Entanglement of distinguishable quantum memories

Time-resolved photon detection can be used to generate entanglement between distinguishable photons. This technique can be extended to entangle quantum memories that emit photons with different frequencies and identical temporal profiles without the loss of entanglement rate or fidelity. We experimentally realize this process using remotely trapped ${}^{171}{\mathrm{Yb}}^{+}$ ions where heralded entanglement is generated by interfering distinguishable photons. This technique may be necessary for future modular quantum systems and networks that are composed of heterogeneous qubits.

Figure 1

(a) The energy-level diagram of the ${}^{171}{\mathrm{Yb}}^{+}$ quantum memory. Photon generation (blue dashed) and collection (red dotted) transitions are labeled along with the microwave transitions (green solid) used to analyze the entangled memory state. ${\sigma }^{\pm }$ polarized light is emitted by each memory before being converted to the linear basis by a $\lambda /4$ wave plate. (b) Experimental setup including quantum memories, photon collection optics, and a partial Bell state analyzer. The analyzer consists of a 50:50 nonpolarizing beam splitter (50:50 BS), two polarizing beam splitters (PBSs), and four photomultiplier tubes (PMTs).

Figure 2

(a) In the conventional memory-memory entanglement configuration, the polarization of photons from both memories are associated with the same atomic state. The resulting photon frequency difference $\Delta \omega$ is limited by the largest magnetic field difference we can apply across the two memories. The ket subscripts represent which memory the state is associated with. (b) By introducing a $\lambda /2$ wave plate to one photon path and rotating that photon's polarization to the orthogonal linear state, the polarizations of the two photons are now associated with atomic states with opposite Zeeman shifts. This technique maximizes $\Delta \omega$ for a given maximum magnetic field magnitude.

Figure 3

(a) Frequency line shapes for indistinguishable $(\Delta \omega =2\pi \times 1.35$ MHz) and distinguishable $(\Delta \omega =2\pi \times 28.35$ MHz) photons with linewidth $\Gamma =1/\tau =2\pi \times 19.6$ MHz. (b) Extracted time-dependent phase evolution of $P^o$ oscillations for the $\left|\Psi \right.〉$ and $\left|\Phi \right.〉$ memory states. We find $\Delta \omega =2\pi \times 1.4\left(2\right)$ MHz for $\left|\Psi \right.〉$ and $\Delta \omega =2\pi \times 27.1\left(1.7\right)$ MHz for $\left|\Phi \right.〉$. The ${\varphi }^{\prime }=\pm \Delta \omega \Delta t+{\varphi }_0$ data have been offset such that ${\varphi }_0=0$ and the error bars correspond to the standard error of the mean.

Figure 4

Entangled memory state fidelity vs maximum time between detector clicks during an entanglement event. For the indistinguishable case where the joint memory state is $\left|\Psi \right.〉$, the fidelity is nearly constant for all values of $\Delta t_{\text{max}}$. For the $\left|\Phi \right.〉$ state, which is associated with distinguishable photons, there is a clear increase in fidelity for $\Delta t_{\text{max}}<2\pi /\Delta \omega \approx 35$ ns. Error bars correspond to the standard error of the mean.

Figure 5

(a) $P_{\left|\Phi \right.〉}^o$ $\left({\varphi }_D=\pi \right)$ as a function of analysis pulse phases ${\varphi }_a$ and ${\varphi }_b$ for varying values of photon detection time difference $\Delta t$. The sinusoids are incoherent due to their time-dependent phase shifts. (b) We postprocess the entangled state by shifting the analysis phases ${\varphi }_a+{\varphi }_b\to {\varphi }_a+{\varphi }_b+\Delta \omega \Delta t$ using the experimentally measured photon frequency difference $\Delta \omega$ and $\Delta t$. The resulting parity oscillations are in phase. Here, the fit serves as a guide to the eye. (c) Fidelity of the entangled memory state for the original (blue squares) and phase-shifted (black diamonds) data. Fidelity loss due to the time-dependent phase is significantly reduced for the latter. All error bars correspond to the standard error of the mean.