Two-dimensional topological quantum walks in the momentum space of structured light

Abstract

Quantum walks are powerful tools for quantum applications and for designing topological systems. Although they are simulated in a variety of platforms, genuine two-dimensional realizations are still challenging. Here we present an innovative approach to the photonic simulation of a quantum walk in two dimensions, where walker positions are encoded in the transverse wavevector components of a single light beam. The desired dynamics is obtained by means of a sequence of liquid-crystal devices, which apply polarization-dependent transverse "kicks" to the photons in the beam. We engineer our quantum walk so that it realizes a periodically-driven Chern insulator, and we probe its topological features by detecting the anomalous displacement of the photonic wavepacket under the effect of a constant force. Our compact, versatile platform offers exciting prospects for the photonic simulation of two-dimensional quantum dynamics and topological systems.

Published version of the manuscript

References in corpus (46)

• Berry Phase Effects on Electronic Properties
• Topological Photonics
• Topological Field Theory of Time-Reversal Invariant Insulators
• Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media
• Topological phases of non-Hermitian systems
• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• A Quantum Random Walk Search Algorithm
• Non-Bloch Band Theory of Non-Hermitian Systems
• Universal computation by quantum walk
• Quantum walks of correlated particles
• Non-Hermitian Chern bands
• Quantum walks: a comprehensive review
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Dynamical quantum phase transitions: a review
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Observation of topologically protected bound states in a one dimensional photonic system
• Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
• Exploring Topological Phases With Quantum Walks
• Quantum transport simulations in a programmable nanophotonic processor
• Anderson localization of entangled photons in an integrated quantum walk
• Strongly Correlated Quantum Walks in Optical Lattices
• A 2D Quantum Walk Simulation of Two-Particle Dynamics
• Discrete single-photon quantum walks with tunable decoherence
• Decoherence and disorder in quantum walks: From ballistic spread to localization
• Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
• Topological singularities and the general classification of Floquet-Bloch systems
• Artificial gauge fields in materials and engineered systems
• Experimental Two-dimensional Quantum Walk on a Photonic Chip
• Simulating dynamic quantum phase transitions in photonic quantum walks
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Photonic quantum walk in a single beam with twisted light
• Quantum walks and wavepacket dynamics on a lattice with twisted photons
• Two-photon quantum walk in a multimode fiber
• Electric quantum walks with individual atoms
• Dynamical moments reveal a topological quantum transition in a photonic quantum walk
• Quantum walks of correlated photon pairs in two-dimensional waveguide arrays
• Photon spin-to-orbital angular momentum conversion via an electrically tunable $q$-plate
• Extracting the Chern number from the dynamics of a Fermi gas: Implementing a quantum Hall bar for cold atoms
• Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
• Experimental Quantum Fast Hitting on Hexagonal Graphs
• Quantum Walk in Momentum Space with a Bose-Einstein Condensate
• Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin
• Measurement of Chern numbers through center-of-mass responses
• A synthetic gauge field for two-dimensional time-multiplexed quantum random walks
• Experimental realisation of a delayed-choice quantum walk
• Alternate two-dimensional quantum walk with a single-qubit coin

Cited by in corpus (43)

• Realization of an anomalous Floquet topological system with ultracold atoms
• Nonseparable states of light: From quantum to classical
• Roadmap on structured waves
• Non-Bloch $\mathcal{P}\mathcal{T}$ symmetry breaking in non-Hermitian Photonic Quantum Walks
• Ultra-sensitive measurement of transverse displacements with structured light
• A comprehensive review on developments of synthetic dimensions
• Ultra-long quantum walks via spin-orbit photonics
• Quantum walks of two correlated photons in a 2D synthetic lattice
• Topological Anderson phase in quasi-periodic waveguide lattices
• Fidelity susceptibility near topological phase transitions in quantum walks
• Topological swing in Bloch oscillations
• Bulk detection of time-dependent topological transitions in quenched chiral models
• Synthetic dimensions for topological and quantum phases: Perspective
• Bloch-Landau-Zener dynamics induced by a synthetic field in a photonic quantum walk
• Generation of hyperentangled states and two-dimensional quantum walks using $J$- ($q$)- plates and polarization beamsplitters
• Topological chiral modes in random scattering networks
• Quantized Hall drift in a frequency-encoded photonic Chern insulator
• Toward simulation of topological phenomenas with one-, two- and three-dimensional quantum walks
• Linking topological features of the Hofstadter model to optical diffraction figures
• Electrically tunable liquid-crystal metasurfaces with patterned birefringence and dichroism
• Tunable Aharonov-Bohm-like cages for quantum walks
• The Coming Decades of Quantum Simulation
• Quantum walk on a graph of spins: magnetism and entanglement
• Large-scale free-space photonic circuits in two dimensions
• Second-order topological insulator in a coinless discrete-time quantum walk
• Topological spin-orbit-coupled fermions beyond rotating wave approximation
• Manifestation of the Berry connection in chiral lattice systems
• Generation of the Complete Bell Basis via Hong-Ou-Mandel Interference
• Photonic random walks with traps
• High-fidelity state transfer via quantum walks from delocalized states
• Nonlocal transfer of high-dimensional unitary operations
• Non-Hermitian dynamical topological winding in photonic mesh lattices
• History states of one-dimensional quantum walks
• Retrieving space-dependent polarization transformations via near-optimal quantum process tomography
• Optical realization of one-dimensional generalized split-step quantum walks
• Programmable non-Hermitian photonic quantum walks via dichroic metasurfaces
• Quantum process tomography of structured optical gates with convolutional neural networks
• Two-Dimensional Quantum Walk of Correlated Photons
• Quantum walk with coherent multiple translations induces fast quantum gate operations
• Compact and programmable large-scale optical processor in free space
• Continuous-time quantum walks on a defective lattice: Boosting the spreading of delocalized states through Parrondo's strategy
• Classical structured light analogy of quantum squeezed state
• Engineering qubit dynamics in open systems with photonic synthetic lattices