Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Nature Photonics

Space-time-topological events in photonic quantum walks

Joshua Feis, Sebastian Weidemann, Tom Sheppard, Hannah M. Price, Alexander Szameit

Published Apr 4, 2025• 37 citations
Publisher

Abstract

Abstract Time is, figuratively and literally, becoming the new dimension for crystalline matter. In a key recent advance, temporal and spatiotemporal crystals that exhibit periodicity in time and space-time, respectively, were reported, with unique properties such as spectra containing gaps not only in energy but also in momentum. Conversely, the field of topological physics, which has led to celebrated discoveries such as topological insulators featuring protected conducting surface states with immunity to backscattering, has so far been based on the notion of energy gaps and spatial boundaries only. Fundamentally rethinking the role of time, which in contrast to space exhibits a unique unidirectionality called the ‘arrow of time’, thus promises a new dimension for topological physics, setting paradigms of time and space-time topology based on the topological properties of momentum and energy–momentum gaps. Indeed, previous work has shown simulations of states which arise through the topology of momentum gaps and localize at temporal interfaces. Here we enter this new dimension of time and space-time topology. First, using discrete-time quantum walks on synthetic photonic lattices in coupled optical fibre loops, we observe such time topological states. We find a time-topological invariant and establish its relation to the observed time topological states. Transcending the separate concepts of space and time topology, we then propose and implement a system with an energy–momentum gap and introduce the concept of space-time topology, leading to topological states that are localized in both space and time, thus forming space-time topological events. We demonstrate that these are associated with unique effects such as causality-suppressed coupling or the limited collapse of space-time localization. Our study provides a model of time and space-time topology, highlighting an interplay of momentum and energy gap topology with applicability beyond photonics. In the field of topological physics, we anticipate a new role of causality and non-Hermiticity inspired by time and space-time topology. These concepts further invite exploration of connections to other fields where the arrow of time plays an important role. Moreover, our results enable the topological shaping of waves in space and time, with applications in spatiotemporal wave control for imaging or communication and topological lasers, for example.

DOI
10.1038/s41566-025-01653-w

Related papers

Spatiotemporal Topological Phase Transition in non-Hermitian Photonic System

Zimeng Zeng, Zhuoyang Li, Jiayao Liu +2 more

While energy band topology in spatial photonic crystals (PCs) and momentum-band topology in temporal crystals have each served as powerful probes of topological phases in their respective domains, their unification in a static platform remains unexplored. In this Letter, we bridge this gap by introducing a waveguide assisted non-Hermitian SSH model, in which controlled tuning of loss and coupling drives PT-symmetry breaking and enables a continuous transition between energy- and momentum-gap regimes. This allows us to construct a complete spatiotemporal topological phase diagram in a unified parameter space. By mapping this phase diagram onto a spatially graded PC, we experimentally observe multiple Bloch momentum-band gaps and a continuous spatiotemporal topological transition via translating across the static sample, enabling real-time control over the evolution pathway of the band topology. Our work creates a versatile, bias-free platform for exploring synthetic spacetime physics and opens new avenues for controlling light via non-Hermitian band engineering.

physics.opticsCross-listedarXiv:2602.05475•Feb 6, 2026

Scattering theory of topological phases in discrete-time quantum walks

Brian Tarasinski, János K. Asbóth, Jan P. Dahlhaus

One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analyzed using the Floquet operator in momentum space. In this work, we introduce an alternative approach to topology which is based on the scattering matrix of a quantum walk, adapting concepts from time-independent systems. For quantum walks with gaps in the quasienergy spectrum at 0 and $\ensuremath{\pi}$, we find three different types of topological invariants, which apply dependent on the symmetries of the system. These determine the number of protected boundary states at an interface between two quantum-walk regions. Quantum walks with an unequal number of leftward and rightward shifts per cycle are characterized by the number of perfectly transmitting unidirectional modes they support, which is equal to their nontrivial quasienergy winding. Our classification provides a unified framework that includes all known types of topology in one-dimensional discrete-time quantum walks and is very well suited for the analysis of finite-size and disorder effects. We provide a simple scheme to directly measure the topological invariants in an optical quantum-walk experiment.

arXiv:1401.2673•Physical Review A•Apr 25, 2014•69 citations

Quantum electrodynamics of photonic time crystals

Junhyeon Bae, Kyungmin Lee, Bumki Min +1 more

Photonic time crystals host a variety of intriguing phenomena, from wave amplification and mixing to exotic band structures, all stemming from the time-periodic modulation of optical properties. While these features have been well described classically, their quantum manifestation when coupled to an atomic electric dipole has remained elusive. Here, we introduce a quantum electrodynamical model of photonic time crystals that reveals a deeper connection between classical and quantum pictures: the classical momentum gap arises from a localization-delocalization quantum phase transition in a Floquet-photonic synthetic lattice. Leveraging an effective Hamiltonian perspective, we pinpoint the critical momenta and highlight how classical exponential field growth manifests itself as wave-packet acceleration in the quantum synthetic space. Remarkably, when a two-level atom is embedded in such a photonic time crystal, its Rabi oscillations undergo irreversible decay to a half-and-half mixed state-a previously unobserved phenomenon driven by photonic delocalization within the momentum gap, even with just a single frequency mode. Our findings establish photonic time crystals as versatile platforms for studying nonequilibrium quantum photonics and suggest new avenues for controlling light matter interactions through time domain engineering.

arXiv:2501.03106•Nature Communications•Dec 19, 2025•7 citations

Topological Nodal Lines for Tailored Light-Matter Entanglement

Revista, Zen, PHYSICS, 10

This paper explores the novel interplay between topological nodal lines in photonic and matter systems and their potential for engineering tailored light-matter entanglement. Topological nodal lines, characterized by closed loops of band degeneracies in momentum space, offer a robust platform for manipulating quantum states due to their inherent protection against local perturbations. We propose and investigate theoretical frameworks for realizing such topological features in systems amenable to strong light-matter coupling, including photonic crystal structures and superconducting circuits coupled to artificial atoms. By harnessing the unique dispersion properties and Berry phases associated with nodal lines, we demonstrate how specific entanglement protocols can be optimized, enabling deterministic generation of entangled photons, robust entanglement transfer, and the creation of highly non-classical states. Our methodology involves detailed analysis of band structures, topological invariants, and light-matter interaction Hamiltonians, coupled with numerical simulations to predict the entanglement fidelity and robustness. The findings suggest that topological nodal lines provide an unprecedented degree of control over the spatial and spectral properties of entangled light and matter states, paving the way for advanced quantum technologies such as fault-tolerant quantum computing, quantum communication, and quantum sensing with enhanced capabilities. This work highlights a promising avenue for integrating condensed matter topology with quantum optics, forging new pathways for fundamental research and practical applications.

•Nov 28, 2025•0 citations

Photonic quantum information and quantum walks

Matthew A. Broome

Controlling quantum states of light is of central importance to many fields of modern physics. The technology to do so underpins the only feasible means for long-distance quantum communication using quantum-key-distribution, and plays a pivotal role in the application of quantum computing, quantum metrology and investigations of fundamental physics. Motivated by these applications, in this thesis we present a number of experimental results that demonstrate an enhanced level of control over photonic states. First, we tackle one of the most important technological issues currently facing the field, namely the creation of pure multi-photon Fock states from pulsed parametric downconversion. Our technique shows a marked improvement over previous photon sources when employed for quantum information tasks. At a more foundational level, we experimentally examine the properties of quantum correlations in the temporal domain, where our results highlight surprising differences between its spatial-domain counterpart of multipartite entanglement. Finally, we experimentally implement single- and multi-photon quantum walks in the discrete- and continuous-time regimes respectively. Quantum walks have received much attention in recent years due to their vast applicability in quantum information science, especially for quantum simulation and emulation. On this front we use the quantum walk formalism to perform a full experimental simulation of topological phases in a 1-dimensional configuration. Aside from being the first demonstration of topological phases in this regime, our system exhibits unprecedented control over the topological properties in a quantum system. As such we are able to observe the exotic behaviour of trapped bound states, and discover the new phenomenon of paired bound states—a feature unique to periodically driven systems.

•Jan 1, 2012•0 citations

Global topological protection of entanglement in integrated photonic quantum walks

Anonymous, Yonatan Plotnik, Alexander Palatnik +4 more

Photon entanglement is a fundamental resource for quantum technologies, yet it is extremely fragile especially in large quantum circuitry, which is necessary for quantum information processing and computing. We propose an integrated scheme for direct topological protection of entanglement, enabling robust transport of entangled photonic states, even when the photon dynamically evolves during propagation. Our platform relies on a two-dimensional discrete-time quantum walks in synthetic dimensions, supporting topological edge states at the interface between distinct domains. Thus far, in all previous approaches for exploiting topology to protect entanglement, the protection was linked to the position of the photon in the actual structure. In contrast, our scheme relies on a synthetic temporal dimension (time bins) where the entangled state is always reproduced, despite fluctuations or variations that may emerge in the system. Thus, our scheme provides precise temporal control important for synchronization and timing in quantum computation. By suppressing phase-sensitive errors—the most critical noise source in photonic platforms—our approach can lower the physical error rate below fault-tolerance thresholds and reduce the overhead typically required for scalable quantum information processing. The robustness to errors arises from the fact that the entangled state is preserved through correlations in the synthetic (temporal) dimension. As a result, we ensure that at specific designated times, the emergent state faithfully reproduces the initial entangled state, despite the photon having taken any dynamically evolving paths. This approach establishes a robust framework for directly protecting entanglement.

Physical Review Research•Jul 23, 2026•0 citations
Abstract Time is, figuratively and literally, becoming the new dimension for crystalline matter. In a key recent advance, temporal and spatiotemporal crystals that exhibit periodicity in time and space-time, respectively, were reported, with unique properties such as spectra containing gaps not only in energy but also in momentum. Conversely, the field of topological physics, which has led to celebrated discoveries such as topological insulators featuring protected conducting surface states with immunity to backscattering, has so far been based on the notion of energy gaps and spatial boundaries only. Fundamentally rethinking the role of time, which in contrast to space exhibits a unique unidirectionality called the ‘arrow of time’, thus promises a new dimension for topological physics, setting paradigms of time and space-time topology based on the topological properties of momentum and energy–momentum gaps. Indeed, previous work has shown simulations of states which arise through the topology of momentum gaps and localize at temporal interfaces. Here we enter this new dimension of time and space-time topology. First, using discrete-time quantum walks on synthetic photonic lattices in coupled optical fibre loops, we observe such time topological states. We find a time-topological invariant and establish its relation to the observed time topological states. Transcending the separate concepts of space and time topology, we then propose and implement a system with an energy–momentum gap and introduce the concept of space-time topology, leading to topological states that are localized in both space and time, thus forming space-time topological events. We demonstrate that these are associated with unique effects such as causality-suppressed coupling or the limited collapse of space-time localization. Our study provides a model of time and space-time topology, highlighting an interplay of momentum and energy gap topology with applicability beyond photonics. In the field of topological physics, we anticipate a new role of causality and non-Hermiticity inspired by time and space-time topology. These concepts further invite exploration of connections to other fields where the arrow of time plays an important role. Moreover, our results enable the topological shaping of waves in space and time, with applications in spatiotemporal wave control for imaging or communication and topological lasers, for example.
While energy band topology in spatial photonic crystals (PCs) and momentum-band topology in temporal crystals have each served as powerful probes of topological phases in their respective domains, their unification in a static platform remains unexplored. In this Letter, we bridge this gap by introducing a waveguide assisted non-Hermitian SSH model, in which controlled tuning of loss and coupling drives PT-symmetry breaking and enables a continuous transition between energy- and momentum-gap regimes. This allows us to construct a complete spatiotemporal topological phase diagram in a unified parameter space. By mapping this phase diagram onto a spatially graded PC, we experimentally observe multiple Bloch momentum-band gaps and a continuous spatiotemporal topological transition via translating across the static sample, enabling real-time control over the evolution pathway of the band topology. Our work creates a versatile, bias-free platform for exploring synthetic spacetime physics and opens new avenues for controlling light via non-Hermitian band engineering.
One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analyzed using the Floquet operator in momentum space. In this work, we introduce an alternative approach to topology which is based on the scattering matrix of a quantum walk, adapting concepts from time-independent systems. For quantum walks with gaps in the quasienergy spectrum at 0 and $\ensuremath{\pi}$, we find three different types of topological invariants, which apply dependent on the symmetries of the system. These determine the number of protected boundary states at an interface between two quantum-walk regions. Quantum walks with an unequal number of leftward and rightward shifts per cycle are characterized by the number of perfectly transmitting unidirectional modes they support, which is equal to their nontrivial quasienergy winding. Our classification provides a unified framework that includes all known types of topology in one-dimensional discrete-time quantum walks and is very well suited for the analysis of finite-size and disorder effects. We provide a simple scheme to directly measure the topological invariants in an optical quantum-walk experiment.
Photonic time crystals host a variety of intriguing phenomena, from wave amplification and mixing to exotic band structures, all stemming from the time-periodic modulation of optical properties. While these features have been well described classically, their quantum manifestation when coupled to an atomic electric dipole has remained elusive. Here, we introduce a quantum electrodynamical model of photonic time crystals that reveals a deeper connection between classical and quantum pictures: the classical momentum gap arises from a localization-delocalization quantum phase transition in a Floquet-photonic synthetic lattice. Leveraging an effective Hamiltonian perspective, we pinpoint the critical momenta and highlight how classical exponential field growth manifests itself as wave-packet acceleration in the quantum synthetic space. Remarkably, when a two-level atom is embedded in such a photonic time crystal, its Rabi oscillations undergo irreversible decay to a half-and-half mixed state-a previously unobserved phenomenon driven by photonic delocalization within the momentum gap, even with just a single frequency mode. Our findings establish photonic time crystals as versatile platforms for studying nonequilibrium quantum photonics and suggest new avenues for controlling light matter interactions through time domain engineering.
This paper explores the novel interplay between topological nodal lines in photonic and matter systems and their potential for engineering tailored light-matter entanglement. Topological nodal lines, characterized by closed loops of band degeneracies in momentum space, offer a robust platform for manipulating quantum states due to their inherent protection against local perturbations. We propose and investigate theoretical frameworks for realizing such topological features in systems amenable to strong light-matter coupling, including photonic crystal structures and superconducting circuits coupled to artificial atoms. By harnessing the unique dispersion properties and Berry phases associated with nodal lines, we demonstrate how specific entanglement protocols can be optimized, enabling deterministic generation of entangled photons, robust entanglement transfer, and the creation of highly non-classical states. Our methodology involves detailed analysis of band structures, topological invariants, and light-matter interaction Hamiltonians, coupled with numerical simulations to predict the entanglement fidelity and robustness. The findings suggest that topological nodal lines provide an unprecedented degree of control over the spatial and spectral properties of entangled light and matter states, paving the way for advanced quantum technologies such as fault-tolerant quantum computing, quantum communication, and quantum sensing with enhanced capabilities. This work highlights a promising avenue for integrating condensed matter topology with quantum optics, forging new pathways for fundamental research and practical applications.
Controlling quantum states of light is of central importance to many fields of modern physics. The technology to do so underpins the only feasible means for long-distance quantum communication using quantum-key-distribution, and plays a pivotal role in the application of quantum computing, quantum metrology and investigations of fundamental physics. Motivated by these applications, in this thesis we present a number of experimental results that demonstrate an enhanced level of control over photonic states. First, we tackle one of the most important technological issues currently facing the field, namely the creation of pure multi-photon Fock states from pulsed parametric downconversion. Our technique shows a marked improvement over previous photon sources when employed for quantum information tasks. At a more foundational level, we experimentally examine the properties of quantum correlations in the temporal domain, where our results highlight surprising differences between its spatial-domain counterpart of multipartite entanglement. Finally, we experimentally implement single- and multi-photon quantum walks in the discrete- and continuous-time regimes respectively. Quantum walks have received much attention in recent years due to their vast applicability in quantum information science, especially for quantum simulation and emulation. On this front we use the quantum walk formalism to perform a full experimental simulation of topological phases in a 1-dimensional configuration. Aside from being the first demonstration of topological phases in this regime, our system exhibits unprecedented control over the topological properties in a quantum system. As such we are able to observe the exotic behaviour of trapped bound states, and discover the new phenomenon of paired bound states—a feature unique to periodically driven systems.
Photon entanglement is a fundamental resource for quantum technologies, yet it is extremely fragile especially in large quantum circuitry, which is necessary for quantum information processing and computing. We propose an integrated scheme for direct topological protection of entanglement, enabling robust transport of entangled photonic states, even when the photon dynamically evolves during propagation. Our platform relies on a two-dimensional discrete-time quantum walks in synthetic dimensions, supporting topological edge states at the interface between distinct domains. Thus far, in all previous approaches for exploiting topology to protect entanglement, the protection was linked to the position of the photon in the actual structure. In contrast, our scheme relies on a synthetic temporal dimension (time bins) where the entangled state is always reproduced, despite fluctuations or variations that may emerge in the system. Thus, our scheme provides precise temporal control important for synchronization and timing in quantum computation. By suppressing phase-sensitive errors—the most critical noise source in photonic platforms—our approach can lower the physical error rate below fault-tolerance thresholds and reduce the overhead typically required for scalable quantum information processing. The robustness to errors arises from the fact that the entangled state is preserved through correlations in the synthetic (temporal) dimension. As a result, we ensure that at specific designated times, the emergent state faithfully reproduces the initial entangled state, despite the photon having taken any dynamically evolving paths. This approach establishes a robust framework for directly protecting entanglement.