Ultrafast electric control of cavity mediated single-photon and photon-pair generation with semiconductor quantum dots

Employing the ultrafast control of electronic states of a semiconductor quantum dot in a cavity, we introduce an approach to achieve on-demand emission of single photons with almost perfect indistinguishability and photon pairs with near ideal entanglement. Our scheme is based on optical excitation off resonant to a cavity mode followed by ultrafast control of the electronic states using the time-dependent quantum-confined Stark effect, which then allows for cavity-resonant emission. Our theoretical analysis considers cavity-loss mechanisms, the Stark effect, and phonon-induced dephasing, allowing realistic predictions for finite temperatures.

Figure 1

(a) Quantum dot (QD)-cavity system with electronic ground state $|G\rangle$, exciton states $|X_H\rangle$ and $|X_V\rangle$, and biexciton state $|B\rangle$, with binding energy $E_{\text{bind}}$ and single- and two-photon optical selection rules as indicated. The exciton state degeneracy may be lifted by fine structure splitting $E_{\text{fsp}}$. Electric tuning of exciton and biexciton energies via the quantum-confined Stark effect is also indicated. The shift in energy for the biexciton is assumed twice as large as for the excitons. (b) Illustration of the quantum-confined Stark effect that is induced for finite external electric field $F\ne 0$. A time-dependent external field allows ultrafast control of the exciton and biexciton energies. (c) Sketch of the temporal sequence used for the coherent excitation pulse, electric tuning of electronic resonance frequencies, and resulting photon emission.

Figure 2

Pulsed optical excitation of the quantum dot (QD)-cavity system with and without ultrafast electric control. Two scenarios are shown: (a) exciton excitation (top) and (c) biexciton excitation (bottom) with exciton, biexciton (solid lines) and cavity photon populations given (dashed lines). The cavity loss is $\kappa =g$ with $g=66\mu \mathrm{eV}$, resulting in a Q factor of $\approx 20.000$. The excitation pulses are centered at $15\mathrm{ps}$ with a pulse width of $\sigma =5\mathrm{ps}$. The insets illustrate the three different configurations studied, the dashed lines mark the cavity resonance, and the red arrows indicate the control of the electronic levels. In the electric tuning case, a linear electronic control starting at $t_0=25\mathrm{ps}$ with total magnitude of $\mathrm{\Delta }E=1\text{meV}$ transforms the static off-resonant case (orange) into the resonant case (blue) over a period of $10\mathrm{ps}$. Thus, in that case, excitation occurs while the electronic transitions are detuned from the cavity resonance, and efficient photon emission starts at about $t_1=35\mathrm{ps}$ when the electric control restores the resonance condition with the cavity mode. This dynamic scenario (green) combines robust resonant exciton and biexciton initialization with the cavity-enhanced photon emission, which without the electronic control would be mutually exclusive. The resulting spectra in (b) and (d) inherit the slightly redshifted and asymmetric emission characteristics compared with the resonantly pumped case.

Figure 3

Emission probability for (a) and (c) the horizontally polarized cavity photon and (b) and (d) the corresponding quantum properties for different cavity loss $\kappa \in [0.5g,4g]$. For the photon emitted from the exciton, the single-photon indistinguishability is shown. For the photon emitted from the biexciton in a direct two-photon emission process, the concurrence as a measure for the polarization entanglement is displayed. The electrically controlled emission (solid lines) is compared with the spontaneous emission from the resonant decay of an initially fully excited exciton or biexciton, respectively, without the use of an excitation pulse (dashed lines) and resonantly pumped case, as illustrated in Fig. 2 above (dotted lines).

Figure 4

Emission probability for (a) and (c) the horizontally polarized cavity photon and (b) and (d) the corresponding quantum properties for different temperatures $T\in [0\mathrm{K},10\mathrm{K}]$. For the photon emitted from the exciton, the single-photon indistinguishability is shown. For the direct two-photon biexciton to ground state transition, the concurrence as a measure for the polarization entanglement is displayed. The electrically controlled emission (solid lines) is compared with the spontaneous emission from the resonant decay of an initially fully excited exciton or biexciton, respectively, without the use of an excitation pulse (dashed lines) and resonantly pumped case, as illustrated in Fig. 2 above (dotted lines).

Figure 5

Normalized emission spectra for the case with electric control for (a) and (c) exciton and (b) and (d) biexciton. Parameters as in Fig. 3. For comparison (black lines), the emission spectra for the resonant decay case for initially fully excited exciton and biexciton, respectively, are overlayed. For the electrically controlled case, a redshifted photon emission from the exciton is observed, also showing an asymmetry for the Rabi-split emission peaks. Note that, for mirrored energy configurations, the reverse control will result in a blueshift in emission energy instead.