Creating excitonic entanglement in quantum dots through the optical Stark effect

We show that two initially nonresonant quantum dots may be brought into resonance by the application of a single detuned laser. This allows for control of the interdot interactions and the generation of highly entangled excitonic states on the picosecond time scale. Along with arbitrary single-qubit manipulations, this system would be sufficient for the demonstration of a prototype excitonic quantum computer.

Figure 1

Laser-induced anticrossing in the {∣01⟩,∣10⟩} subspace, for fixed ratio ${\Omega }_1∕{\Omega }_2=0.55$. Eigenvalues are calculated from Eq. (4) with ${\delta }_1=292.59\mathrm{meV}$, ${\delta }_2=290.59\mathrm{meV}$, and $V_{\mathrm{F}}=0.1\mathrm{meV}$.

Figure 2

Populations of the four states ∣00⟩, ∣01⟩, ∣11⟩, and ∣10⟩ calculated from Eq. (2) with input ∣01⟩, ${\rho }_{nm}=⟨nm\mid \rho \mid nm⟩$, $V_{\mathrm{F}}=0.1\mathrm{meV}$, and $V_{\mathrm{XX}}=0$. Dashed line: state evolution when the laser is always on. The Rabi frequencies and detunings of the laser are given by ${\Omega }_2=40.96\mathrm{meV}$, ${\Omega }_1=0.55{\Omega }_2$, ${\Omega }_2∕2{\delta }_1=0.07$, and ${\delta }_1-{\delta }_2=2\mathrm{meV}$. Dotted line: state evolution when the same laser is on for a time of $\pi ∕\left(4V_{\mathrm{eff}}\right)$ and then turned off. The small oscillations in population in the $\pi ∕\left(4V_{\mathrm{eff}}\right)$ pulse case after the laser is switched off are due to some residual coupling between the dots which can be suppressed by increasing the energy selectivity ${\delta }_1-{\delta }_2$. Solid line: state evolution when the laser is always off. In this case the state is almost purely ∣01⟩ throughout.

Figure 3

(a) Numerical simulation of the four populations for an input state ∣01⟩ and a $\pi ∕\left(4V_{\mathrm{eff}}\right)$ pulse. The simulation uses Eq. (8), which does not rely on the RWA and includes exciton decay, but not pure dephasing. The decay rates for dots 1 and 2 are given by ${\Gamma }_1={\tau }_1^{-1}={\left(331\mathrm{ps}\right)}^{-1}$ and ${\Gamma }_2={\tau }_2^{-1}={\left(100\mathrm{ps}\right)}^{-1}$, respectively. All other parameters are the same as for Fig. 2 except ${\delta }_1-{\delta }_2=2.18\mathrm{meV}$, to account for the extra shifts, and ${\omega }_l=1500\mathrm{meV}$. (b) Entanglement of formation of the input state ∣01⟩ as a function of time for a $\pi ∕\left(4V_{\mathrm{eff}}\right)$ laser pulse and for a series of different decay rates. We keep a constant ratio of ${\Gamma }_1∕{\Gamma }_2={\mid {\mathbf{d}}_1∕{\mathbf{d}}_2\mid }^2={({\Omega }_1∕{\Omega }_2)}^2$. The calculations are made by using Eqs. (8, 9, 10).