Optical spin readout method in a quantum dot using the ac Stark effect

We propose a method to read out the spin state of an electron in a quantum dot in a Voigt geometry magnetic field using cycling transitions induced by the ac Stark effect. We show that cycling transitions can be made possible by a red-detuned, circularly polarized cw laser, which modifies the spin eigenstates and polarization selection rules via the ac Stark effect. A Floquet-Liouville supermatrix approach is used to calculate the time evolution of the density matrix under the experimental conditions of a spin readout operation. With an overall detection efficiency of 2.5%, the readout is a single-shot measurement with a fidelity of 76.2%.

Figure 1

Energy level structure of a charged quantum dot with (a) no magnetic field, (b) a Faraday magnetic field, and (c) a Voigt magnetic field. Dipole-allowed transitions are shown with solid lines; weakly allowed transitions are shown with dashed lines.

Figure 2

Splitting of the electron and trion spin states due to the Zeeman effect (left) and the ac Stark effect (right). The trion eigenfrequencies are plotted relative to the zero-field transition resonance frequency ${\omega }_0/2\pi$ (dashed), for a fixed laser detuning of ${\mathrm{\Delta }}_1/2\pi =2000\text{GHz}$.

Figure 3

Evolution of eigenstate frequencies as a function of first magnetic field, and then Rabi frequency with a fixed magnetic field of 0.1 T and detuning ${\mathrm{\Delta }}_1/2\pi =2000\text{GHz}$. The diagram to the right shows the energy level structure in the pseudo-Faraday configuration. Allowed transitions are shown as solid lines and labeled with their polarizations. Weakly allowed transitions are shown as dashed lines.

Figure 4

Evolution of the branching ratio from the Voigt configuration $(B_x=0.1\text{T})$ to the pseudo-Faraday configuration. In the pseudo-Faraday configuration, the branching ratio is 0.02.

Figure 5

Spin readout operation under ${\sigma }_{-}$ resonant excitation. In (a) and (b) the two initial conditions are the $z-$ electron state (solid red curve) and the $z+$ electron state (dashed blue curve). (a) Photon emission rate after ${\sigma }_{-}$ resonant excitation begins. (b) Average number of photons detected as a function of detection window duration. (c) Fidelity of the spin measurement as a function of detection window duration. The vertical dashed line indicates the optimum detection window.