Atom-Atom Entanglement by Single-Photon Detection

A scheme for entangling distant atoms is realized, as proposed in the seminal paper by [C. Cabrillo et al., Phys. Rev. A 59, 1025 (1999)]. The protocol is based on quantum interference and detection of a single photon scattered from two effectively one meter distant laser cooled and trapped atomic ions. The detection of a single photon heralds entanglement of two internal states of the trapped ions with high rate and with a fidelity limited mostly by atomic motion. Control of the entangled state phase is demonstrated by changing the path length of the single-photon interferometer.

Figure 1

Experimental procedure for entanglement generation. (a) The fluorescence of the two ions is overlapped using a distant mirror which sets the effective distance between them to $d=1$ meter. A half wave plate (HWP), a polarizing beam splitter (PBS), single-mode fiber (SMF), beam splitter (BS), piezoelectric transducer (PZT) and a single-mode optical fiber select the polarization and the spatial mode before an avalanche photodiode (APD1). A nonpolarizing beam splitter and an additional avalanche photodiode (APD2) can be inserted to form a Hanbury Brown–Twiss setup. See details in main text. (b) Level scheme of ${}^{138}\mathrm{Ba}^{+}$ including the wavelengths of the lasers used in our experiment. (c) Experimental sequence. Spontaneous Raman scattering to $|e⟩$ triggers emission of a single photon from the two atoms. Upon successful detection of a ${\sigma }^{-}$ photon, state analysis comprising coherent radio-frequency (rf) pulses at 11 MHz, and electron shelving to the $5D_{5/2}$ level are performed. See details in main text.

Figure 2

Characterization of the entangled state. (a) Two-atom state populations after the detection of a ${\sigma }^{-}$ photon showing that the total probability of measuring the state with a single excitation is 90%. (b) Parity measurements as a function of the rf phase. Trace (ii) corresponds to the measurement of the atomic populations after two global rotations ${\widehat{R}}^g(\pi /2,\varphi ){\widehat{R}}^g(\pi /2,\pi /2)$. In the measurement of trace (i) only a single global rf pulse ${\widehat{R}}^g(\pi /2,\varphi )$ is applied. The dashed line shows the threshold for entanglement, estimated from the measured diagonal terms. (c) Real part of the coherence between the $|ge⟩$ and $|eg⟩$ states as a function of the phase of the optical path difference between the two ions.