Proposed Coupling of an Electron Spin in a Semiconductor Quantum Dot to a Nanosize Optical Cavity

We propose a scheme to efficiently couple a single quantum dot electron spin to an optical nano-cavity, which enables us to simultaneously benefit from a cavity as an efficient photonic interface, as well as to perform high fidelity (nearly 100%) spin initialization and manipulation achievable in bulk semiconductors. Moreover, the presence of the cavity speeds up the spin initialization process beyond the GHz range.

Figure 1

(a) Scanning electron microscope image of a bimodal photonic-crystal nanocavity fabricated in a GaAs membrane with embedded quantum dots. The scale bar is 500 nm. Due to the $C_6$ symmetry of the cavity, it can support two orthogonally polarized near-degenerate modes. (b) The schematics and the optical transitions of a four-level system arising when a magnetic field is applied in the Voigt configuration [plot (a)] to a QD charged with a single electron. The states $|1⟩$ and $|2⟩$ are superpositions of electron spin up and down, and the states $|3⟩$ and $|4⟩$ are trion states with both electron spins and superposition of hole spins. The cavity mode $a$ has $H$ polarization [plot (a)] and can couple to transitions $|1⟩\to |4⟩$ and $|2⟩\to |3⟩$, while the cavity mode $b$ has $V$ polarization and can drive the transitions $|1⟩\to |3⟩$ and $|2⟩\to |4⟩$.

Figure 2

Photoluminescence spectra of the coupled QD spin-cavity system as a function of the magnetic field (a) for a QD-cavity system with $\kappa /2\pi =5\mathrm{GHz}$ and $g/2\pi =20\mathrm{GHz}$. (b) Similar PL spectra for $g/2\pi =\kappa /2\pi =20\mathrm{GHz}$. (c), (d) Energy splitting between all the QD transitions as a function of the magnetic field without (c) and with (d) a cavity in the absence of losses ($\kappa =0$).

Figure 3

(a) Initialization fidelity $|{\rho }_{11}-{\rho }_{22}|$ as a function of the cavity mode $b$ frequency ${\Delta }_b={\omega }_b-{\omega }_0$ and the pump laser wavelength ${\Delta }_l={\omega }_l-{\omega }_0$. The white point marks the situation where we get optimal spin initialization fidelity [the situation shown in (b)]: the pump laser is tuned to the QD transition $|1⟩\to |4⟩$, and the cavity mode $b$ is tuned to the transition $|2⟩\to |4⟩$. Here the double arrows denote cavity fields and the single arrows denote the laser). (c) The spin initialization as a function of time for different cavity detunings ${\Delta }_{c2}$, with the laser being fixed at the transition frequency ${\omega }_{14}({\Delta }_l\sim 2\kappa )$. ${\Delta }_{c2}$ is changed from 0 to $2\kappa$. We note that the spin-initialization time is only around $40/\kappa \sim 300\mathrm{ps}$. Parameters for simulation: $g/2\pi =\kappa /2\pi =20\mathrm{GHz}$ at a magnetic field of 5 T.

Figure 4

(a) The steady-state spin population (${\rho }_{11}-{\rho }_{22}$) as a function of the laser Rabi frequency (${\Omega }_h={\Omega }_v$). All the population is initially in state $|1⟩$, and a 5 ps laser pulse excites the system. Three different pulse detunings are used. Rabi oscillations between two spin states are observed. (b) $\mathrm{Tr}[({\rho }^{(1,2)}{)}^2]$ as a function of the laser Rabi frequency. The process becomes coherent [$\mathrm{Tr}[({\rho }^{(1,2)}{)}^2]\sim 1$] when the detuning of the pulse from the QD-cavity system is large. Parameters for simulation: $g/2\pi =\kappa /2\pi =20\mathrm{GHz}$ at a magnetic field of 5 T.