Photonic Bloch oscillations of correlated particles
Open accessAbstract
A photonic realization of Bloch oscillations (BOs) of two correlated electrons that move on a one-dimensional periodic lattice, based on spatial light transport in a square waveguide array with a defect line, is theoretically proposed. The signature of correlated BOs, such as frequency doubling of the oscillation frequency induced by particle interaction, can be simply visualized by monitoring the spatial path followed by an optical beam that excites the array near the defect line.
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TL;DR
This Letter theoretically proposes a photonic realization of Bloch oscillations (BOs) for two correlated electrons, mapped onto spatial light transport in a square waveguide array with a diagonal defect line. Numerical simulations show that when the two particles initially occupy the same site, the BO frequency is doubled relative to the independent-particle case.
Key findings
- For two electrons initially far apart (n₀ = 10, m₀ = 0), the wave packet undergoes ordinary two-dimensional BOs in a homogeneous region of the array without touching the defect line, with period T_B = 2π/(Fa) ≃ 2.25 cm.
- For two electrons initially on the same site (n₀ = m₀ = 0), the beam centroid shows a frequency-doubled component of the BO, associated with excitation of localized (bounded) two-electron singlet states at the defect line n = m.
- The frequency-doubled component is most pronounced at U ∼ 4κ — the interaction strength at which the two lattice bands begin to separate — and vanishes in the low- and strong-coupling limits.
- The two-electron spectrum for U ≠ 0 splits into two bands: a delocalized band spanning −4κ < E < 4κ and a defect band spanning U < E < √(U² + 16κ²), which separate once U exceeds 4κ.
Methods
- Theoretical proposal: the Hubbard Hamiltonian for two opposite-spin electrons on a 1D tight-binding lattice under a dc force is mapped, via a Wannier-state expansion, onto coupled-mode equations for a 2D square waveguide array with a transverse index gradient and a defect line at n = m.
- Numerical simulations of the paraxial wave equation in a 5 cm long array with λ = 980 nm, n_s = 1.522, Δn = 0.01, Δn₁ = 0.01035, a = 8.6 µm, R = (30/√2) cm, and 3 µm core radius; estimated parameters κ = 3.977 cm⁻¹, U ≃ 4κ, Fa = 2.7973 cm⁻¹.
- Input Gaussian beam with w = 1.3; comparison of the numerically computed beam centroid ⟨n(s)⟩ against the wave-packet centroid from the coupled-mode equations.
Limitations
- Not stated in the paper: the Letter presents no explicit limitations section.
- Evident from the text: the work is purely theoretical — no experimental realization is reported, and the proposed femtosecond-laser-written fused-silica structure is only suggested as a possible implementation.
- Evident from the text: the analysis is restricted to two electrons in a singlet configuration with opposite spins, and the frequency-doubling result is drawn from numerical simulation rather than measurement.
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Claims the paper makes
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- Findingown data§ Photonic Bloch oscillations of correlated particles · p. 3
The numerically computed beam centroid curves are well approximated by the corresponding wave packet centroid curves obtained by numerical simulations of the coupled-mode equations (2).
“The curves are well approximated by the corresponding ones for the wave packet centroid 〈 n ( t ) 〉 = ∑ n,m ( n -n 0 ) | c n,m ( t ) | 2 obtained by numerical simulations of the coupled mode equations (2), which are depicted by the solid curves in the figures.”
Quote in the paperNot a substantial claim - Findingreasoning§ Photonic Bloch oscillations of correlated particles · p. 3
For two electrons initially far apart from each other, the wave packet undergoes two-dimensional Bloch oscillations in a homogeneous region of the array, without touching the defect line.
“while for two electrons initially far apart each other the wave packet undergoes two-dimensional BOs in a homogeneous region of the array, without touching the defect line Y [see Fig.2(b)]”
Quote in the paperSubstantial claim - Findingown data§ Photonic Bloch oscillations of correlated particles · p. 3
Numerical simulations of the paraxial wave equation show a doubling of the oscillation frequency when the lattice is initially excited at the defect line.
“clearly showing the doubling of the oscillation frequency when the lattice is initially excited at the defect line [compare Figs.2(a) and 3(a)].”
Quote in the paperSubstantial claim - Findingreasoning§ Photonic Bloch oscillations of correlated particles · p. 2
The spatial period of Bloch oscillations is T_B = 2π/(Fa) ≃ 2.25 cm.
“The spatial period of BOs is T B = 2 π/ ( Fa ) ≃ 2 . 25 cm.”
Quote in the paperNot a substantial claim - Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 1
The motion of two interacting electrons moving on a one-dimensional tight-binding lattice subjected to an external dc force F is described by the Hubbard Hamiltonian.
“The motion of two interacting electrons moving on a one-dimensional tight-binding lattice subjected to an external dc force F is described by the Hubbard Hamiltonian (see, for instance, [16,17])”
Quote in the paperSubstantial claim0 of 2 sources checked
- Interpretationnone given§ Photonic Bloch oscillations of correlated particles · p. 1
A photonic realization of Bloch oscillations of two correlated electrons moving on a one-dimensional periodic lattice, based on spatial light transport in a square waveguide array with a defect line, is theoretically proposed.
“A photonic realization of Bloch oscillations (BOs) of two correlated electrons that move on a one-dimensional periodic lattice, based on spatial light transport in a square waveguide array with a defect line, is theoretically proposed.”
- Also stated in: § Photonic Bloch oscillations of correlated particles · p. 1 · plain
“In this Letter a photonic realization of BOs for two correlated electrons is proposed, which is based on light transport in a two-dimensional square waveguide array with a defect line.”
Quote in the paperSubstantial claim - Also stated in: § Photonic Bloch oscillations of correlated particles · p. 1 · plain
- Interpretationcitation§ Photonic Bloch oscillations of correlated particles · p. 2
The relative contributions of the fundamental and frequency-doubled components of the Bloch oscillations basically depend on the relative excitation of bounded and unbounded states from the initial wave packet.
“The relative contributions of fundamental and frequency double components of the BOs basically depends on the relative excitation of bounded and unbounded states from the initial wave packet.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17] Dias, 2007, Phys. Rev. B source
Not checked in the free run.
- Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 1
For many particles, the onset of Bloch oscillations is greatly affected by particle interactions.
“For many particles, the onset of BOs is greatly affected by particle interactions [15-19]”
Quote in the paperSubstantial claim0 of 5 sources checked- cites [15] Buchleitner, 2003, Phys. Rev. Lett. source
Not checked in the free run.
- cites [16] Claro, 2003, Phys. Rev. B source
Not checked in the free run.
- cites [17] Dias, 2007, Phys. Rev. B source
Not checked in the free run.
- cites [18] Freericks, 2008, Phys. Rev. B source
Not checked in the free run.
- cites [19] Khomeriki, 2010, Phys. Rev. A source
Not checked in the free run.
- Interpretationreasoning§ Photonic Bloch oscillations of correlated particles · p. 1
A photonic realization of the Hubbard Hamiltonian for two electrons can be obtained by expanding the state vector of the system as a superposition of Wannier states.
“A photonic realization of the Hubbard Hamiltonian (1) for two electrons can be readily obtained after expanding the state vector of the system | ψ ( t ) 〉 as a superposition of Wannier states”
Quote in the paperSubstantial claim- The authors state this as an assumption: The two electrons have opposite spins (singlet state), so as to allow double occupancy of the on-site orbital.
- Interpretationnone given§ Photonic Bloch oscillations of correlated particles · p. 2
If n0 = m0, the initial wave packet describes two electrons that initially occupy the same site and thus strongly interact.
“Note that, if n 0 = m 0 , the wave packet describes two electrons that initially occupy the same site and thus strongly interact.”
Quote in the paperSubstantial claim - Premisenone given§ Photonic Bloch oscillations of correlated particles · p. 1
One of the main limitations of photonic Bloch oscillations so far realized is that they mimic the motion of single particles solely.
“One of the main limitations of photonic BOs so far realized is to mimic the motion of single particles solely.”
Quote in the paperSubstantial claim - Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 2
The two bands start to separate when the interaction U increases above 4κ.
“These two bands starts to separate when the interaction U increases above 4 κ [see Fig.1(b)].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [16] Claro, 2003, Phys. Rev. B source
Not checked in the free run.
- Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 2
For U = 0, there exists a single tight-binding band of energy -4κ < E < 4κ, which is precisely the energy band of a single electron on a two-dimensional square lattice.
“For U = 0, there exists a single tight-binding band of energy -4 κ < E < 4 κ , which is precisely the energy band of a single electron on a two-dimensional square lattice.”
Quote in the paperSubstantial claim0 of 2 sources checked - Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 2
The first band, covering the range -4κ < E < 4κ, corresponds to delocalized Bloch states which are scattered off by the defect line n = m.
“The first one, which covers the range -4 κ < E < 4 κ [band 1 in Fig.1(b)], corresponds to delocalized Bloch states which are scattered off by the defect line n = m .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [16] Claro, 2003, Phys. Rev. B source
Not checked in the free run.
- Interpretationreasoning§ Photonic Bloch oscillations of correlated particles · p. 2
Coupled-mode equations (2) are obtained from the optical Schrödinger equation in the tight-binding approximation and neglecting cross coupling, provided that time t is replaced by the spatial curvilinear distance s and a forcing F = 2πn_s/(√2 Rλ) is assumed.
“Coupled-mode equations (2) are obtained from Eq.(3) in the tight-binding approximation and neglecting cross coupling, provided that time t is replaced by the spatial curvilinear distance s and a forcing F = 2 πn s / ( √ 2 Rλ ) is assumed.”
Quote in the paperSubstantial claim - Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 2
For a non-vanishing interaction U, the energy spectrum of the two-electron Hamiltonian in the absence of the external force is composed of two bands.
“For a non-vanishing interaction U , the energy spectrum is composed by two bands [16].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [16] Claro, 2003, Phys. Rev. B source
Not checked in the free run.
- Interpretationreasoning§ Photonic Bloch oscillations of correlated particles · p. 2
If |n0 - m0| is much larger than w, the initial wave packet describes two electrons that are initially separated from each other.
“Conversely, if | n 0 -m 0 | is much larger than w , the initial wave packet describes two electrons that are initially separated each other.”
Quote in the paperSubstantial claim - Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 2
If the two electrons initially occupy the same site (n0 = m0), Bloch oscillations develop a frequency-doubled component which is more pronounced at intermediate couplings.
“Conversely, if the two electrons initially occupy the same site, i.e. for n 0 = m 0 , BOs develop a frequency doubled component which is more pronounced at intermediate couplings.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17] Dias, 2007, Phys. Rev. B source
Not checked in the free run.
- Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 2
The second band, covering the range U < E < √(U2+16κ2), is related to the appearance of defect modes which are localized at the n = m interface.
“The second band [band 2 in Fig.1(b)], which covers the range U < E < √ U 2 +16 κ 2 , is related to the appearance of defect modes which are localized at the n = m interface”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [16] Claro, 2003, Phys. Rev. B source
Not checked in the free run.
- Interpretationown data§ Photonic Bloch oscillations of correlated particles · p. 1
The signature of correlated Bloch oscillations, such as frequency doubling of the oscillation frequency induced by particle interaction, can be simply visualized by monitoring the spatial path followed by an optical beam that excites the array near the defect line.
“The signature of correlated BOs, such as frequency doubling of the oscillation frequency induced by particle interaction, can be simply visualized by monitoring the spatial path followed by an optical beam that excites the array near the defect line.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Photonic Bloch oscillations of correlated particles · p. 2
In the optical lattice realization, the independent Bloch oscillations of separated electrons are explained by the two-dimensional wave packet motion remaining confined in a homogeneous region of the lattice and not touching the defect line n = m, thus realizing a two-dimensional Bloch oscillation motion.
“In the optical lattice realization of Fig.1(a), such a result can be simply explained by observing that in this case the two-dimensional wave packet motion basically remains confined in a homogeneous region of the lattice and does not touches the defect line n = m , thus realizing a twodimensional BOs motion.”
Quote in the paperSubstantial claim - Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 2
The frequency doubling is associated with the excitation of bounded states of two electrons in a singlet configuration, i.e. the localized modes at the defect line m = n.
“As discussed in Ref. [17], such frequency doubling is associated with the excitation of bounded states of two electrons in a singlet configuration (i.e. the localized modes at the defect line m = n ).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17] Dias, 2007, Phys. Rev. B source
Not checked in the free run.
- The authors state this as an assumption: The two electrons have opposite spins (singlet state), so as to allow double occupancy of the on-site orbital.
- Interpretationown data§ Photonic Bloch oscillations of correlated particles · p. 3
Such an optical setting should provide an experimentally accessible laboratory tool for the observation of interaction-induced frequency doubling of Bloch oscillations.
“Such an optical setting should provide an experimentally accessible laboratory tool for the observation of interaction-induced frequency doubling of BOs.”
Quote in the paperSubstantial claim
- May combine two claims. 5
- Classified as probably not a substantial claim. 3
May combine two claims.
Findingown data§ Photonic Bloch oscillations of correlated particles · p. 2The values of the coupling constant κ, propagation constant shift U and gradient parameter Fa entering the coupled-mode equations (2) are estimated to be κ = 3.977 cm−1, U ≃ 4κ, and Fa = 2.7973 cm−1.
“The values of coupling constant κ , propagation constant shift U and gradient parameter Fa entering in the coupled-mode equations (2) are estimated to be κ = 3 . 977 cm -1 , U ≃ 4 κ , and Fa = 2 . 7973 cm -1 , respectively.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ Photonic Bloch oscillations of correlated particles · p. 3For the two interacting electrons, the wave packet remains strongly localized near the defect line, exciting the defect modes at the interface.
“for the two interacting electrons the wave packet remains strongly localized near the defect line, exciting the defect modes at the interface [Fig.3(b)].”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationreasoning§ Photonic Bloch oscillations of correlated particles · p. 2When the external force F is applied and the two electrons are initially separated, the two particles basically undergo independent Bloch oscillations with a characteristic period T_B = 2π/(Fa), provided that the amplitude of the Bloch oscillations is smaller than the electronic separation.
“When the external force F is applied, in the latter case the two particles basically undergo independent BOs with a characteristic period given by T B = 2 π/ ( Fa ), provided that the amplitude of BOs is smaller than the electronic separation.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Interpretationcitation§ Photonic Bloch oscillations of correlated particles · p. 1Such a structure could be realized by femtosecond laser writing in fused silica, in which the defect line is readily obtained by varying the writing speed of the laser beam.
“Such a structure could be realized, for instance, by femtosecond laser writing in fused silica, in which the defect line is readily obtained by varying the writing speed of the laser beam (see, for instance, [6,20]).”
Quote in the paperNot a substantial claim0 of 2 sources checkedProbably not a substantial claim: may not pass S3 (load-bearing).
Interpretationnone given§ Photonic Bloch oscillations of correlated particles · p. 2The Gaussian initial condition of the two electrons is readily realized in the optical system by initial excitation of the array, at the s = 0 input plane, with a Gaussian beam of spot size wa at normal incidence at the lattice sites (n0, m0).
“Such an initial condition is readily realized in the optical system by initial excitation of the array, at the s = 0 input plane, with a Gaussian beam of spot size wa with normal incidence at the lattice sites ( n 0 , m 0 )”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S4 (based).
Premisenone given§ Photonic Bloch oscillations of correlated particles · p. 1Experiments aimed to observe Bloch oscillations of few correlated electrons or bosons are rather difficult to perform in semiconductor superlattices or cold atoms, where the many-particle regime is generally of easier access.
“Experiments aimed to observe BOs of few correlated electrons or bosons are rather difficult to be performed in semiconductor superlattices or cold atoms, where the many particle regime is generally of easier access.”
Quote in the paperNot a substantial claimMay combine two claims.
Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 2The frequency-doubled component is more pronounced for U ∼ 4κ, i.e. at the interaction strength at which the two lattice bands start to separate, whereas it vanishes in the low and strong coupling limits.
“In particular, the frequency-doubled component is more pronounced for U ∼ 4 κ , i.e. at the interaction strength at which the two lattice bands starts to separate each other, whereas it vanishes in the low and strong coupling limits [17].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17] Dias, 2007, Phys. Rev. B source
Not checked in the free run.
May combine two claims.
Premisecitation§ Photonic Bloch oscillations of correlated particles · p. 1Novel phenomena are predicted for Bloch oscillations of few interacting particles, such as the frequency doubling of Bloch oscillations of two correlated electrons.
“interesting novel phenomena are predicted for BOs of few interacting particles [16, 17, 19], such as the frequency doubling of BOs of two correlated electrons [16,17].”
Quote in the paperSubstantial claim0 of 3 sources checked
The authors state this as an assumption.
The two electrons have opposite spins (singlet state), so as to allow double occupancy of the on-site orbital.
“In order to allow for double occupancy of the on-site orbital, the two electrons are assumed to have opposite spins (singlet state).”
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Longhi, S. (2012) · Physical Review B · doi:10.1103/physrevb.86.075144 · Cited by 24 · see citing works
Self-citationTopology and Interactions in the photonic Creutz and Creutz-Hubbard ladders
Zurita, J., Creffield, C. E., & Platero, G. (2020) · Docta Complutense (Universidad Complutense de Madrid) · Cited by 22 · see citing works
Anyons in one-dimensional lattices: a photonic realization
Longhi, S., & Valle, G. D. (2012) · Optics Letters · doi:10.1364/ol.37.002160 · Cited by 22 · see citing works
Self-citationTunneling control of strongly correlated particles on a lattice: a photonic realization
Longhi, S., & Valle, G. D. (2011) · Optics Letters · doi:10.1364/ol.36.004743 · Cited by 20 · see citing works
Self-citationProbing the effect of interaction in Anderson localization using linear photonic lattices
Lee, C., Rai, A., Noh, C., & Angelakis, D. G. (2014) · Physical Review A · doi:10.1103/physreva.89.023823 · Cited by 21 · see citing works
Arbitrary synthetic dimensions via multiboson dynamics on a one-dimensional lattice
Cheng, D., Peng, B., Wang, D., Chen, X., Yuan, L., & Fan, S. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033069 · Cited by 19 · see citing works
Gorlach, M. A., Liberto, M. F. D., Recati, A., Carusotto, I., Poddubny, A. N., & Menotti, C. (2018) · Physical Review A · doi:10.1103/physreva.98.063625 · Cited by 17 · see citing works
Multi-particle quantum walks on 3D integrated photonic chip
Zhou, W.-H., Wang, X.-W., Ren, R.-J., Fu, Y.-X., Chang, Y.-J., Xu, X.-Y., Tang, H., & Jin, X.-M. (2024) · Light: Science & Applications · doi:10.1038/s41377-024-01627-7 · Cited by 16 · see citing works
Photonic lattice simulation of dissipation-induced correlations in bosonic systems
Rai, A., Lee, C., Noh, C., & Angelakis, D. G. (2015) · Scientific Reports · doi:10.1038/srep08438 · Cited by 15 · see citing works
Many-body dynamic localization of strongly correlated electrons in ac-driven Hubbard lattices
Longhi, S. (2012) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/24/43/435601 · Cited by 13 · see citing works
Self-citationBloch oscillations of multimagnon excitations in a Heisenberg XXZ chain
Liu, W., Ke, Y., Zhang, L., & Lee, C. (2019) · Physical Review A · doi:10.1103/physreva.99.063614 · Cited by 13 · see citing works
Acoustic Bound Pairs under Nonreciprocal Two-Body Interactions
Pu, Z., Xi, Y., Tang, Y., Lu, J., Deng, W., Cheng, H., Ke, M., Chen, S., & Liu, Z. (2026) · Physical Review Letters · doi:10.1103/xr3h-j9pv · Cited by 11 · see citing works
Nonlinear wave-packet dynamics resonantly driven by AC and DC fields
Pereira, A. L. S., Lyra, M. L., de Moura, F. A. B. F., Neto, A. R., & Dias, W. S. (2018) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2018.04.016 · Cited by 9 · see citing works
Klein tunneling of two correlated bosons
Longhi, S., & Della Valle, G. (2013) · The European Physical Journal B · doi:10.1140/epjb/e2013-40154-8 · Cited by 9 · see citing works
Self-citationTwo-body bound and edge bound states in a ladder lattice with synthetic flux
Zheng, Y., & Yang, S.-J. (2023) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/1361-6455/acd66f · Cited by 8 · see citing works
Classical simulation of the Hubbard-Holstein dynamics with optical waveguide lattices
Longhi, S., & Valle, G. D. (2011) · Physical Review B · doi:10.1103/physrevb.84.155101 · Cited by 7 · see citing works
Self-citationEffects of Peierls phases in open linear chains
Marques, A. M. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.115156 · Cited by 6 · see citing works
Anti-Newtonian dynamics and self-induced Bloch oscillations of correlated particles
Longhi, S. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/11/113076 · Cited by 6 · see citing works
Self-citationThe role of on-site and nearest-neighbor interactions in the correlated two-particles quantum walk
Peixoto, A., & Dias, W. S. (2016) · Solid State Communications · doi:10.1016/j.ssc.2016.04.027 · Cited by 6 · see citing works
Dias, W. S., de Moura, F. A. B. F., & Lyra, M. L. (2016) · Physical Review A · doi:10.1103/physreva.93.023623 · Cited by 6 · see citing works
Anti-Newtonian dynamics and self-induced Bloch oscillations of correlated particlesPreprint
Longhi, S. (2016) · Cited by 6 · see citing works
Self-citationPeixoto, A., Dias, W. S., Lyra, M. L., & de Moura, F. A. B. F. (2013) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2013.10.039 · Cited by 3 · see citing works
A photonic crystal realization of a phase driven two-level atom
Rodríguez-Lara, B. M., Cárdenas, A. Z., Soto, F., & Moya-Cessa, H. M. (2012) · Optics Communications · doi:10.1016/j.optcom.2012.11.072 · Cited by 5 · see citing works
Zhang, H. P., & Song, Z. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.064310 · Cited by 3 · see citing works
Observing two-particle Anderson localization in linear disordered photonic lattices
Xing, Y., Zhao, X., Lü, Z., Liu, S., Zhang, S., & Wang, H.-F. (2021) · Optics Express · doi:10.1364/oe.446007 · Cited by 3 · see citing works
Quench field sensitivity of two-particle correlation in a Hubbard model
Zhang, X. Z., Lin, S., & Song, Z. (2016) · Scientific Reports · doi:10.1038/srep27189 · Cited by 3 · see citing works
Lasmar, Z., Sajna, A. S., Lee, S., & Kurzyński, P. (2018) · Physical Review A · doi:10.1103/physreva.98.062105 · Cited by 3 · see citing works
Cooperative bound states in quantum walks of interacting particles
Oliveira, M. F. V., SANTOS, M. S., Bertoldo-Coêlho, M., de Moura, F. A. B. F., & Dias, W. S. (2024) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2024.129697 · Cited by 2 · see citing works
Engineered Kerr nonlinearities for precise quantum control of Fock states
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Non-diffracting optical Bloch oscillations in hexagonal photonic lattices
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Electron pairing in periodic potentials under an external electric field
Gaul, C., Rodríguez, A., Lima, R. P. A., & Domínguez-Adame, F. (2013) · Physical Review B · doi:10.1103/physrevb.87.224306 · Cited by 1 · see citing works
Formation of generalized Wannier-Stark ladders: Theorem and applications
Zhang, H. P., & Song, Z. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.014313 · Cited by 1 · see citing works
Two-Dimensional Quantum Walk of Correlated PhotonsPreprint
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Photon pair generation in quadratic waveguide arrays: A classical optical simulation
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Classical Optical Simulation of Bi-Photon Generation in Quadratic Waveguide Arrays
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Acoustic Bound Pair States in the Continuum Induced by Off-Site Two-Body Interactions
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- Authors
- Longhi, S.
- Affiliations
- Politecnico di Milano (IT)
- Corresponding author
- Longhi, Stefano
- ORCID
- Longhi, Stefano
- Venue
- Optics Letters
- Publisher
- Optica Publishing Group
- Published
- 2011-08-15
- Volume
- 36
- Issue
- 16
- Pages
- 3248
- ISSN
- 0146-9592 (ISSN-L)
- 1539-4794
- OpenAlex
- W2065847930
- Semantic Scholar
- e7f14a6b77d81666313d29a256d1cbf770b42c14
- Cited by
- 61
- References
- 21
- Citations by year
- 2026: 4 · 2025: 2 · 2024: 5 · 2023: 4 · 2021: 3 · 2020: 4 · 2019: 3 · 2018: 4 · 2017: 2 · 2016: 7 · 2015: 1 · 2014: 4 · 2013: 6 · 2012: 10
- FWCI
- 5.37
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Optics Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Virtual Community of Pathological Anatomy (University of Castilla La Mancha) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Italian Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) (PRIN-2008-YCAAK)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Photonic Systems
- Physical Sciences › Physics and Astronomy › Acoustics and Ultrasonics › Random lasers and scattering media
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Keywords
- correlated electrons, electron-electron interaction, one-dimensional periodic lattice, line defects, second harmonic generation
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