Magnon-photon strong coupling for tunable microwave circulators

Na Zhu, Xu Han, Chang-Ling Zou, Mingrui Xu, and Hong X. Tang

Phys. Rev. A 101, 043842 – Published 28 April 2020

Abstract

We present a generic theoretical framework to describe nonreciprocal microwave circulation in a multimode cavity magnonic system and assess the optimal performance of practical circulator devices. We show that high isolation ( $> 56$ dB), extremely low insertion loss ( $< 0.05$ dB), and flexible bandwidth control can be potentially realized in high-quality-factor superconducting cavity based magnonic platforms. These circulation characteristics are analyzed with materials of different spin densities. For high-spin-density materials such as yttrium iron garnet, the strong-coupling operation regime can be harnessed to obtain a broader circulation bandwidth. We also provide practical design principles for a highly integratable low-spin-density material (vanadium tetracyanoethylene) for narrow-band circulator operation, which could benefit noise-sensitive quantum microwave measurements. This theory can be extended to other coupled systems and provide design guidelines for achieving tunable microwave nonreciprocity for both classical and quantum applications.

Received 8 December 2019
Accepted 23 March 2020

DOI:https://doi.org/10.1103/PhysRevA.101.043842

Physics Subject Headings (PhySH)

Magnetization dynamics Magnons Polaritons Superconductivity

Magnetic insulators Magnetic semiconductors Strongly correlated systems

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Na Zhu , Xu Han, Chang-Ling Zou^*, Mingrui Xu, and Hong X. Tang^†

Department of Electrical Engineering, Yale University, New Haven, Connecticut 06520, USA

^*Present address: Department of Optics, University of Science and Technology of China, Hefei 230026, China.
^†hong.tang@yale.edu

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Vol. 101, Iss. 4 — April 2020

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Images

Figure 1
(a) Schematic diagram of the device. The superconducting ring resonator supports both counterclockwise (ccw; $a_{ccw}$ ) and clockwise (cw; $a_{cw}$ ) rotating microwave modes. A ferrimagnetic disk (gray color) with similar dimension is placed on top of the superconducting ring and biased perpendicularly. There are three straight waveguides with threefold geometrical symmetry inductively coupled with the ring resonator. (b) The schematic shows the magnon-photon coupling, where the microwave mode $a_{ccw}$ is coupled with the magnon mode $m$ with the coupling strength $g_{ccw}$ , while mode $a_{cw}$ is coupled with magnon mode via a different coupling strength $g_{cw}$ . $κ_{ccw}, κ_{cw}$ , and $κ_{m}$ are the total dissipation rates for mode $a_{cw}, a_{ccw}$ , and $m$ , respectively.
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Figure 2
(a) and (b) are the mapping of the transmission ${| S_{21} |}^{2}$ and ${| S_{12} |}^{2}$ , respectively, as a function of $Δ_{m}$ and $Δ_{c}$ , under strongly coupled conditions with $κ_{e} / 2 π = 600$ MHz, $2 g / 2 π = 1200$ MHz. The mode splitting at the on-resonance condition is around $2 g$ . Under different detunings $Δ_{m} / 2 π = \pm 0.87$ GHz, the transmission spectra are plotted in (c) [(d)] when YIG is biased with magnetic resonance lower (higher) than the microwave resonance.
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Figure 3
The 20 dB isolation ratio ( $| iso . |$ ) bandwidth is plotted in (a) as a function of $g / 2 π$ and $κ / 2 π$ , where the black dashed lines are contour lines of 20, 50, 100, and 200 MHz $| iso . |$ bandwidth, respectively. The magnon frequency detuning $Δ_{m}$ is chosen at each $κ$ and $g$ to maximize the isolation bandwidth. (b) When $g / 2 π$ is set to be 1200 MHz, the insertion loss (IL) as a function of $κ_{i} / 2 π$ , for different $κ_{e} / 2 π$ is plotted. The colored lines in (b) correspond to the colored circles in (a).
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Figure 4
(a) and (b) are the mappings of the transmission ${| S_{21} |}^{2}$ and ${| S_{12} |}^{2}$ , respectively, as a function of $Δ_{m}$ and $Δ_{c}$ . The $V {[TCNE]}_{2}$ -based circulator is weakly coupled with $g / 2 π = 100$ MHz and $κ_{e} / 2 π = 600$ MHz. (c) plots the full scattering parameters, showing low $| IL |$ and high $| iso . |$ being achieved simultaneously [corresponding to the bias condition shown by the dashed white line in (a) and (b)].
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Figure 5
(a) Transmission spectra of $V {[TCNE]}_{2}$ -based circulator when the ccw and cw modes have different total external coupling rates ( $κ_{ccw, e} / 2 π = 600$ MHz, $κ_{cw, e} / 2 π = 720$ MHz). The solid lines are transmission $S$ parameters when the $Δ_{m}$ is 0.21 GHz, while the dashed lines are the transmission parameters when the magnon detuning remains the same as in the symmetrical $V {[TCNE]}_{2}$ circulator. (b) Transmission spectra when the external coupling rates to each waveguide are nondegenerate. The solid and dashed lines denote the $S$ parameters under the optimized and unoptimized magnon detunings, respectively.
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