Engineering energy-time entanglement from resonance fluorescence

Abstract

Resonance fluorescence from a coherently driven two-level emitter is a minimal quantum optical field that combines phase coherence with single-photon-level nonlinearity. Here we show that it can be engineered, using only passive linear interferometry, into energy-time entanglement. By injecting resonance fluorescence from a single quantum dot into an asymmetric Mach--Zehnder interferometer operated near destructive interference of the single-photon component, we generate an output field whose coincidence statistics are dominated by the simultaneous two-photon contribution |2> and the temporally separated photon-pair contribution |11>. In a Franson geometry, these two sectors are resolved on the coincidence-delay axis, and both exhibit high-visibility nonlocal interference fringes and violate the Clauser--Horne--Shimony--Holt Bell inequality. Our results reveal a general route for engineering entanglement from resonance fluorescence using passive optics.

Figures (12)

• Figure 1: Interferometric synthesis of time--energy entanglement. The RF field from a coherently driven two-level emitter is injected into an asymmetric Mach--Zehnder interferometer (AMZI) with phase set to $\pi$. Destructive interference suppresses the probability of single-photon terms from $\mathcal{O}(p_1)$ to $\mathcal{O}(p_1^2)$, reshaping the output toward prominence of two-photon components: a same-bin pair $\ket{2}$ ($\ket{02}$ or $\ket{20}$) and a time-bin pair $\ket{11}$ separated by the interferometer delay imbalance $\tau_p$. Because the emission time of each RF photon is indeterminate prior to detection, the temporal superposition of these two-photon amplitudes yields time--energy entanglement. $p_0$ and $p_1$ are the probabilities of the vacuum and one-photon components, respectively, satisfying $p_0 + p_1 = 1$.
• Figure 2: Experimental setup and state preparation.a, RF source: an InAs QD in a low-reflectivity micropillar cavity under cw resonant excitation. b, State-preparation AMZI. c, Franson analyser. d, High-resolution spectra of the raw RF (blue) and the field after the state-preparation AMZI (red); traces are vertically offset for clarity. e, Second-order autocorrelation functions $g^{(2)}_{HBT}(\Delta t)$ of the raw RF (blue) and the AMZI-prepared output (red). Abbreviations: FBS, fiber beam splitter; PBS, polarizing beam splitter; BS, beam splitter; MR, mirror; QWP/HWP, quarter-/half-wave plate; FC, fiber coupler; PZT, piezoelectric transducer; SNSPD, superconducting nanowire single-photon detector.
• Figure 3: Franson interference.a, Measured second-order correlation functions between detectors $A_1$ and $B_1$ for phase settings $\phi_A + \phi_B = 0$ and $\pi$. b and c, Measured two-dimensional correlation maps with $\phi_B = 0$ (b) and $\phi_B = \pi/2$ (c). An excitation power of $\bar{n}=0.01$ was used for the measurements in a--c. d and e, Corresponding theoretical simulations for b and c, respectively.
• Figure 4: Franson interference fringes.a--d, Interference curves of the coincidence counts $N(\phi_A,\phi_B)$ extracted at time delays of 0, $\pm\tau_p$, and $\pm\tau_m$, $\pm(\tau_p+\tau_m)$ respectively, with $\phi_B$ fixed at 0 and $\pi/2$. The solid dots represent the experimental data, and the solid lines are the fitting results.
• Figure 5: CHSH Bell inequality violation.a, Correlation functions at coincidence delays of $0$ and $\pm\tau_p$ for $\bar{n}=0.01$. b, Excitation-power dependence of the CHSH $S$ parameters extracted at coincidence delays of $0$ (red) and $\pm\tau_p$ (blue). c, Excitation-power dependence of the second-order autocorrelation $g^{(2)}_{\mathrm{HBT}}(0)$ of the AMZI-prepared output at $0$ (red) and $\pm\tau_p$ (blue) delays. Inset: $g^{(2)}_{\mathrm{HBT}}(0)$ of the raw RF versus $\bar{n}$.