Creating Polarization-Entangled Photon Pairs from a Semiconductor Quantum Dot Using the Optical Stark Effect

In typical epitaxial quantum dots (QDs) the ideally degenerate optical excitons are energy split, preventing the formation of two-photon entanglement in a biexciton decay. We use an external field, here a continuous-wave laser tuned to the QD in the ac Stark limit, to cancel the splitting and create two-photon entanglement. Quantum-state tomography is used to construct the two-photon density matrix. When the splitting is removed it satisfies well-known entanglement tests. Our approach shows that polarization-entangled photons can be routinely produced in semiconductor nanostructures.

Figure 1

Single QD emission spectrum. The biexcitonic (excitonic) transitions give rise to the left (right) spectrum. The two doublets are spectrally separated by $E_B/2\pi \hslash \approx 460\mathrm{GHz}$ ($\Delta \lambda \approx 1.3\mathrm{nm}$).

Figure 2

(a) Experimental setup. (b) Energy diagram in the presence of the near-resonant tuning laser. (c) Spectra of the evolution of the exciton (left) and biexciton (right) transitions with increasing tuning laser intensity, $I$. When $I=3I_0$ (uppermost spectra), the overlapped configuration sketched in (b) is achieved. $I_0=\Omega /2\pi \approx 8.3\mathrm{GHz}$.

Figure 3

(a) Real and imaginary parts of the two-photon density matrix, tomographically reconstructed from 16 coincidence measurements. No tuning laser is applied. (b) Same as in (a), but with a near-resonant laser that creates fine-structure overlap as in Fig. 2c. Off-diagonal matrix elements appear and the state is now inseparable (entangled). (c) Spectra of exciton emission with detection set to $D$ (diagonal), $L$ (left-circular), and $R$ (right-circular) polarizations, without tuning laser. (d) Same as in (c), but with the tuning laser adjusted to create fine-structure overlap, as in (b). (e) Correlation contrast in different polarization bases under tuned condition as in (b) and (d). Correlation contrast in $R/L$ basis under blue (f) and red (g) detuned conditions, i.e., when the laser does not create fine-structure overlap.

Figure 4

QD spectra and density matrices for QD2 under different tuning conditions. (a) Without any applied near-resonant laser. (b) With a laser that creates conditions of spectral overlap. (c) With a laser that purposefully increases the fine structure splitting by reversing the polarity of the laser detuning.