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Journal of Physics Condensed Matter

Dissecting quantum pathways in two-dimensional correlation spectroscopy of semiconductors

Lijun Yang, Shaul Mukamel

Published Sep 1, 2008• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/20/39/395202

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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.
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)).
Abstract Pathway selectivity in quantum spectroscopy with entangled photons is a powerful spectroscopic tool. Phase‐matched signals involving classical light contain contributions from multiple material pathways, whereas quantum spectroscopy may allow the selection of individual pathways. 2D electronic‐vibrational spectroscopy (2DEVS) is a four‐wave mixing technique which employs visible and infrared entangled photons. It is showed how the three contributing pathways—ground state bleach, excited state absorption, and excited state emission—can be separated by photon‐number‐resolved coincidence measurements. Entangled photons thus reveal spectral features not visible in the classical signal, with an enhanced spectral resolution.
Abstract Two-dimensional coherent spectroscopy (2DCS) combined with dual-comb technology offers unprecedented resolution for probing many-body interactions and correlations in atomic vapors, yet its application to high-order multi-quantum transitions remains challenging due to weaker nonlinear signals and phase instability. Here, we demonstrate a triple-quantum dual-comb 2DCS technique that achieves λ/110 phase stability through digital correction, enabling the observation of velocity-synchronized Dicke states in a thermal rubidium vapor. By resolving collective hyperfine resonances of ⁸⁵Rb and ⁸⁷Rb isotopes with 100 MHz spectral resolution, we reveal that triple-quantum dipole-dipole correlations (0.95) surpass double-quantum counterparts (0.90), indicating tighter velocity matching in higher-order Dicke states. This work establishes a pathway for manipulating multi-atom correlations in Doppler-broadened systems and extends 2DCS to research the many-body interaction in semiconductor exciton and 2D materials.
Optical multidimensional coherent spectroscopy is a powerful tool for studying structure and dynamics in complex systems, such as semiconductors. In optical two-dimensional coherent spectroscopy (2DCS), where the spectrum is presented in a two-dimensional (2D) plane with two frequency axes, an important advantage is the ability to isolate quantum pathways by unfolding a one-dimensional spectrum onto a 2D plane. For many systems, however, the quantum pathways are only partially separated in a 2D spectrum. In order to completely isolate the quantum pathways, we extend 2DCS into a third dimension to generate three-dimensional (3D) spectra in which the spectrum is further unfolded. A 3D spectrum provides complete and well-isolated information of the third-order optical response of the system. The information can be used to fully characterize the quantum pathways and to determine the system’s Hamiltonian. Quantitative knowledge of the Hamiltonian enables prediction and control of quantum processes. For instance, such information is essential for deterministic control and improved performance of coherent control schemes.