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arXiv:1612.04803 · Physical Review A

Limitations of two-level emitters as nonlinearities in two-photon controlled-phase gates

Anders Nysteen, Dara P. S. McCutcheon, Mikkel Heuck, Jesper Mørk, Dirk Englund

Published Jun 5, 2017• 21 citations
arXivHTMLPDF

Abstract

We investigate the origin of imperfections in the fidelity of a two-photon controlled-phase gate based on two-level-emitter nonlinearities. We focus on a passive system that operates without external modulations to enhance its performance. We demonstrate that the fidelity of the gate is limited by opposing requirements on the input pulse width for one- and two-photon-scattering events. For one-photon scattering, the spectral pulse width must be narrow compared with the emitter linewidth, while two-photon-scattering processes require the pulse width and emitter linewidth to be comparable. We find that these opposing requirements limit the maximum fidelity of the two-photon controlled-phase gate to $84%$ for photons with Gaussian spectral profiles.

DOI
10.1103/physreva.95.062304

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arXiv:2110.02960•npj Quantum Information•Sep 7, 2022•13 citations
We investigate the origin of imperfections in the fidelity of a two-photon controlled-phase gate based on two-level-emitter nonlinearities. We focus on a passive system that operates without external modulations to enhance its performance. We demonstrate that the fidelity of the gate is limited by opposing requirements on the input pulse width for one- and two-photon-scattering events. For one-photon scattering, the spectral pulse width must be narrow compared with the emitter linewidth, while two-photon-scattering processes require the pulse width and emitter linewidth to be comparable. We find that these opposing requirements limit the maximum fidelity of the two-photon controlled-phase gate to 8484%84 for photons with Gaussian spectral profiles.
In this thesis we investigate few-photon non-linearities in all-optical, on-chip circuits, and we discuss their possible applications in devices of interest for quantum information technology, such as conditional two-photon gates and single-photon sources. In order to propose efficient devices, it is crucial to fully understand the non-equilibrium dynamics of strongly interacting photons. Employing both numerical and analytical approaches we map out the full scattering dynamics for two photons scattering on a two-level emitter in a one-dimensional waveguide. The strongest non-linear interaction arise when the emitter is excited the most, which occurs for incoming photon pulses with a spectral bandwidth comparable to the emitter linewidth. For two identical, counter-propagating photons, the emitter works as a non-linear beam splitter, as the emitter induces strong directional correlations between the scattered photons. Even though the non-linearity also alters the pulse spectrum due to a four-wave mixing process, we demonstrate that input pulses with a Gaussian spectrum can be mapped to the output with up to 80 % fidelity. Using two identical two-level emitters, we propose a setup for a deterministic controlled-phase gate, which preserves the properties of the two incoming photons with almost 80 %, limited by spectral changes induced by the non-linearity and phase modulations upon scattering. Another setup for a controlled-phase operation is suggested with two coupled ring resonators exploiting a strong second-order material non-linearity. By dynamically trapping the first of two temporally separated photons in the non-linear resonator, the scattering of the second photon is altered. Due to the trapping, the undesired aforementioned non-linear effects are avoided, but the gate performance is now limited by the capturing process. Semiconductor quantum dots (QDs) are promising for realizing few-photon non-linearities in solid-state implementations, although coupling to phonon modes in the surrounding lattice have significant influence on the dynamics. By accounting for the commonly neglected asymmetry between the electron and hole wavefunction in the QD, we show how the phonon-assisted transition rate to a slightly detuned optical mode may be suppressed. This is achieved by properly matching the electrical carrier confinement with the deformation potential interaction, where the suppression only occurs in materials where the deformation potential interaction shifts the electron and hole bands in the same direction. We demonstrate also how the phonon-induced effects may be altered by placing the QD inside an infinite slab, where the confinement of the phonons is modified instead. For a slab thickness below ∼ 70 nm, the bulk description of the phonon modes may be insufficient. The QD decay rate may be strongly increased or decreased, depending on how the detuning between the QD and the optical mode matches the phonon modes in the slab.
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 F∼99.2%\mathcal{F} \sim 99.2\%F∼99.2% (F∼96%\mathcal{F} \sim 96\%F∼96%) and a success probability of Ps∼99.6%P_s \sim 99.6 \%Ps​∼99.6% (Ps∼98%P_s\sim 98 \%Ps​∼98%) for a Bell-state measurement with N=17N=17N=17 (N=5N=5N=5) scatterings.
We present a fully passive method for implementing a quantum phase gate between two photons traveling in a one-dimensional waveguide. The gate is based on chirally coupled emitters in a three level V configuration, which only interact through the photon field without any external control fields. We describe the (non)linear scattering of the emerging polariton states and show that for near resonant photons the scattering dynamics directly implements a perfect control phase gate between the incoming photons in the limit of many emitters. For a finite number of emitters we show that the dominant error mechanism can be suppressed by a simple frequency filter at the cost of a minor reduction in the success probability. We verify the results via comparison with exact scattering matrix theory and show that the fidelity can reach values F∼99% with a gate success probability of >99% for as few as eight emitters.
In this paper we analyze the performance of photonic CZ gates based on N waveguide-coupled cavities containing two-level emitters. We derive single- and two-photon scattering matrices for one cavity using the input-output formalism of quantum optics and for N>1 cavities using the SLH formalism, allowing us to compute the CZ gate fidelity. We consider two input Gaussian wave packets that are centered on a two-photon transition of the emitter-cavity system, and find a trade-off between optimizing the single-photon and two-photon wave packet shape. While the single-photon wave packet is preserved for large emitter-cavity coupling rates, where there is little overlap with the single-photon transitions, the two-photon wave packet acquires the necessary πππ phase shift for smaller coupling rates, comparable to the cavity decay rate multiplied by the number of cavities. We find that this trade-off limits the CZ gate fidelity to approximately 60% when averaging over all input states.
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.
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.