Generation of fully phase controlled two-photon entangled states

Abstract

Control over the internal states of trapped ions makes them the ideal system to generate single and two-photon states. Coupling a single ion to an optical cavity enables efficient emission of single photons into a single spatial mode and grants control over their temporal shape, phase and frequency. Using the long coherence time of the ion's internal states and employing a scheme to protect the coherence of the ion-cavity interaction, we demonstrate the generation of a two-photon entangled state with full control over the phase. Initially, ion-photon entanglement is generated. A second photon is subsequently generated, mapping the ion's state onto the second photon. By adjusting the drive field the phase of the entangled state can be fully controlled. We implement this scheme in the most resource efficient way by utilizing a single $^{40}$Ca$^+$ ion coupled to an optical cavity and demonstrate the generation of a two-photon entangled stated with full phase control with a fidelity of up to 82\%.

Figures (4)

• Figure 1: Single $^{40}\text{Ca}^{+}$-ions are trapped in a linear Paul trap at the antinode of an optical cavity. The cavity mirrors are placed within the DC end-cap electrodes with an ion-cavity coupling $g_0=2\pi \times0.76$ MHz. The generated photons are sent through two band-pass filters to remove the $894$ nm cavity lock light and subsequently through a pair of waveplates and a PBS whose outputs are each coupled to a single photon detector.
• Figure 2: Experimental pulse sequence for creating entangled photon pairs. The ion is Doppler cooled for $6$$\mathrm{ \mu s}$ before being optically pumped into the S$_{1/2}$,$m_j=-1/2$ state with >95% efficiency. From this state the ion is transferred to the D$_{3/2}$,$m_j=-1/2$ state via STIRAP. A bi-chromatic 850 nm pulse produces an ion-photon entangled state. A second bi-chromatic drive at 854 nm generates a second photon producing a two-photon entangled state.
• Figure 3: Photon detection probability for the two polarization channels for measured entangled pairs. Each photon area is normalized to 1 across both polarizations.
• Figure 4: Detector correlation outcomes for all three measurement bases (H/V, A/D, R/L), used to calculate fidelity of the created (a) $\xspace\left\vert \Psi^- \right\rangle\xspace$ and (b) $\xspace\left\vert \Psi^+ \right\rangle\xspace$ Bell states, showing successful creation of entangled photon pair with fidelity of 0.82 and 0.70 respectively. The gray dashed lines mark the measurement efficiency for a perfect Bell state. (c) and (d) showing contrast measurement in X-basis as phase is scanned to find the optimum. Solid lines are fitted sin curves of form $A \sin(x+\phi)$.