Quantum memory and gates using a $\mathrm{\Lambda }$-type quantum emitter coupled to a chiral waveguide

By coupling a $\mathrm{\Lambda }$-type quantum emitter to a chiral waveguide, in which the polarization of a photon is locked to its propagation direction, we propose a controllable photon-emitter interface for quantum networks. We show that this chiral system enables the swap gate and a hybrid-entangling gate between the emitter and a flying single photon. It also allows deterministic storage and retrieval of single-photon states with high fidelities and efficiencies. In short, this chirally coupled emitter-photon interface can be a critical building block toward a large-scale quantum network.

Figure 1

(a) Chiral scattering of a single photon by a $\mathrm{\Lambda }$-type emitter coupled to a photonic-crystal waveguide, (b) energy levels and the circularly polarized (${\sigma }_{\pm }$) dipole transitions of a $\mathrm{\Lambda }$-type emitter (decaying with a damping rate $\gamma$), and (c) chiral scattering of a single photon by a $\mathrm{\Lambda }$-type emitter coupled to the waveguide. Here $R$ and $T$ represent the reflection and transmission amplitudes of the scattered output modes. For simplicity, we show only a photon entering the waveguide from its left-hand side (say, a forward-propagating photon), although we also consider a backward-propagating photon. The atom is placed at a point of the local in-plane (circular) polarization of the electric field in the waveguide (see Ref. [37] for a pedagogical description of this configuration). The circularly-polarized ${\sigma }_{+}$ (${\sigma }_{-}$) dipole transition couples only to the forward- or backward-propagating modes with the coupling constants ${\mathrm{\Gamma }}_f\left(k\right)=V_f^2\left(k\right)$ or ${\mathrm{\Gamma }}_b\left(k\right)=V_b^2\left(k\right)$, respectively.

Figure 2

Absolute values of the transmission $\left|T\right|$ and reflection $\left|R\right|$ amplitudes versus the detuning $\mathrm{\Delta }$ (in units of the damping rate $\gamma$) between an input photon and the atomic transitions with (a) $\beta =10$, (b) $\beta =30$, and (c) $\beta =50$. Here $\beta =\mathrm{\Gamma }/\gamma$ is the ratio of the coupling constant $\mathrm{\Gamma }$ and the damping rate $\gamma$ describing the enhancement of the directional emission of the atom.

Figure 3

(a) Schematics of the multifunctional quantum interface (MQI) using a $\mathrm{\Lambda }$-type emitter and a 1D waveguide and (b) heralded-entanglement generation and quantum-state transmission between two remote quantum nodes. Here, PBS denotes a polarized beam splitter, OC is an optical circular, and PC is a polarization controller.

Figure 4

(a) The average fidelities ${\overline{F}}_{\mathrm{ent}}$, ${\overline{F}}_{\mathrm{swap}}$, and ${\overline{F}}_{\mathrm{mem}}$ and (b) the average efficiencies ${\overline{\eta }}_{\mathrm{ent}}$, ${\overline{\eta }}_{\mathrm{swap}}$, and ${\overline{\eta }}_{\mathrm{mem}}$ versus the coupling constant $\mathrm{\Gamma }$ (in units of the damping rate $\gamma$). The averages are calculated over all detunings of an input photon, with the Gaussian wave form given by Eq. (28) with ${\sigma }_{\omega }=5\gamma$.

Figure 5

(a) Average fidelities ${\overline{F}}_{\mathrm{ent}}$, ${\overline{F}}_{\mathrm{swap}}$, and ${\overline{F}}_{\mathrm{mem}}$ and (b) average efficiencies ${\overline{\eta }}_{\mathrm{ent}}$, ${\overline{\eta }}_{\mathrm{swap}}$, and ${\overline{\eta }}_{\mathrm{mem}}$ versus the pulse bandwidth ${\sigma }_{\omega }/\gamma$ (in units of the damping rate $\gamma$). These averages are calculated over all detunings of an input photon, with the Gaussian wave form given by Eq. (28) and $\mathrm{\Gamma }/\gamma =50$.