Strong spin-orbit coupling inducing Autler-Townes effect in lead halide perovskite nanocrystals

The study investigates how strong spin-orbit coupling in lead halide perovskites can be exploited to achieve efficient, room-temperature, coherent optical control of excitons over a broad wavelength range. Conventional coherent modulation via the optical Stark effect (OSE) in excitonic two-level systems requires large detuning and weak fields to avoid real excitation, limiting controllability and typically restricting operation to specific wavelengths and low temperatures. Multilevel excitonic schemes (e.g., involving fine-structure splitting, biexcitons, intraexciton, or intersubband transitions) can enhance control but usually demand cryogenic temperatures and pump wavelengths either near the exciton resonance (<1 μm) or in the THz–mid-IR. Lead halide perovskites possess strong spin-orbit coupling that splits conduction bands by ~0.7–1 eV, potentially enabling coherent access to inter-conduction-band (inter-CB) transitions and a multilevel ladder using near-infrared light at room temperature. The research question is whether inter-CB transitions between spin-orbit split states can drive a crossover from two-level OSE to three-level Autler-Townes effect (ATE) to enhance exciton energy shifts and suppress incoherent excitation, thereby enabling effective ultrafast optical modulation in CsPbBr3 nanocrystals at room temperature.

Prior work established the optical Stark effect (OSE) in semiconductor excitons and in two-dimensional materials, enabling valley-selective control but typically under constraints of detuning and temperature. Multilevel coherent phenomena such as Autler-Townes effect (ATE), quantum interference, and electromagnetically induced transparency have been demonstrated in quantum wells and quantum dots via exciton-biexciton, intraexciton, or intersubband transitions, often at cryogenic temperatures and specific wavelength windows (near-resonant near-IR or THz–mid-IR). Lead halide perovskites (LHPs) have shown large room-temperature OSE and possess strong spin-orbit coupling that splits the conduction band into split-off (J=1/2) and higher (J=3/2 heavy and light) states by ~0.7–1 eV—larger than in GaAs and many TMDs. Theory indicates inter-CB transitions are allowed away from the R point due to k·p mixing, and experiments have implicated these transitions in two-photon absorption spectra of perovskites. However, coherent manipulation utilizing spin-orbit split inter-CB transitions had not been explored before this work.

Materials synthesis: CsPbBr3 nanocrystals (NCs) with cuboidal shape were synthesized via a modified hot-injection method under dry nitrogen using Schlenk techniques. A Cs-oleate solution was prepared by heating Cs2CO3 (160 mg), oleic acid (0.5 mL), and 1-octadecene (6 mL) at 150 °C for 30 min and cooling to 100 °C. Separately, PbBr2 (138 mg), oleic acid (1 mL), oleylamine (1 mL), and 1-octadecene (10 mL) were degassed at 100 °C for 30 min under vacuum and then heated to 150 °C, after which 0.8 mL of Cs-oleate was rapidly injected with vigorous stirring. The reaction proceeded for 5 s at 150 °C and was quenched in an ice-water bath. Products were purified and size-selected by precipitation fractionation with centrifugation in dried n-hexane. Transmission electron microscopy determined an average cuboid edge length of 6.9 ± 0.7 nm, placing NCs in the intermediate confinement regime relative to the ~7 nm exciton Bohr diameter. Spectroscopy setup: Circularly polarized pump-probe transient absorption spectroscopy was performed at room temperature. A regenerative amplifier (central wavelength 1028 nm, 10 kHz repetition rate, 300 fs pulse duration) provided beams for pump and probe generation. Pump pulses were produced by an optical parametric amplifier; white-light probe pulses were generated by focusing into water in a 10-mm quartz cell. Probe circular polarizations (σ+ or σ−) were set with an achromatic quarter-wave plate; σ+ pump polarization was generated with a Berek compensator. Probe chirp was calibrated via pump–probe cross-correlation; temporal delay was controlled with a mechanical delay stage. CsPbBr3 NCs dispersed in hexane (1-mm quartz cell) were stirred during measurements to avoid photo-charging. Background signals from hexane were removed by subtracting the transient signal from a hexane reference. Measurement configurations and analysis: Absorption spectra and second derivatives were used to extract the band-edge exciton transition energy and linewidth by fitting with a Gaussian-profile model, yielding E0 = 2.519 eV and FWHM = 0.079 eV. Pump–probe measurements employed σ+ pump with σ+σ+ (co-polarized) or σ+σ− (cross-polarized) probing to isolate selection-rule-dependent responses. Detuning energy Δ was varied broadly (e.g., Δ = 0.16, 0.20, 0.67, 1.06, 1.26, 1.58 eV) while keeping Δ > linewidth to avoid direct excitation; in some cases (e.g., Δ = 0.16 eV) incoherent components with slow decay were observed and subtracted. Pump intensities up to 0.56 GW/cm2 were used. The exciton energy shift δE was estimated from the pump-induced change in absorption Δα using a spectral weight transfer method. Temporal dynamics were examined to confirm that the blueshift occurred only during pump overlap (indicative of coherent OSE/ATE). Modeling and parameter extraction: In the two-level regime, δE was fitted with the OSE expression (including local field corrections) to extract the band-edge transition dipole moment μ. A three-level dressed-state model (rotating-wave approximation) was developed for the observed non-monotonic Δ-dependence, involving the valence-to-split-off conduction transition and inter-CB transitions between spin-orbit split states. The effective Hamiltonian was diagonalized to compute level shifts of |+1/2⟩ and |−1/2⟩ excitonic states under σ+ pumping, reproducing the crossover from two-level OSE to three-level ATE. The inter-CB transition dipole μ′ was extracted by fitting the residual energy shift (measured δE minus two-level δE_Stark) versus pump intensity for large detuning (Δ = 1.26 and 1.58 eV). The Bloch–Siegert shift was neglected as counter-rotating terms are forbidden by angular momentum selection rules in the σ+σ+ configuration. Additional checks included estimating the inter-CB energy spacing Δ_SO from resonant pump–probe measurements of the band-edge exciton and comparing with literature. Coherent versus incoherent (e.g., two-photon absorption) contributions were quantified by their intensity dependences (linear vs quadratic) across detunings.

- The band-edge exciton in CsPbBr3 NCs exhibits a pump-induced blueshift consistent with the optical Stark effect (OSE) at small detuning (e.g., Δ = 0.16–0.67 eV), with dynamics confined to pump–probe temporal overlap. - From two-level OSE fits (including local field correction), the band-edge transition dipole moment is μ ≈ 19 D, about three times larger than in GaAs quantum wells. - As the pump photon energy is lowered into the near-infrared (increasing Δ), the exciton energy shift δE shows a non-monotonic Δ-dependence: after decreasing with Δ as expected for two-level OSE, δE increases strongly for Δ ≳ 1.06 eV. - At Δ = 1.58 eV (ħω ≈ 0.94 eV ≈ 0.37 Eg), δE is enhanced up to about fivefold relative to the two-level OSE prediction at the same intensity (Ipump = 0.56 GW/cm2), indicating a crossover to a three-level Autler–Townes effect (ATE). - The inter-conduction-band (inter-CB) transitions between spin-orbit split states have a large transition dipole moment μ′ ≈ 25 D (extracted from residual δE fits at Δ = 1.26 and 1.58 eV), larger than the band-edge dipole, consistent with their smaller transition energy and k·p mixing away from the R point. - The inter-CB energy spacing (spin-orbit splitting) relevant to the observed effect is estimated as Δ_SO ≈ 0.58 eV from resonant measurements, consistent in magnitude with reported values (~0.8 eV) considering nanocrystal distortions. - The three-level dressed-state model under rotating-wave approximation quantitatively reproduces the Δ-dependent crossover: for small Δ, |+1/2⟩ shifts via hybridization with |−1/2 + ħω⟩ (two-level OSE), while for large Δ and ħω near Δ_SO, hybridization with |+3/2 − ħω⟩ dominates (ATE). - Cross-polarized σ+σ− probing isolates the ATE contribution and shows monotonic increase of δE with Δ, matching model predictions. - Rabi frequency under typical conditions is Ω_R ≈ 14.2 meV at Ipump = 0.56 GW/cm2. - Steady-state absorption analysis yields E0 = 2.519 eV and linewidth (FWHM) = 0.079 eV for the band-edge exciton. - Incoherent two-photon absorption is evident at small detuning (Δ = 0.16 eV; ħω ≈ 0.94 Eg) with quadratic intensity scaling, but is absent at large detuning (Δ = 1.58 eV; ħω < Eg/2), enabling sizable coherent shifts without exciton population or heating. - The enhancement is prominent for pump energies below Eg/2, extending coherent control into the telecommunication-wavelength near-IR at room temperature.

The results demonstrate that strong spin-orbit coupling in CsPbBr3 nanocrystals enables inter-conduction-band transitions with large dipole moments to coherently dress the band-edge exciton, producing a crossover from a two-level optical Stark regime to a three-level Autler–Townes regime as the pump photon energy approaches the spin-orbit splitting. This addresses the central question of how to achieve efficient, room-temperature, multilevel coherent control using near-infrared light: the large μ′ and sizable Δ_SO allow strong hybridization without real excitations, enhancing δE even at large detuning. The σ+σ− selection rules confirm the ATE origin of the enhancement, while the σ+σ+ channel reveals how the inter-CB coupling augments the Stark shift of the |+1/2⟩ exciton state. Importantly, operating at ħω < Eg/2 suppresses incoherent processes like two-photon absorption and avoids phonon resonances, enabling clean, large, and potentially damage-free exciton energy modulation. These findings are significant for ultrafast optical switching and quantum control, broadening the operational wavelength window (into the telecom band) and temperature range (room temperature) for coherent exciton manipulation in perovskite nanomaterials.

This work establishes a novel coherent control scheme in lead halide perovskite nanocrystals wherein strong spin-orbit coupling enables large-dipole inter-conduction-band transitions to induce a crossover from two-level OSE to three-level ATE, yielding enhanced exciton energy shifts at room temperature using near-infrared light. Quantitatively, the band-edge dipole is μ ≈ 19 D, while inter-CB transitions exhibit μ′ ≈ 25 D; the relevant spin-orbit splitting is ~0.58 eV. The approach delivers sizable coherent shifts without incoherent backgrounds for ħω < Eg/2, suggesting pathways to efficient ultrafast optical switching and modulation at telecom wavelengths. Future work could: (i) integrate this control mechanism into device architectures for on-chip modulators; (ii) explore composition and dimensionality tuning across perovskite families to optimize Δ_SO and μ′; (iii) extend modeling to include simultaneous two-photon resonances and counter-rotating terms where allowed; and (iv) investigate coherence times and dephasing mechanisms to maximize modulation speed and fidelity.

The three-level model employs the rotating-wave approximation and neglects counter-rotating (Bloch–Siegert) terms; while selection rules suppress these in the σ+σ+ configuration, they may contribute in other configurations. A deviation between model and experiment appears near pump energies around 1.6 eV, likely due to simultaneous two-photon resonance between |−1/2⟩ and |+3/2⟩ states not captured by the simplified model. Residual incoherent components at small detuning (e.g., Δ = 0.16 eV) required subtraction, indicating real excitations under those conditions. Estimates of spin-orbit splitting (≈0.58 eV) in nanocrystals may differ from single crystals (~0.8 eV) due to structural distortions, and wavevector-dependent mixing outside the R point suggests contributions beyond a simple k ≈ 0 picture.