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npj | nanophotonics Perspective
https://doi.org/10.1038/s44310-024-00034-5
Quantum topological photonics with
special focus on waveguide systems
Check for updates
Jun Gao1, Ze-Sheng Xu1, Zhaoju Yang2, Val Zwiller1& Ali W. Elshaari1
In the burgeoning field of quantum topological photonics, waveguide systems play a crucial role. This
perspective delves into the intricate interplay between photonic waveguides and topological
phenomena, underscoring the theoretical underpinnings of topological insulators and their photonic
manifestations. We highlight key milestones and breakthroughs in topological photonics using
waveguide systems, alongside an in-depth analysis of their fabrication techniques and tunability. The
discussion includes the technological advancements and challenges, limitations of current methods,
and potential strategies for improvement. This perspective also examines the quantum states of light
in topological waveguides, where the confluence of topology and quantum optics promises robust
avenues for quantum communication and computing. Concl uding with a forward-looking view, we aim
to inspire new research and innovation in quantum topological photonics, highlighting its potential for
the next generation of photonic technologies.
Timeline of topological photonics in waveguide
systems
Originating from solid-state physics, the concept of topology is increasingly
being applied in the field of photonics, garnering widespread attention and
giving rise to numerous novel applications. A seminal contribution in this
domain involves the theoretical prediction of topological insulators. The
concept of topological insulators originated with the discovery of the
quantum Hall effect1–5. Although this effect was originally demonstrated in
electronic systems, it could also be realized in bosonic systems (such as
photonics). Through the manipulation of system parameters, t he creation of
an artificial magnetic field is achievable, resulting in the observation of the
quantum Hall effect (QHE) and quantum spin Hall effect (QSHE) within
two-dimensional photonic systems6–10.
Throughout the evolutionary trajectory of topological photonics, the
waveguide platform has assumed a pivotal role (Box 1). Based on photonic
platforms, the unidirectional backscattering-immune topological electro-
magnetic states have been realized by implementing the chiral edge states in
a gyromagnetic photonic-crystal slab, as shown in Fig. 18. In another con-
text, photonic crystals consisting of gyromagnetic materials, such as yttrium
iron garnet (YIG) were applied11. Under an additional uniform magnetic
field B, the gyromagnetic response of the material will induce an effective
magnetic field for photons in the microwave frequency range, which can be
mapped to the Haldane model. Concurrently, in the year of 2009, the first
experimental realization of Su–Schrieffer–Heeger (SSH) model12 in the
photonic context was performed in a photonic superlattice13.Subsequently,
a two-dimensional topological insulator was realized in a Floquet helical
waveguide array through the utilization of the femtosecond laser direct
writing method, as shown in Fig. 19.Thisprogressculminatedinnumerous
milestones in topological insulators such as the Anderson insulator14,fractal
photonic topological insulator15,16, and bimorphic Floquet topological
insulator17.Mostrecently,asignificant advancement was made by intro-
ducing the periodic gain/loss into a two-dimensional system comprising 48
waveguides, the evidence of the existence of a non-Hermitian topological
insulator with a real-valued energy spectrum has been presented in a Floquet
regime, as shown in Fig. 118.
In the meanwhile, coupled resonator optical waveguide (CROW)
system also offers a great platform to study topological insulator phases,
where the direction of propagation of light in each resonator functions as a
spin. A resilient optical delay line featuring topological protection has been
successfully implemented in a silicon photonics platform leveraging the
QHE and QSHE principles10,19. In 2013, an important model of quantum
anomalous Floquet Hall model was proposed20 and realized in the CROW
system to demonstrate topologically protected entanglement emitters21.
Most recently, a fully programmable topological photonic chip was realized
using tunable microring resonators, and the platform showcased the cap-
ability to implement multifunctional topological models22.Anotherkey
modelisatopologicalcrystalline insulator23, which could introduce a
topological quantum optics interface24.
1Department of Applied Physics, KTH Royal Institute of Technology, Albanova University Centre, Roslagstullsbacken 21, 106 91 Stockholm, Sweden. 2School of
Physics, Interdisciplinary Center of Quantum Information, and Zhejiang Key Laboratory of Micro-Nano Quantum Chips and Quantum Control, Zhejiang University,
310027 Hangzhou, Zhejiang Province, China. e-mail: junga@kth.se;zhaojuyang@zju.edu.cn;elshaari@kth.se
npj Nanophotonics | (2024) 1:34 1
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Box 1 | Formation of photonic lattices and fabrication techniques
Photorefractive crystal
Topological photonic lattices can be intricately created using optical
induction135. This process starts with encoding the desired lattice’sphase
information, based on the interference patterns of counterpropagat ing plane
waves, onto a high-resolution spatial light modulator (SLM). When a
continuous-wave laser, typically with a wavelength of 532 nm, illuminates
this encoded SLM, it reconstructs the intended interference wave field.
However, directly using this wave field is challenging due to its diffraction
properties. To address this, the wave field is transformed into the wavevector
domain and filtered to remove undesired components, ensuring only the
first-order diffraction pattern is retained. This filtered wave field is then
converted back, resulting in a smooth, non-diffracting beam perfect for
creating the lattice in a physical sample. The light is then coupled to a
photorefractive crystal to form the lattice, and a signal light at a longer
wavelength is used to probe the propagation dynamics of light in the pho-
tonic lattice. The experimental setupis illustrated in (a), adapted from ref. 136.
Femtosecond laser direct writing technique
Femtosecond laser machining (FLM) utilizes femtosecond laser pulses
focused through high-precision optics, such as aspheric lenses or micro-
scope objectives, onto or into the material. The intense peak power of the laser
triggers nonlinear absorption processes, resulting in localized, permanent
modifications within the material. By moving the material relative to the laser’s
focus using high-precision stages, intricate three-dimensional structures can
be realized. The applications of FLM span various domains, from waveguide
writing to 3D microstructuring and even two-photon polymerization, show-
casing the technique’sflexibility. For waveguide fabrication, FLM enables the
creation of optical channels within glasses and crystals by inducing positive
refractive index changes. This has been extensively explored for producing
single-mode waveguides across a wide spectral range, with properties finely
tunable through the adjustment of laser parameters like pulse energy, scan
speed, and repetition rate. Materials commonly used include pure fused silica
and commercial borosilicate glasses, with fabricated waveguides demon-
strating low propagation and bending losses, making them well-suited for
integrated photonics applications. In 3D microstructuring, FLM allows for the
precise excavation of microtrenches and the creation of hollow micro-
structures by focusing the laser on the material’s surface or by water-assisted
laser ablation. Two-photon polymerization represents another facet of FLM’s
versatility, allowing for additive manufacturing of three-dimensional polymeric
structures with sub-micrometer precision. This process involves the localized
polymerization of a photosensitive resin through nonlinear two-photon
absorption, enabling the creation of complex photonic elements such as
waveguides, couplers, and microdisc resonators.
Top-down CMOS-compatible process
The fabrication process begins with the patterning of the wafer to define
various optical components, such as grating couplers and photonic wave-
guides. This step can be achieved through electron beam lithography or
optical lithography, depending on the required precision and the scale of the
circuits. Electron beam lithography offers high resolution, suitable for intricate
patterns, while optical lithography provides a more cost-effective solution for
large-scale applications. Once the layout is patterned on the wafer, an etch
mask protects certain areas during the etching process. Reactive ion etching
(RIE) can then be used to carve out the optical elements from the silicon
substrate. This etching process is highly controllable, allowing for the precise
definition of waveguide dimensions and the realization of complex optical
structures. To enhance the functionality and efficiency of the devices, certain
components, like grating couplers, may undergo partial etching to improve
the coupling efficiency between the integrated waveguides and external
optical fibers. After the primary structure of the photonic circuits is estab-
lished, a top cladding layer, such as silicon dioxide (SiO
2
), can be deposited
over the devices. This top oxide layer serves multiple purposes: it provides a
symmetric environment for the optical modes, and it also protects the
underlying components from physical damage and contamination. By
leveraging established CMOS processes, this method offers a scalable and
economically viable route to the mass production of integrated photonic
circuits. The process is depicted in the figure with two SEM images show-
casing a 1D lattice with grating couplers, all adapted from refs. 38,137,138.
(a) Experimental setup for creating photonic lattices using computer-
generated holography. (b) Femtosecond laser writing process for realiz-
ing optical lattices through photorefractive effect, 3D micro-structuring,
and two-photon polymerization. (c) Top shows a top-down CMOS-
compatible process to realize nanophotonic lattices. Bottom shows an
SEM image of a 1D photonic lattice with grating couplers to probe the
dynamics in each lattice site. Panels adapted with permission from (a),
ref. 136; (b), ref. 139; (c), refs. 38,137,138.
https://doi.org/10.1038/s44310-024-00034-5 Perspective
npj Nanophotonics | (2024) 1:34 2
Another platform worth mentioning is based on meta-waveguides. In
2013, a photonic analog of a topological insulator was theoretically proposed
using metacrystals, demonstrating the potential for one-way photon
transport without the need for external magnetic fields or breaking time-
reversal symmetry25. Subsequently, in 2015, a simple yet insightful photonic
structure based on a periodic array of metallic cylinders was developed to
emulate spin–orbit interaction through bianisotropy26.Thismeta-
waveguide platform does not suffer from high Ohmic losses and could
potentially be scaled to infrared optical frequencies. This approach has
proven fruitful for topological photonics, as evidenced by numerous
experimental demonstrations27–29.
These insulators maintain insulation within their bulk while permitting
the propagation of waves on their surfaces. They exhibit notable robustness
to disorder and effectively impede back-scattering. The robust demonstra-
tion of the QHE and quantum anomalous Hall effect5,30 in terms of edge
conductivity across various parametersservesasacompellingillustrationof
the predictions within this domain. The topological invariant known as the
Chern number31 plays a crucial role in elucidating the aforementioned
effects. It is the adept application of the winding number (one-dimensional
systems) and the Chern number (even-dimensional systems) that estab-
lishes a profound theoretical foundation for topological photonics
W¼1
2πRBZ AðkÞdk
C¼1
2πiRBZ Tr P∂kxP;∂kyP
hi
d2kð1Þ
where AðkÞ¼iu
k∣∇k∣uk
represents the Berry connection32 in the
momentum–space and Pdenotes the projector operator
PðkÞ¼Pn
i¼1∣uiðkÞuiðkÞ
∣. These topological invariants keep the nature of
the integer and only undergo a change when there is a closure of the band
gap. Despite the myriad differences in properties such as dimensions, the
number of waveguides, and shapes, photonic systems sharing the same
topological invariants can often be categorized into a unified class, exhi-
biting consistent characteristics in key properties. Consequently, these
integers serve as a manifestation of the robust attributes inherent in topo-
logical photonics systems against small continuous perturbations, for
example, the defects in photonic device processing, or small changes in the
refractive index of the material. Building upon this foundation, the
exploration of methods to enhance the nonlinear effects in materials and the
quest for novel invariants that could potentially confer topological protec-
tion to devices have increasingly become noteworthy endeavors within the
realm of topological photonics based on photonics waveguide systems
(Table 1).
In one-dimensional topological photonics systems, the emergence of
topological phases is inevitably associated with the presence of
symmetries33,34. A paramount one-dimensional model is the SSH model
with a Hamiltonian denoted as
^
H¼κ1X
n
i¼1
^
ay
i;A
^
ai;Bþκ2X
n1
i¼1
^
ay
i;B
^
aiþ1;Aþh:c:; ð2Þ
characterized by chiral symmetry. κ
1
and κ
2
denote the intra/inter-cell
hoppingamplitudesinthisdimerizedsystem. Further exploration has been
undertaken in the photonic waveguide system regarding the topology
associated with the winding number (or the Zak phase), including the
interface between two dimer chains with different Zak phases35–37, locali-
zation behavior in SSH model with defects38, superlattice model with more
sites (>2) in a cell39,40 and direct detection of topological invariant41–43.
Originating from the embodiment of topology in two-dimensional
materials, chiral topological photonics also shows its potential rich appli-
cation prospects44. Barik et al. achieved the realization of a chiral quantum
emitter using InAs quantum dots, as shown in Fig. 1,thankstothe
exploration of interface edge modes connecting two topologically distinct
regions. This implementation involved the selective coupling of
900–980 nm white light to the grating coupler, while photons outside the
bandgap dissipated to the bulk24. Additionally, a series of investigations in
chiral topological photonics have been systematically conducted, building
upon photonic waveguide systems45–48.
Another emerging area based on waveguide systems that have
garnered widespread attention is PT-symmetric topological photonics,
which provides a new perspective by conside ring gain and loss in o ptical
systems. This emerging field has attracted considerable attention and
the readers could find many nice review articles on related topics49–54.
Leveraging the novel design motivated by exceptional points, a
Fig. 1 | Timeline showing key experimental milestones in waveguide-based
topological photonic lattices. Shockley-like surface states in photonic
superlattices13. Unidirectional topological electromagnetic states8. Floquet topolo-
gical insulator9. Topological quantum optics interface assisted quantum emitter24.
Topological exceptional state transfer laser55. PT-symmetric photonic topological
insulator realized in a 2-dimensional waveguides array18. Panels adapted with per-
mission from refs. 8,9,13,18,24,55.
https://doi.org/10.1038/s44310-024-00034-5 Perspective
npj Nanophotonics | (2024) 1:34 3
topological laser emitting in two different but topologically linked
transverse profiles is realized through exceptional state transfer within
two waveguides, as shown in Fig. 155. Inspired by the ongoing non-
Hermitian physics in condensed matter, the non-Hermitian photonics,
such as non-Hermitian skin effect incorporating non-Bloch band the-
ory, will follow further56,57, apart from the PT topological insulator and
PT-symmetric lasing58. Finally, we would like to point out another
direction, that is, the interplay between topology and quantum optics
(for instance, see ref. 59), and this is also the focus of this perspective.
Physics of photonic waveguide arrays
Photonic waveguides represent a cornerstone in the field of photonics,
facilitating the controlled propagation of light (Box 2). These structures are
capable of guiding light waves through the modulation of refractive indices,
creating pathways that allow for the efficient transmission of optical signals.
The underlying physics of photonic waveguide arrays is governed by the
interplay between the wave nature of light and the geometrical/material
properties of the waveguides themselves.
The behavior of light within these waveguides is described by Max-
well’s equations, which, under the approximation of a slowly varying
envelope and assuming linear, isotropic, and non-dispersive media, can be
reduced to the Helmholtz equation:
∇2
x;yφðx;y;zÞþ2ikz
∂
∂zφðx;y;zÞk2
zφðx;y;zÞþk2
0n2ðx;yÞφðx;y;zÞ¼0ð3Þ
where ∇2
x;yis the transverse Laplacian, φ(x,y,z) is the electric field envelope,
k
z
is the propagation constant along the z-direction, k
0
is the free space wave
number, and n(x,y) is the refractive index distribution.
The coupling of light between adjacentwaveguidesinanarrayis
described by the coupled-mode theory, which can be simplified under the
tight-binding approximation to yield a set of discrete equations modeling
the evolution of light amplitude in each waveguide:
i∂
∂zφi¼βiφiþκi;i1φi1þκi;iþ1φiþ1ð4Þ
where φ
i
isthewaveamplitudeintheith waveguide, β
i
is the propagation
constant, and κ
i,j
represents the coupling coefficient between the ith and jth
waveguides.
Adjusting the on-site potential (β
i
) and the hopping terms (κ
i,j
)allows
for the meticulous control of light propagation. Variations in the on-site
potential can lead to phase shifts within the waveguides, affecting inter-
ference patterns. Similarly, modifying the hopping terms influences the
extent of light spread across the array, effectively controlling the bandwidth
of the photonic band structure. By engineering the geometry and refractive
index distribution of the waveguide array, it is possible to tailor the pro-
pagation characteristics of light. This framework allows for the exploration
of various phenomena unique to waveguide arrays, such as bandgap for-
mation, localization effects, and the emergence of topological edge states.
In addition to linear propagation, photonic waveguide arrays can
exhibit complex dynamics due to nonlinear effects. When the intensity of
light within the waveguides reaches a certain threshold, nonlinear phe-
nomena such as self-phase modulation and soliton formation can occur.
These effects can be described by introducing nonlinear terms into the
coupled-mode equations, providing a rich avenue for the study of nonlinear
optics in discretized systems. For a comprehensive exploration of the
principles governing light propagation within photonic waveguide arrays,
we kindly refer the readers to refs. 60,61.
Quantum states of light in topological waveguides
To maintain a focused perspective in this discussion, we will limit our
exploration to systems that involve single or arrayed waveguides. This
approach allows us to delve deeply into the specifics of these systems,
examining their unique properties and applications without extending into
Table 1 | Summary of different topological photonics platforms, and their key characteristics
Photonic platform Optical confinement and birefringence Photon generation Dimensionality of the
models
Tunability Transparency Qubit coding
possibilities
Glass (borosilicate,
fused silica)62–64,68–71
Low, Δn≈5×10
−3
−1×10
−2100, low
birefringence
Probabilistic, four-wave
mixing70,101
1D and 2D9,102 Slow, thermo-optic103 0.18–3μm104 Polarization, time-bin,
frequency-bin, path and
OAM105,106
III–V24,44,107 Can be high, in suspended membranes
Δn> 2.5108, with high birefringence
Probabilistic through SPDC,
on-demand using QDs109
1D and 2D110–112 Fast EO modulation, MEMS113 GaAs 1–16 μm, check ref. 114
for GaP, InP, InAs, and InSb
Time-bin, frequency-
bin, path
Silicon-based (Si,
SiN, SiC)10,43,115,116
High, Δn≈210, high birefringence Probabilistic four-wave
mixing, on-demand
defects65,117,
1D and 2D10,35,65,67,115 Thermo-optic, carrier-induced
dispersion (Si), MEMS, phase
change materials118–122
Si 1.1–8μm, SiN
0.40–2.235 μm and SiC
0.37–5.6 μm123–126
Time-bin, frequency-bin,
path, and transverse
mode127,128
Lithium niobate129 High in thin-film LNOI (high birefringence), low
in diffusion-based waveguides (low
birefringence)130
Probabilistic SPDC, on-
demand through hybrid
integration131,132
1D and 2D129 Fast EO modulation133 0.4–5.2 μm134 Time-bin, frequency-
bin, path
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npj Nanophotonics | (2024) 1:34 4
the broader and more complex landscape of other optical systems. The
generation of single and entangled photon pairs are cornerstones for
quantum communication and computing. Entangled photon pairs emerge
primarily from non-linear optical phenomena like spontaneous four-wave
mixing and spontaneous parametric down-conversion. On the other hand,
on-demand single photons are generated from atomic-like transitions in
quantum dots, color centers, and 2-D emitters. As the exploration in
quantum photonics forges ahead, it becomes increasingly clear that
addressing the efficiency and quality of entangled photon-pair sources, and
the uniformity and purity of single-photon sources are pivotal challenges.
Box 2 | Tunability and control of photonic lattices
Photonic waveguide systems present considerable tunability across
various parameters. Serving as the fundamental unit, a waveguide
embodies two inherent characteristics: the hopping term and on-site
potential, as depicted in (a). The modulation of the gaps between
neighboring waveguides enables the adjustment of the hopping rate via
evanescent coupling fields. Conversely, manipulation of the physical
dimensions of the waveguide facilitates control over the on-site potential.
By incorporating the propagation direction (z-axis) of photonic lattices, a
helical structured waveguide is introduced to break z-reversal symmetry.
This temporal modulation, as depicted in (b), facilitates the realization of
one-way edge states propagating in photonic Floquet topological
insulators9, which has spurred experimental investigations into Floquet
systems140–142. By leveraging the flexibility of 3D laser fabrication, wave-
guides can be arranged in a specialized geometry, which allows eva-
nescent coupling to occur exclusively in a designated direction, see one
example in (c) ref. 143. This operation is in line with non-Abelian wave
physics and greatly enriches the classification of topological
physics144,145. Another emerging research field to broaden topological
photonics is to introduce the loss of Hermiticity, which describes energy
exchanges with an open system. A crucial aspect of non-Hermitian
Hamiltonians is the simultaneous presence of on-site gain and loss.
However, certain quasi-PT-symmetric systems can be realized using
passive photonic lattices with partly lossless and partly lossy structures,
as depicted in (d)146. On-site losses are introduced by depositing chro-
mium on top of waveguides, and it has been proved that this system
exhibits identical evolution dynamics to that of a system with gain and
loss, albeit with a global exponential damping factor.147. Last but not
least, it is possible to interface a quantum emitter with nano-scale
waveguide systems, opening up new possibilities to tailor light–matter
interaction and enable novel quantum-electrodynamics experiments, for
which the readers can refer to ref. 148.
(a) Schematic diagram of photonic waveguide systems with hopping
terms and on-site modulation. (b) 2D honeycomb photonic lattice made
of helical waveguides. (c) Schematic and microscope photograph of a
two-dimensional photonic lattice to realize non-Abelian Thouless
pumping. (d) Schematic of a waveguide array with Cr deposited on top to
introduce loss and study non-Hermitian systems. (e) Single photon
emitter interfaced with nanophotonic structures. Panels adapted with
permission from (b), ref. 9; (c), ref. 143; (d), ref. 146; (e), ref. 148.
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npj Nanophotonics | (2024) 1:34 5
Surmounting these obstacles will not only enhance our understanding of the
quantum world but also open avenues for more practical and scalable
applications in quantum technologies.
Early theoretical studies highlighted the potential of photonic topolo-
gical insulators to maintain the integrity of fragile multiphoton states in
quantum walks62, which is vital for applications like Boson sampling, a
process known for its potential exponential speedup in certain algorithms.
In waveguide systems, topological protection of the two-photon state
against decoherence was demonstrated63. The study reveals that in the
topologically nontrivial boundary state of a photonic chip, two-photon
quantum-correlated states are effectively preserved, exhibiting high cross-
correlation and a strong violation of the Cauchy–Schwarz inequality by up
to 30 standard deviations. These findings highlight the robustness of
topological protection against factors like photon wavelength difference and
distinguishability. Moreover, the study in ref. 64 reports high-visibility
quantum interference of single-photon topological states within an inte-
grated photonic circuit, where two topological boundary states at the edges
of a coupled waveguide array are brought together to interfere and undergo
a beamsplitter operation. This process results in the observation of
Hong–Ou–Mandel interference with a visibility of 93.1 ± 2.8%, demon-
strating the nonclassical behavior of topological states. This significant
achievement illustrates the practical feasibility of generating and controlling
highly indistinguishable single-photon topological states. To confirm the
resilience of topological biphoton states against disorder, the work in ref. 65
fabricated structures with varying levels of introduced disorder. The mea-
sured Schmidt number remains close to 1, underlined by the topology’s
assurance of a single localized mode. These results not only underscore the
importance of quantum correlation robustness but also spotlight the
potential advantages of topological methods in quantum information sys-
tems. Entanglement protection was also demonstrated in refs. 66,67.Inthe
latter, the team demonstrates topological protection of spatially entangled
biphoton states. Utilizing the SSH model, the system exhibits strong loca-
lization of topological modes and spatial entanglement between them under
varying levels of disorder, underscores the topological nature of these
entangled states. The topological protection was extended to systems with
quasi-crystal structures and sawtooth lattice, the non-classical features are
safeguarded against decoherence caused by diffusion in interconnected
waveguides and from the environment noise disturbances68,69. Similar ideas
were extended to the generation of squeezed light70,akeycomponentin
quantum sensing and information processing. Due to the weak optical
nonlinearity and limited interaction volume in bulk crystals, the study uses
waveguide arrays to increase nonlinearity. The topologically protected
pump light enables the waveguide lattice to operate effectively as a high-
quality quantum squeezing device. In addition to path-entanglement,
topological protection was realized for polarization-entangled photon pairs
in a waveguide array lattice71. Additionally, in another waveguide-based
system that utilizes valley photonic crystals (VPCs), topological protection
of frequency entangled photons was realized72. The photon pairs were
generated by four-wave mixing (FWM) interactions in topological valley
states, propagating along interfaces between VPCs. Furthermore, theoretical
studies showed that topological protection can be extended to dual degrees
of freedom, specifically time and energy73. Such a demonstration highlights
the potential of topologically protected quantum states in photonic systems,
particularly for applications operating at telecommunication wavelengths.
In addition to photon pairs based on non-linear interactions, sig-
nificant progress has been made in engineering the topological properties of
photonic circuits hosting on-demand single photon sources and potentially
solid-state optical memories. In a recent study24, the authors successfully
demonstrate a powerful interface between single quantum emitters and
topologically robust photonic edge states, a significant achievement at the
intersection of quantum optics and topological photonics. Utilizing a device
composed of a thin GaAs membrane with epitaxially grown InAs quantum
dots acting as quantum emitters, the team creates robust counter-
propagating edge states at the boundary of two distinct topological photonic
crystals. A key result of their experiment is the demonstration of chiral
emission of a quantum emitter into these modes, confirming their robust-
ness against sharp bends in the photonic structure. This research not only
exemplifies the successful coupling of single quantum emitters with topo-
logical photonic states but also highlights the potential of these systems in
developing quantum optical devices that inherently possess built-in pro-
tection. Moreover, the work in ref. 74 developed a chiral quantum optical
interface by integrating semiconductor quantum dots into a valley-Hall
topological photonic crystal waveguide, showcasing the interface’scap-
ability to support both topologically trivial and non-trivial modes. The
convergence of nanophotonics with quantum optics has led to the emer-
gence of chiral light–matter interactions, a phenomenon not addressed in
conventional quantum optics frameworks. This interaction, stemming from
the strong confinement of light within these nanostructures, results in a
unique relationship where the local polarization of light is intricately linked
to its propagation direction. This leads to direction-dependent emission,
scattering, and absorption of photons by quantum emitters, forming the
basis of chiral quantum optics. Such advancements promise novel func-
tionalities and applications, including non-reciprocal single-photon devices
with deterministic spin–photon interfaces44. The study showcases the
potential of chiral quantum photonics in ref. 75. It successfully demonstrates
that the helicity of a quantum emitter’s optical transition determines the
direction of single-photon emission in a glide-plane photonic-crystal
waveguide. The implications of this research are vast, including the con-
struction of non-reciprocal photonic elements like single-photon diodes
and circulators.
Topological protection of quantum resources
The field of topological photonics, inspired by groundbreaking concepts in
quantum mechanics and solid-state physics, promised a revolution in
controlling light propagation in photonic systems. The notion of harnessing
topological properties to create backscattering-immune waveguides pre-
sented a paradigm shift, particularly in developing efficient quantum
resources and enhancing photonic system performances. In nanophotonic
waveguides, the precision of fabrication is challenged by the occurrence
nanometer-level imperfections along the etched sidewalls. These imper-
fections, significantly smaller than the fabricated unit-cell, for example, in
photonic crystal waveguide systems, cast doubt on the efficacy of employing
topological protection strategies for quantum resources76.Theback-
scattering mean free path (ξ) is essential for assessing photonic waveguides
against nanostructural imperfections. It marks the threshold between effi-
cient transmission with minimal scattering and significant backscattering
when waveguide length (L) exceeds ξ.Suchafigure of merit is imperative for
substantiating the advantages of topological over conventional transport at
the nanoscale77. Recent experimental evidence in ref. 76,showedsignificant
backscattering in valley-Hall topological waveguides despite record low-loss
waveguides. The persistence of backscattering raises fundamental questions
about our understanding of light–matter interaction in topologically
structured photonic environments. This necessitates rethinking the mate-
rials and designs used in photonic quantum technologies, potentially
shifting focus towards alternative mechanisms for achieving topological
protection. Addressing these challenges requires exploring beyond con-
ventional topological paradigms. This might involve investigating new
classes of materials, such as magneto-optic systems, to break time-reversal
symmetry at optical frequencies. Despite these challenges, topologically
non-trivial systems with non-broken time-reversal symmetry have been
shown to outperform topologically trivial ones for certain disorder
strength77. Such structures can offer a viable foundation for novel quantum
logic architectures, resource robustness, non-reciprocal photonic elements,
and efficient spin–photon coupling44,78,79 (Fig. 2).
Quantum topological photonics: Looking ahead
What next for topological quantum photonics? As the field of quantum
topological photonics continues to mature, the journey ahead is lined with
both challenges and opportunities34,80–83. Building on the foundation laid by
pioneering research in this field, the future direction is poised to explore
https://doi.org/10.1038/s44310-024-00034-5 Perspective
npj Nanophotonics | (2024) 1:34 6
novel paradigms and technologies that could further revolutionize photo-
nics and quantum information processing. One of the most promising
frontiers is the development of active tuning and dynamic control
mechanisms within topological photonic structures84. Current research has
predominantly focused on passive systems, where the topological properties
are fixed once fabricated. However, the integration of active materials or
mechanisms that allow for real-time control of topological features can
dramatically enhance the versatility of photonic devices, and create synthetic
dimensions85. Such advancements could enable reconfigurable photonic
circuits, adaptable computing architectures, and dynamic communication
networks. For instance, integrating electro-optic or thermo-optic materials
into topological waveguides could provide a means to dynamically tune the
band structure, thus controlling the propagation and interaction of photons
in these systems86. Additionally, incorporating magneto-optic materials into
topological photonics offers a powerful approach to breaking time-reversal
symmetry87. Hybrid integration could pave the way for devices that exploit
magnetic fields to control photonic states88. The exploration of materials
with strong magneto-optical responses at room temperature and their
seamless integration into photonic chips will be crucial in this endeavor89.
With regard to quantum sources, the challenge that remains is enhancing
the efficiency and uniformity of quantum sources, such as single-photon
emitters and entangled photon pairs. Efforts should be directed toward
improving the coupling efficiency between quantum emitters and photonic
structures, minimizing losses, and increasing the purity of quantum states90.
Research in developing more efficient non-linear materials for photon pair
generation, along with better fabrication techniques for quantum dots and
other emitters, will be vital91–94. The integration of topological photonics
with quantum optics and information processing has already demonstrated
significant potential. The next step is to develop complex quantum photonic
systems that leverage topological protection for enhanced performance and
new functionalities, with careful investigation of the figures of merits, and to
benchmark their superior performance to topologically trivial devices. On a
more fundamental level, future research should also focus on discovering
new topological phases and experimenting with a wider range of materials.
The exploration of 2D materials, such as graphene and transition metal
dichalcogenides, offers exciting prospects for hosting topologically pro-
tected states with unique properties and building systems that rely on the
interplay between electronic and photonic states78,95. Lastly, it is crucial to
address fundamental questions raised by recent experimental observations,
such as the persistence of coherent backscattering in topologically protected
systems. This will require a deeper theoretical understanding of light–matter
interactions in topologically structured environments and might lead to the
development of new theoretical models and simulation tools. Moreover, the
fusion of non-Hermitian physics with topological insulators reveals a ple-
thora of novel phenomena and offers more approaches to optical device
design. By harnessing the intricate balance of gain and loss within photonic
systems, non-Hermitian topological photonics paves the way for manip-
ulating topological states in unprecedented manners. Recent advancements
and applications include the manipulation of topological phase transitions
and the skin effect96. Additionally, quantum topological time crystals
represent a transformative advancement in the manipulation of temporal
properties for photonic applications. It leverages the periodic modulation of
material properties, which give s rise to dispersion relations characterized by
bands separated by momentum gaps, resulting in a class of non-
conservation energy states due to broken time-translation symmetry.
Quantum topological time crystals are poised to enable exciting new devices,
including detectors of entangled states and generation of cluster states97.
Additionally, the concept of gain and time crystals can be combined,
leading to amplified emission and lasing with narrowing radiation linewidth
over time98. The research into such crystals, with loss/gain and temporal
modulation, not only revisits the classical understanding of light–matter
interaction but also proposes the intriguing concept of non-resonant, tun-
able lasers. These lasers, devoid of the traditional resonance requirements,
can draw operational energy from the external modulation of the medium,
presenting a versatile approach to laser design. Moreover, the study of
strongly correlated photonic systems introduces a novel dimension to our
understanding of quantum topological states. A standout achievement in
this domain is the experimental realization of Laughlin states using light99.
Fig. 2 | Topological protection of quantum resources. a Topological protection of
biphoton states65.bTopological protection of path entanglement62.cTopological
protection of continuous frequency entangled biphoton states72.dTopological
protection of two-photon states against the decoherence in diffusion63.eAnderson
localization of entangled photons in an integrated quantum walk66.fTopological
light–matter interface75. Panels adapted with permission from
refs. 62,63,65,66,72,75.
https://doi.org/10.1038/s44310-024-00034-5 Perspective
npj Nanophotonics | (2024) 1:34 7
The control over light-matter interactions can have implications for dif-
ferent quantum technologies ranging from quantum computing to novel
topological quantum devices.
In the rapidly advancing field of quantum topological photonics, the
intersection of theoretical innovation and practical application paints a
promising yet challenging future. This domain, rich with potential, stands at
the forefront of revolutionizing information processing, communication
technologies, and quantum computing, thanks to its predicted robustness
against disturbances and its ability to manipulate light in novel ways.
However, the path forward is not without its hurdles. Fabrication imper-
fections, scalability of systems, and the integration of quantum sources with
topological structures remain significant challenges that demand meticu-
lous attention and creative solutions. Additionally, the complexities of non-
Hermitian dynamics, the realization of time crystals in practical settings, and
harnessing the full potential of strongly correlated photonic systems require
a deeper understanding and more sophisticated experimental techniques.
Despite these challenges, the field of quantum topological photonics holds
significant promise for advancing technology and science. As we continue to
navigate its complexities, the potential for transformative breakthroughs
remains vast, paving the way for a new era of photonic applications and
discoveries.
Received: 22 March 2024; Accepted: 15 July 2024;
References
1. Ando, T., Matsumoto, Y. & Uemura, Y. Theory of Hall effect in a two-
dimensional electron system. J. Phys. Soc. Jpn. 39, 279–288 (1975).
2. Laughlin, R. B. Quantized Hall conductivity in two dimensions. Phys.
Rev. B 23, 5632–5633 (1981).
3. Thouless, D. J. Quantization of particle transport. Phys. Rev. B 27,
6083–6087 (1983).
4. von Klitzing, K. The quantized Hall effect. Rev. Mod. Phys. 58,
519–531 (1986).
5. Klitzing, K. V., Dorda, G. & Pepper, M. New method for high-
accuracy determination of the fine-structure constant based on
quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).
6. Raghu, S. & Haldane, F. D. M. Analogs of quantum-Hall-effect edge
states in photonic crystals. Phys. Rev. A 78, 033834 (2008).
7. Wang, Z., Chong, Y. D., Joannopoulos, J. D. & Soljačić,M.
Reflection-free one-way edge modes in a gyromagnetic photonic
crystal. Phys. Rev. Lett. 100, 013905 (2008).
8. Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić, M. Observation
of unidirectional backscattering-immune topological
electromagnetic states. Nature 461, 772–775 (2009).
9. Rechtsman, M. C. et al. Photonic floquet topological insulators.
Nature 496, 196–200 (2013).
10. Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. Imaging
topological edge states in silicon photonics. Nat. Photon 7,
1001–1005 (2013).
11. Poo, Y., Wu, R.-x, Lin, Z., Yang, Y. & Chan, C. T. Experimental
realization of self-guiding unidirectional electromagnetic edge
states. Phys. Rev. Lett. 106, 093903 (2011).
12. Su, W. P., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene.
Phys. Rev. Lett. 42, 1698–1701 (1979).
13. Malkova, N., Hromada, I., Wang, X., Bryant, G. & Chen, Z.
Observation of optical Shockley-like surface states in photonic
superlattices. Opt. Lett. 34, 1633–1635 (2009).
14. Stützer, S. et al. Photonic topological Anderson insulators. Nature
560, 461–465 (2018).
15. Yang, Z., Lustig, E., Lumer, Y. & Segev, M. Photonic floquet
topological insulators in a fractal lattice. Light Sci. Appl. 9,
128 (2020).
16. Biesenthal, T. et al. Fractal photonic topological insulators. Science
376, 1114–1119 (2022).
17. Pyrialakos, G. G. et al. Bimorphic floquet topological insulators. Nat.
Mater. 21, 634–639 (2022).
18. Fritzsche, A. et al. Parity-time-symmetric photonic topological
insulator. Nat. Mater. 23, 377–382 (2024).
19. Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical
delay lines with topological protection. Nat. Phys. 7, 907–912 (2011).
20. Liang, G. & Chong, Y. Optical resonator analog of a two-dimensional
topological insulator. Phys. Rev. Lett. 110, 203904 (2013).
21. Dai, T. et al. Topologically protected quantum entanglement
emitters. Nat. Photon 16, 248–257 (2022).
22. Dai, T. et al. A programmable topological photonic chip. Nat. Mater.
23, 928–936 (2024).
23. Wu, L.-H. & Hu, X. Scheme for achieving a topological photonic
crystal by using dielectric material. Phys. Rev. Lett. 114,
223901 (2015).
24. Barik, S. et al. A topological quantum optics interface. Science 359,
666–668 (2018).
25. Khanikaev, A. B. et al. Photonic topological insulators. Nat. Mater.
12, 233–239 (2013).
26. Ma, T., Khanikaev, A. B., Mousavi, S. H. & Shvets, G. Guiding
electromagnetic waves around sharp corners: topologically
protected photonic transport in metawaveguides. Phys. Rev. Lett.
114, 127401 (2015).
27. Chen, W.-J. et al. Experimental realization of photonic topological
insulator in a uniaxial metacrystal waveguide. Nat. Commun. 5,
5782 (2014).
28. Cheng, X. et al. Robust reconfigurable electromagnetic pathways
within a photonic topological insulator. Nat. Mater. 15,
542–548 (2016).
29. Bisharat, D. J. & Sievenpiper, D. F. Electromagnetic-dual
metasurfaces for topological states along a 1d interface. Laser
Photon Rev. 13, 1900126 (2019).
30. Liu, C.-X., Zhang, S.-C. & Qi, X.-L. The quantum anomalous hall
effect: theory and experiment. Annu. Rev. Condens. Matter Phys. 7,
301–321 (2016).
31. Chern, S.-S. Characteristic classes of hermitian manifolds. Ann.
Math. 47,85–121 (1946).
32. Berry, M. V. Quantal phase factors accompanying adiabatic
changes. Proc. R. Soc. Lond. A. Math. Phys. Sci. 392,45–57 (1984).
33. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev.
Mod. Phys. 82, 3045–3067 (2010).
34. Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91,
015006 (2019).
35. Blanco-Redondo, A. et al. Topological optical waveguiding in silicon
and the transition between topological and trivial defect states.
Phys. Rev. Lett. 116, 163901 (2016).
36. Cheng, Q., Pan, Y., Wang, Q., Li, T. & Zhu, S. Topologically protected
interface mode in plasmonic waveguide arrays. Laser Photonics
Rev. 9, 392–398 (2015).
37. Bleckmann, F., Cherpakova, Z., Linden, S. & Alberti, A. Spectral
imaging of topological edge states in plasmonic waveguide arrays.
Phys. Rev. B 96, 045417 (2017).
38. Gao, J. et al. Observation of Anderson phase in a topological
photonic circuit. Phys. Rev. Res. 4, 033222 (2022).
39. Midya, B. & Feng, L. Topological multiband photonic superlattices.
Phys. Rev. A 98, 043838 (2018).
40. Wang, Y. et al. Experimental topological photonic superlattice. Phys.
Rev. B 103, 014110 (2021).
41. Wang, Y. et al. Direct observation of topology from single-photon
dynamics. Phys. Rev. Lett. 122, 193903 (2019).
42. Jiao, Z.-Q. et al. Experimentally detecting quantized zak phases
without chiral symmetry in photonic lattices. Phys. Rev. Lett. 127,
147401 (2021).
43. Xu, Z.-S. et al. Direct measurement of topological invariants in
photonic superlattices. Photonics Res. 10, 2901–2907 (2022).
https://doi.org/10.1038/s44310-024-00034-5 Perspective
npj Nanophotonics | (2024) 1:34 8
44. Lodahl, P. et al. Chiral quantum optics. Nature 541, 473–480 (2017).
45. Mittal, S., Ganeshan, S., Fan, J., Vaezi, A. & Hafezi, M. Measurement
of topological invariants in a 2d photonic system. Nat. Photon 10,
180–183 (2016).
46. Hauff, N. V., Le Jeannic, H., Lodahl, P., Hughes, S. & Rotenberg, N.
Chiral quantum optics in broken-symmetry and topological photonic
crystal waveguides. Phys. Rev. Res. 4, 023082 (2022).
47. Barik, S., Karasahin, A., Mittal, S., Waks, E. & Hafezi, M. Chiral
quantum optics using a topological resonator. Phys. Rev. B 101,
205303 (2020).
48. Parappurath, N., Alpeggiani, F., Kuipers, L. & Verhagen, E. Direct
observation of topological edge states in silicon photonic crystals:
spin, dispersion, and chiral routing. Sci. Adv. 6, eaaw4137
(2020).
49. Wang, C. et al. Non-Hermitian optics and photonics: from classical
to quantum. Adv. Opt. Photon 15, 442–523 (2023).
50. Özdemir, Ş. K., Rotter, S., Nori, F. & Yang, L. Parity–time symmetry
and exceptional points in photonics. Nat. Mater. 18, 783–798
(2019).
51. Nasari, H., Pyrialakos, G. G., Christodoulides, D. N. & Khajavikhan,
M. Non-Hermitian topological photonics. Opt. Mater. Express 13,
870–885 (2023).
52. El-Ganainy, R. et al. Non-Hermitian physics and pt symmetry. Nat.
Phys. 14,11–19 (2018).
53. Feng, L., El-Ganainy, R. & Ge, L. Non-Hermitian photonics based on
parity–time symmetry. Nat. Photon 11, 752–762 (2017).
54. Wang, Q. & Chong, Y. Non-hermitian photonic lattices: tutorial.
JOSA B 40, 1443–1466 (2023).
55. Schumer, A. et al. Topological modes in a laser cavity through
exceptional state transfer. Science 375, 884–888 (2022).
56. Xia, S. et al. Nonlinear tuning of pt symmetry and non-hermitian
topological states. Science 372,72–76 (2021).
57. Sun, Y. et al. Photonic floquet skin-topological effect. Phys. Rev.
Lett. 132, 063804 (2024).
58. Hodaei, H., Miri, M.-A., Heinrich, M., Christodoulides, D. N. &
Khajavikhan, M. Parity-time–symmetric microring lasers. Science
346, 975–978 (2014).
59. Deng, J. et al. Observing the quantum topology of light. Science 378,
966–971 (2022).
60. Garanovich, I. L., Longhi, S., Sukhorukov, A. A. & Kivshar, Y. S. Light
propagation and localization in modulated photonic lattices and
waveguides. Phys. Rep. 518,1–79 (2012).
61. Smirnova, D., Leykam, D., Chong, Y. & Kivshar, Y. Nonlinear
topological photonics. Appl. Phys. Rev. 7, 021306 (2020).
62. Rechtsman, M. C. et al. Topological protection of photonic path
entanglement. Optica 3, 925–930 (2016).
63. Wang, Y. et al. Topological protection of two-photon quantum
correlation on a photonic chip. Optica 6, 955–960 (2019).
64. Tambasco, J.-L. et al. Quantum interference of topological states of
light. Sci. Adv. 4, eaat3187 (2018).
65. Blanco-Redondo, A., Bell, B., Oren, D., Eggleton, B. J. & Segev, M.
Topological protection of biphoton states. Science 362,
568–571 (2018).
66. Crespi, A. et al. Anderson localization of entangled photons in an
integrated quantum walk. Nat. Photon 7, 322–328 (2013).
67. Wang, M. et al. Topologically protected entangled photonic states.
Nanophotonics 8, 1327–1335 (2019).
68. Wang, Y. et al. Quantum topological boundary states in quasi-
crystals. Adv. Mater. 31, 1905624 (2019).
69. Zhou, W.-H. et al. Topologically protecting quantum resources with
sawtooth lattices. Opt. Lett. 46, 1584–1587 (2021).
70. Ren, R.-J. et al. Topologically protecting squeezed light on a
photonic chip. Photon Res. 10, 456–464 (2022).
71. Wang, Y. et al. Topologically protected polarization quantum
entanglement on a photonic chip. Chip 1, 100003 (2022).
72. Jiang, Z., Ding, Y., Xi, C., He, G. & Jiang, C. Topological protection of
continuous frequency entangled biphoton states. Nanophotonics
10, 4019–4026 (2021).
73. Jiang, Z., Xi, C., He, G. & Jiang, C. Topologically protected
energy–time entangled biphoton states in photonic crystals. J. Phys.
D: Appl. Phys. 55, 315104 (2022).
74. Mehrabad, M. J. et al. Chiral topological photonics with an
embedded quantum emitter. Optica 7, 1690–1696 (2020).
75. Söllner, I. et al. Deterministic photon-emitter coupling in chiral
photonic circuits. Nat. Nanotechnol. 10, 775–778 (2015).
76. Rosiek, C. A. et al. Observation of strong backscattering in valley-
hall photonic topological interface modes. Nat. Photon 1–7 (2023).
77. Arregui, G., Gomis-Bresco, J., Sotomayor-Torres, C. M. & Garcia, P.
D. Quantifying the robustness of topological slow light. Phys. Rev.
Lett. 126, 027403 (2021).
78. Gong, S.-H., Alpeggiani, F., Sciacca, B., Garnett, E. C. & Kuipers, L.
Nanoscale chiral valley-photon interface through optical spin–orbit
coupling. Science 359, 443–447 (2018).
79. Mittal, S., Goldschmidt, E. A. & Hafezi, M. A topological source of
quantum light. Nature 561, 502–506 (2018).
80. Yan, Q. et al. Quantum topological photonics. Adv. Opt. Mater. 9,
2001739 (2021).
81. Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat.
Photon 8, 821–829 (2014).
82. Segev, M. & Bandres, M. A. Topological photonics: where do we go
from here? Nanophotonics 10, 425–434 (2020).
83. Price, H. et al. Roadmap on topological photonics. J. Phys.: Photon
4, 032501 (2022).
84. Ota, Y. et al. Active topological photonics. Nanophotonics 9,
547–567 (2020).
85. Lustig, E. & Segev, M. Topological photonics in synthetic
dimensions. Adv. Opt. Photon. 13, 426–461 (2021).
86. Zhang, Y. et al. High-speed electro-optic modulation in topological
interface states of a one-dimensional lattice. Light Sci. Appl. 12,
206 (2023).
87. Bahari, B. et al. Nonreciprocal lasing in topological cavities of
arbitrary geometries. Science 358, 636–640 (2017).
88. Elshaari, A. W., Pernice, W., Srinivasan, K., Benson, O. & Zwiller, V.
Hybrid integrated quantum photonic circuits. Nat. Photon 14,
285–298 (2020).
89. Shoji, Y. & Mizumoto, T. Waveguide magneto-optical devices for
photonics integrated circuits. Opt. Mater. Express 8,
2387–2394 (2018).
90. Moody, G. et al. 2022 roadmap on integrated quantum photonics. J.
Phys.: Photon 4, 012501 (2022).
91. Aharonovich, I., Englund, D. & Toth, M. Solid-state single-photon
emitters. Nat. Photon 10, 631–641 (2016).
92. Senellart, P., Solomon, G. & White, A. High-performance
semiconductor quantum-dot single-photon sources. Nat.
Nanotechnol. 12, 1026–1039 (2017).
93. Arakawa, Y. & Holmes, M. J. Progress in quantum-dot single photon
sources for quantum information technologies: a broad spectrum
overview. Appl. Phys. Rev. 7, 021309 (2020).
94. Caspani, L. et al. Integrated sources of photon quantum states
based on nonlinear optics. Light Sci. Appl. 6, e17100 (2017).
95. Chen, P. et al. Chiral coupling of valley excitons and light through
photonic spin–orbit interactions. Adv. Opt. Mater. 8, 1901233 (2020).
96. Yan, Q. et al. Advances and applications on non-Hermitian
topological photonics. Nanophotonics 12, 2247–2271 (2023).
97. Arkhipov, R., Arkhipov, M. & Rosanov, N. Generation and control of
population difference gratings in a three-level hydrogen atomic
medium using half-cycle attosecond pulses. Phys. Rev. A 109,
063113 (2024).
98. Lyubarov, M. et al. Amplified emission and lasing in photonic time
crystals. Science 377, 425–428 (2022).
https://doi.org/10.1038/s44310-024-00034-5 Perspective
npj Nanophotonics | (2024) 1:34 9
99. Clark, L. W., Schine, N., Baum, C., Jia, N. & Simon, J. Observation of
Laughlin states made of light. Nature 582,41–45 (2020).
100. Allsop, T., Dubov, M., Mezentsev, V. & Bennion, I. Inscription and
characterization of waveguides written into borosilicate glass by a
high-repetition-rate femtosecond laser at 800 nm. Appl. Opt. 49,
1938–1950 (2010).
101. Ren, R.-J. et al. 128 identical quantum sources integrated on a single
silica chip. Phys. Rev. Appl. 16, 054026 (2021).
102. Weimann, S. et al. Topologically protected bound states in photonic
parity–time-symmetric crystals. Nat. Mater. 16, 433–438 (2017).
103. Chaboyer, Z., Stokes, A., Downes, J., Steel, M. & Withford, M. J.
Design and fabrication of reconfigurable laser-written waveguide
circuits. Opt. Express 25, 33056–33065 (2017).
104. Malitson, I. H. Interspecimen comparison of the refractive index of
fused silica. Josa 55, 1205–1209 (1965).
105. Chen, Y. et al. Mapping twisted light into and out of a photonic chip.
Phys. Rev. Lett. 121, 233602 (2018).
106. Chen, Y. et al. Vector vortex beam emitter embedded in a photonic
chip. Phys. Rev. Lett. 124, 153601 (2020).
107. Rao, M. et al. Single photon emitter deterministically coupled to a
topological corner state. Light Sci. Appl. 13, 19 (2024).
108. Liu, F. et al. High Purcell factor generation of indistinguishable on-
chip single photons. Nat. Nanotechnol. 13, 835–840 (2018).
109. Orieux, A., Versteegh, M. A., Jöns, K. D. & Ducci, S. Semiconductor
devices for entangled photon pair generation: a review. Rep. Prog.
Phys. 80, 076001 (2017).
110. Guo, A. et al. Observation of p t-symmetry breaking in complex
optical potentials. Phys. Rev. Lett. 103, 093902 (2009).
111. St-Jean, P. et al. Lasing in topological edge states of a one-
dimensional lattice. Nat. Photon 11, 651–656 (2017).
112. Parto, M. et al. Edge-mode lasing in 1d topological active arrays.
Phys. Rev. Lett. 120, 113901 (2018).
113. Dietrich, C. P., Fiore, A., Thompson, M. G., Kamp, M. & Höfling, S.
GaAs integrated quantum photonics: towards compact and multi-
functional quantum photonic integrated circuits. Laser Photonics
Rev. 10, 870–894 (2016).
114. Adachi, S. Optical dispersion relations for GaP, GaAs, GaSb, InP,
InAs, InSb, Al
x
Ga
1−x
As, and In
1−x
Ga
x
As
y
P
1−y
.J. Appl. Phys. 66,
6030–6040 (1989).
115. Mittal, S. et al. Topologically robust transport of photons in a
synthetic gauge field. Phys. Rev. Lett. 113, 087403 (2014).
116. Liu, Y. et al. Topological corner states in a silicon nitride photonic
crystal membrane with a large bandgap. Opt. Lett. 49,
242–245 (2024).
117. Redjem, W. et al. Single artificial atoms in silicon emitting at telecom
wavelengths. Nat. Electron. 3, 738–743 (2020).
118. On, M. B. et al. Programmable integrated photonics for topological
Hamiltonians. Nat. Commun. 15, 629 (2024).
119. Saxena, A., Manna, A., Trivedi, R. & Majumdar, A. Realizing tight-
binding Hamiltonians using site-controlled coupled cavity arrays.
Nat. Commun. 14, 5260 (2023).
120. Chen, R. et al. Non-volatile electrically programmable integrated
photonics with a 5-bit operation. Nat. Commun. 14, 3465 (2023).
121. Gyger, S. et al. Reconfigurable photonics with on-chip single-
photon detectors. Nat. Commun. 12, 1408 (2021).
122. Liu, K., Ye, C. R., Khan, S. & Sorger, V. J. Review and perspective on
ultrafast wavelength-size electro-optic modulators. Laser Photon
Rev. 9, 172–194 (2015).
123. Palik, E. D. Handbook of Optical Constants of Solids Vol. 3
(Academic Press, 1998).
124. Wang, S. et al. 4H-SiC: a new nonlinear material for midinfrared
lasers. Laser Photon Rev. 7, 831–838 (2013).
125. Muñoz, P. et al. Silicon nitride photonic integration platforms for
visible, near-infrared and mid-infrared applications. Sensors 17,
2088 (2017).
126. Smith, J. A., Francis, H., Navickaite, G. & Strain, M. J. Sin foundry
platform for high performance visible light integrated photonics. Opt.
Mater. Express 13, 458–468 (2023).
127. Mohanty, A. et al. Quantum interference between transverse spatial
waveguide modes. Nat. Commun. 8,1–7 (2017).
128. Feng, L.-T. et al. Transverse mode-encoded quantum gate on a
silicon photonic chip. Phys. Rev. Lett. 128, 060501 (2022).
129. Yang, Y. et al. Programmable high-dimensional Hamiltonian in a
photonic waveguide array. Nat. Commun. 15, 50 (2024).
130. Zhu, D. et al. Integrated photonics on thin-film lithium niobate. Adv.
Opt. Photon 13, 242–352 (2021).
131. Aghaeimeibodi, S. et al. Integration of quantum dots with lithium
niobate photonics. Appl. Phys. Lett. 113, 221102 (2018).
132. Zhao, J., Ma, C., Rüsing, M. & Mookherjea, S. High quality entangled
photon pair generation in periodically poled thin-film lithium niobate
waveguides. Phys. Rev. Lett. 124, 163603 (2020).
133. Zhang, M. et al. Electronically programmable photonic molecule.
Nat. Photon 13,36–40 (2019).
134. Qi, Y. & Li, Y. Integrated lithium niobate photonics. Nanophoton 9,
1287–1320 (2020).
135. Petrović, M. et al. Solitonic lattices in photorefractive crystals. Phys.
Rev. E 68, 055601 (2003).
136. Wang, P., Fu, Q., Konotop, V. V., Kartashov, Y. V. & Ye, F.
Observation of localization of light in linear photonic quasicrystals
with diverse rotational symmetries. Nat. Photonics 18,
224–229 (2024).
137. Su, Y., Zhang, Y., Qiu, C., Guo, X. & Sun, L. Silicon photonic platform
for passive waveguide devices: materials, fabrication, and
applications. Adv. Mater. Technol. 5, 1901153 (2020).
138. Gao, J. et al. Experimental probe of multi-mobility edges in
quasiperiodic mosaic lattices. arXiv preprint
arXiv:2306.10829 (2023).
139. Corrielli, G., Crespi, A. & Osellame, R. Femtosecond laser
micromachining for integrated quantum photonics. Nanophotonics
10, 3789–3812 (2021).
140. Shen, S., Kartashov, Y. V., Li, Y. & Zhang, Y. et al. Floquet edge
solitons in modulated trimer waveguide arrays. Phys. Rev. Appl. 20,
014012 (2023).
141. Pan, Y., Chen, Z., Wang, B. & Poem, E. Floquet gauge anomaly
inflow and arbitrary fractional charge in periodically driven
topological-normal insulator heterostructures. Phys. Rev. Lett. 130,
223403 (2023).
142. Wu, S. et al. Floquet πmode engineering in non-hermitian waveguide
lattices. Phys. Rev. Res. 3, 023211 (2021).
143. Sun, Y.-K. et al. Non-Abelian Thouless pumping in photonic
waveguides. Nat. Phys. 18, 1080–1085 (2022).
144. Chen, Y. et al. Non-abelian gauge field optics. Nat. Commun. 10,
3125 (2019).
145. Zhang, X., Zangeneh-Nejad, F., Chen, Z.-G., Lu, M.-H. &
Christensen, J. A second wave of topological phenomena in
photonics and acoustics. Nature 618, 687–697 (2023).
146. Pan, M., Zhao, H., Miao, P., Longhi, S. & Feng, L. Photonic zero
mode in a non-hermitian photonic lattice. Nat. Commun. 9,
1308 (2018).
147. Ornigotti, M. & Szameit, A. Quasi-symmetry in passive photonic
lattices. J. Opt. 16, 065501 (2014).
148. Lodahl, P., Mahmoodian, S. & Stobbe, S. Interfacing single photons
and single quantum dots with photonic nanostructures. Rev. Mod.
Phys. 87, 347 (2015).
Acknowledgements
The authors would like to thank Dr. Daniel Leykam for helpful discussions.
J.G. acknowledges support from Swedish Research Council (Ref.: 2023-
06671 and 2023-05288), Vinnova Project (Ref.: 2024-00466) and the Göran
Gustafsson Foundation, A.W.E. acknowledges supporting Knut and Alice
https://doi.org/10.1038/s44310-024-00034-5 Perspective
npj Nanophotonics | (2024) 1:34 10
Wallenberg (KAW) Foundation through the Wallenberg Centre for Quantum
Technology (WACQT), and Vinnova quantum kick-start project 2021, and
Light-Neuro 2023. V.Z. acknowledges support from the KAW and VR. Z.Y.
acknowledges the support from the National Key Research and Develop-
ment Programof China (No. 2022YFA1404203,2023YFA1406703), National
Natural Science Foundation of China (No. 12174339), and Zhejiang Pro-
vincial Natural Science Foundation of China (Grant No. LR23A040003).
Author contributions
All authors participated in the writing and reviewing of the manuscript.
Competing interests
The authors declare no competing interests.
Additional information
Correspondence and requests for materials should be addressed to
Jun Gao, Zhaoju Yang or Ali W. Elshaari.
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