A versatile setup for symmetry-resolved ultrafast dynamics of quantum materials

TL;DR

The paper presents a table-top, all-optical symmetry-resolved RA setup capable of tracking ultrafast symmetry changes in quantum materials with high signal-to-noise. It combines linear and nonlinear (SHG) RA within a near-normal incidence geometry using a single rotating ultrabroadband half-wave plate, enabling straightforward, low-footprint alignment and flexible wavelength, repetition-rate, and temperature control. Theoretical RA formalism connects birefringence and order parameters through $I_{sig}(\Theta)=I_{DC}+I_4\cos(4\Theta+\Psi_4)+I_8\cos(8\Theta+\Psi_8)$ with $\eta^2=(1-\rho)/(1+\rho)$, allowing direct interpretation of symmetry changes; the setup is validated through static and time-resolved measurements on PCMO showing a COO-driven C2 symmetry transition near $T_{COO}\approx330$ K and ultrafast dynamics with recombination influenced by repetition rate, plus SHG-RA on GaAs revealing pump-induced amplitude changes without symmetry breaking. The work demonstrates that table-top optical methods can match key insights from XFEL/e-beam techniques for symmetry-driven phenomena and introduces a path toward low-fluence, single-photon SHG detection via SPD for weak signals. Overall, the platform offers a versatile, accessible route to symmetry-resolved dynamics with practical implications for studying a wide range of quantum materials.

Abstract

Correlated phenomena occur in quantum materials because of the delicate interplay between internal degrees of freedom, leading to multiple symmetry-broken quantum phases. Resolving the structure of these phases is a key challenge, often requiring facilities equipped with x-ray free-electron lasers and electron sources that may not be readily accessible to the average user. Table-top sources that offer alternative means are therefore needed. In this work, we present an all-optical, table-top setup that enables symmetry-resolved studies using linear and nonlinear spectroscopies. We demonstrate the versatility of the setup with chosen examples that underscore the importance of tracking symmetries and showcase the strengths of the setup, which offers a large tunable parameter space.

Figures (10)

• Figure 1: Schematic of linear and non-linear rotational anisotropy setup. BS: beam-splitter; TDG: timing and delay generator; CC: chopper-controller; OPA: optical parametric amplifier; $\mathrm{PD_{sig/ref}}$: signal/reference photodiode; L: lens; W: wedge prism; CL: cylindrical lens; WGP: broadband wire-grid polariser; HWP: broadband half-wave plate. Pol: polarizer; DAQ: data acquisition.
• Figure 2: (a). Signal ($I_{sig}$) from a birefringent sample for ten consecutive scans as recorded by the DAQ system. Traces have random initial phases as denoted by the dashed line and need to be sorted before they can be averaged. The signals are vertically offset for clarity (b). The zero-crossing signal for each scan is shown as a vertical line. The label denotes the scan number out of ten measurements. Inset: locations of the zero-crossing which are used to shift and align the patterns before averaging (c). Signals from the reference diode, ($I_{ref}$) which are used for intensity normalization (d). Simulated normalized pump signal through the chopper demonstrating the alternating OFF and ON nature used for sorting the time-resolved data into respective Pump-OFF and Pump-ON bins.
• Figure 3: (a). Measured signal to characterize the degree of possible anisotropy solely due to optical elements carried out by placing a silver mirror in the sample plane and plotted in polar form. The circular pattern that emerges demonstrates very low anisotropic contribution and high isotropy. See text for more details (b). Measurement, repeated by placing a polarizer in the setup. (c). Measured traces resulting from cross-correlation between 800 nm pump and different probe wavelengths. The fits are given by the black dashed lines (d). Extracted FWHM width of the traces shown in panel (c) denoting the estimated time resolution as a function of probe wavelength. The average estimated value for instrument resolution of $\approx75$ fs is given as the dashed horizontal line.
• Figure 4: (a). Crystal structure of PCMO; Green denotes Ca/Pr atoms; purple: Mn, and red: oxygen atoms (b). Representative anisotropy and corresponding fit of measured birefringence at 200 K. (c). The change in anisotropy at selected temperatures represented in the form of polar plots. The amplitude reduces and a rotation of the pattern emerges. (d). Comparison between the measured temperature dependence of the order parameter from this work and that reported in the literature showing a good agreement between the two datasets. Data in gray is taken from Fig. 2 of Ref. Porer2020 with permission. Inset: Dependence of the $\Psi_4$ parameter which denotes the phase shift of the order parameter against temperature.
• Figure 5: (a). Typical 2D tr-RA map of PCMO at 300 K plotting intensity changes as function of time and angle following excitation using 800 nm pump (b-d). relative changes in reflectivity for two different fluences and three repetition rates (e-g). Corresponding changes in the order parameter as function of fluence and repetition rate.