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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Transmission through a two dimensional quantum metamaterial

R. D. Wilson, M. J. Everitt, John H. Samson, S. E. Salelev, Alexandre M. Zagoskin, Timothy P. Spiller

Published May 6, 2013• 0 citations
Publisher

Abstract

We begin to explore the possibilities offered by two-dimensional quantum metamaterials by considering the transmission across a prototypical system, that is a square array of coupled qubits (two level quantum systems). We construct a simple model that accounts for the input and detection of propagating excitations in the system. We find that even a limited degree of control through an applied field can allow the tunability between distinctly different regimes of transmission properties.

DOI
10.1117/12.2018057

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A quantum metamaterial can be implemented as a quantum coherent one-dimensional array of qubits placed in a transmission line. The properties of quantum metamaterials are determined by the local quantum state of the system. Here we show that a spatially periodic quantum state of such a system can be realized without direct control of the constituent qubits, by their interaction with the initializing (``priming'') pulses sent through the system in opposite directions. The properties of the resulting quantum photonic crystal are determined by the choice of the priming pulses. This proposal can be readily generalized to other implementations of quantum metamaterials.
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Quantum metamaterials provide a promising potential test bed for probing the quantum-classical transition. We propose a feasible and scalable architecture for a solid-state quantum metamaterial. This consists of an ensemble of superconducting flux qubits inductively coupled to a superconducting transmission line. We make use of a quasi-classical model to study the transmission properties of the proposed architecture and we also discuss the possibilities for experimentation with this type of extended quantum system.
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We report a theoretical study of the ac response of superconducting quantum metamaterials (SQMs), i.e., an array of qubits (two-level systems) embedded in a low-dissipative resonator. By making use of a particular example of a SQM, namely the array of charge qubits capacitively coupled to the resonator, we obtain a second-order phase transition between an incoherent (the high-temperature phase) and coherent (the low-temperatures phase) state of photons. This phase transition in many aspects resembles the paramagnetic-ferromagnetic phase transition. The critical temperature of the phase transition, ${T}^{\ensuremath{\star}}$, is determined by the energy splitting of two-level systems $\ensuremath{\delta}$, number of qubits in the array NNN, and the strength of the interaction $\ensuremath{\eta}$ between qubits and photons in the cavity. We obtain that the photon states manifest themselves by resonant drops in the frequency-dependent transmission $D(\ensuremath{\omega})$ of electromagnetic waves propagating through a transmission line weakly coupled to the SQM. At high temperatures the $D(\ensuremath{\omega})$ displays a single resonant drop, and at low temperatures a peculiar double-resonance response has to be observed. The physical origin of such a resonant splitting is the quantum oscillations between two coherent states of photons of different polarizations.