Coherent Transfer of Light Polarization to Electron Spins in a Semiconductor

We demonstrate that the superposition of light polarization states is coherently transferred to electron spins in a semiconductor quantum well. By using time-resolved Kerr rotation, we observe the initial phase of Larmor precession of electron spins whose coherence is transferred from light. To break the electron-hole spin entanglement, we utilized the big discrepancy between the transverse $g$ factors of electrons and light-holes. The result encourages us to make a quantum media converter between flying photon qubits and stationary electron-spin qubits in semiconductors.

Figure 1

The operating principle of our QMC scheme from photon polarization to electron-spin polarization. (a) State vectors representing a photon polarization in a Poincaré sphere and an electron-spin polarization in a Bloch sphere with the phase definitions used in Fig. 3. (b) Schematic diagrams of the experimental setup and the relevant energy levels together with optical spin selection rules under an in-plane magnetic field $B_x$ that forms a $\mathsf{V}$-shaped three-level system consisting of a degenerate electron state and one eigenstate of nondegenerate light-hole (LH) states. The photon bandwidth ($\Delta {\omega }_{\mathrm{ph}}$) should be larger than the electron Zeeman splitting ($\Delta E_e$) but smaller than the LH Zeeman splitting ($\Delta E_{\mathrm{LH}}$).

Figure 2

(a) PL (blue) and PLE (red) spectra detected at HH exciton emission under $B_x=7\mathrm{T}$. The broken lines show the spectra of the pump (red) and probe (blue) lights. (b) Pump power dependence of the Kerr rotation angle (${\theta }_K$) with $D^{+}$ under $B_x=7\mathrm{T}$ at $\Delta t=12\mathrm{ps}$. Error bars show standard deviation. (c) Temporal evolution of ${\theta }_K$ with six basis polarizations under $B_x=7\mathrm{T}$. Each of the consecutive phase shifts in the cyclic order of $|{\sigma }^{+}⟩$ $(\mathrm{\text{red}})\to |D^{+}⟩$ $(\mathrm{\text{green}})\to |{\sigma }^{-}⟩$ $(\mathrm{\text{blue}})\to |D^{-}⟩$ $(\mathrm{\text{orange}})\to |{\sigma }^{+}⟩$ in $\pi /2$ steps coincides well with that of electron-spin states expected from the pump-light polarizations. In contrast, excitation with the $|H⟩$ (pink) and $|V⟩$ (sky blue) polarization, which correspond to the $B_x$ direction, generate negligible signals. (d) Large-time-scale view of Fig. 2c. (e) HH-excitation case for comparison. Only $|{\sigma }^{\pm }⟩$ excitations generate relatively large signals, indicating that spins are always projected along the $z$ axis.

Figure 3

Time evolution of ${\theta }_K$ as a function of pump-light polarization under $B_x=7\mathrm{T}$. The linear streak pattern indicates coincidence of the phase angle of the electron spins ${\phi }_x^e$ to that of the light polarization ${\phi }_x^{\mathrm{ph}}$. Definitions of the phases are shown in Fig. 1a.

Figure 4

(a) Time evolution of ${\theta }_K$ as a function of $B_x$ with $D^{+}$ pumping. The cut of ${\theta }_K$ at $B_x=4$  is shown by the dots fitted to a damped sine function. The dashed curves are the calculated tracks of the $B_x-\Delta t$ values needed to detect electrons aligned to $|\pm z{⟩}_e$ when an electron transverse $g$ factor of $-0.21$ is assumed. (b) ${\theta }_K$ as a function of pump/probe wavelengths with $D^{+}$ at $\Delta t=12\mathrm{ps}$ under $B_x=7\mathrm{T}$. Dots show the pump spectrum of ${\theta }_K$ at the probe wavelength used for all the LH measurements (795.7 nm) with a curve fitted by a two-component Gaussian.