Superconducting circuit optomechanics in topological lattices

Youssefi, Amir; Kono, Shingo; Bancora, Andrea; Chegnizadeh, Mahdi; Pan, Jiahe; Vovk, Tatiana A.; Kippenberg, Tobias J.

doi:10.48550/arxiv.2111.09133

Cited by 1 publication

(2 citation statements)

References 53 publications

(60 reference statements)

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“…In this respect, optomechanical and photonic platforms are ideal candidates to implement NH topological amplification. Specifically, in superconducting circuit optomechanics, directional amplification has been realized in few-mode systems [57,81] and the control of multi-mode arrays recently demonstrated [46]. Nano-optomechanical systems [44,82] as well as multiscale optomechanical crystal structures [45] are also ideal platforms where to implement NH lattice dynamics.…”

Section: Discussionmentioning

confidence: 99%

“…in photonic lattices [34,35], topolectric circuits [36][37][38][39][40], mechanical [41,42] and robotic [43] metamaterials. Especially suitable for implementing our ideas are nano-optomechanical lattices [44,45] and superconducting circuit optomechanics [46], where non-reciprocal couplings, gain and loss can be engineered to a high degree. We also expect our approach to be applicable to more general NH systems, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification

Brunelli¹,

Wanjura²,

Nunnenkamp³

2022

Preprint

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Non-Hermitian (NH) lattice Hamiltonians display a unique kind of energy gap and extreme sensitivity to boundary conditions. Due to the NH skin effect, the separation between edge and bulk states is blurred and the (conventional) bulk-boundary correspondence is lost. Here, we restore the bulk-boundary correspondence for the most paradigmatic class of NH Hamiltonians, namely those with one complex band and without symmetries. We obtain the desired NH Hamiltonian from the (mean-field) unconditional evolution of driven-dissipative cavity arrays, in which NH terms-in the form of non-reciprocal hopping amplitudes, gain and loss-are explicitly modelled via coupling to (engineered and non-engineered) reservoirs. This approach removes the arbitrariness in the definition of the topological invariant, as point-gapped spectra differing by a complex-energy shift are not treated as equivalent; the origin of the complex plane provides a common reference (base point) for the evaluation of the topological invariant. This implies that topologically non-trivial Hamiltonians are only a strict subset of those with a point gap and that the NH skin effect does not have a topological origin. We analyze the NH Hamiltonians so obtained via the singular value decomposition, which allows to express the NH bulk-boundary correspondence in the following simple form: an integer value ν of the topological invariant defined in the bulk corresponds to |ν| singular vectors exponentially localized at the system edge under open boundary conditions, in which the sign of ν determines which edge. Non-trivial topology manifests as directional amplification of a coherent input with gain exponential in system size. Our work solves an outstanding problem in the theory of NH topological phases and opens up new avenues in topological photonics.

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