ARTICLE https://doi.org/10.1038/s42005-019-0266-x OPEN Introducing coherent time control to cavity magnon-polariton modes Tim Wolz 1*, Alexander Stehli1, Andre Schneider 1, Isabella Boventer1,2, Rair Macêdo 3, Alexey V. Ustinov1,4, Mathias Kläui 2 & Martin Weides 1,3* 1234567890():,; By connecting light to magnetism, cavity magnon-polaritons (CMPs) can link quantum computation to spintronics. Consequently, CMP-based information processing devices have emerged over the last years, but have almost exclusively been investigated with single-tone spectroscopy. However, universal computing applications will require a dynamic and on- demand control of the CMP within nanoseconds. Here, we perform fast manipulations of the different CMP modes with independent but coherent pulses to the cavity and magnon sys- tem. We change the state of the CMP from the energy exchanging beat mode to its normal modes and further demonstrate two fundamental examples of coherent manipulation. We first evidence dynamic control over the appearance of magnon-Rabi oscillations, i.e., energy exchange, and second, energy extraction by applying an anti-phase drive to the magnon. Our results show a promising approach to control building blocks valuable for a quantum internet and pave the way for future magnon-based quantum computing research. 1 Institute of Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany. 2 Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany. 3 James Watt School of Engineering, Electronics & Nanoscale Engineering Division, University of Glasgow, Glasgow G12 8QQ, UK. 4 Russian Quantum Center, National University of Science and Technology MISIS, Moscow, Russia 119049. *email: [email protected]; [email protected] COMMUNICATIONS PHYSICS | (2020) 3:3 | https://doi.org/10.1038/s42005-019-0266-x | www.nature.com/commsphys 1 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-019-0266-x he cavity magnon-polariton (CMP)1–4 is a hybrid quasi- strength g: particle arising from strong coupling between photons and ω À ω~ T c g h magnon excitations. It interconnects light with magnetism ¼ : ð Þ ω À ω~ 0 1 presenting itself as an excellent candidate to combine quantum g r m 5,6 fi information with spintronics .The rst CMP-based devices, Here, ω~ and ω~ denote the complex eigenfrequencies of the 7 c r such as a gradient memory and radio-frequency-to-optical cavity and magnon system, respectively. They are defined as transducers8 have already been developed. The latter ones, in ω~ ¼ ω À βω ω~ ¼ ω À αω c cpffiffiffiffiffiffii c and r r i c with barep cavityffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi frequency particular, are crucial devices for a quantum internet, for ω ¼ 1= LC, bare magnon frequency ω ¼ γ jHjðjHjþM Þ, instance, because they bridge microwave-frequency based c r 0 where α, β are damping factors, γ the gyromagnetic ratio of the quantum processors to long range optical quantum networks. Kittel-mode and M its saturation magnetization. Since the Since the recent emergence of this hybrid quasiparticle, three 0 right hand side of Eq. (1) is zero, the equation describes different models, in particular, have helped to unravel the the system during free evolution. The driven case can physicsofCMPsoverthelastyears:first, the picture of two be modeled by inserting two harmonic drive tones coupled oscillators, which is the most intuitive one; the ¼ ðω À φ Þ Fc;m Ac;m cos 0t c;m , one to each line and differing in underlying physics, however, is only revealed from an elec- φ tromagnetic viewpoint, which is the second model and shows a phase and amplitude A. Combining driven case and free phase correlation between cavity and magnon excitation9;and evolution, Eq. (1) can be numerically integrated for various finally, the quantum description of the CMP, which has, for pulse combinations yielding simulated data of our experiments instance, given the theoretical framework for a coupling of (Supplementary Note 2). 10,11 If both subsystems are exactly on resonance, i.e, at their crossing magnons to a superconducting qubit .Manyspectroscopic ω ¼ ω ¼ ω experiments have led to new insights about loss channels3,12,13, point, c r 0, the eigenfrequencies of Eq. (1) are given – ω ¼ ω ξ ¼ð ; Þ their temperature dependence14 16, and to the observation of by ± 0 ± g with the eigenvectors ± 1 ±1 , the so-called 17–19 normal modes. A single, short pulse to the cavity prepares the level attraction . These spectroscopic measurements, ξ ¼ ξ þ ξ ¼ð ; Þ however, are performed under continuous driving, and while system in the non-eigenstate 0;c þ À 1 0 ,knownas they have yielded great physical insight into these hybrid sys- beat mode. The excitation, and therefore the energy, periodically tems, flexible and universal information processing requires the oscillates between cavity and magnon. Hence, the system displays 2,22 – manipulation of such physical states on demand and on classical magnon-Rabi oscillations .Figures1a c illustrate these nanosecond timescales. Despite this necessity for fast manip- different modes in the intuitive picture of two coupled pendula. To ξ ulation, the literature about time resolved experiments with observe the normal modes ± , where no energy is exchanged, one either an yttrium iron garnet (YIG) waveguide20 or has to coherently and simultaneously excite the cavity and magnon CMPs2,7,21,22 is scarce and confined to cavity-pulsing. A system while recording the cavity response. simultaneous and coherent control over both subsystems has yet to be demonstrated, which is the subject of this work. Experimental setup. Our sample consists of a copper reentrant 4 ω = π ¼ : Here, we establish the control over the cavity and magnon cavity resonating at r 2 6 58 GHz. An additional stripline system by using coherent manipulation pulses on the timescale of with a second microwave port is fixed to the bottom of the cavity. nanoseconds. We observe the transition from maximum energy This port allows for the direct manipulation of the magnon mode, exchange to no energy exchange between cavity photons and similar to the work of Wang et al.25 and Boventer et al.19,ina magnons depending on the applied pulses. We employ these YIG sphere with a diameter of 0.5 mm. The sphere is placed close results for a dynamic control of the different modes and for the to the magnetic antinode of the cavity. The cavity’s magnetic rf- extraction of the total energy from the system by destructive field, the stripline rf-field and the external bias field stand all interference within the sample. Moreover, all results are validated perpendicular to each other (Supplementary Note 3), which by numerical simulations. minimizes unwanted crosstalk between the two rf-fields. Mea- surements are performed with a time-domain setup (Fig. 1d) comprising three parts: magnon manipulation, cavity manipula- Results tion, and recording. It enables us to independently but coherently fl Theoretical background. In our experiments the electro- pulse the two subsystems and record the re ected signal, i.e., the magnetic resonance of a copper cavity interacts with the Kittel outgoing photons, of the cavity. Figure 1e depicts the pulse mode - the uniform ferromagnetic resonance (FMR)23 -ofa scheme that we employ to prepare the system in its normal modes YIGsphere mounted inside the cavity. The Landau-Lifshitz- by varying the following two parameters: An arbitrary φ Gilbert (LLG) equation24 describes the Kittel-mode as a mac- phase offset between the pulses, and the applied power Àiωt Δ2 ¼ 2 = 2 rospin with dynamic magnetization mðtÞ¼me in an ratio Am Ac , allowing for an amplitude matching and thus external magnetic field H. The cavity resonance can be mod- equal excitation of cavity and magnon system. Unless otherwise eled as an RLC circuit, with resistor R, inductance L and stated, the manipulation pulses are 10 ns short. This results in a capacitance C. Following the model proposed by Bai et al.9,a bandwidth of the pulses much larger than the linewidths of cavity linear coupling between both systems arises from their mutual and magnon. However, only the ratio of stored energy is of back actions, leading to a phasecorrelation.Thechanging importance and we chose such short drive tones to only set the magnetization of the FMR induces an electric field in the cavity initial state of the system and to not drive the CMP into its steady according to Faraday’slaw.FollowingAmpère’slaw,thecavity state response. field gives rise to a cavity current, which produces a magnetic rf-field (radio frequency) hðtÞ¼heÀiωt driving the FMR. System characterization.Asafirst step, we characterize the system Combining the LLG, the RLC equation and Maxwell’slaws,we spectroscopically. The avoided level crossing data (Fig. 2a) show a obtain a system of coupled equations for h and m (Supple- coupling strength of g=2π ¼ 24:6 MHz, as theoretically expected mentary Note 1). If both subsystems are close to resonance, for this cavity magnon-system14, and identical decay rates (Sup- κ = π ¼ : these equations can be simplified to the eigenvalue equations of plementary Note 4) at the crossing point of crp 2 2 1MHzdue two coupled harmonic oscillators with constant coupling to equal hybridization. We hence conclude that our system is 2 COMMUNICATIONS PHYSICS | (2020) 3:3 | https://doi.org/10.1038/s42005-019-0266-x | www.nature.com/commsphys COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-019-0266-x ARTICLE ξþ (ξÀ), which is characteristic for the normal modes9. These a d DAC ADC ξ+ results are in excellent agreement with numerical simulation of Eq. (1), which can be found in Supplementary Note 5. M C Transition to normal modes. We also monitor the transition ξ ξ from 0 to ± directly at the crossing point with the same pulse Cavity sequence (Fig.