High Tc superconducting THz metamaterial for ultra-strong coupling in

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High Tc superconducting THz metamaterial for ultra-strong coupling in magnetic field Janine Keller, Giacomo Scalari, Felice Appugliese, Elena Mavrona, Shima Rajabali, Martin J. Süess, Mattias Beck, and Jerome Faist ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01025 • Publication Date (Web): 04 Oct 2018 Downloaded from http://pubs.acs.org on October 7, 2018

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High

TC

superconducting THz metamaterial

for ultra-strong coupling in magnetic eld Janine Keller *, Giacomo Scalari **, Felice Appugliese, Elena Mavrona, Shima Rajabali, Martin J. Süess, Mattias Beck, and Jérôme Faist∗ ETH Zürich, Institute of Quantum Electronics, Auguste-Piccard-Hof 1, Zürich 8093, Switzerland E-mail: *[email protected],**[email protected] Keywords: High Tc superconductor, metamaterial, terahertz, ultra-strong coupling, focused ion beam (FIB), Landau polaritons, cyclotron

Abstract We fabricate high temperature superconducting metasurfaces from Yttrium-BariumCopper-Oxide (YBCO) lms via focused ion beam milling. The design of the complementary split ring resonators yields a high quality factor (up to Q = 31) resonance, which is fully switchable when exploiting the transition from the superconducting to normal conducting state, which is achieved by heating the sample above the critical temperature. Meanwhile, the resonance is continuously visible and frequency stable under the action of a magnetic eld, up to B = 9 T. This makes it an ideal candidate for light-matter coupling experiments with magnetic eld tunable Landau level transitions. We present two techniques to bring the metasurface in close vicinity of a 2D electron gas in an AlGaAs/GaAs QW without direct deposition, and we achieve a normalized vacuum Rabi frequency of ΩR /ωcyc = 24%.

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Dierent regimes of light-matter interactions can be realized, particularly, one can attain the so-called ultra-strong coupling regime when the vacuum Rabi frequency ΩR is approaching a sizeable fraction of the transition frequency of the system. 1 Many platforms have been shown to be suitable to reach such a regime, from intersubband transitions 26 to superconducting quantum circuits 7,8 and organics in cavities. 911 In our group, we established a platform which makes use of magnetic eld tunable matter excitations, the inter-Landau level transitions. 1214 The large optical dipole moment of the cyclotron transition ωcyc is advantageous for attaining the ultra-strong coupling regime 12,14 and recently a coupling beyond unity has been demonstrated 15 based on such a platform. As cavity, metamaterials arrays, specically split ring resonators (SSRs), have been implemented successfully due to their strongly enhanced electric eld in strongly subwavelength volumes. 12,13,15 However, to study some fundamental eects like the recently demonstrated vacuum Bloch-Siegert shift in Landau polaritons, a narrow linewidth is required which can not be provided by standard gold SRRs and has been realized instead with a one dimensional photonic crystal cavity. 16,17 Other theoretical predictions in the ultra-strong coupling regime, such as the emission of vacuum photons upon non-adiabatic modulation, 1 have remained experimentally elusive. One proposed pathway to observe such phenomena is to employ superconducting metamaterials, 18 as one can exploit the switching between the normal conducting and superconducting state to alter the resonance response of the system. 1928 It has been shown that the switching can indeed be achieved on a picosecond timescale in the terahertz frequency region via IR or THz pulses. 2931 However, the stability of the superconducting state of investigated Nb metamaterial structures in magnetic eld is rather poor, i.e. the resonance tunes in frequency and eventually fades out well below B = 1 T. 24,33 To use a switchable Nb superconducting metamaterial to couple to a cyclotron resonance in magnetic eld has been unsuccessful. 33 In the present work, we present an implementation of complementary split ring resonators in Yttrium-Barium-Copper-Oxide (YBCO) lms, where the resonance is very stable in magnetic eld, showing almost no frequency drift up to an explored range of B = 9 T. Additionally, the 2


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metasurface is still fully switchable by going from the superconducting state to the normal conducting state, achieved in this study by heating the sample above the critical temperature. Furthermore, we realize the ultra-strong coupling of the superconducting metasurface to a 2D electron gas (2DEG) via a pure mechanical approach of the two systems. Thus, we are overcoming a longstanding experimental challenge of coupling the two systems, as a direct deposition of the high TC superconductor on the QW would greatly degrade the quality of the 2DEG and is consequently not a viable option.

We use commercially available YBCO lms of 200 nm thickness from Ceraco, deposited on a 500µm thick Sapphire substrate. The lms are specied with a critical temperature of

TC = 88 K and a critical current of jc (77 K) ≥ 2.5 MA/cm2 . We utilize Ga3+ focused ion beam (FIB) milling (ScopeM, FEI Helios 600i) to fabricate the complementary split ring resonator arrays. This method allows to dene a metamaterial array in the pre-deposited high quality YBCO lm and allows freedom in the choice of geometry for each run, thus also useful for rapid prototyping with still well dened and small features. 34 The chosen split ring resonator, shown in a scanning electron micrograph in Figure 1 (a), is an adapted version of our previous work of a Nb superconducting, fully switchable, high quality factor resonator 18 and is placed in an array with a lattice constant of 60 µm. The total number of resonator is

15 x 15 = 225 resonators covering an area of 0.9 x 0.9 mm2 .

We probe the samples in THz time domain spectroscopy (THz-TDS), illuminating a photoconductive switch with a Ti:Sapphire laser with 71 fs pulse duration at 800 nm wavelength and 80 MHz repetition rate at an average power of 500 mW. The transmission through the samples is detected via electro-optic sampling with a 3 mm long ZnTe (110) crystal. To enhance the visibility of the lower frequencies, we have the option to utilize a low pass lter to cut frequencies higher than ∼ 1 THz. In Figure 1 (c), we show the transmission spectra through the YBCO metamaterial array clearly above the critical temperature TC 3


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Figure 1: (a) Scanning electron micrograph (SEM) of one resonator with indicated dimensions. (b) Electric eld distribution for the LC-mode and the dipolar mode of the resonator, simulated with CST microwave studio modeling an Ohmic sheet with resistance RS = 0.245 Ohm/sq and reactance XS = 0.8 Ohm/sq. (c) Transmission spectra of the resonator array at T = 150 K and T = 3 K, both normalized to the transmission at T = 220 K.

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at T = 150 K (red line) and well below TC , at T = 3 K (black line), both normalized to the transmission at T = 220 K. The broadband transmission observed at T = 150 K drastically changes when cooling to T = 3 K into the two resonator modes. The fundamental, LC-mode at fLC = 380 GHz and the higher order mode, the so-called dipolar mode at

fdipolar = 1.4 THz. Both are excited with the THz-polarization across the capacitive gap, as indicated in Fig. 1 (a). In contrast to Nb, with a superconducting gap below 1 THz, 18,33,35 the superconducting gap of YBCO lies in the range of several THz (≈ 20 − 30 meV 36 ), which enables the visibility of the dipolar mode at 1.4 THz. The dipolar mode appears as a double peak, which is due to the coincidence with a lattice mediated mode, the surface plasmon polariton (SPP) mode, which we studied in detail in a previous work. 32 The spacing of the resonators and the refractive index of the thick Sapphire substrate determine the resonance frequency of the SPP-mode. This coinciding additional mode makes it dicult to extract the quality factor of the mode. With a double Lorentzian peak t we can estimate it to be on the order of Q = 6. The electric eld distribution of the LC-resonance and the dipolar mode are shown in Fig. 1 (b), which were simulated with CST Microwave Studio. The YBCO is modeled as an Ohmic sheet with a resistance RS = 0.245 Ohm/sq and reactance XS = 0.8 Ohm/sq, which are in agreement with literature 26,29,37 and were adjusted to t our measured spectrum. The LC-mode has a higher eld enhancement than the dipolar mode and the main eld with an enhancement factor of 70 is in the capacitive gap.

The LC-resonance, as shown in Figure 2 (a), is very stable in frequency with increasing temperature and starts tuning at around 60 K, as expected when the imaginary part of the conductivity of the superconductor is reduced, as observed and discussed in detail in other works. 18,21,26 The linewidth of the LC-resonance in Fig. 1 (c) and Fig. 2 (a) are resolution limited by the Fourier transformation and appear broadened in the spectrum. However, we can extract the quality factor directly from the measured THz-TDS timetrace via a damped 5


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sinusoidal t. The quality factor and amplitude of the LC-resonance are shown in Fig. 2 (b). We reach a quality factor of Q = 25 ± 1 which decreases slowly until it dramatically drops to Q = 6 ± 0.5 at T = 70 K, where also the normalized peak transmission has dropped below 50 %. At T = 80 K, the resonance is not measurable anymore. 3a7 2.5

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Figure 2: (a) Transmission spectra as function of temperature of the resonator array, showing the evolution of the dipolar mode at fdipolar = 1.4 THz and the fundamental LC-mode at fLC = 380 GHz from T = 3 K to 120 K, normalized by the transmission at T = 220 K. The color scale is adapted to each resonance as indicated. (b) Extracted quality factor and normalized transmission of the LC-mode at 380 GHz via damped sinusoidal tting to the time traces, shown as function of temperature. As elaborated in our previous work, 18 the design of the resonator is optimized to have high ohmic losses in the normal conducting state and low radiative coupling with a large kinetic inductance in the superconducting state to achieve a fully switchable metasurface. The kinetic inductance Lk of a superconducting wire is dependent on the aspect ratio of the length and the cross sectional area and scales as f ∝

q

1/((Lg + Lk )C), where C is the capacitance

of the SRR and Lg the inductance. Compared to the original design of the switchable Nb 6


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resonator, 18 we slightly widened the inductive elements to 2 µm to balance out undesired degradation of the superconductor due to ion implantation in the FIB milling process. 34 The observed resonance frequency in YBCO shifts to fLC = 380 GHz and nevertheless remains fully switchable, due to the exploitation of the superconducting to normal state transition. One of the key requirement to be able to utilize such a superconducting metamaterial for ultra-strong coupling with Landau level transitions, is the stability of the resonance under the action of magnetic eld. For switchable Nb resonators in our previous work 18,33 we observed a fast fade-out and frequency tuning in a range of 100 mT, making it impossible to observe a clear anti-crossing with the cyclotron resonance, 33 which is expected at higher magnetic elds. Also in the work of Jin et al 24 with a dierent Nb resonator geometry, the resonance is not stable, tunes in frequency and is greatly reduced below 1 T. In this study, as displayed in Figure 3 (a), we demonstrate that utilizing a high TC superconductor, like the chosen YBCO, enables to achieve a very stable and still switchable metasurface resonance in magnetic elds. We observe a frequency tuning of as little as 6 GHz over the full magnetic eld range up to 9 T. We analyze the quality factor Q = f /δf of the resonance in the time domain by tting a damped sinusoidal function to the measured time traces, example time traces are shown in Figure 3 (b) for B = 0 T, 4 T and 9 T. We show the extracted quality factors with tting error in Figure 3 (c), together with the normalized transmission of the resonance. We report a quality factor as high as Q = 31 ± 1 in this sample for the case of no applied magnetic eld. This quality factor stays constant up to about 1 T before is starts to decrease in a linear manner until it reaches Q = 11.4 ± 0.5 at B = 9 T, where also the transmission has dropped down to 27% of the original transmission at zero magnetic eld. The decrease in quality factor can be directly linked to a decrease in conductivity of the bare YBCO lm 37 under the inuence of magnetic elds. Despite the decrease of the quality factor and transmission, the resonance stays visible at magnetic elds as high as 9 T and is thus suitable for ultra-strong coupling studies in magnetic eld while maintaining the switchable character. 7


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Figure 3: (a) Transmission spectra as function of magnetic eld for the fundamental, LCmode of the resonator at fLC = 380 GHz, measured with low pass lter. (b) Time trace of the LC-mode for B = 0 T, 4 T and 9 T utilizing a low pass lter. (c) Extracted quality factor and normalized transmission of the LC-mode at 380 GHz via damped sinusoidal tting to the time traces, shown as function of magnetic eld.

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Figure 4: (a) Sketch of the sample assembly, placing the 2DEG on top of the resonators. The stack is then held by two metal plates which are screwed together. (b) Transmission spectra as function of magnetic eld showing an anti-crossing of the dipolar mode of the resonator. (c) Transmission spectra measured with additional low pass lter to enhance the visibility of the LC-mode. (d) Single spectra of (b) are shown at the lowest and highest magnetic elds, i.e. B = 0 T (blue line) and B = 5.2 T (green line), as well as at the anti-crossing of the cyclotron and the dipolar resonator mode, B = 2.9 T.

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To achieve strong coupling between the resonator mode and the cyclotron resonance, we bring the quantum well with high mobility 2D electron gas (2DEG) into mechanical contact with the YBCO metasurface on the Sapphire. Thus, we sandwich our two substrates (both with dimensions of 5 x 5 mm2 ) between two metal plates with a circular aperture each, which is 3 mm in diameter on the sample side to couple the THz in and 2.5 mm diameter on the resonator substrate side, where the THz transmission is coupled out. The resonator array in YBCO is facing the 2DEG which is located ∼ 30 nm below the surface, as sketched in Figure 4 (a). We then screw together the two metal plates, with the samples in between, using four screws at the corners. This approach ensures a placement of the metasurface in close vicinity to the 2DEG, which is necessary, as the cyclotron resonance is coupled to the near eld of the split ring resonator capacitor gaps. The near eld of the resonator extends at maximum a few microns in orthogonal direction to the plane of split ring resonators as shown in Refs. 13,15 At the same time, the high quality of the 2DEG is maintained, which would highly degrade if YBCO would be sputtered directly on the 2DEG, as a high substrate temperature (T > 700 ◦ C) is required which lies above the growth temperature of the 2DEG in the molecular beam epitaxy. Measuring the sandwiched structure at T = 3 K in THz-TDS as function of magnetic eld reveals two very clear anti-crossings. In Figure 4 (b) we show the transmission spectra through the sample without low-pass lter, to observe the coupling to the dipolar mode of the resonator. The fundamental LC-mode of the resonator is measured additionally utilizing the low-pass lter to enhance the visibility of the low frequencies, and is displayed in Figure 4 (c). The resonance frequencies of the split ring resonator array are sensitive to the dielectric environment in close vicinity and thus have red shifted upon placing a GaAs sample with a dielectric constant of = 12.94 instead of air. The LC-mode is now at fLC = 300 GHz and the dipolar mode at fdipolar = 1.15 GHz, as can be seen by the frequency of the lower polariton branch at high magnetic elds, detuned from the anti-crossing. 1,1214 The normalized vacuum Rabi frequency ΩR /ωcyc , quantifying the coupling strength, can be determined by 10


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tting the anti-crossing with the so-called Hopeld model, 1,1214 resulting in ΩR /ωcyc = 13% for the dipolar mode and ΩR /ωcyc = 15.5% for the LC-mode. In Fig. 4 (d), single spectra of (b) are shown at the lowest and highest magnetic elds, i.e. B = 0 T (blue line) and

B = 5.2 T (green line), as well as at B = 2.9 T, which corresponds to the position of the anti-crossing of the cyclotron and dipolar resonator mode. Generally, the linewidth of the polaritons is a weighted sum of the linewidths of the two components 38 and at the anticrossing point this would results in the average of the two broadenings. The inuence of inhomogeneous broadening and superradiance 39 has been recently discussed also in the case of ultra-strong coupling of intersubband transitions 40,41 and Landau polaritons. 16 In our case the observed linewidth of the polariton branches of the coupling to the LC-mode should be equal to 12 (Γcyc + ΓLC ) ' 12 (100 GHz + 12 GHz) = 56 GHz but is experimentally limited to

∼ 70 GHz by the reection at the back of the substrate of the 2DEG, which has a typical thickness of 625 µm . For the higher order dipolar mode the linewidths of the upper (UP) and lower polariton (LP) at the anti-crossing are ΓU P = 350 GHz and ΓLP = 210 GHz in respect to an expected value 21 (Γcyc + Γdipolar ) ' 12 (100 GHz + 250 GHz) = 175 GHz. This discrepancy can be attributed partially to the dierent energy distribution of the meta-atom resonant modes with respect to an optical cavity which lead to intrinsically asymmetric line shapes for the polaritons. 42 It has to be mentioned that the presence of the 2DEG in close proximity of the whole superconducting complementary metasurface can also increase the losses with respect to the uncoupled case.

The coupling strength is, among other parameters, governed by the geometrical overlap of the resonator mode with the Landau level transitions in the 2DEG. To evaluate the spacing between the QW and the resonators in the present approach, we characterized the surface roughness of the commercial M-type YBCO lm from Ceraco by atomic force microscopy. The grains, which are also visible in the scanning electron micrograph 1 (a), are at the maximum 100 nm high. We nd a root mean square average of the height deviation (image 11


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Rq) of 13 nm over an area of 20 x 20 µm2 . The surface of the 2DEG is, as it is grown by molecular beam epitaxy, very smooth and has an average roughness of less than 1 nm and no visible height variations. The observed discrepancy of the coupling strength must stem from a long range (mm length scale) change of the substrate thickness which makes a very close alignment of the relatively large surfaces dicult. ba) GaAs

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Figure 5: (a) Sketch of the sample assembly, gluing a 1 x 1 mm2 piece of 2DEG on top of the resonators with nailpolish. (b) Scanning electron micrograph of the glued 2DEG on top of the YBCO/Sapphire. (c) Transmission spectra as function of magnetic eld showing an anti-crossing of the LC-mode of the resonator with a normalized coupling strength of ΩR /ωcyc = 24%. In order to enhance the coupling strength, we reduce the size of the 2DEG substrate to a 12


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1 x 1 mm2 piece. We then deposit a small drop of slightly diluted (with acetone) transparent nailpolish on the resonator array and immediately press the small piece of 2DEG on top. This glues after a short waiting time the 2DEG directly onto the resonator array, as sketched in Fig. 5 (a) and shown with a scanning electron micrograph in Fig. 5 (b). The nailpolish is transparent in the observed THz window and does not remove when cooling the sample. The measured transmission spectra are displayed in Fig. 5 (c) as function of magnetic eld. The now observed coupling strength is ΩR /ωcyc = 24%, a large increase compared to the above observed value of ΩR /ωcyc = 15.5%, despite the fact that the utilized 2DEG is now located even at 90 nm below the surface. We conclude therefore, that the long range height variations are indeed dominating the overall distance between the two interfaces and thus are dominating the coupling strength. However, this technique is much less reliable and reproducible compared to the mechanical coupling using screws and larger substrates. Additionally, the recorded THz-TDS timetrace is more complex as it features pulses arriving at dierent times. A part of the incoming pulse goes through the full stack and a part is passing the piece of 2DEG on the side, as the 2DEG is now smaller than the spot size, and thus carries signal which does not probe the coupled system.

In conclusion, we demonstrate a high TC superconducting metasurface with an optimized resonator design which is switchable by exploiting the transition from the superconducting to the normal conducting state. We analyzed the quality factor and transmission as function of temperature and magnetic eld and nd, that the resonance vanishes above the transition temperature of the superconductor but remains visible at low temperatures under the action of magnetic eld. Thus, we were able to conduct ultra-strong coupling experiments with a superconducting metasurface with Landau level transitions. Thereby, we overcome the technological issue of direct deposition of the superconducting lm and show successfully two techniques, which enable us to observe ultra-strong coupling by bringing the two surfaces in close vicinity, reaching a normalized coupling strength of ΩR /ωcyc = 24%. This platform has a 13


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high potential to reveal interesting phenomena predicted in the ultra-strong coupling regime 1 and enables to gain control over the coupled state. For an investigation of the ground state properties of the ultra-strongly coupled state, one would need to switch the resonance on a fast (∼ picosecond) timescale, 1 which has been demonstrated utilizing THz or IR pulses. 2931 Thus, our superconducting metasurface in combination with the 2DEG might enable the exciting possibility of experimentally accessing new physics. Future investigation will thus be aimed at further increasing the coupling strength, for example employing multiple QW structures, and investigations to switch this specic metasurface design on a fast timescale.

Acknowledgement We are grateful to Oleg Mitrofanov for technical suggestions. The authors acknowledge nancial support from the ERC Advanced grant Quantum Metamaterials in the Ultra Strong Coupling Regime (MUSiC) with the ERC Grant No. 340975. The authors also acknowledge nancial support from the Swiss National Science Foundation (SNF) through the National Centre of Competence in Research Quantum Science and Technology (NCCR QSIT). Support by the ScopeM (Scientic Center for Optical and Electron Microscopy) at ETH Zurich is gratefully acknowledged.

References (1) Ciuti, C.; Bastard, G.; Carusotto, I. Quantum vacuum properties of the intersubband cavity polariton eld. Phys. Rev. B 2005, 72 . (2) Günter, G.; Anappara, A. A.; Hees, J.; Sell, A.; Biasiol, G.; Sorba, L.; De Liberato, S.; Ciuti, C.; Tredicucci, A.; Leitenstorfer, A.; Huber, R. Sub-cycle switch-on of ultrastrong light-matter interaction. Nature 2009, 458, 178181. (3) Anappara, A. A.; De Liberato, S.; Tredicucci, A.; Ciuti, C.; Biasiol, G.; Sorba, L.; 14


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Beltram, F. Signatures of the ultrastrong light-matter coupling regime. Phys. Rev. B

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For table of contents use only manuscript title: High TC superconducting THz metamaterial for ultra-strong coupling in magnetic eld Authors: Janine Keller, Giacomo Scalari, Felice Appugliese, Elena Mavrona, Shima Rajabali, Martin J. Süess, Mattias Beck and Jerome Faist

GaAs 2DEG YBCO

Transmission

2.5

Dipolar mode

2.0

T=3K

1.5

T = 150 K

0.5 0

0.5

1.0 1.5 Frequency (THz)

2.0

2.5 max

Transmission

0.45

Frequency (THz)

Sapphire

SPP lattice mode

1.0 LC-mode

31 µm

1.1 µm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.35

0.25

0.15

LC-mode 0

0.5

1.5 1 Magnetic field (T)

2

min

Figure 6: We fabricate high temperature superconducting metasurfaces from YttriumBarium-Copper-Oxide (YBCO) lms via focused ion beam milling. The design of the complementary split ring resonators yields a high quality factor (up to Q = 31) resonance, which is fully switchable when exploiting the transition from the superconducting to normal conducting state, which is achieved by heating the sample above the critical temperature. Meanwhile, the resonance is continuously visible and frequency stable under the action of a magnetic eld, up to B = 9 T. This makes it an ideal candidate for light-matter coupling experiments with magnetic eld tunable Landau level transitions. We present two techniques to bring the metasurface in close vicinity of a 2D electron gas in an AlGaAs/GaAs QW without direct deposition, and we achieve a normalized vacuum Rabi frequency of ΩR /ωcyc = 24%.

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High Tc superconducting THz metamaterial for ultra-strong coupling in

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