Inversion recovery of single quantum-dot exciton based qubit

We investigate the coherence decay of a single-exciton-based qubit with electrical readout. Pairs of laser pulses initialize the qubit state and then map the target basis onto the measurement basis, probing the decay of either the population inversion or electronic polarization components of the state vector. A comparison of coherence and population decay confirms that the exciton coherence is lifetime limited by fast voltage-tunable electron tunneling. Optimum coherence times are limited by a heavy-hole tunneling rate slow compared with the repetition rate of the laser.

Figure 1

(a) Schematic of photocurrent measurement. $V_r$ and $V_s$ are the applied and Schottky voltages, respectively. (b) Effect of pulse sequence for $T_1$ (inversion recovery) and $T_2$ (quantum interference) measurements, on the qubit state vector.

Figure 2

Quantum interference measurement for $V_r=0.80\mathrm{V}$. (a) Photocurrent vs time delay for two $\frac{\pi }{2}$ pulses. Inset: quantum interference observed on a fine time scale. (b) Interference amplitude vs time delay. The exponential decay yields $T_2$. Inset: Rabi flop in photocurrent vs single-pulse area.

Figure 3

Inversion recovery measurements. (a) Normalized photocurrent $P\left(\tau \right)=\frac{\mathrm{PC}\left(\tau \right)-\mathrm{PC}\left(0\right)}{2\mathrm{PC}\left(\mathrm{SP}\right)-\mathrm{PC}\left(0\right)}$ versus time delay $\tau$ for excitation with two $\pi$ pulses at various reverse-bias voltages. Traces are offset for clarity. (b) Comparison of $T_1\left(X^0\right)$ and $T_2$ versus reverse voltage. (c) ${\Gamma }_1\left(hh\right)$ slow tunneling rate of heavy holes. The horizontal line indicates the repetition rate of the laser. Inset: energy relaxation scheme of the neutral exciton. ${\Omega }_r$ is the Rabi frequency.

Figure 4

$\star \mathrm{PC}\left(\pi \right)$: photocurrent per pulse measured for a single $\pi$ pulse in electrons per pulse. Dashed line: ideal photocurrent detector efficiency ${\eta }_{\mathit{\text{ideal}}}\left(\mathrm{PC}\right)$. dotted line: probability $p$ that a quantum dot is in the vacuum state when next pulse arrives, calculated using ${\Gamma }_1\left(\mathrm{hh}\right)$ data from Fig. 3c. Solid line: overall photocurrent detection efficiency $\eta \left(\mathrm{PC}\right)$.