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arXiv:cond-mat/0701424 · Physical Review B

Two-dimensional optical spectroscopy of excitons in semiconductor quantum wells: Liouville-space pathway analysis

Lijun Yang, Igor V. Schweigert, Steven T. Cundiff, Shaul Mukamel

Published Mar 2, 2007• 65 citations
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Abstract

We demonstrate how dynamic correlations of heavy-hole and light-hole excitons in semiconductor quantum wells may be investigated by two-dimensional correlation spectroscopy. The coherent response to three femtosecond optical pulses is predicted to yield cross (off-diagonal) peaks that contain direct signatures of many-body two-exciton correlations. Signals generated at various phase-matching directions are compared.

DOI
10.1103/physrevb.75.125302

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We demonstrate how dynamic correlations of heavy-hole and light-hole excitons in semiconductor quantum wells may be investigated by two-dimensional correlation spectroscopy. The coherent response to three femtosecond optical pulses is predicted to yield cross (off-diagonal) peaks that contain direct signatures of many-body two-exciton correlations. Signals generated at various phase-matching directions are compared.
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.
Multidimensional analysis of coherent signals is commonly used in nuclear magnetic resonance to study correlations among spins. These techniques were recently extended to the femtosecond regime and applied to chemical, biological and semiconductor systems. In this work, we apply a two-dimensional correlation spectroscopy technique which employs double-quantum-coherence to investigate many-body effects in a semiconductor quantum well. The signal is detected along the direction k(1)+ k(2)- k(3), where k(1), k(2) and k(3) are the pulse wave vectors in chronological order. We show that this signal is particularly sensitive to many-body correlations which are missed by time-dependent Hartree-Fock approximation. The correlation energy of two-exciton can be probed with a very high resolution arising from a two-dimensional correlation spectrum, where two-exciton couplings spread the cross peaks along both axes of the 2D spectrum to create 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 (-k(1)+ k(2)+ k(3)).
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.
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.