Excitonic Bloch-Siegert shift in CsPbI3 perovskite quantum dots

Abstract

Coherent interaction between matter and light field induces both optical Stark effect and Bloch-Siegert shift. Observing the latter has been historically challenging, because it is weak and is often accompanied by a much stronger Stark shift. Herein, by controlling the light helicity, we can largely restrict these two effects to different spin-transitions in CsPbI₃ perovskite quantum dots, achieving room-temperature Bloch-Siegert shift as strong as 4 meV with near-infrared pulses. The ratio between the Bloch-Siegert and optical Stark shifts is however systematically higher than the prediction by the non-interacting, quasi-particle model. With a model that explicitly accounts for excitonic effects, we quantitatively reproduce the experimental observations. This model depicts a unified physical picture of the optical Stark effect, biexcitonic optical Stark effect and Bloch-Siegert shift in low-dimensional materials displaying strong many-body interactions, forming the basis for the implementation of these effects to information processing, optical modulation and Floquet engineering.

Fig. 1. Spin-selective transition rules and separation of the OSE and BSS in lead halide perovskites.

a Schematic illustration of the crystal structure of CsPbI₃ perovskite phase. b Conduction band (CB) and valence band (VB) edge states coupled to circularly-polarized photons. c Interaction energy diagram of the optical Stark shift driven by a nonresonant σ⁺ photon, which occurs at the VB | − 1/2〉 and CB | + 1/2〉 states. The shift can be detected only with σ⁺σ⁺ pump-probe configuration. d Interaction energy diagram for the Bloch–Siegert shift driven by a nonresonant σ⁺ photon, which occurs at the VB | + 1/2〉 and CB | −1/2〉 states and can be detected only with σ⁺σ⁻ pump-probe configuration.

Fig. 2. Characterization of CsPbI₃ QDs.

a A representative transmission electron microscopy (TEM) image. b Steady–state absorption spectrum, with the band-edge exciton peak at ~1.98 eV. c Broadband transient absorption (TA) spectra at varying delay times, pumped at 2.64 eV (470 nm), displaying negligible photoinduced absorption in the near infrared region. Inset is a scheme showing the forbidden nature of the intra-CB transition from band-edge spin-orbit split-off states to higher-energy light and heavy electron states.

Fig. 3. Optical Stark (σ⁺σ⁺) and Bloch–Siegert (σ⁺σ⁻) shifts in CsPbI₃ QDs.

Time-zero transient absorption (TA) spectra obtained with σ⁺σ⁺ (blue) and σ⁺σ⁻ (red) pump-probe configurations with pump photon energies at (a) 1.74 eV (714 nm), (b) 1.21 eV (1027 nm), and (c) 0.805 eV (1540 nm). The incident pump intensities are indicated in each panel. d, e, f Temporal profiles of the signals reported in a–c. Note that the 1.74 eV pump pulse has been spectrally filtered using a grating in order to avoid resonant excitation, and consequently the pulse duration is broadened. g σ⁺σ⁻ TA spectra under varying pump intensities of 0.792 eV (1565 nm) photon. h Nominal Bloch–Sigert shift (blue hexagons) as a function of the incident pump intensity, calculated from the spectral-weight-transfer in g. The red solid line is a linear fit.

Fig. 4. Excitonic Bloch–Siegert shift in CsPbI₃ QDs.

a Ratio between the normal Bloch–Siegert and optical Stark shifts measured with σ⁺σ⁻ and σ⁺σ⁺ configurations, respectively (gray balls). The red solid line is the prediction by a non-interacting, quasi-particle model (Eq. (3)), whereas the blue solid line is obtained using our excitonic model (Eq. (4)) with μ₀₁ = 34 D, μ₁₂ = 28 D and E_XX = 65 meV. By setting μ₀₁ = μ₁₂ and E_XX = 0, our excitonic model (black dashed line) reduces to the quasi-particle model. The error bars are obtained from the standard variations of σ⁺σ⁺ and σ⁺σ⁻ signals in the range of ±40 fs around time-zero. b States and optical selection rules under the excitonic representation. c Equilibrium matter states (solid lines) and Floquet states (dashed lines) driven by a nonresonant σ⁺ photon, whose angular momenta are indicated by their colors. Other Floquet states are not shown because their interactions with matter states are against angular momentum conservation. The shift of the biexciton state |X₊, X_-〉 is not considered here as we are experimentally probing the shift of single-exciton transitions. There are 9 states in total in the interaction Hamiltonian.