Spin dynamics of a Mn atom in a semiconductor quantum dot under resonant optical excitation

We analyze the spin dynamics of an individual magnetic atom (Mn) inserted in a II-VI semiconductor quantum dot under resonant optical excitation. In addition to standard optical pumping expected for a resonant excitation, we show that for particular conditions of laser detuning and excitation intensity, the Mn spin population can be trapped in the state which is resonantly excited. This effect is modeled considering the coherent spin dynamics of the coupled electronic and nuclear spin of the Mn atom optically dressed by a resonant laser field. This “spin population trapping” mechanism is controlled by the combined effect of the coupling with the laser field and the coherent interaction between the different Mn spin states induced by an anisotropy of the strain in the plane of the quantum dot.

Figure 1

Scheme of the optical transitions and their polarizations in a quantum dot containing an individual magnetic atom and 0 (Mn), 1 (X-Mn), or 2 (X${}_2$-Mn) excitons. The exciton states are split by the exchange interaction with the Mn spin whereas in the ground (Mn) and biexciton (X${}_2$-Mn) states the energy levels results from the fine and hyperfine structure of the Mn spin. A direct resonant excitation of the biexciton is performed by a pulsed two-photon absorption through an intermediate virtual state whereas X-Mn states are resonantly excited by a tunable CW laser.

Figure 2

Photoluminescence spectra of a Mn-doped quantum dot (QD1) obtained under a two-photon resonant absorption of a picosecond laser pulse (blue). The resonant creation of the biexciton (X${}_2$-Mn) is only possible for a linearly polarized excitation (red) whereas almost no photoluminescence is observed for circularly polarized pulses (black). The influence on the Mn spin population of a CW control laser (green) in resonance with the exciton (X-Mn) levels can be detected in the intensity distribution of X${}_2$-Mn. Inset: Photoluminescence intensity of one X-Mn line versus the intensity of the pulsed linearly polarized excitation. The $P^2$ dependence is characteristic of a two-photon absorption.

Figure 3

(a) Map of the intensity of X${}_2$-Mn on QD1 versus the energy of the linearly polarized CW resonant excitation on X-Mn for a linearly polarized detection of the two-photon PL of X${}_2$-Mn. (b) PL spectra of X${}_2$-Mn obtained for a resonant CW excitation on (i) and (ii). (c) PL spectra of X${}_2$-Mn under CW excitation on (ii) at zero field (red) and under a transverse magnetic field $B_x=0.22$ T (black). (d) PL spectra of X-Mn (black) and intensity of each X${}_2$-Mn lines versus the CW laser excitation energy scanned across X-Mn.

Figure 4

Map of the intensity of X${}_2$-Mn in QD2 versus the energy of the CW resonant excitation on X-Mn for co- (a) and cross- (c) circular CW excitation and detection of X${}_2$-Mn. (b) and (d) present the corresponding intensity curves of X${}_2$-Mn for the spin states $S_z=+5/2$ (1) and $S_z=-5/2$ (6).

Figure 5

High-resolution intensity map of X${}_2$-Mn versus the energy of a single-mode resonant excitation scanned around $|J_z=-1,S_z=+5/2\rangle$ for co- (a) and cross- (c) circular excitation on X-Mn and detection on X${}_2$-Mn (QD2). (b) and (d) present the corresponding intensity curves of X${}_2$-Mn for the spin states $S_z=-5/2$ and $S_z=+5/2$.

Figure 6

Scheme of the energy levels and transition rates involved in the resonant excitation model (see text). $\hslash {\Omega }_R$ is the energy coupling with the laser, ${\gamma }_d=1/{\tau }_d$ is a pure dephasing rate of the exciton, ${\Gamma }_{\mathrm{Mn}}=1/{\tau }_{\mathrm{Mn}}$ is the spin relaxation rate of the Mn, ${\Gamma }_r=1/{\tau }_r$ is the optical recombination rate of the exciton. A relaxation rate of the exciton-Mn complex ${\Gamma }_{\mathrm{relax}}=1/{\tau }_{\mathrm{relax}}$ is used for an effective description of the optical pumping effect.

Figure 7

Calculated population of the six electronic spin states of a Mn versus the detuning $\delta$ of the CW control laser around the X-Mn state $|J_z=-1,S_z=+5/2,I_z\rangle$ for different Rabi energies: (a) $\hslash {\Omega }_R=12.5\mu \mathrm{eV}$, (b) $\hslash {\Omega }_R=25\mu \mathrm{eV}$, and (c) $\hslash {\Omega }_R=50\mu \mathrm{eV}$. The relaxation times are ${\tau }_{\mathrm{Mn}}=250$ ns, ${\tau }_r=0.25$ ns, ${\tau }_{\mathrm{relax}}=60$ ns, ${\tau }_d=100$ ps, and the Mn fine-structure parameters ${\mathcal{D}}_0=7\mu \mathrm{eV}$ and $E=0.35\mu \mathrm{eV}$.

Figure 8

Calculated population of the six spin states of the Mn versus the detuning $\delta$ of the CW laser around the X-Mn states $|J_z=-1,S_z=+1/2,I_z\rangle$ (a), $|J_z=-1,S_z=+3/2,I_z\rangle$ (b), and $|J_z=-1,S_z=+5/2,I_z\rangle$ (c) at a fixed Rabi energy $\hslash {\Omega }_R=25\mu \mathrm{eV}$. The relaxation times are ${\tau }_{\mathrm{Mn}}=250$ ns, ${\tau }_r=0.25$ ns, ${\tau }_{\mathrm{relax}}=60$ ns, ${\tau }_d=100$ ps and the Mn fine-structure parameters ${\mathcal{D}}_0=7\mu \mathrm{eV}$ and $E=0.35\mu \mathrm{eV}$.

Figure 9

(a) Calculated population of $S_z=+5/2$ versus the CW laser detuning $\delta$ around $|J_z=-1,S_z=+5/2,I_z\rangle$: (a) for different values of the in-plane anisotropy of the strain $E$ at a fixed Rabi energy $\hslash {\Omega }_R=25\mu \mathrm{eV}$ and (b) for different transverse magnetic field $B_x$ with $E=0.35\mu \mathrm{eV}$ and $\hslash {\Omega }_R=12.5\mu \mathrm{eV}$. The inset shows the transverse magnetic field dependence of the peak population of $S_z=+5/2$. The relaxation times are ${\tau }_{\mathrm{Mn}}=250$ ns, ${\tau }_r=0.25$ ns, ${\tau }_{\mathrm{relax}}=60$ ns, ${\tau }_d=100$ ps and the magnetic anisotropy ${\mathcal{D}}_0=7\mu \mathrm{eV}$.

Figure 10

(a) PL of X-Mn in QD3 (black). The green curve is the spectra of the single-mode laser used for the power dependence presented in (b). The blue curve presents the intensity of X${}_2$-Mn for the spin state $S_z=+5/2$ versus the energy of the $\sigma$ single-mode laser scanned around the low-energy line of X-Mn. (b) PL intensity of the high ($S_z=-5/2$, black squares) and low ($S_z=+5/2$, red circles) energy lines of X${}_2$-Mn versus the square root of the intensity $P$ of the resonant CW laser (quantity proportional to the laser electric field). (c) PL spectra of X${}_2$-Mn for two slightly different excitation energies: excitation energy pointed by the red arrow in (a) (red curve) and by the black arrow in (a) (black curve). (d) PL spectra of X${}_2$-Mn for two different excitation power: excitation power pointed by the red arrow in (b) (red curve) and by the black arrow in (b) (black curve). (e) Calculated power dependence of the different spin states populations for an excitation detuned by $\delta =-40\mu \mathrm{eV}$ from $|J_z=-1,S_z=+5/2,I_z\rangle$. The parameters used in the calculation are ${\tau }_{\mathrm{Mn}}=250$ ns, ${\tau }_r=0.25$ ns, ${\tau }_{\mathrm{relax}}=60$ ns, ${\tau }_d=100$ ps, ${\mathcal{D}}_0=7\mu \mathrm{eV}$, and $E=0.35$ $\mu \mathrm{eV}$.