Topological framework for directional amplification in driven-dissipative cavity arrays

Wanjura, Clara C.; Brunelli, Matteo; Nunnenkamp, Andreas

doi:10.1038/s41467-020-16863-9

Cited by 123 publications

(113 citation statements)

References 65 publications

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“…In particular, the quantity introduced below displays quantized plateaus that precisely match spectral winding numbers, making it possible to distinguish between one nontrivial point-gap topology from another. This is a true advance as compared with earlier interesting attempts where signal amplification was only used to probe NHSE under OBC 39,40 .…”

Section: Resultsmentioning

confidence: 88%

“…Such correspondence between spectral winding numbers and quantized response is arguably broader in scope than in the case of momentum-space topology, because spectral winding does not even require translational invariance. Our results are relevant to a number of current experimental platforms of non-Hermitian systems 30,31,33,39,[59][60][61] . In the context of classical electrical circuits, we have shown that a quantized response can be easily extracted from extremely experimentally accessible impedance measurements.…”

Section: Discussionmentioning

confidence: 86%

“…Notably, spectral winding as a topological feature is not directly related to quantum physics and is hence a classical concept. Furthermore, the notion of classical response can be also a property of the Green's function alone, which has been recently shown to exhibit exponential growth in the presence of nontrivial spectral winding numbers [39][40][41] . While nontrivial complex energy winding is in principle well defined for quantum systems, it is most physically relevant in classical settings like mechanical, photonic, plasmonic, and electrical systems where non-Hermiticity does not present significant measurement difficulties 30,31,42 .…”

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confidence: 99%

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Quantized classical response from spectral winding topology

Lee

et al. 2021

Nat Commun

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Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge states as their topological winding. In this work, we discover the totally new paradigm of quantized classical response, which is based on the spectral winding number in the complex spectral plane, rather than the winding of eigenstates in momentum space. Such quantized response is classical insofar as it applies to phenomenological non-Hermitian setting, arises from fundamental mathematical properties of the Green’s function, and shows up in steady-state response, without invoking a conventional linear response theory. Specifically, the ratio of the change in one quantity depicting signal amplification to the variation in one imaginary flux-like parameter is found to display fascinating plateaus, with their quantized values given by the spectral winding numbers as the topological invariants.

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Section: Resultsmentioning

confidence: 88%

Section: Discussionmentioning

confidence: 86%

mentioning

confidence: 99%

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Quantized classical response from spectral winding topology

Lee

et al. 2021

Nat Commun

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“…Devices that exploit the rotational inertia of the resonator, such as chiral structures [ 34 , 35 , 36 , 37 , 38 ] or gyroscopic spinners [ 29 ], are the most popular designs of directional amplifiers in periodic structures, where the longitudinal motion of the finite size mass elements is coupled to their rotation, following a spin. Directional amplification systems have also been implemented in other scientific fields, such as quantum information processing [ 39 ] in terms of controlling amplification and directionality of electromagnetic signals [ 40 ] as well as in photonic systems [ 41 , 42 ]. However, a different approach has been followed in those cases.…”

Section: Introductionmentioning

confidence: 99%

2D Dynamic Directional Amplification (DDA) in Phononic Metamaterials

2021

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Phononic structures with unit cells exhibiting Bragg scattering and local resonance present unique wave propagation properties at wavelengths well below the regime corresponding to bandgap generation based on spatial periodicity. However, both mechanisms show certain constraints in designing systems with wide bandgaps in the low-frequency range. To face the main practical challenges encountered in such cases, including heavy oscillating masses, a simple dynamic directional amplification (DDA) mechanism is proposed as the base of the phononic lattice. This amplifier is designed to present the same mass and use the same damping element as a reference two-dimensional (2D) phononic metamaterial. Thus, no increase in the structure mass or the viscous damping is needed. The proposed DDA can be realized by imposing kinematic constraints to the structure’s degrees of freedom (DoF), improving inertia and damping on the desired direction of motion. Analysis of the 2D lattice via Bloch’s theory is performed, and the corresponding dispersion relations are derived. The numerical results of an indicative case study show significant improvements and advantages over a conventional phononic structure, such as broader bandgaps and increased damping ratio. Finally, a conceptual design indicates the usage of the concept in potential applications, such as mechanical filters, sound and vibration isolators, and acoustic waveguides.

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“…We shall, as customary in the context of quantum optics [4][5][6], define a coherent feedback loop as one where a set of output modes, interacting with a system at an input-output interface, may be manipulated through quantum CP maps and then fed back into a system as input modes at another interface. This approach is similar to that used in the established field of "cascaded quantum systems," where the output of one system is used as the input of another [7][8][9][10], and of the related "all-optical" feedback [11], the difference being that here the output is fed back into the system from whence it came.…”

Section: Introductionmentioning

confidence: 99%

Ultimate squeezing through coherent quantum feedback

Harwood

Serafini

2020

Phys. Rev. Research

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Coherent feedback is the use of feedback loops not involving any measurements for the purpose of quantum control. This can be contrasted to measurement-based feedback where the feedback signal is directed by the result of measurements upon the system. Here, we develop a general framework to describe interferometric coherent feedback loops and prove that, under any such scheme, the steady-state squeezing of a bosonic mode subject to a rotating wave coupling with a white-noise environment and to any quadratic Hamiltonian must abide by a noise-dependent bound that reduces to the 3-dB limit at zero temperature. Such a finding is compared, at fixed dynamical parameters, with the performance of homodyne continuous monitoring of the output modes, which allows one to beat coherent feedback and the 3-dB limit under certain dynamical conditions.

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Topological framework for directional amplification in driven-dissipative cavity arrays

Cited by 123 publications

References 65 publications

Quantized classical response from spectral winding topology

Quantized classical response from spectral winding topology

2D Dynamic Directional Amplification (DDA) in Phononic Metamaterials

Ultimate squeezing through coherent quantum feedback

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