Ion Crystal Transducer for Strong Coupling between Single Ions and Single Photons

A new approach for the realization of a quantum interface between single photons and single ions in an ion crystal is proposed and analyzed. In our approach the coupling between a single photon and a single ion is enhanced via the collective degrees of freedom of the ion crystal. Applications including single-photon generation, a memory for a quantum repeater, and a deterministic photon-photon, photon-phonon, or photon-ion entangler are discussed.

Figure 1

Schematic of the setup. (a) Chain of $N$ ions in cavity with incoming photon and two pairs of off-axis lasers comprising a quadrupole field. (b) Ionic level scheme. States $|0⟩$ and $|1⟩$ are metastable states (e.g., $3D_{5/2}$ and $4S_{1/2}$ in ${}^{40}\mathrm{Ca}^{+}$), and $|e⟩$ is an excited state (e.g., the $4P_{3/2}$ state in the same ion). For step I, the transition $|0⟩\to |e⟩$ is coupled by a single photon with the effective Rabi frequency $g_0\sqrt{N}$. The ${\Omega }_1$ laser is directed perpendicularly to the chain. For step II, the states $|0⟩$ and $|1⟩$ are coupled by a quadrupole transition. (c) Coupling to a phonon mode. The harmonic energy level of the phonon excitations, e.g., of the c.m. mode, is denoted for different internal states. The singly excited phonon mode can be addressed by a transition frequency that is red detuned from the bare ionic transitions by the frequency of the phonons ${\omega }_{\mathrm{pn}}$ by a quadrupole transition. The laser scheme for this part is depicted in (a).

Figure 2

(a) Process fidelity $F_1$ for the transfer of one phonon onto one collective excitation versus the number of ions $N$. The parameters used are ${\Omega }_{\max }={10}^{-2}\omega$, $\eta =0.1$, $\tilde{\eta }=0.4$. The line is an average to guide the eye. (b) Fidelity $F_2$ for the transfer of one collective excitation to one photon versus the number of ions $N$. The parameters used are ${\Omega }_1=50\kappa$, $\Gamma =10\kappa$, $\Delta =0$. The lines are averages to guide the eye.