Controlling core-hole lifetime through an x-ray planar cavity
Xin-Chao Huang, Xiang-Jin Kong, Tian-Jun Li, Zi-Ru Ma, Hong-Chang Wang, Gen-Chang Liu, Zhan-Shan Wang, Wen-Bin Li, Lin-Fan Zhu
aa r X i v : . [ phy s i c s . a t o m - ph ] J a n Controlling core-hole lifetime through an x-ray planar cavity
Xin-Chao Huang, Xiang-Jin Kong, Tian-Jun Li, Zi-Ru Ma, Hong-Chang Wang, Gen-Chang Liu, Zhan-Shan Wang, Wen-Bin Li, ∗ and Lin-Fan Zhu, Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics,University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China Department of Physics, National University of Defense Technology,Changsha, Hunan 410073, People’s Republic of China Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0DE, UK MOE Key Laboratory of Advanced Micro-Structured Materials,Institute of Precision Optical Engineering (IPOE), School of Physics science and Engineering,Tongji University, Shanghai 200092, People’s Republic of China (Dated: January 28, 2021)It has long been believed that core-hole lifetime (CHL) of an atom is an intrinsic physical property, andcontrolling it is significant yet is very hard. Here, CHL of the 2 p state of W atom is manipulated experimentallythrough adjusting the emission rate of a resonant fluorescence channel with the assistance of an x-ray thin-filmplanar cavity. The emission rate is accelerated by a factor linearly proportional to the cavity field amplitude, thatcan be directly controlled by choosing different cavity modes or changing the angle offset in experiment. Thisexperimental observation is in good agreement with theoretical predictions. It is found that the manipulatedresonant fluorescence channel even can dominate the CHL. The controllable CHL realized here will facilitatethe nonlinear investigations and modern x-ray scattering techniques in hard x-ray region.PACS: 32.80.-t, 32.80.Qk, 42.50.Ct, 32.30.Rj, 78.70.Ck. The particularity of an inner-shell excitation or ionizationis to produce a core vacancy, which has a finite lifetime, i.e.,the so-called core-hole lifetime (CHL), and then it decaysinto lower-lying states. There are two main relaxation path-ways, i.e., radiative (fluorescence) and non-radiative (Augerdecay or autoionization) channels, and the CHL is determinedby the total decay rate of all relaxation channels. Normally,Auger effect dominates the decay routes of K shell for low-Z atoms [1] and L and M shells for higher-Z atoms [2], sothe CHL is sometimes called Auger lifetime. The CHL haslong been considered as an intrinsic factor and controlling itis very difficult because the relaxation channels are hard to bemanipulated with common methods.Nevertheless, an adjustable CHL is strongly desired, sinceCHL changes are useful to detect ultrafast dynamics. An ad-justable CHL is needed to give a deep insight to nonlinearlight-matter interaction with the advent of x-ray free electronlaser (XFEL), since the ratio of CHL to XFEL pulse widthdoes matter for multiphoton ionization [3], two-photon ab-sorption [4], population inversion [5] and stimulated emis-sion [6, 7]. CHL is also a key factor in resonant x-ray scatter-ing (RXS) process [8], where the dynamics of the core-excitedstate is controlled by the duration time which is determined byboth energy detuning and CHL [10]. Because of a lack of anefficient method to manipulate CHL experimentally, the con-trolling schemes for duration time were based on the energydetuning up to now [11–16]. The dynamics of the core-excitedstate determines the application range for RXS techniques,e.g., resonant inelastic x-ray scattering (RIXS) [9]. SinceCoulomb interaction between core-hole and valence electronsonly exists during the existence of core-excited state, the rela- ∗ [email protected] † [email protected] tive timescale between CHL and elementary excitations gov-erns the effectiveness of indirect RXIS [17–19], especially forcharge and magnon excitations [18, 20–23]. In time-resolvedRIXS (tr-RIXS), CHL also needs to be flexibly adjusted forpursuing higher time resolution [24–27]. Therefore, a con-trollable CHL will be very useful thus is strongly wished for,from both fundamental and application perspectives.Because CHL is determined by the total decay rate of all re-laxation channels, controlling CHL means manipulatable de-cay channels, at least one of them, which is a challengingtask. Stimulated emission channel could be opened by in-tense and short x-ray pulses to accelerate CHL [6, 7], whilesuch scheme can only be implemented in XFEL. The presentwork proposes another scheme that controls the spontaneousemission channel. R. Feynman once said, the theory behindchemistry is quantum electrodynamics (QED) [28], indicat-ing that the spontaneous emission rate of atom depends onthe environment (photonic density of states). A cavity is suchan outstanding system to robustly structure environment andmodify the spontaneous emission rate in visible wavelengthregime [29, 30], as known cavity-QED. With the dramaticprogress of new generation x-ray source and thin-film technol-ogy, cavity-QED effect in hard x-ray range was demonstratedby the laboratory of thin film planar cavity with nuclear en-sembles [31–36] or electronic resonance [37], which breedsthe new field of x-ray quantum optics [38].In this work, a controllable CHL for 2 p state of W atomis realized through adjusting the emission rate of a resonantfluorescence channel with the assistance of an x-ray thin-filmplanar cavity. WSi has a remarkable white line around theL III edge of W, which is a resonant channel and generallyknown to be associated with an atomic-like electric dipole al-lowed transition, from an inner shell 2 p to an unoccupied level5 d [37, 39, 40]. Inside the cavity, the emission rate of the reso-nant channel depends on the photonic density of states wherethe atom locates, which can be modified by the cavity fieldamplitude in experiment. Because the thin-film planar cav-ity can only enhance the photonic density of states, but notsuppress it, only CHL shortening is realized in the present ex-periment. As long as the cavity effect is strong enough, thetotal decay rate will have measurable changes and lead to ancontrollable CHL. Driving (1+Re( (cid:1) )) (cid:2) re γ ie ResonantFluo. InelasticFluo. g e f White Line L (cid:3) / (cid:0) L III M /M Band (a)(b) (c)
CCDCollimatorX-Ray θ th Fig. 1. The schematic for controlling core-hole lifetime. (a) Cavitysample and measurement setup. The cavity has a structure of Pt (2.1nm)/C (18.4 nm)/WSi (2.8 nm)/C (18.0 nm)/Pt (16.0 nm)/Si , andthe middle-right inset shows the energy-level of L III edge of atom W.The sample is probed by a monochromatic x-ray, and the resonantfluorescence is measured in the reflection direction by a CCD andthe inelastic fluorescence signals are collected by an energy-resolvedfluorescence detector. The distance between collimator and samplesurface is 31.0 mm, and the hole diameter and the length of the col-limator are 2.8 mm and 20.1 mm. An example of full range fluores-cence spectrum is shown in inset at top-left side, and the grey regioncorresponds to the fluorescence photon energy of L α line. The in-set at top-right side is the reflectivity curve with an incident energydetuning 30 eV from E , and the pink solid bar indicates the criticalangle of Pt (0.46 degree). (b) The values of Re( η ) and Im( η ) as afunction of incident angle, which is calculated by a transfer matrixformulism. (c) The simplified energy levels of W. The driving is la-beled by the blue arrow, and the cavity enhanced emission is labeledby the red thick arrow. The inelastic fluorescence decay is labeled bythe red thin arrow. Fig. 1(a) depicts the cavity structure used in the presentwork. The thin-film cavity is made of a multilayer of Pt andC. The top and bottom layers of Pt with a high electron densityare used as mirrors. The layers of C in the middle with a lowelectron density are used to guide the x-ray and to stack thecavity space. In this design, at certain incident angles θ th be-low the critical angle of Pt, x-ray can resonantly excite specificcavity guided modes where dips in the reflectivity curve ap-pear as shown in the top-right inset of Fig. 1(a). In the presentwork, θ th are θ =0.218 ◦ , θ =0.312 ◦ and θ =0.440 ◦ for the1 st , 3 rd and 5 th odd orders of cavity mode. Then the couplingbetween the cavity and atom is built by embedding a thin layerof WSi at the middle of the cavity where the cavity field am-plitudes are the strongest. The field distributions of the 1 st , 3 rd and 5 th orders of cavity mode are sketched in Fig. 1(a).As shown in the middle-right inset of Fig. 1(a), the inner shell energy-level system is different from the simple two-level one, and both resonant channel and incoherent processessuch like inelastic radiative channels (Auger decay channelsis not exhibited here) can annihilate the core vacancy state, sothe decay width is determined by the total decay rates of allrelaxation channels. Excited by the incoming x-ray field, theatomic dipole emits the resonant fluorescence through the res-onant channel, and the resonant response could be written asa simple form of Lorentz function, f = − f i γ re / δ + i ( γ re / + γ in / ) (1)The electronic continuum in higher energy range is not con-sidered here. f is a constant, and δ is the energy detuningbetween the incident x-ray energy E and the white line tran-sition energy E . γ re is the natural spontaneous emission rateof the resonant channel, while γ in is the incoherent decay ratewhich sums two branches: the radiative decay rate of inelasticchannels γ ie and the non-radiative decay rate of Auger process γ A , i.e., γ in = γ ie + γ A . It is clear that the inverse core-holelifetime is expressed by the natural width as γ = γ re + γ in .Cavity strengthens the photonic density of states [29, 41] atthe position of the radiating atom, so the resonant fluorescencewill be enhanced. Applying the transfer matrix combined witha perturbation expansion method (SM Sec. I), the resonantfluorescence in the reflection direction is solved as, r a = − id f × | a z a | γ re / δ + δ c + i ( γ c + γ ) / d is the thickness of the atomic layer, and | a z a | is the fieldintensity where the atom locates. It can be seen that Eq. (2)still has a Lorentzian resonant response, while contains addi-tional cavity effects: the cavity enhanced emission rate γ c andthe cavity induced energy shift δ c , γ c = d f γ re × Re ( η ) δ c = d f γ re × Im ( η ) η = pq (3)Thus the emission rate is enhanced by a factor of Re( η ), where p and q are the field amplitudes corresponding to the wavescattered from up (down) direction into both up and down di-rections at the position of atomic layer (Sec. I of SM). Notehere that the photonic density of states is directly related tothe cavity field amplitudes [32, 41], so Eq. (3) conforms tothe typical cavity Purcell effect [30] which describes the well-known linear relation between lifetime shortening and pho-tonic density of states strengthening. It is clear that the realpart of η is an essential factor to control the enhanced emis-sion rate, and the energy shift is modified by the image part of η . The real and image parts of η as a function of incident an-gle are depicted in Fig. 1(b), and γ c and δ c are simultaneouslymodified by the incident angle around the mode angles, whichhas been observed by Haber et al recently [37]. On the otherhand, Fig. 1(b) suggests that the strongest enhanced emissionrate can be achieved without introducing additional energyshift by exactly choosing the angles of odd orders of cavitymode, which will be more convenient to study the individualinfluence of the CHL on core-hole dynamics (SM Sec. IV).The fully controllable resonant channel makes an adjustabletotal inverse core-hole lifetime, Γ n = γ c + γ re + γ ie + γ A (4)where all four contributions are included, herein γ c is the cav-ity enhanced emission rate, and γ = γ re + γ ie + γ A is the naturalinverse CHL as the sum of three branches: the natural sponta-neous emission rate of the resonant fluorescence channel, theradiative decay rate of inelastic fluorescence channels and theAuger decay rate. γ is a fixed value which can be obtainedfrom the experimental spectrum at a large incident angle (Fig.S3 of SM), i.e., γ / γ c is large enough, thiscontrollable part will dominate the CHL.As shown in the simplified energy levels in Fig. 1(c), thecore-hole lifetime determines the linewidth of inelastic scat-tering, i.e, the fluorescence spectrum. We employ a RXS for-malism known as Kramers-Heisenberg equation to characterthe inelastic scattering [8, 9] as, F i f (cid:18) ⇀ k , ⇀ k ′ , ω , ω ′ (cid:19) = h f | ˆ D ′ | n i h n | ˆ D | i i δ + i Γ n / | i i = (cid:12)(cid:12)(cid:12) g , ⇀ k E , the final state | f i = (cid:12)(cid:12)(cid:12)(cid:12) f , ⇀ k ′ (cid:29) , and the intermediate state | n i = | e , i . ⇀ k is the wavevector and ˆ D is the transition operator. For the present system,an intermediate state and a final state are considered, since wechoose the L III white line transition and measure L α with en-ergy E ′ . Eq. (5) indicates that CHL changes can be monitoredby the inelastic fluorescence spectrum, and in the present workL α line (L α is much stronger than L α ) is chosen to obtainthe inelastic fluorescence spectra.The measurement was performed on the B16 Test beamlinein Diamond Light Source. Monochromatic x-ray from a dou-ble crystal monochromator was used to scan the incident x-rayenergy, and two small apart slits were used to obtain a goodcollimation beam with a small vertical beam size of about 50 µ m. The multilayer was deposited onto a polished siliconwafer (100) using DC magnetron sputtering method which ispopular to fabricate diverse cavity structures [31–37]. Beforesample fabrication, the deposition rate was calibrated care-fully to guarantee the layer thickness with a good accuracy ofbetter than 1 ˚A. The size of the wafer is 30 ×
30 mm whichis larger than the footprint to avoid the beam overpassing thesample length. As shown in the top-right inset of Fig. 1(a),the θ − θ rocking curve with an incident energy detuning 30eV from the white line position was measured firstly to findthe desired specific incident angles corresponding to the 1 st ,3 rd and 5 th orders of the guided modes, i.e., the corresponding reflection dips. For a given incident angle, the incident energy E was scanned from 10161 eV to 10261 eV across the tran-sition energy E =10208 eV. Then the reflectivity correspond-ing to the resonant channel was measured by a CCD detector,and the inelastic fluorescence lines were measured simultane-ously by a silicon drift detector ( Vortex ) with a resolution ofabout 180 eV at a perpendicular direction. In front of the fluo-rescence detector, a collimator guarantees a constant detectedarea of the sample, and the footprint bw / sin θ on the samplesurface is determined by the beam width bw and the incidentangle, so the inelastic fluorescence intensities need to be nor-malized by taking into account a geometry factor [43]. Thestrongest L α fluorescence lines (L α at 8398 eV and L α at8335 eV) of W are far from the white line (10208 eV) andother weak fluorescence lines (9951 eV of L β , 7387 eV of L l and other negligible lines), so L α can be extracted separatelyfrom the energy-resolved fluorescence spectrum.Firstly, the 1 st , 3 rd and 5 th orders are exactly chosen to con-trol the CHL without introducing additional energy shift, andthe results are depicted in Fig. (2). Fig. 2(a) shows the experi-mental and theoretically fitted reflectivity curves. The presenttheoretical model for resonant fluorescence does not take intoaccount the influence of the absorption edge due to its natureof the electronic continuum, and the continuum overlaps withthe right side of the white line. The sudden increase of theabsorption coefficient changes the refractive index and dra-matically alters the cavity properties [37]. So the data below10220 eV are selected for fitting (labeled by the green region).Above 10220 eV, the theoretical results diverge from the ex-perimental datum. The reflection coefficient includes the con-tributions from two pathways (SM Sec. II): the first one of r is from the multilayer cavity itself that the photon does notinteract with the resonant atom, and the second one of r a isfrom the resonant atom inside the cavity, i.e., the resonant flu-orescence. The linewidth of the cavity is much larger than theone of atom, which means that r is more like a flat continuumstate and r a is more like a sharp discrete state [34, 44]. There-fore, the reflectivity spectrum is a result of Fano interference.It can be seen from Fig. 2(a) that the profile of the reflectivityspectra shows Fano line-shape. The reflectivity spectra givethe values of ( γ c + γ ) / st , 3 rd and 5 th orders of the cavity mode.Fig. 2(b) shows the experimental and fitted inelastic flu-orescence spectra of L α as a function of incident x-ray en-ergy for the 1 st , 3 rd and 5 th orders. The inelastic fluorescencespectrum is fitted by a custom function combining a simpleLorentz function L ( E ) with a Heaviside step function H ( E ) (SM Sec.III), herein L ( E ) with a linewidth Γ n / H ( E ) is used to describe the absorptionedge. The fitted values of Γ n / γ c = Γ n − γ is even larger than γ in the 1 st order, indicating that the ad-justable resonant channel breaks the limitation of Auger pro-cesses and unchangeable radiative decay channels and domi- Fig. 2. (a) The measured and theoretical reflectivity spectra for the1 st , 3 rd and 5 th orders as a function of incident photon energy. Thered solid line is the theoretically fitted result. (b) The measured andfitted inelastic fluorescence spectra of L α as a function of incidentphoton energy. The solid lines in pink, red, green and blue are thefitted result, Lorentzian resonance line, electronic continuum line andthe flat background respectively. nantly determines CHL. A behavior of widening linewidth iscross-checked by L l and L β lines (SM Fig. S5). Incident Photon Energy A ng l e O ff s e t ( - d e g r ee ) Incident Photon Energy (eV)
Incident Photon Energy (eV) st order 3 rd order 5 th orderIntensity Intensity Intensity Fig. 3. The inelastic fluorescence spectra of L α as functions of in-cident photon energy and angle offset. Angle offset is the deviationbetween the incident angle and the θ ( θ , θ ). The measured inelastic fluorescence 2D spectra are shownin Fig. 3 for selected incident angles around the mode an-gles of the 1 st , 3 rd and 5 th orders ( θ =0.218 ◦ , θ =0.312 ◦ and θ =0.440 ◦ respectively). As discussed in Eq. (3), CHLand the cavity induced energy shift are simultaneously con-trolled by the incident angle. When the incident angle scansacross the mode angle, a phenomenon of firstly increasing tomaximum at the mode angle then decreasing of the inverseCHL will be observed along with an additional energy shift,which is demonstrated by Fig. 3. For the 3 rd order, the maxi-mum linewidth does not seem to be where the angle offset is0, this may due to the occasionally angle shift from the insta-bilities of the goniometer or sample holder. Note here that Fig.3 suggests a way to continuously modify CHL but introduceadditional energy shift.As predicted in Eq. (3), the enhanced emission rate γ c islinearly connected with the real part of the cavity filed ampli-tude η , and this is the essential to discuss the magnitude of in-verse CHL. It should be noted here that the present method tocontrol CHL is different from the scenario of stimulated emis-sion [6, 7] where a non-linear relationship between the stim-ulated emission rate and the x-ray field intensity is expected.The present scheme actually employs a cavity to manipulatethe enhanced spontaneous emission whose decay rate is lin-early determined by the photonic density of states. The inelas- Δ θ = -3 deg 036 A Δ θ =-4×10 -3 deg 036 A Δ θ =-6×10 -3 deg012 L α F l uo . I n t e n s it y ( ) Δ θ =0 deg 036 A Δ θ =0 deg 036 Δ θ =0 deg10170 10200 10230 10260012 Δ θ =4×10 -3 deg 10170 10200 10230 10260036 Incident Photon Energy (ev) Δ θ =6×10 -3 deg 10170 10200 10230 10260036 th Order3 rd Order1 st Order Δ θ =6×10 -3 deg γ c ( e V ) Re( η ) (a)(b) Fig. 4. (a) The measured and fitted inelastic fluorescence spectraof L α for selected angle offsets. (b) Enhanced emission rate γ c asa function of Re ( η ) . The values of γ c are derived from the fittedlinewidth Γ n as γ c = Γ n − γ , and the values of Re ( η ) are obtained bytransfer matrix calculation. The dashed blue line is a linear fitting ofthe experimental dots to guide the eyes. tic fluorescence spectra in Fig. 3 are fitted to get the values of Γ n , and some selected spectra are shown in Fig. 4(a). Thenthe values of γ c are obtained based on Eq. (4), and the valuesof Re ( η ) are calculated by the transfer matrix formulism. Agood linear relationship between γ c and Re ( η ) is depicted inFig. 4(b) which is consistent with the prediction of Eq. (3).From the general viewpoint of cavity-QED in opticalregime, the inelastic channel is an incoherent process whichaccelerates the decoherence, so it is regarded as a defect forthe system [45]. However, the inelastic channel is a natu-ral character and widely exists in atomic inner-shell systems,herein we demonstrate it can be very useful to monitor CHLchanges, enriching the picture of cavity effect.In conclusion, the core-hole lifetime for 2 p state of Wis manipulated experimentally through constructing an x-raythin-film planar cavity system. The core-hole lifetime directlydepends on the cavity field amplitude at the position of Watom (SM Sec. I and [42]), which can be adjusted by choos-ing the different orders of cavity mode or varying the incidentangle offset. With a high quality cavity sample, the core-holelifetime is conveniently manipulated in experiment. Notablyfor the case of the 1 st order, the decay rate of the resonantchannel is even stronger than the natural inverse core-holelifetime which is dominated by the Auger process for L III shellof atom W in common scenarios. Moreover, the inelastic flu-orescence spectra are utilized as a good monitor to reflect thecore-hole lifetime changes. The cavity structure is suitable fora wide range of x-ray energy from few to tens of keV, so thepresent scheme could be extended to a lot of elements whichhave resonant fluorescence channel. Utilizing the present cav-ity technique, the duration time of RXS process can be con-trolled not only by the energy detuning, but also by the core-hole lifetime, which will enrich the physical studies for RXS(SM Sec. VI) in future. Combing with the high-resolution ∼
100 meV analyzer [46], a cavity-manipulating RXS is ex-pected to be achievable.This work is supported by National Natural Science Foun-dation of China (Grants No. U1932207), and the NationalKey Research and Development Program of China (GrantsNo. 2017YFA0303500 and 2017YFA0402300). The exper-iment was carried out in instrument B16 of Diamond LightSource Ltd (No. MM21446-1), United Kingdom. Authorsthank Xiao-Jing Liu for fruitful discussion. [1] P. Auger, Comptes Rendus , 65 (1925).[2] M. O. Krause, J. Phys. Chem. Ref. Data , 307 (1979).[3] H. Fukuzawa, S.-K. Son, K. Motomura, et al. , Phys. Rev. Lett. , 173005 (2013).[4] K. Tamasaku, E. Shigemasa, Y. Inubushi, et al. , Phys. Rev. Lett. , 083901 (2018).[5] H. Yoneda, Y. Inubushi, K. Nagamine, et al. , Nature , 446(2015).[6] B. Wu, T. Wang, C. E. Graves, et al. , Phys. Rev. Lett. ,027401 (2016).[7] Z. Chen, D. J. Higley, M. Beye, et al. , Phys. Rev. Lett. ,137403 (2018).[8] F. Gel’mukhanov and H. ˚Agren, Phys. Rep. , 87 (1999).[9] L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill,and J. van den Brink, Rev. Mod. Phys. , 705 (2011).[10] F. Gel’mukhanov, P. Sałek, T. Privalov, and H. ˚Agren, Phys.Rev. A , 380 (1999).[11] P. Skytt, P. Glans, J.-H. Guo, K. Gunnelin, C. S˚athe, J. Nord-gren, F. K. Gel’mukhanov, A. Cesar, and H. ˚Agren, Phys. Rev.Lett. , 5035 (1996).[12] R. Feifel, A. Baev, F. Gelmukhanov, et al. , Phys. Rev. A ,022707 (2004).[13] V. Kimberg, A. Lindblad, J. S¨oderstr¨om, O. Travnikova,C. Nicolas, Y. P. Sun, F. Gel’mukhanov, N. Kosugi, andC. Miron, Phys. Rev. X , 011017 (2013).[14] R. Feifel and M. N. Piancastelli, J. Electron Spectrosc. Relat.Phenom. , 10 (2011).[15] P. Morin and C. Miron, J. Electron Spectrosc. Relat. Phenom. , 259 (2012).[16] C. Miron and P. Morin, Handbook of High-Resolution Spec-troscopy (Wiley, Chichester, UK, 2011) pp. 1655–1690.[17] L. J. P. Ament, F. Forte, and J. van den Brink, Phys. Rev. B , 115118 (2007).[18] L. J. P. Ament, G. Ghiringhelli, M. M. Sala, L. Braicovich, andJ. van den Brink, Phys. Rev. Lett. , 117003 (2009).[19] M. Dean, R. Springell, C. Monney, et al. , Nat. Mater. ,850C854 (2012).[20] J. van den Brink, Euro. Phys. Lett. , 47003 (2007).[21] M. W. Haverkort, Phys. Rev. Lett. , 167404 (2010).[22] C. Jia, K. Wohlfeld, Y. Wang, B. Moritz, and T. P. Devereaux,Phys. Rev. X , 021020 (2016).[23] T. Tohyama and K. Tsutsui, Inter. J. Mod. Phys. B , 1840017(2018).[24] M. P. Dean, Y. Cao, X. Liu, et al. , Nat. Mat. , 601 (2016).[25] Y. Wang, M. Claassen, C. D. Pemmaraju, C. Jia, B. Moritz, andT. P. Devereaux, Nat. Rev. Mat. , 312 (2018).[26] Y. Chen, Y. Wang, C. Jia, B. Moritz, A. M. Shvaika, J. K. Fre-ericks, and T. P. Devereaux, Phys. Rev. B , 104306 (2019).[27] M. Buzzi, M. F¨orst, R. Mankowsky, and A. Cavalleri, Nat. Rev.Mat. , 299 (2018).[28] F. Richard, QED: The strange theory of light and matter (Princeton University Press, USA, 1985).[29] M. S. Tomaˇs, Phys. Rev. A , 2545 (1995).[30] J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. , 565 (2001).[31] R. R¨ohlsberger, K. Schlage, B. Sahoo, S. Couet, and R. R¨uffer,Science , 1248 (2010).[32] R. R¨ohlsberger, H.-C. Wille, K. Schlage, and B. Sahoo, Nature , 199 (2012).[33] K. P. Heeg, H.-C. Wille, K. Schlage, et al. , Phys. Rev. Lett. ,073601 (2013).[34] K. P. Heeg, C. Ott, D. Schumacher, H.-C. Wille, R. R¨ohlsberger,T. Pfeifer, and J. Evers, Phys. Rev. Lett. , 207401 (2015).[35] K. P. Heeg, J. Haber, D. Schumacher, et al. , Phys. Rev. Lett. , 203601 (2015).[36] J. Haber, X. Kong, C. Strohm, et al. , Nat. Photon. , 720(2017).[37] J. Haber, J. Gollwitzer, S. Francoual, M. Tolkiehn, J. Strempfer,and R. R¨ohlsberger, Phys. Rev. Lett. , 123608 (2019).[38] B. W. Adams, C. Buth, S. M. Cavaletto, et al. , J. Mod. Optic. , 2 (2013).[39] M. Brown, R. E. Peierls, and E. A. Stern, Phys. Rev. B , 738(1977).[40] P. S. P. Wei and F. W. Lytle, Phys. Rev. B , 679 (1979).[41] R. R¨ohlsberger, K. Schlage, T. Klein, and O. Leupold, Phys.Rev. Lett. , 097601 (2005).[42] X.-C. Huang, Z.-R. Ma, X.-J. Kong, W.-B. Li, and L.-F. Zhu,J. Opt. Soc. Am. B , 745 (2020).[43] W. Li, J. Zhu, X. Ma, H. Li, H. Wang, K. J. Sawhney, andZ. Wang, Rev. Sci. Instrum. , 053114 (2012).[44] X.-J. Liu, L.-F. Zhu, Z.-S. Yuan, et al. , Phys. Rev. Lett. ,193203 (2003).[45] A. F. Van Loo, A. Fedorov, K. Lalumi`ere, B. C. Sanders,A. Blais, and A. Wallraff, Science , 1494 (2013).[46] J. Hill, D. Coburn, Y.-J. Kim, T. Gog, D. Casa, C. Kodituwakku,and H. Sinn, J. Synchrotron Radiat.14