High fidelity photon-photon gates by scattering off a two-level quantum emitter

Abstract

We present a scheme for implementing a high-fidelity non-linear phase shift on a photonic state. The scheme is based on repeated scattering off a two-level quantum emitter embedded in a chiral or one-sided waveguide. The waveguide is equipped with elements inducing second-order dispersion and temporal phase shifts, which effectively form a harmonic trap and confine the photon pulses to a Gaussian shape. The same quantum emitter can be used for each scattering, and thus, only one quantum emitter is needed in this scheme. To illustrate the application of our scheme for photonic quantum computing and quantum communication, we analyze the implementation of a control-Z gate and a deterministic Bell-state analyzer for photonic qubits. Through numerical optimization, we show that we can reach a control-Z gate fidelity of $\mathcal{F} \sim 99.2\%$ ($\mathcal{F} \sim 96\%$) and a success probability of $P_s \sim 99.6 \%$ ($P_s\sim 98 \%$) for a Bell-state measurement with $N=17$ ($N=5$) scatterings.

Figures (4)

• Figure 1: A schematic illustration of the main components of our phase gate protocol. a) A two-photon or single-photon pulse is scattered off a two-level quantum emitter embedded in a chiral waveguide. Due to dispersion and spectral entanglement induced by the two-level system, the pulses leave the device distorted. b) Adding a harmonic trap for the light pulse through the sequential evolution of a second-order dispersive element ($p^2$) and a temporally varying phase (EOM) between the repeated scatterings mitigates the distortion effects on the input pulses. Thus, the pulses will leave the device undistorted through the switch (SW) after accumulating the desired phase.
• Figure 2: Illustration of the circuit for implementing the control-Z gate. The circuit interferes the $\ket{11}_{AB}$ component, leading to $\ket{20}$ and $\ket{02}$ components subject to the desired phase shift, whereas the other components travel as independent photons. The subsequent beamsplitter recombines the modes and yields the control-Z gate.
• Figure 3: a) Infidelity of the gate as a function of the number of scatterings, with the harmonic trap (red) and without (blue). b) Optimal bandwidth $\sigma$ in units of the decay rate $\Gamma$ of the two-level system, and c) the optimal detuning in units of $\Gamma$. d) Optimal trapping parameters $\lambda_1$ (purple) and $\lambda_2$ (green) in units of the decay rate $\Gamma$.
• Figure 4: a) The photon sorting device. The photon(s) enter the $\hat{a}$-mode and split on a $50/50$ beam splitter. They then enter the cascade scattering plus harmonic trap loop and leave after $N$-rounds. After the final beam splitter, if a one-photon pulse is sent in, it will leave through the $\hat{a}$-mode again; however, if a two-photon pulse is sent in, the photons will leave through the $\hat{b}$-mode. b) Photon sorting device without a temporal trap, the photon(s) scatter only once between the beam splitters. After one scattering, the sorting is not perfect, and thus, if the photon(s) leave the $\hat{a}$ mode, we scatter once more. This can then be cascaded $N$-times. c) Illustration of the Bell-state analyzer circuit, $PS$ stands for photon sorter. d) Failure probability $P_f$ as a function of the number of scatterings, with the photon sorter using a harmonic trap in a) (red), the photon sorter without a trap in b) (blue), and the proposal in Ref of Witthaut et al. AndersPhotonSorter (black).