Experimental measurement of the Berry curvature from anomalous transport
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TL;DR
This paper reports the first direct optical measurement of Berry curvature by tracking anomalous wavepacket transport in a photonic mesh lattice made from two coupled fibre loops. The measured Berry curvature for a Floquet band agrees well with theory and demonstrates that wavepacket dynamics can map local band geometry without reconstructing eigenstates.
Key findings
- The authors directly observed Berry-curvature-induced anomalous displacement in an optical system, which they describe as the first such direct measurement in photonics and the first full tomography of Berry curvature from anomalous transport.
- For a wavepacket centred near \(Q = 0.1\pi\) with phase gradient \(\phi_0 = \pi/50\), they measured an anomalous displacement of up to about 1 position over 200 time steps.
- The reconstructed Berry curvature captured the expected symmetry, sign, and magnitude over much of the band, including the relation \(\Omega^1_{\phi,Q} = -\Omega^2_{\phi,Q}\) between the two bands.
- The method worked even along trajectories approaching band singularities, although measurements became meaningless after population transfer at the singularity.
Methods
- Pulses at \(\lambda = 1{,}555\) nm were injected into two coupled fibre loops with average round-trip time \(T \approx 5{,}200\) ns and loop-length difference corresponding to \(\Delta T \approx 35.4\) ns; pulse width was 25 ns, limiting unambiguous sequences to about \(T/\Delta T \approx 147\) pulses.
- A time-dependent phase modulation with alternating sign every round trip engineered Floquet quasi-energy bands; the phase magnitude was slowly ramped to pump the wavepacket, and the centre-of-mass shift was measured for opposite phase gradients \(\pm \phi_0\) to isolate Berry curvature from group velocity.
- Wavepackets with narrow momentum spread \(\Delta Q \approx 0.05\pi\) were prepared over 200 steps and measured over the next 200 steps; \(Q\) was scanned from \(-\pi\) to \(\pi\) in steps of \(0.05\pi\), measurements were averaged over about 25 realizations, and Berry curvature was extracted by numerical differentiation after a moving-average filter with span 5.
Limitations
- The paper states that the bands are not gapped, so adiabatic evolution across the full parameter space breaks down and the quantized Thouless-pumping relation is not applicable; near band-touching points adiabaticity fails and the protocol no longer gives meaningful measurements after population transfer.
- The paper notes that sequence length is limited to roughly 147 pulses by the need to label pulses unambiguously, and that additional components introduce losses of about 8 dB per round trip, compensated by erbium-doped fibre amplifiers; the experiments use classical coherent bright light and do not rely on quantum effects.
- Evident from the text: the Berry curvature reconstruction depends on numerical differentiation and smoothing of the measured centre-of-mass shift, and the main demonstration is a proof-of-principle in one photonic platform, with a second modulation example relegated to Supplementary Information.
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Claims the paper makes
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- Findingreasoning§ Experimental measurement of the Berry curvature from anomalous transport
With the alternating phase modulation, the two bands satisfy cos θ = 1/2(cos Q - cos φ).
“cos θ = 1 2 (cos Q -cos ϕ) (6)”
Quote in the paperSubstantial claim - Findingown data§ Experimental measurement of the Berry curvature from anomalous transport
The work provides the first direct measurement or observation of Berry curvature effects in an optical system.
“This is both the first direct observation of Berry curvature effects in an optical system, and a proof-ofprinciple demonstration that wavepacket dynamics can serve as a high-resolution tool for mapping out geometric properties.”
- Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · boosted
“In this Letter, we go beyond previous experiments to provide the first direct measurement of the Berry curvature in an optical system.”
Quote in the paperSubstantial claim - Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · boosted
- Findingreasoning§ Experimental measurement of the Berry curvature from anomalous transport
The separation of timescales allows clearly separated pulse sequences, so each pulse can be labelled by two integers (m,n).
“Thanks to the separation of all of these timescales, we observe clearly separated sequences of pulses over time (see Fig. 1), so that each pulse can be straightforwardly labelled by two integers (m, n)”
Quote in the paperSubstantial claim - Findingown data§ Experimental measurement of the Berry curvature from anomalous transport
The local Berry curvature is mapped directly from anomalous transport for the first time by discrete differentiation of the lateral shift.
“We exploit this to map out the local Berry curvature directly from anomalous transport for the first time, by performing a discrete differentiation of the lateral shift n j (M) as (see Fig. 3c)”
Quote in the paperSubstantial claim - Findingreasoning§ Experimental measurement of the Berry curvature from anomalous transport
Without phase shift, the quasi-energy band structure satisfies cos θ = 1/2(cos Q - 1).
“cos θ = 1 2 (cos Q -1)(5)”
Quote in the paperNot a substantial claim
- Findingown data§ Experimental measurement of the Berry curvature from anomalous transport
The same experimental protocol applied to a second modulation and pumping sequence confirms the method's general applicability.
“The general applicability of this method is further confirmed in Supplementary Information 8, where the same experimental protocol is applied to a second example of modulation and pumping sequence.”
Quote in the paperNot a substantial claim - Findingreasoning§ Experimental measurement of the Berry curvature from anomalous transport
The centre-of-mass of the Gaussian wavepacket evolves with a total velocity equal to the group velocity plus an anomalous velocity due to Berry curvature.
“The centre-of-mass of the Gaussian envelope then evolves along the 1D lattice with a total velocity v j (M) = v G j (ϕ (M) , Q) + ∂ϕ(M) ∂M Ω ϕ(M),Q j (9 ) where the first term is the usual group velocity from the band dispersion and the second is the anomalous velocity due to the Berry curvature.”
Quote in the paperSubstantial claim - Findingown data§ Experimental measurement of the Berry curvature from anomalous transport
The authors experimentally show that wavepacket dynamics can be used to directly map out Berry curvature.
“Here, we experimentally demonstrate that the wavepacket dynamics can be used to directly map out the Berry curvature.”
- Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · plain
“Our high-resolution observation of the wavepacket dynamics then allows us to map out the Berry curvature for an optical energy band for the first time.”
- Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · boosted
“we have demonstrated that anomalous wavepacket dynamics can provide an important experimental tool for mapping out the local geometrical properties of energy bands.”
Quote in the paperSubstantial claim - Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · plain
- Findingnone given§ Experimental measurement of the Berry curvature from anomalous transport
The wavepacket evolution can be measured after each discrete time step, providing high time resolution.
“As the most important advance of our work, the wavepacket evolution can be measured after each discrete time step, allowing for unprecedented high time resolution of the dynamics.”
Quote in the paperSubstantial claim - Findingown data§ Experimental measurement of the Berry curvature from anomalous transport
The work demonstrates the first full tomography of the Berry curvature of a geometrical energy band from measurements of anomalous displacement of a coherent classical wavepacket.
“We also demonstrate the first full tomography of the Berry curvature of a geometrical energy band from measurements of the anomalous displacement of a coherent classical wavepacket.”
Quote in the paperSubstantial claim - Findingown data§ Experimental measurement of the Berry curvature from anomalous transport
The experiment measures an anomalous displacement of up to about 1 position over 200 time steps for a wavepacket centred at Q = 0.1π with phase gradient φ0 = π/50.
“experimentally we measure an anomalous displacement of up to approximately 1 position over 200 time steps for a wavepacket centred around Q = 0.1π subject to a phase gradient of ϕ 0 = π/50.”
Quote in the paperSubstantial claim - Findingcitation§ Experimental measurement of the Berry curvature from anomalous transport
The Berry curvature leads to an anomalous displacement of the wavepacket in the 1D geometric charge pump.
“where the Berry curvature leads to an anomalous displacement of the wavepacket.”
- Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · plain
“Due to this pumping, the wavepacket moves along the 1D 'photonic mesh lattice' , with an anomalous velocity contribution 1,[23][24][25] due to the Berry curvature”
Quote in the paperSubstantial claim0 of 1 sources checked- cites 1,[23][24][25]
Not checked in the free run.
- Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · plain
- Findingreasoning§ Experimental measurement of the Berry curvature from anomalous transport
The method can measure Berry curvature even along trajectories that eventually hit band singularities.
“Due to the 'on the fly' tracking of the wavepacket, we can measure the Berry curvature even along trajectories that eventually hit band singularities.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Experimental measurement of the Berry curvature from anomalous transport
The method can be applied to complex systems with many bands and degrees of freedom where full eigenstate determination is experimentally challenging.
“Consequently, our method can be easily applied to complex systems with many bands and degrees of freedom, where a full determination of the eigenstates would be experimentally challenging.”
Quote in the paperSubstantial claim - Premisecitation§ Experimental measurement of the Berry curvature from anomalous transport
A semi-classical wavepacket moves as a coherent object with an additional anomalous Hall velocity due to Berry curvature at its centre-of-mass when an external force is applied or control parameter pumped.
“In the simplest case, a semi-classical wavepacket moves as a coherent object governed by classical equations of motion with an additional 'anomalous' Hall velocity due to the geometrical Berry curvature at its centre-ofmass, as an external force is applied or as the control parameter is pumped 1,4 .”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [1] Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010). source
Not checked in the free run.
- cites [4] Chang, M.-C. & Niu, Q. Berry phase, hyperorbits, and the Hofstadter spectrum. Phys. Rev. Lett. 75, 1348–1351 (1995). source
Not checked in the free run.
- Premisecitation§ Experimental measurement of the Berry curvature from anomalous transport
The anomalous transport can be understood as Berry curvature acting like a magnetic field in parameter space.
“As highlighted further below, this anomalous transport can be understood physically as the Berry curvature acting like a magnetic field in parameter space [5][6][7] .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [5][6][7]
Not checked in the free run.
- Study design and conductreasoning
The wavepacket preparation produces a sufficiently small spectral width ΔQ ≈ 0.05π to map out the local Berry curvature.
“Thus, for 200 time steps a wavepacket with a width of ≈8 positions with respect to the full-width at half-maximum of the intensity is generated, which provides a sufficiently small spectral width Q ≈ 0.05π to map out the local Berry curvature.”
Quote in the paperSubstantial claim - Premisenone given§ Experimental measurement of the Berry curvature from anomalous transport
Before this work, a direct measurement of Berry curvature in photonics had not been realized.
“However, while the existence of such edge states is linked to the non-trivial global topological properties of bulk bands, a direct measurement of the Berry curvature itself has so far not been realized.”
Quote in the paperSubstantial claim - Study design and conductcitation
The appropriate eigenstate for a given Bloch momentum Q is excited by applying phase φ = Q during diffusive motion and φ = (Q ± π)/2 for the last time step before propagation.
“To excite a specific Bloch momentum Q, we apply a phase of ϕ = Q during the diffusive motion and a phase of ϕ = (Q ± π) /2 for the last time step before the actual propagation.”
- Also stated in: § Additional information · plain
“As discussed in refs 34,37, in this way, the appropriate eigenstate corresponding to a Bloch momentum Q is excited.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [34] Wimmer, M. et al. Optical diametric drive acceleration through action–reaction symmetry breaking. Nat. Phys. 9, 780–784 (2013). source
Not checked in the free run.
- cites [37] Regensburger, A. et al. Photon propagation in a discrete fiber network: an interplay of coherence and losses. Phys. Rev. Lett. 107, 233902 (2011). source
Not checked in the free run.
- Also stated in: § Additional information · plain
- Interpretationreasoning§ Experimental measurement of the Berry curvature from anomalous transport
For a gapped band, integrating the measured Berry curvature over the effective 2D parameter space would give the topological Chern number.
“For a gapped band, this technique would straightforwardly give the topological Chern number (equation ( 12)) when we integrate the measured Berry curvature over the effective 2D parameter space.”
Quote in the paperSubstantial claim - Study design and conductcitation§ Experimental measurement of the Berry curvature from anomalous transport
The time-reversal protocol comparing propagation under +φ0 and -φ0 separates Berry curvature from group velocity effects.
“To cleanly separate Berry curvature from group velocity effects, we apply a variant of the 'time-reversal' protocol 36 and compare the propagation (see Fig. 3a) under a reversal of the sign of the phase magnitude (that is, +ϕ 0 and -ϕ 0 ) to find”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [36] Price, H. M. & Cooper, N. R. Mapping the Berry curvature from semiclassical dynamics in optical lattices. Phys. Rev. A 85, 033620 (2012). source
Not checked in the free run.
- Study design and conductown data§ Experimental measurement of the Berry curvature from anomalous transport
A periodic phase modulation in one loop engineers Floquet quasi-energy bands whose eigenstates depend on Bloch momentum Q and control parameter φ.
“We then apply a periodic phase modulation in one loop to engineer Floquet quasi-energy bands, in which the eigenstates depend on both the 1D 'Bloch momentum' , Q, and on a control parameter, ϕ, given by the amplitude of the phase modulation.”
Quote in the paperSubstantial claim - Study design and conductcitation§ Experimental measurement of the Berry curvature from anomalous transport
The setup uses a time-multiplexing linear optical scheme with two coupled fibre loops of different lengths.
“In our experiment, we employ a time-multiplexing, linear optical scheme based on two coupled fibre loops of different lengths 31,32 as shown in Fig. 1a.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [31] Schreiber, A. et al. Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010). source
Not checked in the free run.
- cites [32] Regensburger, A. et al. Parity-time synthetic photonic lattices. Nature 488, 167–171 (2012). source
Not checked in the free run.
- Study design and conductcitation§ Experimental measurement of the Berry curvature from anomalous transport
In the photonic mesh lattice setup, pulses in two coupled optical fibre loops simulate a wavepacket in a 1D lattice.
“In our 'photonic mesh lattice' set-up 31,32 , pulses are injected into two coupled optical fibre loops, so that the temporal evolution of the outgoing pulse-train envelope simulates a wavepacket in a 1D lattice.”
- Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · plain
“Based on the labelling of pulses according to (m, n), the evolution of light can be mapped to a 1+1-dimensional lattice as depicted in Fig. 1b,c”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [31] Schreiber, A. et al. Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010). source
Not checked in the free run.
- cites [32] Regensburger, A. et al. Parity-time synthetic photonic lattices. Nature 488, 167–171 (2012). source
Not checked in the free run.
- The authors state this as an assumption: Dispersion effects are neglected in the model.
- The authors state this as an assumption: The pulse shape does not depend on the specific route taken through the loops.
- Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · plain
- Premisereasoning§ Experimental measurement of the Berry curvature from anomalous transport
A local non-zero Berry curvature can have striking physical effects in both 2D systems and 1D pumps regardless of whether the global Chern number is non-trivial.
“A local non-zero Berry curvature can have striking physical effects in both 2D systems and 1D pumps, regardless of whether the global topological Chern number is non-trivial.”
Quote in the paperSubstantial claim
- May combine two claims. 10
- Classified as probably not a substantial claim. 7
May combine two claims.
Findingown data§ Experimental measurement of the Berry curvature from anomalous transportThe Berry curvature for these bands is singular where the two bands touch but otherwise takes large non-zero positive and negative values across the effective 2D parameter space.
“As shown in Fig. 2d, this Berry curvature is singular at points where the two bands touch but otherwise can take large non-zero positive and negative values across the effective 2D parameter space.”
Quote in the paperSubstantial claimMay combine two claims.
Findingreasoning§ Experimental measurement of the Berry curvature from anomalous transportThe two bands are periodic in Q and θ and have a band-touching at Q = ±π.
“leading to two bands that are periodic in both Q and θ as expected in a Floquet system, with a band-touching at the edge of the 1D Brillouin zone where Q = ±π”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown data§ Experimental measurement of the Berry curvature from anomalous transportThe experimental reconstruction captures the main features of Berry curvature, including overall symmetry and sign, quantitative magnitude over much of the band, and the complementarity Ω1 = -Ω2.
“as can be seen, the main features of the Berry curvature are well captured, such as the overall symmetry and sign, the quantitative magnitude over much of the band and the predicted complementarity of the two bands 1,26 (that is, Ω ϕ,Q 1 = -Ω ϕ,Q 2 ).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [1] Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010). source
Not checked in the free run.
- cites [26] Fläschner, N. et al. Experimental reconstruction of the Berry curvature in a Floquet Bloch band. Science 352, 1091–1094 (2016). source
Not checked in the free run.
May combine two claims.
Findingown data§ Experimental measurement of the Berry curvature from anomalous transportNear Q ≈ 0, Berry curvature can be extracted until the singularity at φ = π; after that, population transfer to the other band makes the measurement no longer meaningful.
“Close to the centre of the Brillouin zone (Q ≈ 0), for example, we can extract the Berry curvature until the singularity is hit at ϕ = π; afterwards, part of the population is transferred to the other band and the measurement is no longer meaningful.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).
Interpretationcitation§ Experimental measurement of the Berry curvature from anomalous transportThe method's versatility should allow it to be applied in configurations including systems with gain and loss and/or nontrivial topological invariants.
“This versatility of this scheme should allow it to be applied in a variety of configurations, including systems with gain and loss 32 and/or nontrivial topological invariants.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [32] Regensburger, A. et al. Parity-time synthetic photonic lattices. Nature 488, 167–171 (2012). source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Study design and conductown dataThe error bars in Fig. 2e are estimated from the spectral width ΔQ ≈ 0.05π horizontally and the 95% confidence fit uncertainty vertically.
“The error bars depicted in Fig. 2e are estimated by the spectral width Q ≈ 0.05π of the initial excitation in the horizontal direction and by the uncertainty of the fit procedure for a 95% confidence level in the vertical direction.”
Quote in the paperNot a substantial claimMay combine two claims.
Study design and conductreasoning§ Experimental measurement of the Berry curvature from anomalous transportThe integer labelling is limited to sequences shorter than the round-trip time, limiting the maximum number of pulses in a sequence to about 147.
“Of course, this picture is restricted to sequences shorter than the round trip time in order for the assignment of integers to be unambiguous; this limits the maximum number of pulses in a given sequence to T / T ≈ 147.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductreasoning§ Experimental measurement of the Berry curvature from anomalous transportDispersive effects in the optical fibres are typically unimportant even over 400 round trips.
“Thanks to the long pulse-width, T pulse , dispersive LETTERS effects in the optical fibres are typically unimportant, even over 400 round trips, corresponding to 400 km of propagation.”
Quote in the paperNot a substantial claimMay combine two claims.
Study design and conductreasoning§ Experimental measurement of the Berry curvature from anomalous transportThe experiments use classical coherent bright light pulses and do not rely on quantum effects.
“In general, the use of these amplifiers destroys quantum correlations; however, all experiments here are performed with a classical, coherent bright light pulse and do not rely on quantum effects.”
Quote in the paperNot a substantial claimMay combine two claims.
Premisereasoning§ Experimental measurement of the Berry curvature from anomalous transportThe topological Thouless pumping limit is recovered for a filled gapped band after a complete adiabatic pump cycle, with the shift quantized as the Chern number.
“We note that the limit of topological Thouless pumping can be recovered from this expression, if we consider the motion of a filled and gapped energy band after a complete adiabatic pump cycle.Then, the shift is quantized as an integer 3”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [3] Thouless, D. J. Quantization of particle transport. Phys. Rev. B 27, 6083–6087 (1983). source
Not checked in the free run.
May combine two claims.
Study design and conductreasoning§ Experimental measurement of the Berry curvature from anomalous transportIn the experiment, the energy bands are not gapped, so the assumption of adiabatic evolution across the entire 2D parameter space breaks down and the quantized Thouless pumping expression is not applicable.
“In our experiment, however, we consider a system in which the energy bands are not gapped and so the assumption of adiabatic evolution across the entire 2D parameter space breaks down and equation ( 12) is not applicable.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationown data§ Experimental measurement of the Berry curvature from anomalous transportThe method measures Berry curvature directly from wavepacket dynamics without requiring full reconstruction of band eigenstates.
“with the significant advantage that it does not require a full reconstruction of the band eigenstates as an intermediate step.”
- Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · plain
“After exciting an initial eigenstate, no further information about the eigenstates is required as we directly measure the Berry curvature from its physical consequences on wavepacket dynamics”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [26] Fläschner, N. et al. Experimental reconstruction of the Berry curvature in a Floquet Bloch band. Science 352, 1091–1094 (2016). source
Not checked in the free run.
- cites [27] Li, T. et al. Bloch state tomography using Wilson lines. Science 352, 1094–1097 (2016). source
Not checked in the free run.
- Also stated in: § Experimental measurement of the Berry curvature from anomalous transport · plain
Classified as probably not a substantial claim.
Premisecitation§ Experimental measurement of the Berry curvature from anomalous transportThe integral of Berry curvature over the 2D Brillouin zone determines the Chern number, a global topological invariant underlying quantization of Hall transport for a filled 2D band.
“In a twodimensional (2D) quantum Hall system, for example, the integral of the Berry curvature over the 2D Brillouin zone determines the Chern number: a global topological invariant that underlies the quantization of Hall transport for a 2D filled energy band 2 .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [2] Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982). source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ Experimental measurement of the Berry curvature from anomalous transportThouless showed an analogous topological quantization of particle transport in a 1D band insulator when the lattice potential is slowly and periodically modulated.
“As first explained by Thouless 3 , there can be an analogous topological quantization of particle transport in a 1D band insulator, when the lattice potential is 'pumped' , that is, is slowly and periodically modulated in time.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [3] Thouless, D. J. Quantization of particle transport. Phys. Rev. B 27, 6083–6087 (1983). source
Not checked in the free run.
Classified as probably not a substantial claim.
Study design and conductnone given§ Experimental measurement of the Berry curvature from anomalous transportThe slow variation of the phase magnitude adiabatically pumps the system provided the rate φ0 is sufficiently small compared with the bandgap.
“while the slow variation in equation ( 8) adiabatically 'pumps' the system, provided that the rate ϕ 0 is sufficiently small compared with the bandgap.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The slow variation of the phase magnitude adiabatically pumps the system when the rate is sufficiently small compared with the bandgap.
Probably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductown dataThe measured propagation was averaged over approximately 25 realizations to reduce noise.
“To reduce the noise limit of the data acquisition, the measured propagation was averaged over approximately 25 realizations.”
Quote in the paperNot a substantial claim
The authors state this as an assumption.
Dispersion effects are neglected in the model.
“we have neglected here dispersion effects and assumed that the pulse shape does not depend on the specific route taken.”
The authors state this as an assumption.
The pulse shape does not depend on the specific route taken through the loops.
“we have neglected here dispersion effects and assumed that the pulse shape does not depend on the specific route taken.”
The authors state this as an assumption.
The slow variation of the phase magnitude adiabatically pumps the system when the rate is sufficiently small compared with the bandgap.
“while the slow variation in equation ( 8) adiabatically 'pumps' the system, provided that the rate ϕ 0 is sufficiently small compared with the bandgap.”
Claims other papers make about this one
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The topological invariant was already employed in Ref. 28 to characterize crystalline topological superconductors.
“Our topological invariant, which was already employed in Ref. 28 to characterize crystalline topological superconductors”
From Topolectrical-circuit realization of topological corner modes (2018) · cites this paper as [28]
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Colloquium : Synthetic quantum matter in nonstandard geometries
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Shan, Q., Yu, D., Li, G., Yuan, L., & Chen, X. (2020) · Electromagnetic waves · doi:10.2528/pier20083101 · Cited by 19 · see citing works
Simulating topological materials with photonic synthetic dimensions in cavities
Yang, M., Xu, J., Li, C., & Guo, G. (2022) · Quantum Frontiers · doi:10.1007/s44214-022-00015-9 · Cited by 18 · see citing works
Observation of Berry curvature in non-Hermitian system from far-field radiation
Yin, X., Chen, Y., Zhang, X., Zhang, Z., Noda, S., & Peng, C. (2025) · Nature Communications · doi:10.1038/s41467-025-58050-8 · Cited by 18 · see citing works
Optical Neural Network Based on Synthetic Nonlinear Photonic Lattices
Pankov, A. V., Vatnik, I. D., & Sukhorukov, A. A. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.17.024011 · Cited by 18 · see citing works
Extracting non-Abelian quantum metric tensor and its related Chern numbers
Ding, H.-T., Zhu, Y.-Q., He, P., Liu, Y.-G., Wang, J.-T., Zhang, D.-W., & Zhu, S.-L. (2022) · Physical Review A · doi:10.1103/physreva.105.012210 · Cited by 18 · see citing works
Tera-sample-per-second arbitrary waveform generation in a synthetic dimension
Guan, Y., Zhang, J., Li, L., Cao, R., Wang, G., Chen, J., Wang, X., Guan, B., & Yao, J. (2023) · Communications Physics · doi:10.1038/s42005-023-01383-x · Cited by 17 · see citing works
Enhancement of Chiral-Induced Spin Selectivity via Circularly Polarized Light
Liu, W., Chen, J., & Dou, W. (2025) · The Journal of Physical Chemistry C · doi:10.1021/acs.jpcc.5c02365 · Cited by 16 · see citing works
Wang, D., Yang, B., Zhang, R.-Y., Chen, W.-J., Zhang, Z.-Q., Zhang, S., & Chan, C. T. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.043602 · Cited by 16 · see citing works
Observation of Time Reversed Light Propagation by an Exchange of Eigenstates
Wimmer, M., & Peschel, U. (2018) · Scientific Reports · doi:10.1038/s41598-018-20577-w · Cited by 15 · see citing works
Self-citationFrequency diffraction management through arbitrary engineering of photonic band structures
Qin, C., Wang, B., & Lu, P. (2018) · Optics Express · doi:10.1364/oe.26.025721 · Cited by 15 · see citing works
Probing Bulk Band Topology from Time Boundary Effect in Synthetic Dimension
Xu, H. S., Dong, Z., Yuan, L., & Jin, L. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.163801 · Cited by 14 · see citing works
Topological quantum phase transitions driven by a displacement field in twisted MoTe 2 bilayers
Sharma, P. A., Peng, Y., & Sheng, D. N. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.125142 · Cited by 14 · see citing works
Guiding Trojan light beams via Lagrange points
Luo, H., Wei, Y., Wu, F. O., Pyrialakos, G. G., Christodoulides, D. N., & Khajavikhan, M. (2024) · Nature Physics · doi:10.1038/s41567-023-02270-6 · Cited by 13 · see citing works
Bound-Extended Mode Transition in Type-II Synthetic Photonic Weyl Heterostructures
Song, W., Lin, Z., Ji, J., Sun, J., Chen, C., Wu, S., Huang, C., Yuan, L., Zhu, S. N., & Li, T. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.143801 · Cited by 13 · see citing works
Qin, C., Han, Y., Wang, S., Zhao, L., Liu, M., Li, Y., Hu, X., Liu, C., Wang, B., Longhi, S., et al. (2024) · Nature Communications · doi:10.1038/s41467-024-49747-3 · Cited by 13 · see citing works
Manifestation of the Berry curvature in geophysical ray tracing
Perez, N., Delplace, P., & Venaille, A. (2021) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2020.0844 · Cited by 13 · see citing works
- Authors
- Wimmer, M., Price, H. M., Carusotto, I., & Peschel, U.
- Affiliations
- Friedrich-Alexander-Universität Erlangen-Nürnberg (DE)
- University of Trento (IT)
- Friedrich Schiller University Jena (DE)
- Corresponding author
- Peschel, Ulf
- Venue
- Nature Physics
- Published
- 2017-02-27
- Volume
- 13
- Issue
- 6
- Pages
- 545-550
- ISSN
- 1745-2473 (ISSN-L)
- 1745-2481
- OpenAlex
- W2524593142
- Cited by
- 225
- References
- 37
- Citations by year
- 2026: 16 · 2025: 27 · 2024: 34 · 2023: 26 · 2022: 26 · 2021: 29 · 2020: 24 · 2019: 15 · 2018: 22 · 2017: 6
- FWCI
- 8.99
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Nature Physics (publishedVersion)
- University of Birmingham Research Portal (University of Birmingham) (publishedVersion, other-oa)
- arXiv (Cornell University) (submittedVersion)
- Iris (University of Trento) (submittedVersion)
- arXiv (Cornell University)
- Funders
- European Commission (656093)
- Deutsche Forschungsgemeinschaft (PE 523/14-1, GRK2101, /14-1)
- Erlangen Graduate School of Advanced Optical Technologies
- Provincia Autonoma di Trento
- Horizon 2020 Framework Programme (640800)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- Berry curvature, wave packet dynamics, anomalous transport, one-dimensional photonic crystals, optical pulses, topological invariants, Berry phase
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