Two-photon controlled-phase gates enabled by photonic dimers

Photons are appealing as flying quantum bits due to their low-noise, long coherence times, light-speed transmission, and ease of manipulation at the single-qubit level using standard optical components such as beam splitters and waveguides. The challenge in optical quantum information processing has been the realization of two-qubit gates for photonic qubits due to the lack of highly efficient optical Kerr nonlinearities at the single-photon level. To date, only probabilistic two-qubit photonic controlled-phase gates based on linear optics and projective measurement using photon detectors have been demonstrated. Here we show that a high-fidelity frequency-encoded deterministic two-photon controlled-phase gate can be achieved by exploiting the strong photon-photon correlation enabled by photonic dimers, and the unique nonreciprocal photonic propagation in chiral quantum nanophotonic systems.

Figure 1

Schematic diagram of a chiral two-level system (TLS). The chiral photon-quantum dot interaction can be induced via either the Zeeman splitting by a magnetic field [11, 13], or by selective placement of the quantum dot at a chiral point in the reciprocal waveguide [12].

Figure 2

Probability density plot and phase shift for resonant photons. (a) Single-photon case. Green curve indicates the numerical $\pi$ phase shift. (b) Density plot for the two-photon case. (c) Phase shift of the outgoing two-photon state. Parameters for the scattering processes: $\sigma =1.5v_g/\mathrm{\Gamma }$ (for instance, if the atomic spontaneous emission time is $1/\mathrm{\Gamma }\approx 0.1$ ns, the pulse duration is $6\sigma /v_g\approx 0.9$ ns), and $\gamma =0$.

Figure 3

Schematic diagram of the two-photon controlled-phase gate.

Figure 4

Numerical results of average gate fidelity $\overline{F}$ and phase shift ${\theta }_1,{\theta }_2$. (a) $\overline{F}$ and (b) ${\theta }_1,{\theta }_2$ as a function of photon pulse width $\sigma$ in the absence of atomic dissipation $\gamma =0$. (c) $\overline{F}$ and (d) ${\theta }_1,{\theta }_2$ as a function of atomic dissipation $\gamma$ at $\sigma \mathrm{\Gamma }/v_g=1.5$.