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arXiv:1909.05751 · Physical Review Letters

Controlled-Phase Gate Using Dynamically Coupled Cavities and Optical Nonlinearities

Mikkel Heuck, Kurt A. Jacobs, Dirk Englund

Published Apr 20, 2020• 81 citations
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Abstract

We show that relatively simple integrated photonic circuits have the potential to realize a high fidelity deterministic controlled-phase gate between photonic qubits using bulk optical nonlinearities. The gate is enabled by converting travelling continuous-mode photons into stationary cavity modes using strong classical control fields that dynamically change the effective cavity-waveguide coupling rate. This architecture succeeds because it reduces the wave packet distortions that otherwise accompany the action of optical nonlinearities [J. Shapiro, Phys. Rev. A 73, 062305 (2006)PLRAAN1050-294710.1103/PhysRevA.73.062305; J. Gea-Banacloche, Phys. Rev. A 81, 043823 (2010)PLRAAN1050-294710.1103/PhysRevA.81.043823]. We show that high-fidelity gates can be achieved with self-phase modulation in χ^{(3)} materials as well as second-harmonic generation in χ^{(2)} materials. The gate fidelity asymptotically approaches unity with increasing storage time for an incident photon wave packet with fixed duration. We also show that dynamically coupled cavities enable a trade-off between errors due to loss and wave packet distortion. Our proposed architecture represents a new approach to practical implementation of quantum gates that is room-temperature compatible and only relies on components that have been individually demonstrated.

DOI
10.1103/physrevlett.124.160501

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We show that relatively simple integrated photonic circuits have the potential to realize a high fidelity deterministic controlled-phase gate between photonic qubits using bulk optical nonlinearities. The gate is enabled by converting travelling continuous-mode photons into stationary cavity modes using strong classical control fields that dynamically change the effective cavity-waveguide coupling rate. This architecture succeeds because it reduces the wave packet distortions that otherwise accompany the action of optical nonlinearities [J. Shapiro, Phys. Rev. A 73, 062305 (2006)PLRAAN1050-294710.1103/PhysRevA.73.062305; J. Gea-Banacloche, Phys. Rev. A 81, 043823 (2010)PLRAAN1050-294710.1103/PhysRevA.81.043823]. We show that high-fidelity gates can be achieved with self-phase modulation in χ^{(3)} materials as well as second-harmonic generation in χ^{(2)} materials. The gate fidelity asymptotically approaches unity with increasing storage time for an incident photon wave packet with fixed duration. We also show that dynamically coupled cavities enable a trade-off between errors due to loss and wave packet distortion. Our proposed architecture represents a new approach to practical implementation of quantum gates that is room-temperature compatible and only relies on components that have been individually demonstrated.
A central goal in photonic quantum information processing is the ability to perform high-fidelity logic gates between multiple optical qubits. Here, we present our recent theoretical work on using optical nonlinearities to implement controlled-phase gates between two optical qubits. Our approach is based on using dynamically coupled cavities to convert photons travelling in a waveguide into highly confined cavity modes. This conversion enables very strong interactions between photons in quasi-monochromatic modes, which enables high fidelity gates. We will discuss gate protocols based on second- and third order nonlinear materials as well as interactions with two-level emitters.
We study theoretically the interaction between two photons in a nonlinear cavity. The photons are absorbed into the cavity by an effective tuning of its input-output coupling via external control of a coupling to a second, strongly output-coupled cavity mode. Such ``dynamically coupled'' cavities, which can be implemented using bulk ${\ensuremath{\chi}}^{(2)}$ and ${\ensuremath{\chi}}^{(3)}$ nonlinearities, enable incoming photon wave packets to be absorbed into the cavity with high fidelity when the duration of the control is similar to that of the wave packets. Further, this configuration can be used to avoid limitations in the photon-photon interaction time set by the delay-bandwidth product of passive cavities and enables the elimination of wave-packet distortions caused by dispersive cavity transmission and reflection. We consider three kinds of nonlinearities, two arising from ${\ensuremath{\chi}}^{(2)}$ and ${\ensuremath{\chi}}^{(3)}$ materials and one due to an interaction with a two-level emitter. To analyze the input and output of few-photon wave packets, we use a Schr\"odinger-picture formalism in which traveling-wave fields are discretized into infinitesimal time bins. We suggest that dynamically coupled cavities provide a very useful tool for improving the performance of quantum devices relying on cavity-enhanced light-matter interactions such as single-photon sources and atomlike quantum memories with photon interfaces. As an example, we present simulation results showing that high-fidelity two-qubit entangling gates may be constructed using any of the considered nonlinear interactions.
Abstract We propose an architecture for achieving high-fidelity deterministic quantum logic gates on dual-rail encoded photonic qubits by letting photons interact with a two-level emitter (TLE) inside an optical cavity. The photon wave packets that define the qubit are preserved after the interaction due to a quantum control process that actively loads and unloads the photons from the cavity and dynamically alters their effective coupling to the TLE. The controls rely on nonlinear wave mixing between cavity modes enhanced by strong externally modulated electromagnetic fields or on AC Stark shifts of the TLE transition energy. We numerically investigate the effect of imperfections in terms of loss and dephasing of the TLE as well as control field miscalibration. Our results suggest that III-V quantum dots in GaAs membranes is a promising platform for photonic quantum information processing.
We propose a compact and highly efficient scheme for solid-state photonic quantum gates. At the core of our scheme is a $SWA{P}^{\ensuremath{\phi}}$ gate based on giant Cooper-pair-based optical nonlinearity we predict in a semiconductor-superconductor structure, selectively introducing a phase to the $|{\mathrm{\ensuremath{\Psi}}}_{+}\ensuremath{\rangle}$ Bell state. We theoretically demonstrate this scheme on a practical device based on a superconducting contact coupled to a GaAs/AlGaAs waveguide structure. We model the Cooper-pair-induced nonlinear change of the refractive index showing strong nonlinearities at energies close to the superconducting gap inside a semiconductor band. We calculate the fidelity of the proposed $SWA{P}^{\ensuremath{\phi}}$ gate, as well as the sensitivity of the gate to device parameters. As short photon wave packets are crucial for efficient higher-order interactions, we investigate the integrated fidelity for short wave packets with different central wavelengths and bandwidths, providing limiting factors as well as possible optimizations. This theoretically demonstrated concept can pave the way toward practical realizations of scalable photonic quantum circuits.
We propose a scheme for high-fidelity photonic controlled-phase gates using a Rydberg blockade in an ensemble of atoms in an optical cavity. The gate operation is obtained by first storing a photonic pulse in the ensemble and then scattering a second pulse from the cavity, resulting in a phase change depending on whether the first pulse contained a single photon. We show that the combination of a Rydberg blockade and optical cavities effectively enhances the optical nonlinearity created by the strong Rydberg interaction and makes the gate operation more robust. The resulting gate can be implemented with cavities of moderate finesse, allowing for highly efficient processing of quantum information encoded in photons. As an illustration, we show how the gate can be employed to increase the communication rate of quantum repeaters based on atomic ensembles.
We report the construction of a passive, deterministic and near-unity-fidelity controlled-πππ-phase gate for single-photon wavepackets with a node comprising a two-level emitter and a small number of cavities. The proposed gate is rooted in the concept of time-reversal symmetric photon transport, which makes the entire photon transport process into a perfect absorption and re-emission process. Consequently, it can circumvent the longstanding issue of wavepacket distortion inherent in photonic phase gates employing nonlinear media. Moreover, such time-reversal symmetric transport ensures the nonlinear πππ phase shift by a single two-level emitter for the two-photon case. We develop analytical solutions to reveal the temporal dynamics of the nonlinear photon transport and to optimize the gate structure. Notably, the gate fidelity can exceed 99\% for a node with only four cavities for both single-photon and two-photon operations. Moreover, the proposed gate architecture is compatible with the platforms of integrated photonics.