 2 − k 3 (double quantum coherence). Simulations demonstrate how the resolution of 2DCS signals in GaAs quantum wells may be enhanced by spectrally selecting desired Liouville-space pathways. Pulse-shaping techniques may be used to further enhance the resolution.
The correlated behavior of electrons determines the structure and optical properties of molecules, semiconductors, and other systems. Valuable information on these correlations is provided by measuring the response to femtosecond laser pulses, which probe the very short time period during which the excited particles remain correlated. The interpretation of four-wave-mixing techniques, commonly used to study the energy levels and dynamics of many-electron systems, is complicated by many competing effects and overlapping resonances. Here we propose a coherent optical technique, specifically designed to provide a background-free probe for electronic correlations in many-electron systems. The proposed signal pulse is generated only when the electrons are correlated, which gives rise to an extraordinary sensitivity. The peak pattern in two-dimensional plots, obtained by displaying the signal versus two frequencies conjugated to two pulse delays, provides a direct visualization and specific signatures of the many-electron wave functions.
We present the experimental and simulation results of two-dimensional optical coherent correlation spectroscopy signals along the phase-matching direction k(I) = -k(1) + k(2) + k(3) projected on the two-dimensional (2D) (Omega(3),Omega(2)) plane corresponding to the second and third delay periods. Overlapping Raman coherences in the conventional (Omega(3),Omega(1)) 2D projection may now be clearly resolved. The linewidths of the heavy-hole (HH) and light-hole (LH) excitonic Raman coherence peaks are obtained. Further insights on the higher-order (beyond time-dependent Hartree-Fock) correlation effects among mixed (HH and LH) two excitons can be gained by using a cocircular pulse polarization configuration.
Our recent work on optical two-dimensional coherent spectroscopy (2DCS) of semiconductor materials is reviewed. We present and compare two approaches that are appropriate for the study of semiconductor nanostructures. The first one is based on a non-collinear geometry, where the Four-Wave-Mixing (FWM) signal is detected in the form of a radiated optical field. This approach works for samples with translational symmetry, such as Quantum Wells (QWs), or large and dense ensembles of Quantum Dots (QDs). The second method is based on a collinear geometry, where the FWM is detected in the form of a photocurrent. This second approach enables 2DCS of samples where translational symmetry is broken, such as single QDs, nanowires, or nanotubes, and small ensembles thereof. For each method, we provide an example of experimental results obtained on semiconductor QWs. In particular, it is shown how 2DCS can reveal coherent excitonic coupling between adjacent QWs.