The optical Stark effect is a coherent light–matter interaction describing the modification of quantum states by non-resonant light illumination in atoms, solids and nanostructures. Researchers have strived to utilize this effect to control exciton states, aiming to realize ultra-high-speed optical switches and modulators. However, most studies have focused on the optical Stark effect of only the lowest exciton state due to lack of energy selectivity, resulting in low degree-of-freedom devices. Here, by applying a linearly polarized laser pulse to few-layer ReS2, where reduced symmetry leads to strong in-plane anisotropy of excitons, we control the optical Stark shift of two energetically separated exciton states. Especially, we selectively tune the Stark effect of an individual state with varying light polarization. This is possible because each state has a completely distinct dependence on light polarization due to different excitonic transition dipole moments. Our finding provides a methodology for energy-selective control of exciton states.


When a semiconducting system is excited by a laser pulse with photon energy lower than that of exciton transition, a virtual optical transition is invoked resulting in so-called photon-dressed states1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16. It usually interacts repulsively with original states, leading to the characteristic blue-shift of the exciton energy spectrum. Along with the fact that the coherent interaction can only take place during the time duration of an ultra-short laser pulse, such a unique feature makes this phenomena, the so-called excitonic optical Stark effect, ideal for ultrafast optical switches and modulators3,4,5,6,7,8,9,10,12,13,14,15,16,17,18. So far, however, there has been no strategy for energy-selective control of exciton states. More specifically, in conventional semiconductors such as GaAs-based quantum wells, most relevant studies have been focused only on the lowest exciton state (for example, heavy-hole exciton), because it was impossible to selectively measure the optical Stark shift of the higher state (for example, light-hole exciton), as illustrated in Fig. 1a (refs 459,1112). Thus, this effect still lacks practicality, with possible applications such as wavelength-selective optoelectronics. In this regard, if it is possible to selectively control the Stark shift of more than one exciton state, it shall be a technological breakthrough for novel optical devices with high degree-of-freedom and functionality.

Figure 1: Light-polarization-dependent optical Stark effect of excitons in ReS2.

(a,b) Comparison of excitonic optical Stark effect in conventional semiconductors (a) and ReS2 (b). X1 and X2 are the lowest two exciton states and G indicates the ground state. In conventional semiconductors (a), such as GaAs-based quantum wells, X1 and X2 correspond to heavy-hole and light-hole excitons, respectively. Pump photon energy should be smaller than that of the lower-lying X1 transition to avoid real transition (see black arrows). Dashed lines represent the energy levels of unperturbed states. Unlike conventional semiconductors, energy-selective optical Stark effect is possible in ReS2 by choosing proper polarization configurations of pump and probe light (see main text). (c) A schematic illustrating the pump-probe experiment of few-layer ReS2. Bluish-green (yellow) dots are Re (S) atoms. Two electron (?)—hole (+) pairs represent anisotropic excitons, X1 (blue) and X2 (red). The light-polarization-dependent optical Stark effect is measured by varying polarization of the linearly polarized pump (red field) and probe (white field) pulses. Inset: optical image of few-layer ReS2. Yellow thick lines (main panel and inset) indicate the crystal b axis. Red graph shows the AFM height profile of the ReS2 sample along the red dashed line. Scale bar, 15 μm. (d) Polarization-dependent absorption spectra of few-layer ReS2. (e) Corresponding spectral weights of Lorentzian contributions of X1 (blue dots) and X2 (red dots). Yellow line represents the b-axis. Solid fit lines are proportional to cos2(θ?θmax)with offset, where θmax values are polarization angles of the excitons (19° for X1 and 87° for X2).

In the past few years, two-dimensional transition metal dichalcogenides (2D TMDs) have gained intensive attention due to their outstanding excitonic properties, arising from strong confinement and reduced dielectric screening19,20,21. It has recently been discovered that the optical Stark shift of excitons in different valleys in momentum space can be determined by changing helicity of light in monolayer group VI TMDs (WS2 and WSe2) in a completely selective manner13,14. Since the valley excitons at K (K′) point in these studies are energetically indistinguishable, however, it can be said that no experimental approaches for energy-selective optical Stark effect of excitons have been made.

ReS2 is a member of a recently emerged family of group VII 2D TMDs22,23,24,25,26,27,28,29. Unlike molybdenum and tungsten dichalcogenides, group VI TMDs with hexagonal structure, ReS2 exhibits reduced in-plane crystal symmetry with a distorted 1T structure forming Re atom chains (bluish green dots in Fig. 1c) aligned along the b axis (yellow thick line in Fig. 1c)23. Remarkably, the unique symmetry leads to the anisotropic linear polarization of excitons, as illustrated by the blue and red electron–hole pairs in Fig. 1cFigure 1d shows the polarization (θ)-resolved absorption spectra of few-layer (7–8 layers) ReS2 with linearly polarized light (where θmeasures the polarization angle with respect to the b axis, see the inset of Fig. 1c). The absorption peaks, labeled as X1 and X2, arise from the two lowest, energetically nondegenerate direct exciton states near Γ point27 and show strong polarization dependence as reported by Aslan et al.28 Corresponding θ-dependent Lorentzian spectral weights clearly reveal their linear nature (Fig. 1c). Importantly, these excitons are polarized at different angles (θ19° and87° for X1 and X2, respectively)28, making it possible to access individual exciton states selectively by choosing the appropriate polarization of light. In view of the excitonic optical Stark effect, therefore, it can be expected that these two exciton states will be selectively controlled by tuning light polarization as depicted in Fig. 1b; the optical Stark shift will predominantly occur at the X1 (X2) state when the polarizations of pump and probe light are parallel with its orientation angle of 19° (87°), as shown in the middle (right) panel of Fig. 1b.

In this work, by using ultrafast optical pump-probe spectroscopy, we control the optical Stark effect of the two direct exciton states in a light-polarization-selective manner. Based on the excitons’ linearly polarized nature and anisotropy, we selectively measure the shift of the two energetically nondegenerate states by manipulating the angle of the linearly polarized pump and probe light. We gradually tune the Stark shift for X1 and X2, which obviously has different light-polarization dependence. This is possible because the transition dipole moment of each excitonic state depends on completely different angles of light polarization. Our findings offer a foundation for energy-selective control of quantum states in excitonic systems.


Observation of the optical Stark effect in ReS2

Few-layer (7–8 layers) ReS2 flakes were mechanically exfoliated onto sapphire substrates as shown in the inset ofFig. 1c (see Method). We chose to study few-layer ReS2 over monolayer due to the following reasons: the difference between the polarization angle of X1 and X2 is larger in the few-layer (70°) than in the monolayer (45°), and the relative oscillator strength of the X1 transition is extremely small compared with the X2 transition in the few-layer28. These features indicate that the monolayer is less favourable in experimentally distinguishing the optical response of the individual excitons.

We measured the pump-induced change in the transmission of probe light (differential transmission, DT) as a function of pump–probe time delay (τ) in pump–probe experiments (see Methods). Polarization-controlled pump and probe beams were both linearly polarized. All measurements were performed at low temperature (78?K) because exciton linewidths in ReS2 are significantly narrowed with decreasing temperature22 (see Supplementary Figs 1–3 andSupplementary Note 1 for room temperature measurements of bilayer ReS2 with circularly polarized probe).

We first explore the detailed DT response with co-linear pump–probe configuration at θ=70° to confirm the optical Stark effect of both X1 and X2 excitons. Two absorption peaks due to X1 and X2 are observed near 1.53 and 1.59?eV, respectively, which is in well agreement with a prior study28(Fig. 2a). To measure the optical Stark shifts of these two states, we excited the sample with pump photon energy detuned to 90?meV below X1 transition (that is, pump photon energy=1.44?eV) and monitored the time-resolved DT dynamics. Before analyzing the results, it is instructive to note the spectral signature of the optical Stark effect. As illustrated in Fig. 2b, when an absorption resonance is blue-shifted, the corresponding DT signal shows a positive-to-negative sign change near the resonance energy, resulting in a similar shape to the first derivative of the absorption. Indeed, we observed positive-to-negative sign changes of DT near X1 and X2 at τ=0?fs (Fig. 2c), indicating blue shifts of both exciton resonances. We also see that the transient shifts of excitons occur only during the pump laser time duration. Such a fast response cannot arise from the slow dynamics of photo-generated excitons. Instead, it stems from the coherent interaction of the material with ultra-short pulse, namely the excitonic optical Stark effect. This is corroborated by the DT time-traces (Fig. 2d) which show strong spike-like signals due to transient shifts of excitons near τ=0?fs (see Supplementary Fig. 4 and Supplementary Note 2 for further confirmation). The spike-like peaks are followed by slow DT signals arising from pump-excited real carrier dynamics5,6,13. We eliminate this effect when estimating the magnitude of Stark shifts in the discussion below (see Supplementary Fig. 5 andSupplementary Note 3).

Figure 2: Observation of the optical Stark effect in few-layer ReS2.

Figure 2

(a) Absorption spectrum with light polarization angle of θ=70°. (b) Schematic illustration of DT spectrum (black line) due to Stark shift for an exciton state. Gray and blue lines indicate unperturbed and blue-shifted absorption resonances, respectively. (c,d) Transient DT dynamics with a co-polarized pump–probe configuration (θ=70°) (c) and time traces at two different probe photon energies (d).

Energy-selective optical Stark effect

With this understanding, we now investigate the selectively tunable optical Stark effect of excitons. For this purpose, we measure the DT spectra at τ=0?fs while varying pump–probe polarization configuration, with pump photon energy detuned to 90?meV below the X1 level and fluence fixed at 230?μJ?cm?2. First, to measure the Stark shift of X1 in a selective manner, the probe polarization angle was fixed at θ=20°, at which X1 is predominantly coupled with light and X2 has a negligible transition dipole moment (see the equilibrium absorption spectrum in the top panel of Fig. 3a). Under this condition, we observed that the co-linearly polarized pump–probe pulses cause an absorption-derivative-like DT response (middle panel, Fig. 3a) only at the spectral region dominated by X1(blue-shaded area), indicating selective optical Stark effect of X1. The DT spectrum has slight asymmetry and broad background, originating from the pump-excited real carriers discussed above (Supplementary Note 3). The amplitude of the Stark signal becomes small when the pump is orthogonally polarized to the probe, as shown in the bottom panel of Fig. 3a, showing reduced blue shift. This can be explained by the anisotropic optical selection rule of X1, which show very weak coupling with pump light with the polarization of θ=110° (Fig. 1e). In a similar manner, we selectively measure the optical Stark shift of X2. At a fixed probe polarization of θ=90°, at which X2 dominates the optical response (top panel in Fig. 3b), clear absorption-derivative-like DT response due to optical Stark shift of X2 is observed at co-polarized pump–probe configuration (middle panel in Fig. 3b). Similar to the X1’s response, it shows decrease in amplitude at the cross-polarized pump–probe configuration (bottom panel in Fig. 3b).

Figure 3: Exciton-selective optical Stark effect controlled by light polarization.

Figure 3

(a,b) Equilibrium absorption spectra with light polarization angle of θ=20° (top panel in a) and θ=90° (top panel in b). Black dots (middle panels) and gray dots (bottom panels) are transient DT spectra at τ=0?fs with co-polarized and cross-polarized pump-probe configurations, respectively. Probe polarization angles are fixed at θ=20° (a) and θ=90° (b). Pump photon energy is 1.44?eV with fluence of 230?μJ?cm?2. The blue- (red-) shaded area represents the spectral region where DT signal is dominated by the shift of the X1 (X2) state. (c,d) Pump-polarization-dependent optical Stark shifts of X1(blue dots in c) and X2 (red dots in d) with fixed probe polarizations of θ=20° and θ=90°, respectively. The solid lines are fits.

These results enlighten us of significant benefits of ReS2 in terms of selective optical control of excitons. Firstly, as shown in the middle panels of Fig. 3a,b, it is possible to measure the shift of a certain exciton state in a completely exclusive manner, indicating high exciton selectivity. More importantly, the results also reveal energy selectivity, considering that the two exciton states possess well-separated energy levels (note that the spectral distance between the two exciton resonances are larger than the sum of their half linewidths, see Supplementary Fig. 6). In particular, the higher-lying exciton state (X2) can be selectively modulated without being disturbed by the lower-lying exciton (X1) (Fig. 3b). Such unique functionality is absent in other materials, such as semiconductor quantum wells, carbon nanotubes and group VI TMDs. Schematics in Fig. 1b summarize these findings.

For a more comprehensive understanding of this effect, we measured the pump-polarization-dependent DT spectra while tuning the angle of pump polarization continuously at τ=0?fs, and estimated corresponding magnitudes of exciton resonance shifts for X1 (ΔE1, blue dots in Fig. 3c) and X2 (ΔE2, red dots in Fig. 3d) with fixed probe polarizations of θ=20° and of θ=90°, respectively (see Supplementary Fig. 7 for measured DT spectra and Supplementary Note 3 for details of the fitting procedure). The Stark shift is maximized (minimized) when pump polarization is parallel (perpendicular) to the orientation angle of each exciton. As indicated by the solid lines in Fig. 3c,d, the gradual changes of ΔEi (i=1, 2) as a function of pump polarization (θpump) can be well fit with a simple function , setting θmax,i(at which  is maximized) to the individual excitons’ original polarizations (that is, θmax,1=19° for X1 and θmax,2=87° for X2). Here, a and b are the fitting parameters. These results clearly indicate that the polarization-dependent optical Stark shifts of each exciton states directly follow their own spatial orientations. Such behavior can be understood by the following simple relation. In the semi-classical picture, the optical Stark shift of an individual exciton state can be approximated as , where μ is the transition dipole moment between the ground and the exciton state, ? is the electric field of the pump light, X and pumpare the energy of the excitonic transition and pump light, respectively. Considering the proportionality of μ2 to the oscillator strength, the observed θpump dependence of ΔEi is well explained by the light-polarization-dependent spectral-weights (see Fig. 1e) for each excitonic absorption. Note that we obtained similar results with a circularly polarized probe in bilayer ReS2 (Supplementary Note 1). The strengths of the optical Stark effect ()12,14 for X1 and X2 are about 17 D2 and 15 D2 at co-linear pump–probe polarization configurations, respectively (1D≈3.3 × 10?30C·m). These values are of the same order of magnitude as that of group VI TMD (45 D2; ref. 14).


This work reveals functionalities of group VII 2D TMD ReS2 for ultrafast optical applications. By utilizing the characteristic anisotropy of excitons, we can selectively tune the optical Stark shift of two energetically nondegenerate exciton states by manipulating light polarization. We emphasize that such advantages basically originate from the unique in-plane crystal anisotropy of group VII TMDs, which is absent in group VI 2D TMDs (for example, MoS2, MoSe2, WS2 and WSe2). Of course, group VII TMDs are not the only material family exhibiting anisotropic property of excitons; there are several systems possessing anisotropic excitonic properties (such as carbon nanotubes (CNTs) and black phosphorus (BP))12,30,31,32. However, both of them lack polarization-dependent exciton selectivity so that energy-selective optical Stark effect cannot be expected. For CNTs, since the anisotropy of excitonic transition arises simply from the geometrical alignment, all excitonic transitions should have same polarization dependence12. For BP, there is only one prominent excitonic transition with distinct anisotropy30. Thus, group VII TMDs are ideals material platforms for testing the energy selective control of the excitonic optical Stark effect.


Sample preparation

The ReS2 few-layer flake on a sapphire substrate was prepared by polydimethylsiloxane (PDMS)-assisted mechanical exfoliation from bulk crystals (HQ graphene).

Ultrafast spectroscopy

Ultrafast pump–probe spectroscopy was based on the 250?KHz Ti:sapphire regenerative amplifier laser system (Coherent RegA 9050). Pump pulses of 860?nm with filtered 10?nm (time duration200?fs) bandwidth were obtained by the second harmonic generation of an optical parametric amplifier’s idler output pulses (coherent OPA). White-light-continuum probe pulses were generated by focusing 800?nm pulses to a sapphire disk. The linear polarizations of pump and probe pulses were controlled by sets of polarizers and half-wave plates. We measured pump-induced percent change in the transmission of probe light (ΔT/T). All measurements were performed at 78?K.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


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Selectively tunable optical Stark effect of anisotropic excitons in atomically thin ReS2


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