Extracting Past-Future Vacuum Correlations Using Circuit QED

We propose a realistic circuit QED experiment to test the extraction of past-future vacuum entanglement to a pair of superconducting qubits. The qubit $P$ interacts with the quantum field along an open transmission line for an interval $T_{\mathrm{on}}$ and then, after a time-lapse $T_{\mathrm{off}}$, the qubit $F$ starts interacting for a time $T_{\mathrm{on}}$ in a symmetric fashion. After that, past-future quantum correlations will have transferred to the qubits, even if the qubits do not coexist at the same time. We show that this experiment can be realized with current technology and discuss its utility as a possible implementation of a quantum memory.

Figure 1

Experimental proposal for past-future entanglement extraction. (a) Time evolution of our protocol: the qubit $P$ interacts with the vacuum field ($\Delta \psi$) for a time $T_{\mathrm{on}}$. After a certain time $T_{\mathrm{off}}$ with no interaction, a second qubit $F$ interacts with the field getting entangled with the qubit $P$. (b) Switchable coupling design: a flux qubit (top ring) is coupled to the field $\Delta \psi$ by ways of two loops. Varying the magnetic fluxes ${\Phi }_2$ and ${\Phi }_3$, we deactivate the qubit-field coupling.

Figure 2

(a) Diagram of the different spacetime regions. (b) Concurrence vs. $T_{\mathrm{on}}$ and $T_{\mathrm{off}}$ for $g=g_P=g_F$, $\Omega ={\Omega }_P={\Omega }_F=2\pi \times 1\mathrm{GHz}$, $g/\Omega =0.19$, $r/\lambda =0.125$. Significant entanglement is generated at both sides of the lines that discriminate between regions. (c) Concurrence vs. $T_{\mathrm{on}}$ with $T_{\mathrm{off}}$ fixed and vice versa along the blue lines shown in b. The peaks match the position of the region edges. Entanglement is generated in region I and III for three different values of the coupling strength $g/\Omega =0.09$ (blue, solid), 0.15 (red, dashed), and 0.19 (black, dotted) and $T_{\mathrm{off}}=0$. $T_{\mathrm{off}}$ with $T_{\mathrm{on}}=0.02\mathrm{ns}$. $\Omega$ and $r$ are the same as in b. The generated entanglement displays a remarkable symmetry for regions I and III.

Figure 3

Same as in Fig. 2b except for $r/\lambda =2$ and $g/\Omega =0.09$. Entanglement is restricted to region II for long distances.