and D). At the left grating, we observed only
the emission from the s– branch, whereas at
the right grating, we observed only the emission
from the s+ branch. These results establish the
chiral emission and spin-momentum locking
of the emitted photons and provide strong evidence that the emitter is coupling to topological
edge states that exhibit unidirectional transport.
Such chiral coupling is in direct analogy to one-dimensional systems (16, 24, 25); however, the
waveguided modes of our structure originate
from two-dimensional topology. As a result, the
topological edge mode should exhibit robustness
to certain deformations, such as bends.
To establish this topological robustness, we
analyzed the propagation of emitted photons in
the presence of a bend. We introduced a 60° bend
into the structure, as shown in Fig. 4A, and performed measurements similar to those in Fig. 3.
Again, we observed that emitted photons prop-
agate in opposite directions in a chiral fashion
and arrive at the grating associated with their
respective polarization (Fig. 4, B and C). The
preservation of the chiral nature of the emission
demonstrates an absence of back-reflection at
the bend, which would result in a strong signal
for both polarizations at the left grating. We
also confirmed that these routed photons are
single photons by performing a second-order
correlation measurement for photons collected
from both ends of the waveguide, which exhibits
strong antibunching (Fig. 4, D and E). The ro-
bustness in this system is due to C6v symmetry,
and the boundary and disorder can break this
symmetry and lead to backscattering of the edge
modes. In the supplementary materials, we anal-
yze the effect of certain types of disorder on the
transmission properties of the edge modes and
show that the unidirectional propagation is robust.
The full characterization of robustness, beyond
numerical simulations and the tight-binding model
(26), requires further study.
In this work, we demonstrated coupling be-
tween single quantum emitters and topologically
robust photonic edge states. Our approach opens
new prospects at the interface of quantum optics
and topological photonics. In the context of chiral
quantum optics, one can explore new regimes of
dipole emission in the vicinity of topological
photonic structures and exploit the robustness
of the electromagnetic modes (16). Furthermore,
in a chiral waveguide, photon-mediated interac-
tions between emitters are location-independent
(27). This property could facilitate the coupling
of multiple solid-state emitters via photons while
overcoming scalability issues associated with ran-
dom emitter position, enabling large-scale super-
radiant states and spin-squeezing. Ultimately,
such an approach could constitute a versatile
platform to explore many-body quantum physics
at a topological edge (28), create chiral spin
networks (27, 29), and realize fractional quan-
tum Hall states of light (30, 31).
REFERENCES AND NOTES
1. J. Dalibard, F. Gerbier, G. Juzeli nas, P. Öhberg, Rev. Mod. Phys.
83, 1523–1543 (2011).
2. C. Eckardt, Rev. Mod. Phys. 89, 011004 (2017).
3. M. Hafezi, J. M. Taylor, Phys. Today 67, 68–69 (2014).
4. L. Lu, J. D. Joannopoulos, M. Soljačić, Nat. Photonics 8,
5. L. Kane, T. C. Lubensky, Nat. Phys. 10, 39–45 (2014).
6. J. Paulose, B. G. G. Chen, V. Vitelli, Nat. Phys. 11, 153–156
7. R. Süsstrunk, S. D. Huber, Science 349, 47–50 (2015).
8. Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljacić, Nature 461,
9. X. Cheng et al., Nat. Mater. 15, 542–548 (2016).
10. M. Hafezi, S. Mittal, J. Fan, A. Migdall, J. M. Taylor,
Nat. Photonics 7, 1001–1005 (2013).
11. M. C. Rechtsman et al., Nature 496, 196–200 (2013).
12. M. Hafezi, E. A. Demler, M. D. Lukin, J. M. Taylor, Nat. Phys. 7,
13. L. Pilozzi, C. Conti, Phys. Rev. B 93, 195317 (2016).
14. G. Harari et al., “Topological lasers,” in Conference on Lasers and
Electro-Optics [OSA Technical Digest (online), Optical Society of
America, 2016], FM3A.3.
15. P. St-Jean et al., Nat. Photonics 11, 651–656 (2017).
16. P. Lodahl et al., Nature 541, 473–480 (2017).
17. I. Carusotto, C. Ciuti, Rev. Mod. Phys. 85, 299–366 (2013).
18. J. I. Cirac, H. J. Kimble, Nat. Photonics 11, 18–20 (2017).
19. D. G. Angelakis, Ed., Quantum Simulations with Photons and
Polaritons (Springer International Publishing, 2017).
20. L. H. Wu, X. Hu, Phys. Rev. Lett. 114, 223901 (2015).
21. S. Barik, H. Miyake, W. DeGottardi, E. Waks, M. Hafezi,
New J. Phys. 18, 113013 (2016).
22. Materials and methods are available as supplementary materials.
23. M. Bayer et al., Phys. Rev. B 65, 195315 (2002).
24. J. Petersen, J. Volz, A. Rauschenbeutel, Science 346, 67–71 (2014).
25. I. Söllner et al., Nat. Nanotechnol. 10, 775–778 (2015).
26. T. Kariyado, X. Hu, Sci. Rep. 7, 16515 (2017).
27. H. Pichler, T. Ramos, A. J. Daley, P. Zoller, Phys. Rev. A 91,
28. M. Ringel, M. Pletyukhov, V. Gritsev, New J. Phys. 16, 113030
29. A. Metelmann, A. A. Clerk, Phys. Rev. X 5, 021025 (2015).
30. R. O. Umucalılar, I. Carusotto, Phys. Rev. Lett. 108, 206809 (2012).
31. M. Hafezi, M. D. Lukin, J. M. Taylor, New J. Phys. 15, 063001
The authors acknowledge fruitful discussions with S. Mittal.
All data needed to evaluate the conclusions are present in the
paper and/or the supplementary materials. This research was
supported by the Office of Naval Research, the Air Force
Office of Scientific Research–Multidisciplinary University
Research Initiative (grant FA9550-16-1-0323), the Sloan
Foundation, and the Physics Frontier Center at the Joint
Materials and Methods
Figs. S1 to S5
24 September 2017; accepted 11 December 2017
668 9 FEBRUARY 2018 • VOL 359 ISSUE 6376 sciencemag.org SCIENCE
Fig. 4. Robust transport in two dimensions along a bend. (A) Schematic of a modified topological
waveguide with a bend. (B and C) Photoluminescence collected from points L and R, respectively,
showing only one branch of the quantum dot. (D and E) Second-order correlation measurement
[g2(t), where t is the time delay] data obtained from points L and R, respectively, showing antibunching.
Red dots represent the experimental data, and the black line corresponds to fitting.