Optically Induced Rotation of an Exciton Spin in a Semiconductor Quantum Dot

We demonstrate control over the spin state of a semiconductor quantum dot exciton using a polarized picosecond laser pulse slightly detuned from a biexciton resonance. The control pulse follows an earlier pulse, which generates an exciton and initializes its spin state as a coherent superposition of its two nondegenerate eigenstates. The control pulse preferentially couples one component of the exciton state to the biexciton state, thereby rotating the exciton’s spin direction. We detect the rotation by measuring the polarization of the exciton spectral line as a function of the time difference between the two pulses. We show experimentally and theoretically how the angle of rotation depends on the detuning of the second pulse from the biexciton resonance.

Figure 1

(a) A Bloch sphere representation of the exciton spin state. The circle along (above) the equator describes the precession of an exciton spin initialized at $t=0$ by an $R$-polarized pulse, for $t<\tau$ ($t>\tau$), where at $t=\tau$ an $R$-polarized biexciton pulse is applied. (b) Schematic description of the relevant exciton and biexciton energy levels and the polarization selection rules for the coupling laser field. The symbol $\uparrow$ ($\Downarrow$) represents an electron (heavy hole) with $z$-direction spin projection $\frac{1}{2}$ ($-\frac{3}{2}$). Short (long) symbols represent charge carriers in their ground (first excited) state.

Figure 2

$R$-polarized PL intensity as a function of the photon energy and the time difference between two $R$-polarized laser pulses. The first is tuned into the exciton resonance and the second is detuned by $-63\mu \mathrm{eV}$ from the biexciton resonance. The temporally averaged spectrum is shown at the bottom.

Figure 3

(a) Solid line—measured biexciton PL intensity versus the second pulse detuning, at $\tau =30\mathrm{ps}$. The circles represent the specific energies used for the measurements presented in (b)–(d). The dashed line is the calculated $P_{XX}$ [Eq. (4)], for a pulse of 9 ps FWHM ($\hslash \sigma =145\mu \mathrm{eV}$). (b) Biexciton intensity versus $\tau$ close to [gray (light blue)] and far from (black) resonance. The vertical dashed line denotes $\tau =30\mathrm{ps}$. (c) Solid (dashed) line denotes PL intensity of the $H$ ($V$) component of the exciton doublet versus $\tau$, close to and far from resonance, as in (b). The curves are vertically shifted for clarity. (d) The differences between the PL from the $V$ and $H$ components, normalized by their sum at negative $\tau$, for the energies marked by circles in (a) and specified in $\mu \mathrm{eV}$ next to each curve. Vertical dotted lines present integer spin precession periods $T=h/(34\mu \mathrm{eV})=122\mathrm{ps}$.

Figure 4

Measured (symbols) and calculated (lines) oscillation amplitudes of the exciton polarization versus the detuning $\delta /\sigma$, where $\hslash \sigma =145\mu \mathrm{eV}$ and $\Omega /\sigma =0.35$ ($0.7\pi$ pulse). Dark gray (blue) [light gray (red)] color describes co- [cross-]circularly polarized pulses. Inset: The rotation angles $\theta$ versus the detuning for a $0.7\pi$ pulse.