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[Quentin France](https://orcid.org/0009-0008-3035-966X), [Yunhyeon Jeong](https://orcid.org/0009-0004-0784-9151), Akinori Kamiyama, [Takaaki Mano](https://orcid.org/0000-0002-6955-260X), [Ken-ichi Sasaki](https://orcid.org/0000-0002-0658-4911), [Masahiro Hotta](https://orcid.org/0000-0003-1756-7401), [Go Yusa](https://orcid.org/0000-0003-3053-7629)

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[Electrically Induced Bulk and Edge Excitations in the Fractional Quantum Hall Regime](https://mdr.nims.go.jp/datasets/1ebf00e8-fa3e-4d95-a61e-7a12673e0b74)

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Electrically Induced Bulk and Edge Excitations in the Fractional Quantum Hall RegimeElectrically Induced Bulk and Edge Excitations in the Fractional Quantum Hall RegimeQuentin France ,1,2 Yunhyeon Jeong ,1 Akinori Kamiyama,1 Takaaki Mano,3 Ken-ichi Sasaki ,4Masahiro Hotta ,1,5 and Go Yusa 11Department of Physics, Tohoku University, Sendai 980-8578, Japan2Department of Physics, Sorbonne University, Paris 75005, France3National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan4NTT Basic Research Laboratories and NTT Research Center for Theoretical Quantum Information,NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan5Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan, Republic of China(Received 3 February 2025; revised 5 May 2025; accepted 7 July 2025; published 5 August 2025)We apply a voltage pulse to electrically excite the incompressible region of a two-dimensional electronliquid in the ν ¼ 2=3 fractional quantum Hall state and investigate the collective excitations in both the bulkand edge via photoluminescence spectral energy shifts. Introducing an offset in the voltage pulsesignificantly enhances the excitation signal. Real-space and time-resolved measurements reveal thedynamics of the bulk excitations, with an estimated group velocity of approximately 3 × 104 m=s. Thesebulk excitations align well with the magnetoplasmon model. Because bulk and edge magnetoplasmons arecomposed of two polarization degrees of freedom of the gauge field, our results highlight a connection thatcould serve as a resource for their entanglement—similar to the polarization of a photon—and offer a novelapproach to exploring solid-state analogs of quantum gravity.DOI: 10.1103/4bp5-9rygThe quantum Hall effect is a phenomenon observed in atwo-dimensional electron gas (2DEG) at low temperaturesand under the influence of a strong magnetic field B. In thisregime, the longitudinal resistance drops to zero while theHall resistance becomes quantized. This occurs when thefilling factor ν ¼ neh=eB, which represents the ratio of theelectron density ne to the magnetic flux quantum densityB=ðh=eÞ, is either an integer or a rational fraction [1,2].Here, h and e denote the Planck constant and the elemen-tary charge, respectively. The Hall resistance quantizes todiscrete values of h=νe2. The quantum Hall effect repre-sents the first example of a topological insulator, charac-terized by a bulk energy gap and gapless edge [3]. Bulkexcitations typically require energy above the gap, which,for the integer quantum Hall effect, corresponds to thecyclotron frequency ωc ¼ eB=m�, of the electron with aneffective mass m�. In the fractional quantum Hall (FQH)effect, collective neutral excitations known as magneto-rotons have been both theoretically predicted [4] andexperimentally observed through Raman scattering [5,6]and phonon absorption [7]. Recently, magnetorotonswith wave numbers near zero have been experimentallystudied [8], attracting renewed interest due to their antici-pated behavior as chiral gravitons with spin 2 [9,10].In contrast to the bulk, the edge can be excited withinfinitesimal energy due to the absence of an energy gap.Edge excitations propagate spatially along the edge overlong distances with suppressed dissipation [11–14]. Theseedge excitations, known as “edge magnetoplasmons,” arecharacterized by nearly free propagation with a groupvelocity vg, and their frequency is approximately linearin the wave vector k as ωðkÞ ¼ vgk. The unique propertiesof the edge have inspired proposals for innovative appli-cations, including quantum energy teleportation [13,15–17]and a quantum gravity simulator [17–20] that models anexpanding universe in (1þ 1) dimensions. Furthermore,the correlation between the bulk and the edge is ofsignificant importance when considering a condensedmatter analog of brane world scenario [21] in which thebulk corresponds to an extra dimension for the edge.The bulk-edge correspondence suggests that both thebulk and the edge provide valuable insights into thequantum Hall effect. We focus on extracting complemen-tary information from the bulk excitations of the ν ¼ 2=3FQH state, where the edge modes are known to exhibitconsiderable complexity [22,23]. We intentionally excitedthe bulk by efficiently stimulating the edge using a voltagepulse applied to an electrode connected to both the edgeand the bulk. Using a stroboscopic photoluminescence (PL)microscope [24,25], we captured the dynamics of thesebulk excitations. Our results reveal that the primary bulkPublished by the American Physical Society under the terms ofthe Creative Commons Attribution 4.0 International license.Further distribution of this work must maintain attribution tothe author(s) and the published article’s title, journal citation,and DOI.PHYSICAL REVIEW LETTERS 135, 066203 (2025)0031-9007=25=135(6)=066203(6) 066203-1 Published by the American Physical Societyhttps://orcid.org/0009-0008-3035-966Xhttps://orcid.org/0009-0004-0784-9151https://orcid.org/0000-0002-0658-4911https://orcid.org/0000-0003-1756-7401https://orcid.org/0000-0003-3053-7629https://ror.org/01dq60k83https://ror.org/02en5vm52https://ror.org/026v1ze26https://ror.org/01m2pas06https://ror.org/05bqach95https://crossmark.crossref.org/dialog/?doi=10.1103/4bp5-9ryg&domain=pdf&date_stamp=2025-08-05https://doi.org/10.1103/4bp5-9ryghttps://doi.org/10.1103/4bp5-9ryghttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/excitations consist of magnetoplasmons, which aredynamical electromagnetic gauge fields tightly bound tothe 2DEG under an external static magnetic field.Magnetoplasmons are intrinsically related to magnetoro-tons: the latter are derived from the lowest Landau levelprojection of the Hilbert space [4], while the former can bederived without this approximation [26]. Furthermore, thedispersion relation of magnetoplasmons is expressed asωðkÞ ¼ ωc þ vgk: ð1ÞAs will be shown later in Eq. (2), this vg has a simple formthat is determined solely by the quantized Hall resistanceand the permittivity of GaAs. Additionally, we observedanother type of bulk excitation with a velocity approx-imately an order of magnitude slower than the primary bulkexcitation. This secondary excitation can be interpreted as astrain pulse [27] that represents the bulk counterpart of anedge mode carrying heat [28].The measurements were conducted on a 15-nmGaAs=AlGaAs quantum well (QW). An nþ GaAs sub-strate served as a back gate electrode, allowing ne in theQW to be controlled by applying a voltage, Vb, to the backgate. This configuration enables ν to be set to 2=3 at variousB. The horizontal line labeled as the sample edge in Fig. 1corresponds to the ∼250-nm step of the mesa. The etchedregion in this image is located above this line, while thebulk region containing the 2DEG lies below this line. Theexcitation gate and the two ground pads (Fig. 1) werefabricated by evaporating Ti=Au over the GaAs surface.Scanning stroboscopic PL microscopy and spectroscopy(see Appendix A for more details) [24,25] were used toobserve the bulk and edge responses to the incoming acpulses transmitted through the excitation gate. All mea-surements were conducted at ν ¼ 2=3 and a temperatureT ¼ 40–55 mK unless otherwise specified. The ν ¼ 2=3FQH state exhibits a competition between the Zeeman andCoulomb energies, leading to a degeneracy between thespin-polarized (ferromagnetic) and unpolarized (nonmag-netic) phases at a critical magnetic field Bc. At Bc, a first-order phase transition occurs between these two phases[29–31], forming domains of these phases and their domainboundaries [31]. In our sample, Bc was determined to beapproximately 7.5 T based on the B dependence of the PLspectrum [32] [see Fig. S2 in Supplemental Material (SM)[33] for details]. A voltage pulse was applied to theexcitation gate using an AWG and a dc voltage source,connected via a bias tee (Fig. 1). This voltage pulse (Fig. 5)electrically excites electrons in both the edge and bulk.To maximize the visibility of the edge excitation, weapplied a voltage pulsewith an offsetVoffset and investigatedits impact on the PL spectrum (Fig. 2). The measurementpoint (PointA in Fig. 1)was located x ¼ 25 μmdownstreamfrom the excitation gate and y ¼ 2 μm away from thesample edge (mesa). PL spectra were recorded by varyingthe time delay t between the voltage pulse and the laserpulse, with Voffset as a parameter. Regardless of the Voffset,the PL peak exhibited a distinct blueshift around t ∼ 0.5 nscompared to the PL peak observed at t < 0 ns, when theedge excitation has not yet arrived [Figs. 2(a)–2(h)] [24].To analyze the PL peak energy shift, we fit the PL spectraat a given ðt; x; yÞ using a Lorentzian function and obtainedthe PL peak energy shift ΔEðt; x; yÞ at given ðt; x; yÞ(see Appendix B). Consistent with the PL spectra[Figs. 2(a)–2(h)], ΔE exhibits a distinct blueshift aroundt ∼ 0.5 ns, coinciding with the arrival of the edge excitationat the measurement point. Notably, the maximum value ofΔE increases as a function of Voffset, reaching more thanapproximately 0.1 meV. Based on this observation, weadopted Voffset ¼ 0.5 V for the subsequent experimentsdiscussed below.While scanning the spatial coordinates x and y aroundthe excitation gate, we captured the t dependence of the PLspectra at B ¼ 6 T. Since B < Bc, the ν ¼ 2=3 state is inthe spin-unpolarized phase. By mapping ΔE as a functionof x and y and using t as the time frame, we reconstructedmovies illustrating the propagation of the edge and bulkexcitations (see SM for movies recorded at B ¼ 6.5and 11.5 T).A single frame of the movie corresponds to the real-space map of ΔE at a given t [Figs. 3(a)–3(h)]. When thevoltage pulse is applied to the excitation gate, the PL fromthe downstream side of the edge exhibits a blueshift [darkblue region in Fig. 3(b)]. The edge excitation then prop-agates along the sample edge [dark blue region inFigs. 3(b)–3(e)]. Simultaneously, an excitation near thegate propagates toward the bulk [Figs. 3(b) and 3(c)].Notably, ΔE near the excitation gate redshifts [red regionsin Figs. 3(d)–3(g)], and this negative ΔE region alsospreads into the bulk.VoffsetMagnetic field B5 �mExcitation gateBulkChirality Sample edge (mesa)AWGPoint AyxFIG. 1. Scanning electron microscope image of a typicaldevice. The light and dark gray regions correspond to thedeposited Au electrodes and GaAs surface, respectively. Theexcitation gate is connected to an arbitrary waveform generator(AWG) and a dc voltage source, which provides an offset voltageVoffset to the pulse. The two electrodes connected to the groundand the excitation gate form a coplanar waveguide.PHYSICAL REVIEW LETTERS 135, 066203 (2025)066203-2To focus on the behavior of bulk excitations, in Fig. 3(i),we plot the dependence of ΔE on both t and the y axisperpendicular to the sample edge [see the dotted arrow inFig. 3(a)]. Two distinct modes of bulk excitations areclearly observed, corresponding to the strong blueshift andweak redshift regions. The ΔE at y ¼ 0 as a function of texhibits a sharp positive peak at t ∼ 0.5 ns with an FWHMof ∼1 ns and a negative peak at t ∼ 2–3 ns with an FWHMof ∼2 ns [Fig. 3(j)]. Near the excitation gate, the blueshiftexceeds 0.2 meV. The blueshift region extends toy ∼ 30–40 μm, while the redshift region remains relativelycloser to the excitation gate at y ∼ 20 μm.The group velocity vg of the bulk excitation is deter-mined by the reciprocal of the slope of the peaks in the y-tplot [illustrated by the dotted lines in Fig. 3(j)]. To extractthis, we measured both the steepest and flattest slopes,corresponding to the earlier and later borders of the blue-shifted region, respectively. The vg of the blueshifted peakranges from 104 to 105 m=s, whereas that of the redshiftedpeak is on the order of 103 m=s [Fig. 3(j)]. Overall, the vgof bulk excitations is 1 to 2 orders of magnitude slower thanthat of the edge excitation [24,25]. By moving the meas-urement point farther away from the excitation gate, thetemporal widths of the blueshift and redshift modesbroaden, indicating that the speed of these modes under-goes dispersion. Because the bulk excitations can be seen tospread isotropically in the movies (SM_movie1a.gif andSM_movie1b.gif) and Figs. 3(a)–3(h), we focus on only thevelocity in the y direction.More information about the bulk excitations can beobtained by defining the penetration length lP as thedistance along the y direction from y ¼ 0 to the pointPhoton energy (meV)�E (meV)t (ns)0 2 0 20 20 20 20 20 20 20.1015341532(a) (b) (c) (d) (e) (f) (g) (h)(i) (j) (k) (l) (m) (n) (o) (p)FIG. 2. (a)–(h) Microscopic photoluminescence (PL) spectra at ν ¼ 2=3 and B ¼ 14 T as a function of the time delay t between thevoltage pulse and the laser pulse for Voffset ranging from (a) −0.2 to (h) 0.5 V in 0.1-V steps. The measurement point corresponds to thedownstream side of the edge (Point A in Fig. 1.) (i)–(p) PL peak energy shift, ΔE as a function of t. Each PL spectrum in Figs. 2(a)–2(h)was fitted with a Lorentzian function to determine the PL peak energy at each t. The energy shift ΔE is defined as the deviation of thepeak energy from the average peak energy observed during the time interval from t ¼ −1.38 to −0.645 ns prior to the arrival of the edgeexcitation.0 0.1�0.1Energy shift �E (meV)10 �myy (�m)0 20 400246t (ns)(i)0 0.2�E (meV)(j)104  m/s103 m/s105 m/s0(a) t = 0.84 ns (b) t = 1.68 ns (c) t = 2.52 ns (d) t = 3.36 ns(e) t = 4.2 ns (f) t = 5.04 ns (g) t = 5.88 ns (h) t = 6.72 nsFIG. 3. (a)–(h) Real-spacemapping of the energy shiftΔE captured for several t (see SMmovies). (i)ΔE dependence both on the spatialposition along the y axis [see Fig. 3(a)] and t. (j)ΔE at y ¼ 0. All the data shown in Fig. 3 was measured at B ¼ 6 T with Voffset ¼ 0.5 V.PHYSICAL REVIEW LETTERS 135, 066203 (2025)066203-3where the excitation disappears and the lifetime τ as thetime it takes for the excitation to vanish. Thus, vg ≢ lp=τ.To study lP and τ, we measured the y and t dependence ofthe PL spectra at several B ranging from 6 to 10 T (data notshown). By fitting the experimental data at these B values,we obtained ΔE (see Fig. S1). From the y-t dependence ateach B, we determined the B dependence of lP, τ, and vg,including error estimates, as shown in Figs. 4(a)–4(c) (seeSM for details).Here, we discuss the mechanism of the bulk excitation atthe gate [Fig. 4(d)]. The capacitanceC of the excitation gateexpressed in units of ne is given by εε0=ed ∼ 3.9 ×1011 cm−2=V (see Fig. S3).WhenVoffset ¼ 0.5 V is appliedto the excitation gate, the electron density under the gateincreases by Δne ∼ 2 × 1011 cm−2. Since the density ofstates of the 2DEG is constant as a function of energy, theenergy offset ϵoffset induced by Voffset can be estimatedusing ϵoffset ¼ πℏ2Δne=m� [34] to be ϵoffset ∼ 7 meV forΔne ∼ 2 × 1011 cm−2. When the bulk is at ν ¼ 2=3 at B ¼6 T (10 T), the local electron density under the excitationgate increases to ∼3 × 1011 cm−2 (∼3.6 × 1011 cm−2) dueto Voffset, causing the local ν to increase to ∼2 (∼1.5).Similarly, a pulse amplitude of V0 ¼ 0.2 V results in anenergy change of ϵ0 ∼ 3 meV. The electrons near the edgecan be excited to higher Landau levels because the potentialchange induced by the voltage pulse (Fig. 5) is of the sameorder as the Landau level spacing, which is ∼10 meV(17 meV) at B ¼ 6 T (10 T).The dispersion relation of the magnetoplasmon isgiven by: ωmpðkÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiω2c þ ωpðkÞ2q, where ωpðkÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffinee2k=2εε0m�pis the frequency of the surface plasmonfor the 2DEG. Here, ε is the relative permittivity of GaAsand ε0 is the vacuum permittivity [26,35–38]. Since ωpðkÞsquared is linear in k, vg can be derived from the expansionωmpðkÞ ¼ ωc þ ωpðkÞ2=2ωc þOðk2Þ as [39]vg ¼∂ωmpðkÞ∂k����k∼0¼ νe24εε0h: ð2ÞApart from the environmental factor of ε, vg is determinedby fundamental physical constants, similarly to the quan-tization of Hall resistivity, and depends only on ν. Notably,vg remains unaffected by changes in B, provided that the neis adjusted to maintain constant ν. Taking ε ¼ εðωÞ as thelow-frequency limit of the relative permittivity, with εð0Þ ¼12.4 at ∼50 mK [41], we estimate vg ∼ 5.9 × 104 m=s.This value is consistent with the experimental results,where vg ∼ 1–6 × 104 m=s [Fig. 4(c)].Since magnetoplasmons arise from mixing between adja-cent Landau levels, they provide insights into electron-holesymmetry breaking. If this mixing is neglected, two perspec-tives on the ν ¼ 2=3 state are related by symmetry: (A) holesform a ν ¼ 1=3 state on the fully filled ν ¼ 1 “vacuum” stateof electrons (known as hole-conjugate picture) and (B)electrons form a ν ¼ 2=3 state on the empty ν ¼ 0 vacuumstate. These perspectives, (A) and (B), are closely linked toedgemodels [22]. Magnetoplasmons distinguish these states:the vg of (A) is half that of (B). Despite the absence of explicitB dependence in Eq. (2), the experimentally observed vgexhibits slight dependence onB [Fig. 4(c)], which divides thedata into two distinct regions: a faster vg (∼4 × 104 m=s) forB < 7.5 T and a slower vg (∼2 × 104 m=s) forB > 8 T. Thesuppression of vg with increasing B suggests that the hole-conjugate picture (A), which predicts vg ∼ 3 × 104 m=s,becomes valid when B > 8 T.In addition to vg, there is a possibility that lp and τ arealso related to the edge models. The observed τ remainsrelatively constant (∼4–5 ns) over a wide range of B exceptnear 7 T [Fig. 4(b)], which is close to Bc ¼ 7.5 T. At B ∼Bc it is known that the spin-polarized and spin-unpolarizedphases are degenerate [29–32]. In this regime, “edge” statesform at domain boundaries between different spin phasesdue to the exchange interaction, which induces an energybarrier at the boundaries [31,32]. The exchange-energy-induced edge is gapless, allowing bulk excitations to excitethese edges. Consequently, the lifetime of the bulk exci-tation itself shortens near Bc. We note that although τdecreases, lp slightly increases at Bc [Fig. 4(a)]. Thissuggests that lp is not solely determined by the magneto-plasmon but also includes contributions from the edge atdomain boundaries.Penetration length l P (m)040206 8 10B (T)0246Lifetime  (ns)6 8 10B (T)2460g (10⁴ m/s)(a)6 8 10B (T)(b)(c)yℏ(d)0offsetFcFIG. 4. (a) Dependence of penetration length lP on B. The blueand red markers represent bulk excitations where blueshifts andredshifts were observed, respectively. (b) Dependence of lifetimeτ on B. (c) Dependence of vg on B. (d) Schematic illustration ofthe band diagram of the QW. ϵ and ϵF denote the energy ofelectrons and Fermi energy, respectively. The region y < 0corresponds to the area beneath the excitation gate, and εoffsetrepresent the offset energy induced by Voffset.PHYSICAL REVIEW LETTERS 135, 066203 (2025)066203-4The propagation velocity of the redshift mode is on theorder of 103 m=s and is insensitive to the magnetic field.These characteristics limit its interpretation. This moderesembles a strain pulse composed of coherent acousticphonons in GaAs, which have a group velocity of ∼5 ×103 m=s [42]. It has been reported that such a mode can beexcited through the thermal expansion of solids triggeredby a picosecond light pulse [27]. In our system, the voltagepulse applied to the gate may induce Joule heating throughthe magnetoplasmon excitations, which locally increasesthe temperature and leads to thermal expansion and redshiftof the trion PL.In summary, we electrically excited both the bulk andedge using a voltage pulse and captured spacetime-resolvedimages of the bulk excitation dynamics. Our findings showthat the primary bulk excitations can be explained bymagnetoplasmons, while the secondary excitations corre-spond to a strain pulse. The magnetoplasmons propagatingin the bulk, together with those localized at the edge, fullyspan the two polarization degrees of freedom of the gaugefield. Consequently, magnetoplasmons serve as key col-lective modes that can entangle the bulk and edge.Meanwhile, strain modifies the geometry of the 2DEG.We have reported experimental observations of bulk-edgecoupled magnetoplasmon modes and specific propagationfeatures, which support the proposed interpretation andopen the door for testing high-energy physics ideas in anexperimentally controllable setting. These experimentscould include studies of a solid-state simulator of brane-world cosmology using a quantum Hall system, the holo-graphic principle [43], and bulk-edge correspondence, asexemplified by the AdS/CFT correspondence [44,45].Acknowledgments—The authors are grateful to T.Fujisawa, N. Shibata, J. N. Moore, and T. Takayanagifor the fruitful discussions. This work is supported by aGrant-in-Aid for Scientific Research (GrantsNo. 19H05603, No. 21H05182, No. 21H05188, andNo. 24H00399) from the Ministry of Education, Culture,Sports, Science, and Technology (MEXT), Japan.Data availability—The data that support the findings ofthis Letter are not publicly available upon publicationbecause it is not technically feasible and/or the cost ofpreparing, depositing, and hosting the data would beprohibitive within the terms of this research project. Thedata are available from the authors upon reasonable request.[1] K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45,494 (1980).[2] D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev.Lett. 48, 1559 (1982).[3] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. denNijs, Phys. Rev. Lett. 49, 405 (1982).[4] S. Girvin, A. MacDonald, and P. Platzman, Phys. Rev. B 33,2481 (1986).[5] A. Pinczuk, B. Dennis, L. Pfeiffer, and K. West, Phys. Rev.Lett. 70, 3983 (1993).[6] H. Davies, J. Harris, J. 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The σ− polarizedPL was selectively collected using optics located at themillikelvin region, transmitted through a multimode fiber,and subsequently analyzed using a monochromator andCCD detector [31]. The measurement point, whichcorresponds to the focal point of the microscope, wasfreely movable across the sample using piezoelectricscanners. The time resolution of the stroboscopic PLmeasurement was approximately 300 ps. For more details,refer to the experimental techniques described in [24,25].The light and dark gray regions in Fig. 1 correspond tothe deposited Au electrodes and GaAs surface, respectively.The excitation gate is connected to an arbitrary waveformgenerator (AWG) and a dc voltage source, which providesan offset voltage Voffset to the pulse. The two electrodesconnected to the ground and the excitation gate form acoplanar waveguide.Appendix B: PL spectra and PL peak energy shift—To analyze the PL peak energy shift, we fit the PLspectra at a given ðt; x; yÞ using a Lorentzian function,LðE;Epeak; γ; AÞ ¼AðE − EpeakÞ2 þ γ2; ðB1Þwhere E, Epeak, A, and γ represent the photon energy, thecentral energy of the spectrum, the amplitude, and theFWHM, respectively. In this analysis, the fitted Epeak andA correspond to the estimated PL peak energy andintensity, respectively. We define the average peak energyẼpeak;0 as the mean of five spectra captured before thearrival of the edge excitation. For Figs. 2(i)–2(p), Ẽpeak;0is calculated by averaging the spectra from t ¼ −1.38 to−0.645 ns. The PL peak energy shift ΔEðt; x; yÞ at agiven ðt; x; yÞ is then determined usingΔEðt; x; yÞ ¼ Epeakðt; x; yÞ − Ẽpeak;0ðx; yÞ: ðB2ÞVoltage V (V)0.400 21Time (ns)V0 Voffset0.30.5FIG. 5. Voltage waveform applied to the excitation gate, asmeasured by a 12.5 GHz bandwidth oscilloscope directly con-nected to AWG and the dc source. The interval between themeasurement points is 20 ps. V0 denotes the amplitude of thesquare pulse, with a duration of 0.5 ns.PHYSICAL REVIEW LETTERS 135, 066203 (2025)066203-6https://doi.org/10.1016/0003-4916(76)90226-8https://doi.org/10.1016/0003-4916(76)90226-8https://doi.org/10.1016/0039-6028(80)90533-6https://doi.org/10.1103/PhysRevB.93.125402https://doi.org/10.1063/5.0233487https://doi.org/10.1063/5.0233487https://doi.org/10.1063/1.531249https://doi.org/10.4310/ATMP.1998.v2.n2.a1https://doi.org/10.1088/1126-6708/2009/04/019https://doi.org/10.1088/1126-6708/2009/04/019 Electrically Induced Bulk and Edge Excitations in the Fractional Quantum Hall Regime Acknowledgments Data availability References Appendix A: Experimental details Appendix B: PL spectra and PL peak energy shift