Figure 1

(Color online) (a) Schematic of the proposed CZ gate. Atom $s$ is the target qubit with qubit transition ${\mid g⟩}_s\leftrightarrow {\mid f⟩}_s$ addressed via an rf field. The atom accumulates a $\pi$ phase shift conditioned on the populated cavity mode $s$, which dispersively couples the ${\mid g⟩}_s$ to ${\mid e⟩}_s$ transition. The atoms are coupled to their respective cavity mode with Rabi frequency ${\Omega }_{\alpha }$ and detuned by ${\Delta }_{\alpha }$ $(\alpha =s,q)$. Spectral tuning of atom $q$ allows dynamic and coherent photon switching between the waveguide and the storage cavity. The cavities are coupled with photon-hopping rate $\kappa$, detuned by ${\delta }_q$, and $\gamma$ is the cavity decay rate. (b) Proposed gate design in PBG lattice, missing holes constitute the cavities and waveguide. Red circles denote atoms tuned via, e.g., Stark shift gates (rectangles). (c) Light leakage rate from mode $s$ in the static two-cavity arrangement. Cavity loss is rapid at storage-switch resonance (dashed) and is minimized at two-photon resonance $({\Delta }_q=-{\delta }_q)$ between mode $s$ and atom $q$.Reuse & Permissions

Figure 2

(Color online) (a) Simulation of the CZ gate. The matter qubit (atom $s$) is initialized in ${\mid +⟩}_s$. Step A: A single photon of shape ${\mid f_{\mathrm{in}}^{+}\mid }^2$ (red dotted) is switched into the storage cavity adiabatically (${\mid C_s^{+}\mid }^2$, red dashed). Step B: Dispersive interaction results a phase shift from ${\mid +⟩}_s$ to ${\mid -⟩}_s$ (black dashed). Step C: The photon is returned to the waveguide. The gate fidelity $\mathcal{F}\equiv {\mid C_{\mathrm{out}}^{-}\mid }^2=0.993$ (black solid). ${\mid f_{\mathrm{out}}^{-}\mid }^2$ (black dotted) is the pulse envelope of the output photon. (b) Corresponding atomic tuning control that varies ${\Delta }_q$ between ${\Delta }_q^{\mathrm{off}}$, where the switch has minimal transmittivity and ${\Delta }_q^{\mathrm{on}}$, where ${\mid 1⟩}_s$ is resonant with ${\mid -⟩}_q$. Parameters are $\kappa =\gamma$, ${\Omega }_s=5\kappa$, ${\Omega }_q=20\kappa$, ${\delta }_q=10\kappa$, ${\Delta }_s={10}^3\kappa$, and ${\gamma }_q,{\gamma }_e=0$.Reuse & Permissions

Figure 3

(Color online) Circles denote data points from simulations. Dashed lines are guides for the eye. (a) Success probability for light outcoupling via adiabatic transfer for fixed $T_{\mathrm{sw}}=10∕\kappa$, as a function of cavity decay rate $\gamma ∕\kappa$. (b) Reduction in gate fidelity $\mathcal{F}$ due to premature leakage, as a function of atom-cavity coupling ${\Omega }_q∕\kappa$. The solid curve plots ${(\kappa ∕{\Omega }_q)}^2$, showing a good overlap. (c) $\mathcal{F}$ is calculated for different decoherence rates ${\gamma }_{\beta }$ $(\beta =q,e)$ for the scenario in Fig. 2. The black curve denotes the case where the rates are equal, while other curves distinguish individual contributions. Parameters follow from Fig. 2 unless stated otherwise.Reuse & Permissions