Photon-Photon Entanglement with a Single Trapped Atom

An experiment is performed where a single rubidium atom trapped within a high-finesse optical cavity emits two independently triggered entangled photons. The entanglement is mediated by the atom and is characterized both by a Bell inequality violation of $S=2.5$, as well as full quantum-state tomography, resulting in a fidelity exceeding $F=90\%$. The combination of cavity-QED and trapped atom techniques makes our protocol inherently deterministic—an essential step for the generation of scalable entanglement between the nodes of a distributed quantum network.

Figure 1

Individual ${}^{87}\mathrm{Rb}$ atoms are trapped within the mode of a high-finesse optical cavity (finesse $\approx 3\times {10}^4$) at the intersection of two standing-wave dipole-trap beams. $\mathrm{Lin}\perp \mathrm{lin}$-polarized laser beams provide motional cooling, while beams used for the entanglement scheme are polarized along the cavity axis. The 1030 nm dipole-trap beam and all cooling and excitation beams (labeled as $i\mathrm{\text{−}}j$, where $i$ and $j$ are the hyperfine quantum numbers $F$ and $F^{\prime }$ of the $5S_{1/2}$ and $5P_{3/2}$ states, respectively) are perpendicular to the cavity axis. The cavity output is directed to the photonic state detection apparatus. Also perpendicular to the cavity axis, a CCD camera is used to monitor the atoms within the trap. The displayed image shows three atoms coupled to the mode of the cavity and aligned along the 1030 nm beam. SPCM, single photon counting module; NPBS, nonpolarizing beam splitter; PBS, polarizing beam splitter; $\lambda /4$, quarter-wave plate; $\lambda /2$, half-wave plate.

Figure 2

The experimental procedure. (a) When atoms are first loaded into the cavity, a 300 ms laser pulse is applied for optical cooling. During this time, a camera images the cavity mode to confirm the presence of a single atom. (b–e) The entanglement generation protocol runs at a repetition rate of 50 kHz. (b) Atomic recooling. (c) A $\pi$-polarized laser resonant with the $F=2\leftrightarrow F^{\prime }=2$ transition together with resonant lasers on the $F=1\leftrightarrow F^{\prime }=1$ and $F=1\leftrightarrow F^{\prime }=2$ transitions optically pump the atom to the $|F=2,m_F=0⟩$ Zeeman sublevel. (d) A $\pi$-polarized $F=2\leftrightarrow F^{\prime }=1$ laser transition generates atom-photon entanglement. (e) After a time $\Delta t$, a $\pi$-polarized $F=1\leftrightarrow F^{\prime }=1$ laser maps the quantum state of the atom onto a second photon.

Figure 3

Real and imaginary parts of the measured two-photon density matrix. A semitransparent plane at $\rho =0$ is added to better visualize which elements are positive or negative. This density matrix represents the $|{\Psi }_{\mathrm{PP}}^{-}⟩$ Bell state of the photons with a fidelity of $F=0.902\pm 0.009$.

Figure 4

Measured fidelity and logarithmic negativity as a function of time between the two vSTIRAP sequences. Note that these data are independent from those shown in Fig. 3. The solid line is a Gaussian fit to the negativity $N(\Delta t)$, displayed as $E_N(\Delta t)={log}_2(2N_0{e}^{-(\Delta t/{\tau }_e{)}^2}+1)$, with a resulting entanglement lifetime of ${\tau }_e=5.7\pm 0.2\mu \mathrm{s}$. The insets show the real parts of the density matrices at differing values of $\Delta t$ (all imaginary parts have a magnitude smaller than 0.14). The entanglement lifetime is limited mainly by a loss of phase coherence between the $|1,-1⟩$ and $|1,+1⟩$ states.