Control of Exciton Valley Coherence in Transition Metal Dichalcogenide Monolayers

The direct gap interband transitions in transition metal dichalcogenide monolayers are governed by chiral optical selection rules. Determined by laser helicity, optical transitions in either the $K^{+}$ or $K^{-}$ valley in momentum space are induced. Linearly polarized laser excitation prepares a coherent superposition of valley states. Here, we demonstrate the control of the exciton valley coherence in monolayer ${\mathrm{WSe}}_2$ by tuning the applied magnetic field perpendicular to the monolayer plane. We show rotation of this coherent superposition of valley states by angles as large as 30° in applied fields up to 9 T. This exciton valley coherence control on the ps time scale could be an important step towards complete control of qubits based on the valley degree of freedom.

Figure 1

(a) Schematic of experimental configuration. (b) Valley coherence generation following linearly polarized excitation ${\sigma }_X$ at 1.96 eV probed by through PL emission of $X^0$ at the typical energy 1.75 eV [31] at $T=4\mathrm{K}$. The trion emission and the low energy emission probably linked to localized states are, as expected, unpolarized [30]. (c) Representation of valley coherence (exciton pseudospin) on the Bloch sphere. At $B=0$, no rotation around the equator occurs as shown by the blue arrows. For $B\ne 0$, the exciton pseudospin precesses around the equator during the exciton lifetime. As PL emission times are very short (of the order of $\tau \approx 1\mathrm{ps}$), we probe the pseudospin orientation within the first precession period. The green arrows correspond to the state at a time $\tau$ after initialization, when recombination (pseudospin readout) occurs. By changing the amplitude and the direction of the magnetic field in the $Z$ direction, the valley coherence can be tuned to different points on the equator, compare $S(B_1)$ with $S(B_2)$. (d) The normalized $X^0$ angle dependent intensity polar plots for $B=0$ (black), $B=+9\mathrm{T}$ (red), and $B=-9\mathrm{T}$ (blue). The normalized intensity 0.7 corresponds to the center and 1 to the outermost gray circle. The laser polarization direction (constant for all $B$-field values) is indicated by the black arrow.

Figure 2

(a) Absolute rotation angle of linear polarization of $X^0$ PL for different magnetic field values (red open circles). The gray dashed curve is calculated using $\theta =[\arctan (\mathrm{\Omega }/T_{S2}^{*})/2]$ and they are stressed by the blue open triangles at the experimental magnetic field for comparison. (b) The linear polarization of $X_0$ measured along the fixed direction $X$ and $Y$. The black solid line is the calculated value. Both the gray dashed line and the blue opened triangle in (a) and the black solid line in (b) are calculated by $g=-3.7$, $T_2^{*}=0.37\mathrm{ps}$.