Two-qubit conditional quantum-logic operation in a single self-assembled quantum dot

The four-level exciton/biexciton system of a single semiconductor quantum dot acts as a two-qubit register. We experimentally demonstrate an exciton-biexciton Rabi rotation conditional on the initial exciton spin in a single InGaAs/GaAs dot. This forms the basis of an optically gated two-qubit controlled rotation (CROT) quantum-logic operation where an arbitrary exciton spin is selected as the target qubit using the polarization of the control laser.

Figure 1

(Color online) Schematic diagram of the experimental setup with close up of the pulse shaper.

Figure 2

Implementation of a CROT gate on two exciton based qubits. The QD ground state $|00⟩$, the two orthogonally polarized exciton $\left(X^0\right)$ states $|01⟩$, $|10⟩$, the biexciton $\left(2X^0\right)$ state $|11⟩$, and the biexciton binding energy $\Delta E_B$ are indicated. The CROT operation is performed by an $x$-polarized $\pi$-pulse in resonant with the $X^0-2X^0$ transition. Cases (a)-(d) show the CROT operation on all four pure qubit states. (e) The CROT truth table.

Figure 3

(Color online) Photocurrent spectra. $(○)$ The single-pulse measurement shows the ground state to exciton transition $\left(0-X^0\right)$ and two features from neighboring dots (QD B and QD C). For two-pulse measurements, a linearly polarized preparation pulse prepares the exciton state. $(█)$ With copolarized pulses, the exciton-biexciton transition $\left(X^0-2X^0\right)$ and quenching of the exciton are observed. $(\times )$ With cross polarized pulses the $\left(X^0-2X^0\right)$ transition is suppressed by polarization selection rules.

Figure 4

(Color online) Conditional exciton-biexciton $\left(X^0-2X^0\right)$ Rabi rotation (change in photocurrent vs pulse area for a pulse in resonant with the $X^0-2X^0$ transition). $(○)$ The single-pulse measurement shows no oscillation as the pulse is off-resonant, as in Fig. 2a. For two-pulse measurements, a linearly polarized preparation pulse prepares the $X^0$ state. $(●)$ With copolarized pulses, a Rabi rotation between the $X^0$ and $2X^0$ states is observed [corresponding to Figs. 2c, 2d for pulse areas of $\pi$ and $2\pi$, respectively]. $(\times )$ Polarization selection rules suppress the Rabi rotation for cross polarized pulses, as in Fig. 2b. The corresponding logic states are indicated.

Figure 5

(Color online) Amplitude of the $X^0-2X^0$ Rabi rotation measured as a function of the polarization of the CROT pulse. (a)–(b) Linearly polarized CROT pulse probes exciton created with (a) $x$ and (b) $-45°$ linearly polarized prepulses. (c) An elliptically polarized CROT pulse probes exciton created by ${\sigma }_{+}$ polarized prepulse. Full lines (a)-(c) are fits to data using: $\Delta \text{PC}\propto {\left|⟨A_2|{\widehat{U}}_{\text{fs}}|A_1⟩\right|}^2$. (d) Poincaré sphere representation of exciton spin with spin precession due to fine structure.