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arXiv:2112.08981 · Physical Review A

Driven Gaussian quantum walks

Philip Held, Melanie Engelkemeier, Syamsundar De, Sonja Barkhofen, Jan Sperling, Christine Silberhorn

Published Apr 19, 2022• 7 citations
arXivHTMLPDF

Abstract

Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian quantum walk is introduced. In contrast to typically considered quantum walks in optical settings, we describe the operation of the walk in terms of a nonlinear map rather than a unitary operation, e.g., by replacing a beam-splitter-type coin with a two-mode squeezer, being a process that is controlled and driven by a pump field. This opens previously unattainable possibilities for quantum walks that include nonlinear elements as core components of their operation, vastly extending their range of applications. A full framework for driven Gaussian quantum walks is developed, including methods to dynamically characterize nonlinear, quantum, and quantum-nonlinear effects. Moreover, driven Gaussian quantum walks are compared with their classically interfering and linear counterparts, which are based on classical coherence of light rather than quantum superpositions. In particular, the generation and boost of highly multimode entanglement, squeezing, and other quantum effects are studied over the duration of the nonlinear walk. Importantly, we prove the quantumness of the evolution itself, regardless of the input state. A scheme for an experimental realization is proposed. Furthermore, nonlinear properties of driven Gaussian quantum walks are explored, such as amplification that leads to an ever increasing number of correlated quantum particles, constituting a source of new walkers during the walk. Therefore, a concept for quantum walks is proposed that leads to---and even produces---directly accessible quantum phenomena, and that renders the quantum simulation of nonlinear processes possible.

DOI
10.1103/physreva.105.042210

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Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian quantum walk is introduced. In contrast to typically considered quantum walks in optical settings, we describe the operation of the walk in terms of a nonlinear map rather than a unitary operation, e.g., by replacing a beam-splitter-type coin with a two-mode squeezer, being a process that is controlled and driven by a pump field. This opens previously unattainable possibilities for quantum walks that include nonlinear elements as core components of their operation, vastly extending their range of applications. A full framework for driven Gaussian quantum walks is developed, including methods to dynamically characterize nonlinear, quantum, and quantum-nonlinear effects. Moreover, driven Gaussian quantum walks are compared with their classically interfering and linear counterparts, which are based on classical coherence of light rather than quantum superpositions. In particular, the generation and boost of highly multimode entanglement, squeezing, and other quantum effects are studied over the duration of the nonlinear walk. Importantly, we prove the quantumness of the evolution itself, regardless of the input state. A scheme for an experimental realization is proposed. Furthermore, nonlinear properties of driven Gaussian quantum walks are explored, such as amplification that leads to an ever increasing number of correlated quantum particles, constituting a source of new walkers during the walk. Therefore, a concept for quantum walks is proposed that leads to---and even produces---directly accessible quantum phenomena, and that renders the quantum simulation of nonlinear processes possible.
Quantum walk (QW) provides a versatile tool to study fundamental physics and also to make a variety of practical applications. We here start with the recent idea of nonlinear QW and show that introducing nonlinearity to QW can lead to a wealth of remarkable possibilities, e.g., simulating nonlinear quantum dynamics, thus enhancing the applicability of QW above the existing level for a universal quantum simulator. As an illustration, we show that the dynamics of a nonlinear Dirac particle can be simulated on an optical nonlinear QW platform implemented with a measurement-based-feedforward scheme. The nonlinear evolution induced by the feed-forward introduces a self-coupling mechanism to (otherwise linear) Dirac particles, which accordingly behave as a soliton. We particularly consider two kinds of nonlinear Dirac equations, one with a scalar-type self-coupling (Gross-Neveu model) and the other with a vector-type one (Thirring model), respectively. Using their known stationary solutions, we confirm that our nonlinear QW framework is capable of exhibiting characteristic features of a soliton. Furthermore, we show that the nonlinear QW enables us to observe and control an enhancement and suppression of the ballistic diffusion.
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The has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been based on multi-path interferometric schemes in real space. Here, we report the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons. In contrast to previous implementations, the whole process develops in a single light beam, with no need of interferometers; it requires optical resources scaling linearly with the number of steps; and it allows flexible control of input and output superposition states. Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets. Our demonstration introduces a novel versatile photonic platform for quantum simulations.
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High harmonic generation (HHG) is a highly nonlinear optical process in which radiation from a strong driving field is up-converted into its high-order harmonics. In atomic systems, this nonlinearity manifests itself through the intensity scaling of the emitted harmonics with the driving field strength. Despite the highly nonlinear nature of HHG, when the driving field is prepared in a classical Gaussian state and atomic depletion remains negligible, the quantum statistical properties of the generated harmonics retains classical Gaussian quantum statistics. Driving HHG with bright squeezed vacuum (BSV) light challenges this paradigm, as its enhanced field fluctuations can modify the statistical properties of the generated harmonics. In this work, we investigate the conditions under which BSV-driven HHG gives rise to non-classical Gaussian states, and identify the regimes where this Gaussian description breaks down. For bichromatic driving by a strong coherent field at frequency ωωω and a perturbative BSV field at 2ω2ω2ω, the even-harmonic response is approximately linear in the BSV quadrature, leading to non-classical multimode Gaussian entanglement in the harmonic field. We show that this state can be described as a distributed collective squeezed mode over the even-harmonic manifold, and characterize its covariance matrix, entanglement structure, and quantum teleportation fidelity as an operational benchmark. Our results highlight the potential of non-classically driven HHG as a platform for engineering Gaussian and non-Gaussian states of light in the extreme ultraviolet regime.
Over the last few decades, nonlinear optics has become significantly more nonlinear, traversing nearly a billionfold improvement in energy efficiency, with ultrafast nonlinear nanophotonics in particular emerging as a frontier for combining both spatial and temporal engineering. At present, cutting-edge experiments in nonlinear nanophotonics place us just above the mesoscopic regime, where a few hundred photons suffice to trigger highly nonlinear dynamics. In contrast to classical or deep-quantum optics, the mesoscale is characterized by dynamical interactions between mean-field, Gaussian, and non-Gaussian quantum features, all within a close hierarchy of scales. When combined with the inherent multimode complexity of optical fields, such hybrid quantum-classical dynamics present theoretical, experimental, and engineering challenges to the contemporary framework of quantum optics. In this review, we highlight the unique physics that emerges in multimode nonlinear optics at the mesoscale and outline key principles for exploiting both classical and quantum features to engineer novel functionalities. We briefly survey the experimental landscape and draw attention to outstanding technical challenges in materials, dispersion engineering, and device design for accessing mesoscopic operation. Finally, we speculate on how these capabilities might usher in some new paradigms in quantum photonics, from quantum-augmented information processing to nonclassical-light-driven dynamics and phenomena to all-optical non-Gaussian measurement and sensing. The physics unlocked at the mesoscale present significant challenges and opportunities in theory and experiment alike, and this review is intended to serve as a guide to navigating this new frontier in ultrafast quantum nonlinear optics.