Optical Stark Effect and Dressed Exciton States in a Mn-Doped CdTe Quantum Dot

We report on the observation of spin-dependent optically dressed states and the optical Stark effect on an individual Mn spin in a semiconductor quantum dot. The vacuum-to-exciton or the exciton-to-biexciton transitions in a Mn-doped quantum dot are optically dressed by a strong laser field, and the resulting spectral signature is measured in photoluminescence. We demonstrate that the energy of any spin state of a Mn atom can be independently tuned by using the optical Stark effect induced by a control laser. High resolution spectroscopy reveals a power-, polarization-, and detuning-dependent Autler-Townes splitting of each optical transition of the Mn-doped quantum dot. This experiment demonstrates an optical resonant control of the exciton-Mn system.

Figure 1

Energy scheme of a Mn-doped QD and formation of light-matter hybrid states by a laser field. In the absence of carriers, the Mn fine structure is dominated by the strain-induced magnetic anisotropy, which also splits the biexciton states (${\mathrm{X}}_2\mathrm{Mn}$). The bright exciton levels (X, with kinetic momentum $\pm 1$) are split by the exchange interaction with the Mn (XMn levels). A pump laser tuned to a QD excited state is used to produce PL of any exciton and biexciton states. The Rabi splitting $\hslash {\Omega }_r$ induced on the Mn state by the control laser (circularly polarized ${\sigma }^{+}$) can be probed in the PL of the exciton, while the splitting of XMn is observed in the PL of the biexciton. $(\mathrm{I},n)$, $(\mathrm{II},n)$, $(\mathrm{I},n+1)$, and $(\mathrm{II},n+1)$ are the optically dressed states produced by the mixing of the uncoupled states $(\mathrm{XMn},n-1)$, $(\mathrm{Mn},n)$, $(\mathrm{XMn},n)$, and $(\mathrm{Mn},n+1)$, respectively, where $n$ is the number of photons in the control laser.

Figure 2

Autler-Townes splitting of the emission of $|-1,+5/2⟩$ in a Mn-doped QD (QD1) resonantly excited on $|+1,+5/2⟩$. (a) shows the nonresonant photoluminescence of the QD. The intensity map (c) shows the excitation energy dependence of the Rabi splitting. The corresponding emission line shape is presented in (d). The inset shows the spectral position of the Autler-Townes doublet as a function of the pump detuning. The fit is obtained with a Rabi energy $\hslash {\Omega }_r=180\mu \mathrm{eV}$. The straight lines correspond to the uncoupled exciton and laser energy. The excitation intensity dependence of the Autler-Townes doublet is presented in the intensity map (e). The corresponding emission line shape are presented in (f). The inset shows the evolution of the Rabi splitting as a function of the square root of the pump intensity. A linear increase is observed. (b) presents the circular polarization dependence of the Rabi splitting obtained under resonant excitation.

Figure 3

(a) PL of the exciton and biexciton in a Mn-doped QD (QD2). (b) Autler-Townes splitting of the exciton in QD2 detected on the biexciton PL under resonant excitation of the ground-to-exciton transition for the spin state of the Mn $S_z=+5/2$ (i), $S_z=+3/2$ (ii), and $S_z=+1/2$ (iii) (arrows in the PL of QD2). (c) Emission of the exciton for a dressed exciton-to-biexciton transition. The excitation is tuned around the state $S_z=+3/2$ of the biexciton (iv).

Figure 4

Rabi splitting obtained on mixed bright-dark exciton states in QD2. (a) presents the PL of QD2. The intensity of the lines is influenced by the absorption selectivity of the excited state (see Ref. 14). The corresponding theoretical emission spectra is presented in (b). It is calculated with $J_{e\mathrm{Mn}}=-0.095\mathrm{meV}$, $J_{h\mathrm{Mn}}=0.3\mathrm{meV}$, $J_{eh}=-0.6\mathrm{meV}$, ${ϵ}_{\mathrm{VBM}}=0.1$, ${ϵ}_{\mathrm{VBM}}=0.1$, ${\delta }_2=0.05\mathrm{meV}$, and $T=25\mathrm{K}$ (see Ref. 23 for a detail of the model). (c) presents the laser detuning dependence and the excitation power dependence of the Rabi splitting obtained on mixed bright-dark exciton under excitation on (i). (d) presents the detuning and excitation intensity dependence measured on the high energy transitions associated with the Mn spin states $S_z=+1/2$ and $S_z=+3/2$ under excitation on the mixed dark-bright exciton (ii).