Quantum routing of single optical photons with a superconducting flux qubit

Interconnecting optical photons with superconducting circuits is a challenging problem but essential for building long-range superconducting quantum networks. We propose a hybrid quantum interface between the microwave and optical domains where the propagation of a single-photon pulse along a nanowaveguide is controlled in a coherent way by tuning the electromagnetically induced transparency window with the quantum state of a flux qubit mediated by the spin in a nanodiamond. The qubit can route a single-photon pulse using the nanodiamond into a quantum superposition of paths without the aid of an optical cavity—simplifying the setup. By preparing the flux qubit in a superposition state our cavityless scheme creates a hybrid state-path entanglement between a flying single optical photon and a static superconducting qubit.

Figure 1

(a) Schematic of a hybrid quantum single-photon router at $20\mathrm{mK}$. A single-photon pulse with carrier frequency of ${\omega }_{\text{in}}$ (right moving pulse on top left) inputs to a nanowaveguide, e.g., a nanofiber or a photonic crystal waveguide, from the left. It couples to a nearby single SiV with strength $g$. An external coherent laser field ${\mathrm{\Omega }}_c$ drives a transition in the SiV and creates an EIT window. It can be tuned from less than $\mathrm{k}\mathrm{Hz}$ to many $\mathrm{M}\mathrm{Hz}$. This varying region is large enough for our scheme requiring an energy shift of a few $\mathrm{k}\mathrm{Hz}$. The input pulse partly passes through the SiV (right moving pulse on top right) and is partly scattered backwards (left moving pulse—upside down on top left). The central frequency of the EIT window is modulated by the energy levels of the SiV, which themselves are shifted due to the quantum magnetic field $B$ (outward pointing vectors surrounding the SiV) dependent on the quantum state of the flux qubit, $|e\rangle$ and $|g\rangle$. A classical microwave field, ${\mathrm{\Omega }}_{\mu }$, from a nearby SQUID-terminated transmission line [30, 31], modulates the flux qubit energies quickly in time. The SQUID is also used to isolate the flux noise in the transmission line from the flux qubit [30, 31, 32]. (b) Level diagram of the SiV. The SiV acts as a $\mathrm{\Lambda }$-type configuration with the excited state $|3\rangle$, and two ground states $|2\rangle$ and $|1\rangle$ [33, 34].

Figure 2

Estimation of the magnetic field at the location of the SiV generated by the flux qubit. (a) Schematic of the coiled part of flux qubit to enhance the magnetic field at the SiV location. The flux qubit has a 24-turn coiled edge (helical tube). A $\mu$-metal bowtie flux concentrator (tapered cylinder), with a relative permeability of ${\mu }_r={10}^6$, is inserted inside the coil to greatly enhance the local magnetic field generated by the flux qubit. The SiV (central sphere) is located near to the tip of the concentrator. The surface of the helical coil is about $240\mathrm{n}\mathrm{m}$ away from the $\mu$ metal to avoid any flux noise caused by the flux concentrator. (b) The distribution of magnetic field around the structure in (a) is numerically solved in two-dimensional space with the free software femm4.2. The density plot inset shows the zoomed-in distribution close to the concentrator tips, while the line plot inset shows the distribution along the middle line joining the two tips. The small green ball in the inset indicates the position of the SiV.

Figure 3

Steady-state transmission (blue lines with a maximum at an abscissa of $\pm 2$) and reflection (red lines with a minimum at an abscissa of $\pm 2$) given by Eq. (18) for the excited state (dashed lines) and ground state (solid lines) of the flux qubit. We set ${\mathrm{\Omega }}_c/{\mathrm{\Gamma }}_{\text{wg}}=0.03,\eta /{\mathrm{\Gamma }}_{\text{wg}}={10}^{-3},{\mathrm{\Delta }}_1=0,{\gamma }_f=0,{\mathrm{\Gamma }}^{*}=0,{\xi }_c=1,\text{and}{\xi }_2=0.5$.

Figure 4

(a)–(c) Time evolution of excitations of right (blue lines) and left (red lines) -moving photons with the initial state of the flux qubit (a) in $|g\rangle$, (b) in $|e\rangle$, and (c) in $\left(\right|g\rangle +|e\rangle )/\sqrt{2}$. (d) The coherence for the flux qubit prepared in $\left(\right|g\rangle +|e\rangle )/\sqrt{2}$. The blue solid line shows $\text{Tr}\left[\rho C_{\text{R}}^{†}\right|⌀,g\rangle \langle ⌀,e\left|C_{\text{L}}\right]$ indicating the coherence density modulated by the fast spatial (time) oscillating phase $\mathrm{\Theta }\left(x\right)$. It is fitted by $-|{\overline{\varphi }}_R\left(x\right)\left|\right|{\overline{\varphi }}_L\left(x\right)|e^{i({\eta }_1+{\eta }_3)x+i\phi +i\theta }$ (the purple line). The yellow line is for the real coherence evaluated by $\mathcal{C}\left(x\right)$. In (a), the dashed black line shows the input pulse and the solid black line is for the time-dependent excitation in the source cavity. Other parameters are ${\mathrm{\Omega }}_c/{\mathrm{\Gamma }}_{\text{wg}}=0.03,\eta /{\mathrm{\Gamma }}_{\text{wg}}={10}^{-3},{\mathrm{\Delta }}_1=0,{\mathrm{\Delta }}_2=2\eta ,{\gamma }_f=0,{\mathrm{\Gamma }}^{*}=0,{\xi }_c=1,{\xi }_2=0.5$, and ${\tau }_p{\mathrm{\Gamma }}_{\text{wg}}={10}^4$. ${\mathrm{\Gamma }}_{\text{wg}}/2\pi \approx 300\mathrm{M}\mathrm{Hz}$ for SiV.

Figure 5

Excitations (${\left|{\varphi }_R\right|}^2$, ${\left|{\varphi }_L\right|}^2$), fidelity, $F$, and concurrence, $C$, as a function of the pure dephasing rate ${\mathrm{\Gamma }}^{*}$. Other parameters are ${\mathrm{\Omega }}_c/{\mathrm{\Gamma }}_{\text{wg}}=0.03,\eta /{\mathrm{\Gamma }}_{\text{wg}}={10}^{-3},{\mathrm{\Delta }}_1=0,{\mathrm{\Delta }}_2=2\eta ,{\gamma }_f=0,{\xi }_c=1,{\xi }_2=0.5$, and ${\tau }_p{\mathrm{\Gamma }}_{\text{wg}}={10}^4$. The blue line ($|{\varphi }_R{|}^2$) overlaps with that for $|{\varphi }_L{|}^2$. ${\mathrm{\Gamma }}_{\text{wg}}/2\pi \approx 300\mathrm{M}\mathrm{Hz}$ for SiV.

Figure 6

Schematic diagram for mapping the quantum state from the flux qubit to the photonic qubit.