Three-dimensional electronic spectroscopy of excitons in asymmetric double quantum wells

Abstract

We demonstrate three-dimensional (3D) electronic spectroscopy of excitons in a double quantum well system using a three-dimensional phase retrieval algorithm to obtain the phase information that is lost in the measurement of intensities. By extending the analysis of two-dimensional spectroscopy to three dimensions, contributions from different quantum mechanical pathways can be further separated allowing greater insight into the mechanisms responsible for the observed peaks. By examining different slices of the complete three-dimensional spectrum, not only can the relative amplitudes be determined, but the peak shapes can also be analysed to reveal further details of the interactions with the environment and inhomogeneous broadening. We apply this technique to study the coupling between two coupled quantum wells, 5.7 nm and 8 nm wide, separated by a 4 nm barrier. Coupling between the heavy-hole excitons of each well results in a circular cross-peak indicating no correlation of the inhomogeneous broadening. An additional cross-peak is isolated in the 3D spectrum which is elongated in the diagonal direction indicating correlated inhomogeneous broadening. This is attributed to coupling of the excitons involving the two delocalised light-hole states and the electron state localised on the wide well. The attribution of this peak and the analysis of the peak shapes is supported by numerical simulations of the electron and hole wavefunctions and the three-dimensional spectrum based on a density matrix approach. An additional benefit of extending the phase retrieval algorithm from two to three dimensions is that it becomes substantially more reliable and less susceptible to noise as a result of the more extensive use of a priori information.

Three-dimensional infrared spectroscopy of isotope-diluted ice Ih

“…The multidimensional character permits the simultaneous creation of multiple coherence or multiple population states. In the visible frequency range realizations of three-dimensional spectroscopy feature third-order multi-coherence electronic spectroscopies [45][46][47], as well the corresponding fifthorder 3D techniques [48,49]. In the infrared, threedimensional IR spectroscopy (3D-IR) has been demonstrated as a 3-pulse 5th-order experiment exploring only coherence times [50,51], as well as our implementation that involves five laser interactions and allows one to also observe multiple population times [52][53][54].…”

Multidimensional spectroscopy of photoreactivity

“…As a general extension of 2D spectroscopy, 3D representations provide an even more detailed picture. Coherent 3D spectroscopy has been introduced to infrared spectroscopy (14,15), and recently to electronic spectroscopy for isolating excitonic coherences (16,17), for liquid-and gas-phase model systems (18)(19)(20), and for analyzing photosynthetic lightharvesting (21,22). Regarding these approaches, one has to differentiate between fifth-order experiments (14,15,19) for effects of higher nonlinearity (e.g., three-point frequency-fluctuation correlation functions) (14) and third-order techniques (20)(21)(22)(23)(24), as demonstrated here to unravel photochemical reactions.…”

Multidimensional coherent optical spectroscopy of semiconductor nanostructures: a review

“…In theoretical work, Tokmakoff derived envelope lineshapes in the homogeneous and inhomogeneous limits from the Fourier transform of an absolute-value 2D time-domain solution of the optical Bloch equations [16]. Phenomenological fitting to simulations was used to obtain correlation information [17,18], as well as ratios of dephasing parameters in the presence of many-body effects [19,20], but a method for determining absolute (quantitative and physically meaningful) homogeneous and inhomogeneous broadening parameters from 2D lineshapes has not yet been presented, to the best of our knowledge.…”

“…Phase fluctuations can also be addressed during post-processing of the data, using algorithms inspired from the phase-retrieval methods of frequency-resolved optical gating [70]. The convergence of phase-retrieval algorithms has been shown to improve in the case of 3D spectral data [18].…”