Remote Preparation of an Atomic Quantum Memory

Storage and distribution of quantum information are key elements of quantum information processing and future quantum communication networks. Here, using atom-photon entanglement as the main physical resource, we experimentally demonstrate the preparation of a distant atomic quantum memory. Applying a quantum teleportation protocol on a locally prepared state of a photonic qubit, we realized this so-called remote state preparation on a single, optically trapped ${}^{87}\mathrm{Rb}$ atom. We evaluated the performance of this scheme by the full tomography of the prepared atomic state, reaching an average fidelity of 82%.

Figure 1

Schematic of atom-photon entanglement generation in a spontaneous decay of a single optically trapped ${}^{87}\mathrm{Rb}$ atom. (a) After optical excitation to $F^{\prime }=0$, the atom decays into the ground state manifold $|\uparrow {⟩}_z$, $|\downarrow {⟩}_z$ forming an entangled state between the atomic spin and the polarization of the emitted photon. (b) The emitted photon is collected with a microscope objective, coupled into a 5 m long single-mode optical fiber and guided to the preparation setup shown in Fig. 2. The overall detection efficiency for the photon is about $3\times {10}^{-4}$.

Figure 2

Schematic setup for preparing the state from Eq. (2) on the spatial degree of freedom of the photon and for the subsequent Bell-state measurement. The interferometric phase setting ($\alpha$, $\varphi$) allows to prepare any desired superposition of the spatial modes $|a⟩$ and $|b⟩$ without affecting the polarization degree of freedom. The following PBS, together with the polarization measurement in $|\pm 45°⟩$, basis enable a complete Bell-state analysis in the combined polarization–spatial-mode Hilbert space of the photon.

Figure 3

Tomographic data set of the prepared atomic states for $\alpha =90°$, $\varphi =0–330°$. The figures show the probability $p$ to find the atom in the state $|\uparrow {⟩}_z$ (left), $|\downarrow {⟩}_x=\frac{1}{\sqrt{2}}(|\uparrow {⟩}_z-|\downarrow {⟩}_z)$ (middle), and $|\uparrow {⟩}_y=\frac{1}{\sqrt{2}}(|\uparrow {⟩}_z+i|\downarrow {⟩}_z)$ (right), respectively, after a photon detection in detector 1 (red, filled) and 2 (blue, hollow) (upper row), 3 (green, filled) and 4 (magenta, hollow) (lower row). Each data point is evaluated from 150–350 measurement processes from which we calculate the depicted statistical errors (1 standard deviation). The mean fidelity of the 12 states prepared in this measurement is 82.6%. The acquisition of the full data set was realized within approximately three days at an event rate of 10–20 per min.

Figure 4

Bloch-sphere representation of the states prepared on the atomic qubit. The basis states in the equatorial plane are defined as $|\uparrow {⟩}_x$, $|\downarrow {⟩}_x≔\frac{1}{\sqrt{2}}(|\uparrow {⟩}_z\pm |\downarrow {⟩}_z)$ and $|\uparrow {⟩}_y$, $|\downarrow {⟩}_y≔\frac{1}{\sqrt{2}}(|\uparrow {⟩}_z\pm i|\downarrow {⟩}_z)$. The angles ($\alpha$, $\varphi$) can be interpreted as usual polar coordinates with respect to the $x$ axis. The numbers 1–4 depict the corresponding measurements from Table . The insets exemplarily show measured density matrices of the atomic qubit (real part) for four selected states.