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Unidirectional zero reflection as gauged parity-time symmetry

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 Added by James Gear
 Publication date 2017
  fields Physics
and research's language is English




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We introduce here the concept of establishing Parity-time symmetry through a gauge transformation involving a shift of the mirror plane for the Parity operation. The corresponding unitary transformation on the systems constitutive matrix allows us to generate and explore a family of equivalent Parity-time symmetric systems. We further derive that unidirectional zero reflection can always be associated with a gauged PT-symmetry and demonstrate this experimentally using a microstrip transmission-line with magnetoelectric coupling. This study allows us to use bianisotropy as a simple route to realize and explore exceptional point behaviour of PT-symmetric or generally non-Hermitian systems.



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Parity-Time (PT) symmetric systems have been widely recognized as fundamental building blocks for the development of novel, ultra-sensitive opto-electronic devices. However, arguably one of their major drawbacks is that they rely on non-linear amplification processes that could limit their potential applications, particularly in the quantum realm. In this work, we show both theoretically and experimentally that gain-loss, PT-symmetric systems can be designed by means of linear, time-modulated components. More specifically, by making use of a state-of-the-art, fully reconfigurable electronic platform, we demonstrate that PT-symmetry breaking transitions can be observed by properly modulating the inductance (L) and the capacitance (C) of a single LC circuit. Importantly, the lossless dynamic-variations of the electrical components used in our LC circuits allow us to control the static and periodic (Floquet) regimes of our PT-symmetric system. Our results challenge the conventional wisdom that at least two-oscillator systems are needed for observing PT-symmetric phenomena, and provide a new perspective in the field of synthetic PT symmetry with important implications for sensing, energy transfer and topology.
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A zero index metamaterial (ZIM) can be utilized to block wave (super-reflection) or conceal objects completely (cloaking). The super-reflection device is realized by a ZIM with a perfect electric (magnetic) conductor inclusion of arbitrary shape and size for a transverse electric (magnetic) incident wave. In contrast, a ZIM with a perfect magnetic (electric) conductor inclusion for a transverse electric (magnetic) incident wave can be used to conceal objects of arbitrary shape. The underlying physics here is determined by the intrinsic properties of the ZIM.
We develop a theory of charge-parity-time (CPT) frameness resources to circumvent CPT-superselection. We construct and quantify such resources for spin~0, $frac{1}{2}$, 1, and Majorana particles and show that quantum information processing is possible even with CPT superselection. Our method employs a unitary representation of CPT inversion by considering the aggregate action of CPT rather than the composition of separate C, P and T operations, as some of these operations involve problematic anti-unitary representations.
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In this letter, we consider exact $mu-tau$ reflection symmetries for quarks and leptons. Fermion mass matrices are assumed to be four-zero textures for charged fermions $f = u,d,e$ and a symmetric matrix for neutrinos $ u_{L}$. By a bi-maximal transformation, all the mass matrices lead to $mu-tau$ reflection symmetric forms, which seperately satisfy $T_{u} , m_{u, u}^{*} , T_{u} = m_{u, u}$ and $T_{d} , m_{d,e}^{*} , T_{d} = m_{d,e}$. Reconciliation between the $mu-tau$ reflection symmetries and observed $sin theta_{13}$ predicts $delta_{CP} simeq 203^{circ}$. Moreover, imposition of universal texture $(m_{f})_{11} = 0$ for $f=u,d, u,e$ predicts the normal hierarchy with the lightest neutrino mass $|m_{1}| = 6.26$ or $2.54$ meV.
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