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Register a new userCanonical circuit quantization with linear nonreciprocal devices
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Added by
Adrian Parra-Rodriguez
Publication date
2018
fields
Physics
and research's language is
English
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Nonreciprocal devices effectively mimic the breaking of time-reversal symmetry for the subspace of dynamical variables that they couple, and can be used to create chiral information processing networks. We study the systematic inclusion of ideal gyrators and circulators into Lagrangian and Hamiltonian descriptions of lumped-element electrical networks. The proposed theory is of wide applicability in general nonreciprocal networks on the quantum regime. We apply it to pedagogical and pathological examples of circuits containing Josephson junctions and ideal nonreciprocal elements described by admittance matrices, and compare it with the more involved treatment of circuits based on nonreciprocal devices characterized by impedance or scattering matrices. Finally, we discuss the dual quantization of circuits containing phase-slip junctions and nonreciprocal devices.
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We develop a systematic procedure to quantize canonically Hamiltonians of light-matter models of transmission lines coupled through lumped linear lossless ideal nonreciprocal elements, that break time-reversal symmetry, in a circuit QED set-up. This is achieved through a description of the distributed subsystems in terms of both flux and charge fields. We prove that this apparent redundancy is required for the general derivation of the Hamiltonian for a wider class of networks. By making use of the electromagnetic duality symmetry in 1+1 dimensions, we provide unambiguous identification of the physical degrees of freedom, separating out the nondynamical parts. This doubled description can also treat the case of other extended lumped interactions in a regular manner that presents no spurious divergences, as we show explicitly in the example of a circulator connected to a Josephson junction through a transmission line. This theory enhances the quantum engineering toolbox to design complex networks with nonreciprocal elements.
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Superconducting circuits have become a leading quantum technology for testing fundamentals of quantum mechanics and for the implementation of advanced quantum information protocols. In this chapter, we revise the basic concepts of circuit network theory and circuit quantum electrodynamics for the sake of digital and analog quantum simulations of quantum field theories, relativistic quantum mechanics, and many-body physics, involving fermions and bosons. Based on recent improvements in scalability, controllability, and measurement, superconducting circuits can be considered as a promising quantum platform for building scalable digital and analog quantum simulators, enjoying unique and distinctive properties when compared to other advanced platforms as trapped ions, quantum photonics and optical lattices.
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