Pulse-enhanced two-photon interference with solid state quantum emitters

The ability to entangle distant quantum nodes is essential for the construction of quantum networks and for quantum information processing. For solid-state quantum emitters used as qubits, it can be achieved by photon interference. When the emitter is subject to spectral diffusion, this process can become highly inefficient, impeding the achievement of scalable quantum technologies. We study two-photon interference in the context of a Hong-Ou-Mandel (HOM)-type experiment for two separate quantum emitters, with different detunings with respect to a specific target frequency. We evaluate the second order coherences that characterize photon indistinguishability between the two emitters. We find that the two-photon interference operation that is inefficient in the absence of a control protocol, when the two detunings are different and spectral overlap is lessened, can be highly improved by a periodic sequence of $\pi$ pulses at a set target frequency. Photon indistinguishability in solid state and other quantum emitters subject to spectral diffusion can thus be enhanced by the proposed pulse sequence and similar external control protocols despite the fluctuations in the environment.

Figure 1

Two-photon interference from two distant quantum emitters. Photons from Emitters $E_1$ and $E_2$ at spacetime locations 1 and 2 (respective detunings ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$ measured in the frame rotating at the set target frequency ${\omega }_0$) are sent to input ports of a 50:50 beam splitter and then measured at detectors $D_1$ and $D_2$ at spacetime locations 3 and 4. Indistinguishable photons will coalesce and emerge at the same port (top). This indistinguishability is synonymous with similar spatial temporal and spectral profiles. For high efficiency, the entanglement operation requires overlapping spectra whereas it is inefficient for low spectral overlap (bottom).

Figure 2

Schematic representation of the detection times $t$ and $t+\theta$ on the time axis.

Figure 3

Intensity correlation at the detectors in the absence of a control protocol with two independent emitters with detuning ${\mathrm{\Delta }}_1=3.0\left(\mathrm{\Gamma }\right)$ and ${\mathrm{\Delta }}_2=-4.0\left(\mathrm{\Gamma }\right)$, respectively. The inset shows the emission spectra of individual emitters with detunings ${\mathrm{\Delta }}_1=3.0\left(\mathrm{\Gamma }\right)$ (solid red line) and ${\mathrm{\Delta }}_2=-4.0\left(\mathrm{\Gamma }\right)$ (dashed green line). In the absence of any control protocol, they both have Lorentzian lineshapes centered around their respective detunings [50] and have limited spectral overlap. The intensity correlation vanishes at $\theta =0$ and periodically at $\theta =2n\pi /{\mathrm{\Delta }}_{21}, n$ integer.

Figure 4

Intensity correlation at the detectors when the two emitters, with detunings ${\mathrm{\Delta }}_1=3.0\left(\mathrm{\Gamma }\right)$ and ${\mathrm{\Delta }}_2=-4.0\left(\mathrm{\Gamma }\right)$, respectively, are driven by a periodic sequence of $\pi$ pulses with period $\tau =0.2(1/\mathrm{\Gamma })$. The inset shows the emission spectra of individual emitters with detunings ${\mathrm{\Delta }}_1=3.0\left(\mathrm{\Gamma }\right)$ (solid red line) and ${\mathrm{\Delta }}_2=-4.0\left(\mathrm{\Gamma }\right)$ (dashed green line) when they are driven by the same periodic pulse sequence [43]. The intensity correlation is zero at $\theta =0$ and finite elsewhere.

Figure 5

Intensity correlation at the detectors when the two emitters, with detunings ${\mathrm{\Delta }}_1=3.0\left(\mathrm{\Gamma }\right)$ and ${\mathrm{\Delta }}_2=-4.0\left(\mathrm{\Gamma }\right)$ (blue line), ${\mathrm{\Delta }}_1=3.0\left(\mathrm{\Gamma }\right)$ and ${\mathrm{\Delta }}_2=-2.0\left(\mathrm{\Gamma }\right)$ (red line), ${\mathrm{\Delta }}_1=3.0\left(\mathrm{\Gamma }\right)$ and ${\mathrm{\Delta }}_2=2.0\left(\mathrm{\Gamma }\right)$ (green line), are driven by a periodic sequence of $\pi$ pulses with period $\tau =0.2(1/\mathrm{\Gamma })$.

Figure 6

Intensity correlation at the detectors when the two emitters, with detuning ${\mathrm{\Delta }}_1=3.0\left(\mathrm{\Gamma }\right)$ and ${\mathrm{\Delta }}_2=-4.0\left(\mathrm{\Gamma }\right)$ (blue line), ${\mathrm{\Delta }}_1=3.0\left(\mathrm{\Gamma }\right)$ and ${\mathrm{\Delta }}_2=-2.0\left(\mathrm{\Gamma }\right)$ (red line), ${\mathrm{\Delta }}_1=3.0\left(\mathrm{\Gamma }\right)$ and ${\mathrm{\Delta }}_2=2.0\left(\mathrm{\Gamma }\right)$ (green line), are driven by a periodic sequence of $\pi$ pulses with period $\tau =0.3(1/\mathrm{\Gamma })$.