Superconducting Quantum Metamaterials

Abstract

Quantum metamaterials is a concept bridging the fields of conventional metamaterials and quantum processing in solid state. These are artificial media comprised of quantum coherent, specifically designed unit elements (e.g., qubits), such that the quantum state of these elements can be externally controlled, and that the system maintains quantum coherence on the characteristic times and scales of electromagnetic signal propagation through it. This chapter focuses on quantum metamaterials based on superconducting qubits, which-due to the developments in theory and experimental and fabrication techniques over the last decade-currently provide the most feasible implementation of the concept. IntroductionThe term "quantum metamaterial" was first introduced as a logical extension of a conventional metamaterial in [1, 2], independently and in somewhat different contexts. In [1] it was applied to the plasmonic properties of a stack of 2D layers, each of them thin enough for the motion of electrons in the normal direction to be completely quantized. Therefore "the wavelike nature of matter" had to be taken into account at a single-electron level, but the question of quantum coherence in the system did not arise. On the contrary, in [2] the requirement that their system comprised of artificial atoms (qubits) maintains quantum coherence on the time scale of the electromagnetic pulse propagation across it was made explicit, along with the direct control of the quantum state of at least some qubits, for the reason that it was the coherent quantum dynamics of qubits, that determined the "optical" properties of the system. Currently the term "quantum metamaterial" is being used in both senses (see, e.g., [3][4][5][6][7][8]).

An exactly solvable quantum-metamaterial type model

“…It ought to be emphasized that a finite-dimensional approximation is bound to introduce some artifacts. In particular, the one based on a finite Haar transform will yield a small (and decreasing with the dimension) diagonal component of C. (Note that the infinite dimensional C as defined in (5) has no "diagonal" term.) A representation of C in the Haar basis is illustrated numerically in Fig.…”

“…On the other hand, the theoretical analysis of large quantum systems has been restricted to special, though important, cases (e.g., those of factorized or nearly factorized quantum states), which can be described using standard methods of quantum many-body theory. At the same time, it is already possible to build at least partially quantum coherent arrays of quantum bits, [4,5]. There are reasons to believe that the properties of such systems depend strongly on long-range quantum correlations, [6,7].…”

“…theory. At the same time, it is already possible to build at least partially quantum coherent arrays of quantum bits, [4,5]. There are reasons to believe that the properties of such systems depend strongly on long-range quantum correlations, [6,7].…”