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.
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Notes
- 1.
For a more detailed presentation see [10] and references therein.
- 2.
- 3.
We will be using the Gaussian units throughout, as more convenient for our formalism.
- 4.
The circuits we will be dealing with here do not contain resistive elements. In a general case, they can be taken care of through the so called dissipative function (see [10] and references therein).
- 5.
The distinction is here purely notional—if instead of node fluxes, which are essentially currents, as follows from (13.15), we chose as coordinates the node charges, proportional to the voltages \(V_j\), the roles would have been reversed.
- 6.
The approximation of a factorized wave function, (13.37), is quite a drastic simplification, since it excludes such macroscopic quantum superposition states as \((\dots \otimes |0\rangle \otimes |0\rangle \otimes |0\rangle \otimes \dots ) \pm (\dots \otimes |1\rangle \otimes |1\rangle \otimes |1\rangle \otimes \dots )\). Such GHz-like states are necessary for the realization of, e.g., quantum birefringence. Nevertheless even factorized states should give rise to interesting quantum effects [2], while both their theoretical treatment and experimental realization are significantly simpler.
- 7.
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Acknowledgments
I am greatly indebted to O. Astafiev, M. Everitt, E. Il’ichev, F. Nori, A.L. Rakhmanov, J.H. Samson, S. Saveliev and R.D. Wilson for their inspiring collaboration in developing this field and for many illuminating discussions. This work was supported by a grant from John Templeton Foundation.
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Zagoskin, A.M. (2015). Superconducting Quantum Metamaterials. In: Shadrivov, I., Lapine, M., Kivshar, Y. (eds) Nonlinear, Tunable and Active Metamaterials. Springer Series in Materials Science, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-08386-5_13
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