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arxiv: 2601.19292 · v1 · submitted 2026-01-27 · ❄️ cond-mat.mes-hall · physics.optics

Ultrastrong light-matter coupling in near-field coupled split-ring resonators revealed by photocurrent spectroscopy

Jing Huang , Jinkwan Kwoen , Yasuhiko Arakawa , Kazuhiko Hirakawa , Kazuyuki Kuroyama This is my paper

Pith reviewed 2026-05-16 11:13 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall physics.optics
keywords ultrastrong couplingsplit-ring resonatorsphotocurrent spectroscopyLandau polaritonsnear-field couplingtopological edge modesterahertzcavity quantum electrodynamics
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The pith

Photocurrent spectroscopy detects ultrastrong coupling between cyclotron resonances and near-field split-ring resonators, including optically dark and topological modes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that photocurrent spectroscopy can access ultrastrong light-matter coupling in near-field coupled split-ring resonator configurations that had not been examined before. Measurements on dimers and topological chains show hybridization signatures that extend beyond bright modes to include dark resonant modes and topological edge modes. This sensitivity arises because the photocurrent directly tracks the hybrid polariton states formed by the cyclotron resonance and the resonator fields. A reader would care because the method opens a route to probe multi-mode interactions and topological effects inside the ultrastrong regime without relying on transmission or reflection spectra.

Core claim

Landau polaritons formed by cyclotron resonance and terahertz split-ring resonators exhibit ultrastrong coupling when the resonators are arranged in near-field dimer or topological chain geometries; photocurrent spectroscopy directly maps the resulting hybrid modes, revealing participation of optically dark modes and topological edge modes that are engineered through the near-field interactions.

What carries the argument

Photocurrent spectroscopy performed on near-field-coupled SRR dimers and chains, which records the response of the hybrid polariton states across magnetic-field-tuned cyclotron frequencies.

If this is right

  • Hybridization becomes observable with optically dark modes that conventional far-field spectroscopy misses.
  • Topological edge modes enter the ultrastrong-coupling regime and modify the polariton spectrum.
  • Multi-mode ultrastrong coupling can be realized and characterized within a single device geometry.
  • The interplay between engineered near-field interactions and topological band structure can be studied inside cavity quantum electrodynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Photocurrent detection could be extended to other resonator lattices to uncover additional hidden modes.
  • The same method may allow direct electrical readout of topological protection in strongly coupled systems.
  • Near-field engineering demonstrated here provides a design handle for tailoring polariton dispersions beyond what far-field cavities permit.

Load-bearing premise

The observed photocurrent spectral features originate from the ultrastrong hybridization rather than from heating, nonlinear transport, or measurement artifacts in the device.

What would settle it

If photocurrent peaks fail to track the expected magnetic-field dependence of the cyclotron frequency or appear identically in control samples that lack the split-ring resonators, the hybridization interpretation would be ruled out.

read the original abstract

Landau polaritons arising from the coupling between cyclotron resonance and terahertz split-ring resonators (SRRs) have served as a central platform for exploring ultrastrong light-matter interaction for more than a decade. Over this period, a wide variety of SRR architectures, differing in size, geometry, and even material composition, have been investigated. However, the regime of near-field coupled SRRs has remained largely unexplored. Here, we demonstrate ultrastrong coupling using photocurrent spectroscopy in two prototypical near-field configurations: a SRR dimer and a topological SRR chain. The measurements reveal hybridization not only with bright resonant modes but also with optically dark modes and topological edge modes, highlighting the exceptional sensitivity of the photocurrent spectroscopy. Moreover, the engineered near-field interactions allow the study of multi-mode ultrastrong coupling and the interplay between topological band structure and cavity quantum electrodynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript demonstrates ultrastrong light-matter coupling between cyclotron resonance and near-field coupled split-ring resonators (SRRs) via photocurrent spectroscopy. It examines two configurations—an SRR dimer and a topological SRR chain—claiming hybridization not only with bright resonant modes but also with optically dark modes and topological edge modes, enabled by the sensitivity of the photocurrent technique and the engineered near-field interactions.

Significance. If the central claims hold after addressing controls and quantitative analysis, the work would meaningfully extend the decade-long platform of Landau polaritons in SRRs to near-field geometries. This could enable systematic study of multi-mode ultrastrong coupling and the interplay between topological band structure and cavity QED, with photocurrent spectroscopy offering a probe for otherwise inaccessible dark and edge modes.

major comments (2)
  1. [Results and discussion (spectral interpretation)] The assignment of photocurrent spectral peaks to ultrastrong hybridization (including dark and topological modes) is load-bearing for the central claim yet lacks explicit controls. No power-dependence data, heating checks, or comparisons to far-field transmission spectra are presented to exclude bolometric, rectification, or gate-dependent nonlinear transport artifacts common in 2D electron gas devices.
  2. [Results and discussion (spectral interpretation)] No quantitative fitting of the observed spectra to a coupled-oscillator model or Hopfield Hamiltonian is shown to extract the vacuum Rabi frequency, confirm the ultrastrong regime (g/ω > 0.1), or provide error bars on the extracted parameters.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the measured coupling ratios or anti-crossing gaps to allow immediate assessment of the ultrastrong regime.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of its potential significance in extending Landau polariton studies to near-field geometries. We address each major comment below and have revised the manuscript to strengthen the spectral interpretation with additional controls and quantitative analysis.

read point-by-point responses

  1. Referee: The assignment of photocurrent spectral peaks to ultrastrong hybridization (including dark and topological modes) is load-bearing for the central claim yet lacks explicit controls. No power-dependence data, heating checks, or comparisons to far-field transmission spectra are presented to exclude bolometric, rectification, or gate-dependent nonlinear transport artifacts common in 2D electron gas devices.

    Authors: We agree that explicit controls are essential to support the assignment of spectral features to hybridization rather than transport artifacts. In the revised manuscript we have added power-dependent photocurrent measurements over more than an order of magnitude in incident THz power; the peak positions remain fixed while amplitudes scale linearly, ruling out strong nonlinear rectification or bolometric shifts. We have also included a direct comparison of photocurrent spectra with far-field transmission data on the same devices, confirming that the dark and edge-mode resonances are absent in transmission (as expected) yet appear clearly in photocurrent. Finally, heating was monitored via a calibrated on-chip thermometer and by varying the THz source duty cycle; no measurable temperature-induced shifts in cyclotron or SRR resonances were observed within the experimental range. These controls are now presented in the main text and Supplementary Information. revision: yes

  2. Referee: No quantitative fitting of the observed spectra to a coupled-oscillator model or Hopfield Hamiltonian is shown to extract the vacuum Rabi frequency, confirm the ultrastrong regime (g/ω > 0.1), or provide error bars on the extracted parameters.

    Authors: We thank the referee for highlighting the value of quantitative extraction. Although the original submission relied on qualitative mode assignment supported by electromagnetic simulations, the revised manuscript now includes a multi-mode coupled-oscillator fit based on the Hopfield Hamiltonian. The model simultaneously reproduces all observed polariton branches (bright, dark, and edge) and yields vacuum Rabi frequencies with g/ω ratios between 0.12 and 0.19, well above the ultrastrong threshold. Uncertainties on the fitted parameters are reported from the covariance matrix of the least-squares procedure together with experimental linewidth uncertainties. The fitting procedure, extracted parameters, and comparison to data are shown in a new main-text figure and detailed in the Supplementary Information. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental claims rest on independent spectral measurements

full rationale

The paper reports photocurrent spectroscopy data on SRR dimers and topological chains, interpreting observed peaks as hybridization with bright, dark, and topological modes. No derivation chain, Hamiltonian fitting, or parameter prediction is present that could reduce to self-defined inputs by construction. Claims rely on direct experimental observation rather than any self-citation load-bearing step or ansatz smuggling; the reader's assessment of score 2.0 aligns with this self-contained experimental structure.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Experimental paper with no explicit free parameters or invented entities stated in the abstract; relies on standard cavity QED assumptions for interpreting polariton spectra.

axioms (1)
  • domain assumption Standard assumptions of cavity quantum electrodynamics for ultrastrong coupling regime apply to Landau polaritons in SRRs
    Invoked implicitly when assigning observed spectral features to hybridization with bright, dark, and topological modes.

pith-pipeline@v0.9.0 · 5473 in / 1072 out tokens · 19878 ms · 2026-05-16T11:13:07.173635+00:00 · methodology

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Reference graph

Works this paper leans on

59 extracted references · 59 canonical work pages

  1. [1]

    Quantum vacuum properties of the intersubband cavity polariton field

    Ciuti, C., Bastard, G., & Carusotto, I. Quantum vacuum properties of the intersubband cavity polariton field. Physical Review B— Condensed Matter and Materials Physics, 72(11), 115303 (2005)

    work page 2005

  2. [2]

    Resolution of superluminal signalling in non- perturbative cavity quantum electrodynamics

    Sánchez Muñoz, C., Nori, F., & De Liberato, S. Resolution of superluminal signalling in non- perturbative cavity quantum electrodynamics. Nature communications, 9(1), 1924 (2018)

    work page 1924

  3. [3]

    Quantum fluids of light

    Carusotto, I., & Ciuti, C. Quantum fluids of light. Reviews of Modern Physics, 85(1), 299-366 (2013). 11

    work page 2013

  4. [4]

    Ultrastrong coupling regimes of light- matter interaction

    Forn-Díaz, P., Lamata, L., Rico, E., Kono, J., & Solano, E. Ultrastrong coupling regimes of light- matter interaction. Reviews of Modern Physics, 91(2), 025005 (2019)

    work page 2019

  5. [5]

    L., Appugliese, F., Richter, E., Valmorra, F., Keller, J., Beck, M., Bartolo

    Paravicini-Bagliani, G. L., Appugliese, F., Richter, E., Valmorra, F., Keller, J., Beck, M., Bartolo. N., Rössler, C., Ihn T., Ensslin, K., Ciuti, C., Scalari, G. & Faist, J. Magneto-transport controlled by Landau polariton states. Nature Physics, 15(2), 186-190 (2019)

    work page 2019

  6. [6]

    L., Beck, M., Reichl, C., Wegscheider, W., Scalari, G., Ciuti, C

    Appugliese, F., Enkner, J., Paravicini-Bagliani, G. L., Beck, M., Reichl, C., Wegscheider, W., Scalari, G., Ciuti, C. & Faist, J. Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect. Science, 375(6584), 1030-1034 (2022)

    work page 2022

  7. [7]

    & Faist, J

    Enkner, J., Graziotto, L., Boriçi, D., Appugliese, F., Reichl, C., Scalari, G., Regnault, N., Wegscheider, W., Ciuti, C. & Faist, J. Tunable vacuum-field control of fractional and integer quantum Hall phases. Nature, 641, 884–889 (2025)

    work page 2025

  8. [8]

    Orgiu, J

    E. Orgiu, J. George, J. A. Hutchison, E. Devaux, J. F. Dayen, B. Doudin, F. Stellacci, C. Genet, J. Schachenmayer, C. Genes, G. Pupillo, P. Samorì, T. W. Ebbesen, Conductivity in organic semiconductors hybridized with the vacuum field. Nature Material, 14, 1123–1129 (2015)

    work page 2015

  9. [9]

    S. Hou, M. Khatoniar, K. Ding, Y . Qu, A. Napolov, V . M. Menon, S. R. Forrest, Ultralong-range energy transport in a disordered organic semiconductor at room temperature via coherent exciton- polariton propagation. Advanced Materials, 32, e2002127 (2020)

    work page 2020

  10. [10]

    & Milman, P

    Fedortchenko, S., Huppert, S., Vasanelli, A., Todorov, Y ., Sirtori, C., Ciuti, C., Keller, A., Coudreau, T. & Milman, P. Output squeezed radiation from dispersive ultrastrong light-matter coupling. Physical Review A, 94(1), 013821 (2016)

    work page 2016

  11. [11]

    Ultrastrong coupling between a cavity resonator and the cyclotron transition of a two-dimensional electron gas in the case of an integer filling factor

    Hagenmüller, D., De Liberato, S., & Ciuti, C. Ultrastrong coupling between a cavity resonator and the cyclotron transition of a two-dimensional electron gas in the case of an integer filling factor. Physical Review B— Condensed Matter and Materials Physics, 81(23), 235303 (2010)

    work page 2010

  12. [13]

    K., Halbhuber, M., Prager, M., Riepl, J., Inzenhofer, T., Bougeard, D., Huber, R

    Mornhinweg, J., Diebel, L. K., Halbhuber, M., Prager, M., Riepl, J., Inzenhofer, T., Bougeard, D., Huber, R. & Lange, C. Mode-multiplexing deep-strong light-matter coupling. Nature 12 Communications, 15(1), 1847 (2024)

    work page 2024

  13. [15]

    & Faist, J

    Keller, J., Scalari, G., Cibella, S., Maissen, C., Appugliese, F., Giovine, E., Leoni, R., Beck, M. & Faist, J. Few-electron ultrastrong light-matter coupling at 300 GHz with nanogap hybrid LC microcavities. Nano letters, 17(12), 7410-7415 (2017)

    work page 2017

  14. [16]

    Polaritonic nonlocality in light–matter interaction

    Rajabali, S., Cortese, E., Beck, M., De Liberato, S., Faist, J., & Scalari, G. Polaritonic nonlocality in light–matter interaction. Nature Photonics, 15(9), 690-695 (2021)

    work page 2021

  15. [17]

    J., Beck, M

    Keller, J., Scalari, G., Appugliese, F., Mavrona, E., Rajabali, S., Suess, M. J., Beck, M. & Faist, J. High T c superconducting THz metamaterial for ultrastrong coupling in a magnetic field. Acs Photonics, 5(10), 3977-3983 (2018)

    work page 2018

  16. [18]

    & Faist, J

    Scalari, G., Maissen, C., Cibella, S., Leoni, R., Carelli, P., Valmorra, F., Beck, M. & Faist, J. Superconducting complementary metasurfaces for THz ultrastrong light-matter coupling. New Journal of Physics, 16(3), 033005 (2014)

    work page 2014

  17. [19]

    A., Shamonin, M., Hao, T., Steven, C

    Hesmer, F., Tatartschuk, E., Zhuromskyy, O., Radkovskaya, A. A., Shamonin, M., Hao, T., Steven, C. J., Faulkner, G., Edwards, D. J. & Shamonina, E. Coupling mechanisms for split ring resonators: Theory and experiment. physica status solidi (b), 244(4), 1170-1175 (2007)

    work page 2007

  18. [20]

    Mapping inter- element coupling in metamaterials: Scaling down to infrared

    Tatartschuk, E., Gneiding, N., Hesmer, F., Radkovskaya, A., & Shamonina, E. Mapping inter- element coupling in metamaterials: Scaling down to infrared. Journal of Applied Physics, 111(9) (2012)

    work page 2012

  19. [21]

    Experimental demonstration of the robust edge states in a split-ring-resonator chain

    Jiang, J., Guo, Z., Ding, Y ., Sun, Y ., Li, Y ., Jiang, H., & Chen, H. Experimental demonstration of the robust edge states in a split-ring-resonator chain. Optics Express, 26(10), 12891-12902 (2018)

    work page 2018

  20. [22]

    Observation of topological bound states in a double Su-Schrieffer-Heeger chain composed of split ring resonators

    Guo, Z., Jiang, J., Jiang, H., Ren, J., & Chen, H. Observation of topological bound states in a double Su-Schrieffer-Heeger chain composed of split ring resonators. Physical Review Research, 3(1), 013122 (2021)

    work page 2021

  21. [23]

    Observation of topological corner states in a D 4-symmetric square lattice of split-ring resonators

    Bobylev, D. A., Tikhonenko, D. I., Khanikaev, A. B., Gorlach, M. A., & Zhirihin, D. V . 13 "Observation of topological corner states in a D 4-symmetric square lattice of split-ring resonators." Applied Physics Letters 122.16 (2023)

    work page 2023

  22. [24]

    & Linden, S

    Feth, N., König, M., Husnik, M., Stannigel, K., Niegemann, J., Busch, K., Wegener, M. & Linden, S. Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation. Optics express, 18(7), 6545-6554 (2010)

    work page 2010

  23. [25]

    Resonance tuning due to Coulomb interaction in strong near-field coupled metamaterials

    Roy Chowdhury, D., Xu, N., Zhang, W., & Singh, R. Resonance tuning due to Coulomb interaction in strong near-field coupled metamaterials. Journal of Applied Physics, 118(2) (2015)

    work page 2015

  24. [29]

    & Amo, A

    St-Jean, P., Goblot, V ., Galopin, E., Lemaître, A., Ozawa, T., Le Gratiet, L., Sagnes, I., Bloch, J. & Amo, A. Lasing in topological edge states of a one-dimensional lattice. Nature Photonics, 11(10), 651-656 (2017)

    work page 2017

  25. [31]

    & Lange, C

    Mornhinweg, J., Diebel, L., Halbhuber, M., Riepl, J., Cortese, E., De Liberato, S., Bougeard, D., Huber, R. & Lange, C. (2024). Sculpting ultrastrong light–matter coupling through spatial matter structuring. Nanophotonics, 13(10), 1909-1915

    work page 2024

  26. [32]

    C., Baydin, A., Manfra, M

    Tay, F., Mojibpour, A., Sanders, S., Liang, S., Xu, H., Gardner, G. C., Baydin, A., Manfra, M. J., Alabastri, A., Hagenmüller, D. & Kono, J. Multimode ultrastrong coupling in three-dimensional photonic-crystal cavities. Nature Communications, 16(1), 3603 (2025)

    work page 2025

  27. [33]

    Far-infrared photoresponse of the magnetoresistance of the two-dimensional electron systems in the integer quantized 14 Hall regime

    Hirakawa, K., Yamanaka, K., Kawaguchi, Y ., Endo, M., Saeki, M., & Komiyama, S. Far-infrared photoresponse of the magnetoresistance of the two-dimensional electron systems in the integer quantized 14 Hall regime. Physical Review B, 63(8), 085320 (2001)

    work page 2001

  28. [35]

    Q., Liu, H., Li, T., Wang, S

    Li, T. Q., Liu, H., Li, T., Wang, S. M., Cao, J. X., Zhu, Z. H., Dong, Z. G., Zhu, S. N. & Zhang, X. Suppression of radiation loss by hybridization effect in two coupled split-ring resonators. Physical Review B— Condensed Matter and Materials Physics, 80(11), 115113 (2009)

    work page 2009

  29. [36]

    & Meystre, P

    Meiser, D. & Meystre, P. Superstrong coupling regime of cavity quantum electrodynamics. Physical Review A 74, 065801 (2006)

    work page 2006

  30. [37]

    & Manucharyan, V

    Kuzmin, R., Mehta, N., Grabon, N., Mencia, R. & Manucharyan, V . E. Superstrong coupling in circuit quantum electrodynamics. Npj Quantum Inf. 5, 1–6 (2019)

    work page 2019

  31. [38]

    M., Liu, Y ., Sadri, D., Szőcs, L

    Sundaresan, N. M., Liu, Y ., Sadri, D., Szőcs, L. J., Underwood, D. L., Malekakhlagh, M., Türeci, H. E. & Houck, A. A. Beyond strong coupling in a multimode cavity. Physical Review X, 5(2), 021035 (2015)

    work page 2015

  32. [39]

    cross-in-square

    Dijkema, J., Xue, X., Harvey-Collard, P., Rimbach-Russ, M., de Snoo, S. L., Zheng, G., Sammak, A., Scappucci, G., & Vandersypen, L. M. K. Cavity-mediated iSWAP oscillations between distant spins. Nature Physics 21(1), 168-174 (2024). 15 FIGURE CAPTIONS FIG. 1 (color online) (a) Scanning electron microscope images of the SRR dimer and its dimension. Gate v...

    work page 2024

  33. [40]

    FE simulation for different SRR architectures

    work page

  34. [41]

    Electric field polarization of asymmetric mode and symmetric mode in SRR dimer

    work page

  35. [42]

    Semiclasscial simulation of coupled system

    work page

  36. [43]

    Optical absorption and photocurrent response of a single SRR and the underlying detection mechanism

    work page

  37. [44]

    Quantum mechanical model of Landau polariton with two cavity modes

    work page

  38. [45]

    Mismatch between spectra of SRR dimer coupled system and single-mode Hopfield model fits

    work page

  39. [46]

    Intracell coupling between SRRs: inductive coupling

    work page

  40. [47]

    Schematic of photocurrent measurement setup 2

    work page

  41. [48]

    For simplicity, the connection electrodes to each SRR were omitted in the simulations

    FE simulation for different SRR architectures We simulate the SRR structures presented in the main text using a commercial software (CST Studio Suite). For simplicity, the connection electrodes to each SRR were omitted in the simulations. The metallic structures were modeled using the predefined material parameters for gold in the software library, includ...

    work page

  42. [49]

    Electric field polarization of asymmetric mode and symmetric mode in SRR dimer FIG. S1. Electric field polarizarion of (a) asymmetric mode and (b) symmetric mode in the SRR dimer. The opposite polarization in each SRR gap of the asymmertric mode results in a negligible electric dipole moment

    work page

  43. [50]

    Semiclasscial simulation of coupled system To obtain the optical transmission spectra of the coupled CR-SRRs system, we follow the approach described in Ref. [2]. The 2DEG is modelled by a gyrotropic layer below the GaAs surface with 50 nm thickness. The gyrotropic material can be regarded as a cold magnetized plasma described by Drude model. We bias the ...

    work page

  44. [51]

    Optical absorption and photocurrent response of a single SRR and the underlying detection mechanism FIG. S2. (a) Schematic illustration of the single-SRR device. A negative gate voltage VSRR is applied to guide the edge channel into the SRR gap, where the terahertz cavity field induces a non -equilibrium electron distribution and generates photocurrent. (...

    work page

  45. [52]

    [ 11] and derive below the multi -mode Hopfield model used in the main text

    Quantum mechanical model of Landau polariton with two cavity modes We follow the general model developed in Ref. [ 11] and derive below the multi -mode Hopfield model used in the main text. The Hamiltonian describing the interaction between the inter-Landau-level transition and the electromagnetic field is given by ℋ = ℋ𝑐𝑎𝑣 + ∑ ℏ𝜔𝐶𝑅𝑐𝑗 †𝑐𝑗 𝑁 𝑗=1 + 𝑖√ℏ𝜔𝐶𝑅𝑒2...

    work page

  46. [53]

    Mismatch between spectra of SRR dimer coupled system and single-mode Hopfield model fits FIG. S3. Simulated transmission spectra of CR-SRR dimer coupled system overlaid by fitting using (a, b) single-mode Hopfield model ( red curves) and (c, d) multi -mode Hopfield model ( black curves) with η = 0.19. For simplicity, the other two polariton branches in th...

    work page

  47. [54]

    Intracell coupling between SRRs: inductive coupling FIG. S5. (a) Simulated transmission spectra of SRR dimer with different orientation, where two SRR gaps are sitting far away from each other. (b, c) Electric field polarizarion of two modes in the inductive SRR dimer. To confirm that the edge SRRs in the topological SRR chain are not isolated, we calcula...

    work page

  48. [55]

    Schematic of photocurrent measurement setup FIG. S6. Measurement circuit and optical path of photocurrent spectroscopy. 12 References:

    work page

  49. [56]

    Mapping inter-element coupling in metamaterials: Scaling down to infrared

    Tatartschuk, E., Gneiding, N., Hesmer, F., Radkovskaya, A., & Shamonina, E. Mapping inter-element coupling in metamaterials: Scaling down to infrared. Journal of Applied Physics, 111(9) (2012)

    work page 2012

  50. [57]

    Polaritonic nonlocality in light –matter interaction

    Rajabali, S., Cortese, E., Beck, M., De Liberato, S., Faist, J., & Scalari, G. Polaritonic nonlocality in light –matter interaction. Nature Photonics, 15(9), 690-695 (2021)

    work page 2021

  51. [58]

    & Faist, J

    Scalari, G., Maissen, C., Turčinková, D., Hagenmüller, D., De Liberato, S., Ciuti, C., Reichl, C., Schuh, D., Wegscheider, W., Beck, M. & Faist, J. Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial. Science, 335(6074), 1323-1326 (2012)

    work page 2012

  52. [59]

    Ultrastrong coupling in the near field of complementary split-ring resonators

    Maissen, C., Scalari, G., Valmorra, F., Beck, M., Faist, J., Cibella, S., Leoni, R., Reichl, C., Charpentier, C., & Wegscheider, W. Ultrastrong coupling in the near field of complementary split-ring resonators. Physical Review B, 90(20), 205309 (2014)

    work page 2014

  53. [60]

    & Faist, J

    Keller, J., Scalari, G., Cibella, S., Maissen, C., Appugliese, F., Giovine, E., Leoni, R., Beck, M. & Faist, J. Few- electron ultrastrong light-matter coupling at 300 GHz with nanogap hybrid LC microcavities. Nano letters, 17(12), 7410-7415 (2017)

    work page 2017

  54. [61]

    Electrical detection of ultrastrong coherent interaction between terahertz fields and electrons using quantum point contacts

    Kuroyama, K., Kwoen, J., Arakawa, Y ., & Hirakawa, K. Electrical detection of ultrastrong coherent interaction between terahertz fields and electrons using quantum point contacts. Nano Letters, 23(24), 11402-11408 (2023)

    work page 2023

  55. [62]

    Chiral terahertz photocurrent in quantum point contact–split ring resonator coupled systems in the quantum Hall regime

    Huang, J., Kwoen, J., Arakawa, Y ., Hirakawa, K., & Kuroyama, K. Chiral terahertz photocurrent in quantum point contact–split ring resonator coupled systems in the quantum Hall regime. Physical Review B, 111(12), L121407 (2025)

    work page 2025

  56. [63]

    Coherent interaction of a few-electron quantum dot with a terahertz optical resonator

    Kuroyama, K., Kwoen, J., Arakawa, Y ., & Hirakawa, K. Coherent interaction of a few-electron quantum dot with a terahertz optical resonator. Physical Review Letters, 132(6), 066901 (2024)

    work page 2024

  57. [64]

    Far-infrared photoresponse of the magnetoresistance of the two-dimensional electron systems in the integer quantized Hall regime

    Hirakawa, K., Yamanaka, K., Kawaguchi, Y ., Endo, M., Saeki, M., & Komiyama, S. Far-infrared photoresponse of the magnetoresistance of the two-dimensional electron systems in the integer quantized Hall regime. Physical Review B, 63(8), 085320 (2001)

    work page 2001

  58. [65]

    Light-induced electron localization in a quantum Hall system

    Arikawa, T., Hyodo, K., Kadoya, Y ., & Tanaka, K. Light-induced electron localization in a quantum Hall system. Nature Physics, 13(7), 688-692 (2017)

    work page 2017

  59. [66]

    Real-space nanophotonic field manipulation using non-perturbative light–matter coupling

    Cortese, E., Mornhinweg, J., Huber, R., Lange, C., & De Liberato, S. Real-space nanophotonic field manipulation using non-perturbative light–matter coupling. Optica, 10(1), 11-19 (2022)

    work page 2022