Single-scan acquisition of multiple multidimensional spectra

Abstract

Multidimensional coherent spectroscopy is a powerful tool for understanding the ultrafast dynamics of complex quantum systems. To fully characterize the nonlinear optical response of a system, multiple pulse sequences must be recorded and quantitatively compared. We present a new single-scan method that enables rapid and parallel acquisition of all unique pulse sequences corresponding to first- and third-order degenerate wave-mixing processes. Signals are recorded with shot-noise limited detection, enabling acquisition times of ~2 minutes with ~100 zs phase stability and ~8 orders of dynamic range, in a collinear geometry, on a single-pixel detector. We demonstrate this method using quantum well excitons, and quantitative analysis reveals new insights into the bosonic nature of excitons. This scheme may enable rapid and scalable analysis of unique chemical signatures, metrology of optical susceptibilities, nonperturbative coherent control, and the implementation of quantum information protocols using multidimensional spectroscopy.

Fig. 1.

(a) Experimental setup of the collinear multidimensional Fourier transform spectroscopy apparatus for positive ${\text{t}}_{\text{lab}}$, in which case ${\text{t}}_{\text{lab}}=\tau$. A series of nested Mach–Zehnder interferometers prepares copies of the input pulse using beam splitters (BSs). The interpulse delays $\tau$, $T$, $t$ are controlled by translation stages. The frequencies of the excitation pulses and the LO are each shifted by a unique radio frequency using AOMs before going through single-mode fiber (SMF). A detuned (1020 nm) CW reference laser copropagates and samples the interpulse delays. The nonlinear optical signal is collected in reflection, and a dichroic mirror (DM) separates the signal from the reference laser onto their respective detectors. (b) Signal processing diagram showing the superheterodyne optical frequency receiver for recovery of the multidimensional spectra. The right panel shows the vibrational amplitude spectrum of interferometer arm $A-B$. The intrinsic resolution of the interferometers (<100 zs) is set by the noise floor of this spectrum.

Fig. 2.

(a) Excitation pulse scheme and energy level diagram of the heavy-hole exciton. The sample consists of four 10-nm-wide GaAs/AlGaAs quantum wells above a Bragg mirror. (b–d) Image of normalized signal amplitudes detected at ${\omega }_{\mathrm{3,4,5}}$ showing the 1Q scans for $t_{\text{lab}}=\tau$ and the zero and double quantum scans for $-t_{\text{lab}}=T$. Dashed and labeled contours show the 10% and 1% amplitudes. Dashed lines indicate where $t=t_{\text{lab}}$. (e) Total polarization during time $t$ separated into the different contributions. Quantitative comparison of the linear (C-LO) and one-quantum rephasing $(1\text{Q}-S_{\text{I}})$, one-quantum nonrephasing $(1\text{Q}-S_{\text{II}})$, and one-quantum double-quantum $(1\text{Q}-S_{\text{III}})$ signals as a function of time $t$ at $\tau =0.5$ ps. In this plot there is a reflection at ~4.8 ps.

Fig. 3.

All two-dimensional spectra of the heavy-hole exciton in ${\chi }^3$. The top spectra correspond to (a) the real part of the $1\text{Q}-S_{\text{I}}$ signal, (b) the real part of the $1\text{Q}-S_{\text{II}}$ signal, and (c) the real part of the $1\text{Q}-S_{\text{III}}$ signal. The bottom spectra are real parts of (d) the $0\text{Q}-S_{\text{I}}$ signal, (e) the $0\text{Q}-S_{\text{II}}$ signal, and (f) the $2\text{Q}-S_{\text{III}}$ signal. The peaks in the real spectra exhibit mixed absorptive and dispersive line shapes indicative of exciton–exciton interactions.

Fig. 4.

Double-sided Feynman diagrams representing all pathways describing the evolution of the heavy-hole exciton. The diagrams are grouped by pulse sequence with ${\text{S}}_{\text{I}}$ (top), ${\text{S}}_{\text{II}}$ (middle), and ${\text{S}}_{\text{III}}$ (bottom). The many-body parameters modify the exciton ladder of states.

Fig. 5.

Subset of slices fit to Monte Carlo simulations (blue) to the exciton response (orange). All pulse sequences were fit at the same time to the same parameters. All spectra are normalized with respect to the amplitude of the $(1\text{Q}-S_{\text{I}})$ signal. The real (Re), imaginary (Im), amplitude (Abs) part of diagonal (D) and cross-diagonal (XD) slices from the $1\text{Q}-S_{\text{I,II,III}}$ data sets and simulations. Panels (a-d) show $1\text{Q}-{\text{S}}_{\text{I}}$ slices, panels (e-f) show $1\text{Q}-{\text{S}}_{\text{II}}$ slices, and panels (g-h) show $1\text{Q}-{\text{S}}_{\text{III}}$ slices.

Fig. 6.

Simulations of exciton models as a function of interaction energy/homogeneous linewidth. Plots show the amplitude of the simulated $1\text{Q}-S_{\text{II,III}}$ spectra normalized to the amplitude of the $1\text{Q}-S_{\text{I}}$ spectrum. The different models considered consist of the same value between transition dipoles (dashed lines), enhanced Pauli blocking (square dots), and bosonic dynamics (blue). Values extracted from our data sets are represented by (dot and star), and the ±2σ confidence interval is represented by filled colors.