Unconventional Singularity in Anti-Parity-Time Symmetric Cavity Magnonics

Y. Yang, Yi-Pu Wang, J. W. Rao, Y. S. Gui, B. M. Yao, W. Lu, and C.-M. Hu

Phys. Rev. Lett. 125, 147202 – Published 1 October 2020

Abstract

By engineering an anti-parity-time (anti- $PT$ ) symmetric cavity magnonics system with precise eigenspace controllability, we observe two different singularities in the same system. One type of singularity, the exceptional point (EP), is produced by tuning the magnon damping. Between two EPs, the maximal coherent superposition of photon and magnon states is robustly sustained by the preserved anti- $PT$ symmetry. The other type of singularity, arising from the dissipative coupling of two antiresonances, is an unconventional bound state in the continuum (BIC). At the settings of BICs, the coupled system exhibits infinite discontinuities in the group delay. We find that both singularities coexist at the equator of the Bloch sphere, which reveals a unique hybrid state that simultaneously exhibits the maximal coherent superposition and slow light capability.

Received 15 May 2020
Revised 27 July 2020
Accepted 9 September 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.147202

Physics Subject Headings (PhySH)

Dissipative dynamics Extraordinary optical transmission Magnetization dynamics Magnons Polaritons

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. Yang¹, Yi-Pu Wang ^1,*, J. W. Rao¹, Y. S. Gui ¹, B. M. Yao², W. Lu², and C.-M. Hu ^1,†

¹Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
²State Key Laboratory of Infrared Physics, Chinese Academy of Sciences, Shanghai 200083, People’s Republic of China

^*Yipu.Wang@umanitoba.ca
^†hu@physics.umanitoba.ca

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Vol. 125, Iss. 14 — 2 October 2020

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Images

Figure 1
(a) In a $PT$ symmetric system, two subsystems $a$ and $b$ share the same frequency and balanced loss and gain, and coherently coupled with each other at the rate $J$ . In an anti- $PT$ symmetric system, two subsystems $a$ and $m$ are frequency detuned but share the same loss (or gain), and they dissipatively coupled with each other at the rate $Γ$ . The inset transmission amplitude spectrum indicates the profile of a BIC. (b) Schematic setup of the system designed to realize anti- $PT$ symmetry and singularities. A YIG sphere is placed above the center of the crossline-microwave circuit to realize purely dissipative coupling between the cavity and magnon modes. A grounded loop antenna above the YIG sphere is used to control the damping rate of the magnon mode. External magnetic field $H$ is applied perpendicular to the cavity plane.
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Figure 2
(a),(b) Typical transmission amplitude $| S_{21} |$ and phase $P_{21}$ at $Δ_{H} / 2 π = - 80 MHz$ are plotted as a function of the probing frequency $ω$ . The red and blue arrows mark the magnonlike and cavitylike modes, respectively. (c),(e),(g) The measured transmission amplitude $| S_{21} |$ mappings as a function of the frequency detuning $Δ_{ω} = ω - ω_{ref}$ and field detuning $Δ_{H}$ in the conditions of $α / 2 π = 5.6 MHz < β / 2 π$ , $α / 2 π = 10 MHz = β / 2 π$ , and $α / 2 π = 19.2 MHz > β / 2 π$ . The hot spots with the transmission amplitude approaches zero are two BICs. (d),(f),(h): The group delay $τ_{g}$ mappings. Two BICs emerge as singularities, where the group delay abruptly switches from negative infinity (purple) to positive infinity (red). The vertical red and blue arrows indicate the detuning setting for (a),(b). The calculated eigenfrequency dispersions are coplotted as black curves.
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Figure 3
(a),(c),(e) The real parts of the eigenvalues as a function of the field detuning $Δ_{H}$ in the conditions of $α < β$ (triangles), $α = β$ (circles), and $α > β$ (squares). (b),(d),(f) The imaginary parts of the eigenvalues in corresponding conditions. The eigenvalues are colored by the dominance of cavity mode (blue) and magnon mode (red), grey color is the $50 ∶ 50$ dominance in between. The BICs are observed at zero damping and marked by green arrows. In condition $α = β$ , for $| Δ_{H} / 2 Γ | < 1$ , the system is in the anti- $PT$ symmetry-preserved phase (shaded in gold and marked as APT). For $| Δ_{H} / 2 Γ | > 1$ , the system is in the anti- $PT$ symmetry-broken phase. The EPs are observed at $| Δ_{H} / 2 Γ | = 1$ and marked by orange arrows. The calculated eigenfrequency dispersions are coplotted as black curves.
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Figure 4
The Riemann surfaces of the calculated (a) real and (b) imaginary eigenvalues in the parameter space of field detuning $Δ_{H}$ and damping difference $α - β$ . The EPs are labeled by orange circles, and the measured eigenvalues of conditions $α < β$ , $α = β$ , and $α > β$ are added as triangles, circles, and squares. The position of $BIC -$ is emphasized as green dashed line. Only negative field detuning data are displayed for clarity. (c) We construct the Bloch spheres in the spherical coordinates $θ, φ$ that related to Cartesian coordinates $x$ , $y$ , $z$ . The polar and azimuthal angles are defined in the text. The colorbar is defined by the relative intensity $θ$ , which shows the dominance of cavity mode $| a ⟩$ (blue) and magnon mode $| m ⟩$ (red), with the grey color as the $50 ∶ 50$ dominance in between. (d),(e),(f) The Bloch spheres of conditions $α < β$ , $α = β$ , and $α > β$ . The colored arrows indicate the direction of increasing $Δ_{H}$ . The EPs and BICs are labeled by the orange circles and the green stars. The equator of the Bloch sphere with $θ = π / 2$ is marked by the grey dashed lines. The anti- $PT$ symmetry-preserved phase on the equator is shaded in gold in condition $α = β$ .
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