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Quantum Nanophotonics: Deterministic Photon-based Quantum Logic Gate By Exploiting Few-photon Nonlinearity

Zihao Chen

Published Nov 6, 2019• 0 citations
Publisher

Abstract

Photon-based quantum logic gate has substantial advantages over conventional atom-based designs as a result of a longer coherence time and an inherent compatibility with quantum communication protocol of flying qubits, photons. As a vital logic gate for universal quantum computing, the two-photon controlled-phase gate demands a few-photon nonlinearity, which historically suffers from either an indeterministic nature in the linear optics regime, or a weak nonlinearity within naturally-occurring materials in the nonlinear optics regime. It is intriguing yet challenging to deliver a logic gate design by exploiting a genuine fewphoton nonlinearity. In this dissertation, we study a particular one-dimensional quantum nanophotonic system that offers the desired few-photon nonlinearity through light-matter interactions in the quantum limit (i.e., between light quanta of photons and individual material formation of atoms). Towards this end, we study the exotic photonic trimer state generation to frst demonstrate few-photon nonlinearity. Then we report the breakdown of the non-Hermitian Hamiltonian for correlated multi-photon process to unveil the non-trivial effects of few-photon nonlinearity. Finally by exploiting such a nonlinearity, we present a deterministic two-photon controlled-phase gate proposal, and further showcase universal quantum logic gate designs in quantum nanophotonic systems.

DOI
10.7936/7fg4-3p23

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Photon-based quantum logic gate has substantial advantages over conventional atom-based designs as a result of a longer coherence time and an inherent compatibility with quantum communication protocol of flying qubits, photons. As a vital logic gate for universal quantum computing, the two-photon controlled-phase gate demands a few-photon nonlinearity, which historically suffers from either an indeterministic nature in the linear optics regime, or a weak nonlinearity within naturally-occurring materials in the nonlinear optics regime. It is intriguing yet challenging to deliver a logic gate design by exploiting a genuine fewphoton nonlinearity. In this dissertation, we study a particular one-dimensional quantum nanophotonic system that offers the desired few-photon nonlinearity through light-matter interactions in the quantum limit (i.e., between light quanta of photons and individual material formation of atoms). Towards this end, we study the exotic photonic trimer state generation to frst demonstrate few-photon nonlinearity. Then we report the breakdown of the non-Hermitian Hamiltonian for correlated multi-photon process to unveil the non-trivial effects of few-photon nonlinearity. Finally by exploiting such a nonlinearity, we present a deterministic two-photon controlled-phase gate proposal, and further showcase universal quantum logic gate designs in quantum nanophotonic systems.
To resolve the intrinsic trade-off between the deterministic nature and scalability of controlled phase gate implementation in the linear optics regime, we propose a novel deterministic two-photon controlled phase gate scheme in chiral quantum nanophotonics. The essential ingredient here is that, a non-linear π-phase shift is imprinted during the photonic molecule generations. On one hand, the gate operates in a deterministic way without the assistance of probabilistic ancilla qubit measurement. On the other hand, the gate implementation is of low complexity to be highly scalable. To date, the chiral coupling is readily underpinned by the advent of directional emission technique. Potential implementation platforms include QD, superconducting qubit, Rydberg atom, or N-V center that is coupled to a PhC waveguide, transmission line, or optical fiber.
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.
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.
Photons are ideal carriers of quantum information: they are fast, low-loss, and compatible with mature photonic infrastructure.Linear optical quantum computing exploits these properties but relies on probabilistic measurements and post-selection, incurring an exponential resource overhead that limits scalability [1].Circumventing this bottleneck requires deterministic quantum logic gates, which in turn demand strong, controllable interactions between individual photons.Photons do not interact in free space or in linear optical media.The standard route to attain effective photonphoton interactions is to hybridise photons with interacting matter excitations, forming polaritons.The matter component introduces an interaction-induced anharmonic level shift U into the ladder of polariton states: when one polariton occupies a mode, the next photon sees a shifted resonance (Fig. 1a).The key figure of merit is U/γ, where γ is the total polariton decoherence rate.For U/γ ≪ 1 the nonlinearity is classical; for U/γ ≳ 1 the system enters the quantum nonlinear regime, enabling photon blockade, large conditional phase shifts, and deterministic photonic gates.Atomic Rydberg systems have provided the clearest demonstration of this regime.Atoms excited to Rydberg states -electronic states with large principal quantum numbers n ≫ 1 -possess unique properties [2].Their lifetimes scale as 1/γ ∝ n 3 and transition dipole moments as µ ∝ n 2 , leading to strong dipole-dipole (U ∝ n 4 /r 3 ) or van der Waals (U ∝ n 11 /r 6 ) interactions over long distances r.These interactions can be imprinted onto photons via electromagnetically induced transparency (EIT) [3]: photons hybridise with collective atomic excitations to form slowly propagating Rydberg polaritons that strongly interact with each other over distances of up to tens of micrometres [4].This mechanism has produced photon blockade [5]
Quantum nonlinear optics seeks to harness strong photon-photon interactions for scalable quantum technologies, although dissipative losses still pose a major barrier to near-unity conversion efficiency. Here, we bridge non-Hermitian physics with the quantum nonlinear domain by exploiting perfect absorption to identify and optimize few-photon nonlinear processes. We theoretically investigate two circuit QED systems, operating in the light-matter ultrastrong coupling regime. The first (i) enables simultaneous two-atom excitations by single photons, while the second (ii) realizes the strong coupling between a single-photon and a two-photon Fock states. We demonstrate that, since the strong optical nonlinearities cause quantum spectral features to emerge already at the level of linear response theory, the perfect absorption condition in ∣S11∣|S_{11}|∣S11​∣ enables near-deterministic single-photon down-conversion into (i) a qubit-qubit-correlated pair and (ii) a two-photon pair. We show that the conversion efficiency can be systematically optimized through experimentally accessible parameters, both linked to the emergence of Hermitian subspaces within the effective non-Hermitian Hamiltonians. These findings position non-Hermitian engineering as a broadly applicable route to optimizing quantum devices at the single-photon level, even beyond circuit-QED platforms.
Quantum optical nonlinearities have received growing interest for their key role in quantum information science, quantum simulations, and other quantum technologies. Unfortunately, most materials exhibit very weak optical nonlinearities, virtually non-existent at the single photon level. Nano-scale optical resonators can store light for a long period of time in cubic-wavelength scale volume, and thus present a unique opportunity to enhance the light-matter interaction. Additionally, breakthroughs in materials science allow us to engineer inherently strong nonlinear materials. In this talk, I will present our theoretical and experimental efforts in nonlinear nanophotonics, integrated with atomically thin 2D materials, specifically transition metal dichalcogenides and solution-processed quantum dots. By confining both light and matter in the wavelength scale, we aim to reach the nonlinear regime, where single photons start repelling each other. I will also elaborate on the possibility of scaling this platform to multiple single photon quantum nodes with the possibility of creating a correlated quantum fluid of light.