Enhanced Quantum Interface with Collective Ion-Cavity Coupling

We prepare a maximally entangled state of two ions and couple both ions to the mode of an optical cavity. The phase of the entangled state determines the collective interaction of the ions with the cavity mode, that is, whether the emission of a single photon into the cavity is suppressed or enhanced. By adjusting this phase, we tune the ion-cavity system from sub- to superradiance. We then encode a single qubit in the two-ion superradiant state and show that this encoding enhances the transfer of quantum information onto a photon.

Figure 1

(a) Two ${}^{40}{\mathrm{Ca}}^{+}$ ions in a linear Paul trap couple with equal strength to the mode of a high-finesse optical cavity. A magnetic field orthogonal to the cavity axis defines the quantization axis. Quantum information stored in the ions is manipulated using two 729 nm beams: the global beam couples to both ions, while the addressing beam is focused onto one ion. A 393 nm laser beam drives a cavity-mediated Raman transition, generating a single photon in the cavity. At the cavity output, two wave plates ($\lambda /2$, $\lambda /4$) select the basis in which photon polarization is analyzed. Two avalanche photodiodes (APD1 and APD2) detect the horizontally ($H$) or vertically ($V$) polarized photons at the output of a polarizing beam splitter (PBS). (b) Populations of the states $|S⟩|S⟩$ (red diamonds), $|D⟩|D⟩$ (blue circles), and $|S⟩|D⟩$ or $|D⟩|S⟩$ (green triangles) as a function of the Mølmer–Sørensen gate duration. After $55\mu \mathrm{s}$ (dashed vertical line) a maximally entangled state is generated. Solid lines indicate the ideal time evolution of the gate operation [28]. (c) Oscillations in the parity of the ion populations as a function of the phase of a $\pi /2$ pulse on the $|S⟩\leftrightarrow |D⟩$ transition, following entanglement. The dashed vertical line at phase $1.2\pi$ corresponds to $|{\mathrm{\Psi }}^{+}⟩$. Error bars represent projection noise.

Figure 2

(a) The two ions are prepared in either a separable state $|{\psi }_1⟩$ or $|{\psi }_2⟩$ or an entangled state $|\mathrm{\Psi }(\phi )⟩$ for various values of $\phi$. The global beam then drives a Raman transition between $|S⟩$ and $|D⟩$, generating a single cavity photon for each ion in $|S⟩$. Since $|D^{\prime }⟩$ is decoupled from the cavity interaction, both $|{\psi }_1⟩$ and $|{\psi }_2⟩$ represent a single ion interacting with the cavity. (b) Ratio $r(\phi )$ of the probability to detect a photon for $|\mathrm{\Psi }(\phi )⟩$ to that of $|{\psi }_1⟩$ as a function of the phase $\phi$ for the first $6\mu \mathrm{s}$ of the Raman process. The reference single-ion case is shown as a dashed horizontal line. (c) Temporal shape of the photon at the cavity output as a function of detection time $t$, for the entangled states $|{\mathrm{\Psi }}_{\text{super}}⟩$ (circles) and $|{\mathrm{\Psi }}_{\text{sub}}⟩$ (diamonds) and the single-ion cases $|{\psi }_1⟩$ and $|{\psi }_2⟩$ (up and down triangles, respectively). The temporal photon shapes are calculated by normalizing the detected photon counts per $1\mu \mathrm{s}$ time bin by the number of photon generation attempts. Data are shown until $20\mu \mathrm{s}$, the time scale for which enhancement and suppression are most prominent. Lines are simulations. The shaded area represents the time window used in (b). Error bars represent Poissonian statistics and are mostly smaller than the plot symbols.

Figure 3

(a) A bichromatic Raman transition maps a superposition of $|S⟩$ and $|S^{\prime }⟩$ onto a superposition of single-photon polarization states $|H⟩$ and $|V⟩$. The superposition is encoded either in two entangled ions or in a single ion, with the other ion decoupled in $|D^{\prime }⟩$. (b) Process fidelity for $|{\mathrm{\Psi }}_{\text{super}}⟩$ (filled blue circles) and $|{\psi }_1⟩$ (open black circles) as a function of the photon detection time window. Lines are simulations (continuous line: two entangled ions; dashed line: single-ion case). Inset: absolute value of the process matrix ${\chi }_{ij}$ for $|{\mathrm{\Psi }}_{\text{super}}⟩$ reconstructed from photons detected between 2 and $4\mu \mathrm{s}$, yielding the maximum process fidelity $|{\chi }_{00}|=96.0(3)\%$. Error bars are derived from nonparametric bootstrapping. (c) Cumulative process efficiency for $|{\mathrm{\Psi }}_{\text{super}}⟩$ (filled blue circles) and $|{\psi }_1⟩$ (open black circles) as a function of the photon detection time window. Error bars represent Poissonian statistics and are smaller than the plot symbols.