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physica status solidi (b)

Quantum metamaterials: Electromagnetic waves in Josephson qubit lines

Alexandre M. Zagoskin, A. L. Rakhmanov, Sergey E. Savel'ev, Franco Nori

Published Apr 3, 2009• 25 citations
Publisher

Abstract

Abstract We consider the propagation of a classical electromagnetic wave through a transmission line, formed by identical superconducting charge qubits inside a superconducting resonator. Since the qubits can be in a coherent superposition of quantum states, we show that such a system demonstrates interesting new effects, such as a “breathing” photonic crystal with an oscillating bandgap. Similar behaviour is expected from a transmission line formed by flux qubits. The key ingredient of these effects is that the optical properties of the Josephson transmission line are controlled by the quantum coherent state of the qubits (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200881568

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Abstract We consider the propagation of a classical electromagnetic wave through a transmission line, formed by identical superconducting charge qubits inside a superconducting resonator. Since the qubits can be in a coherent superposition of quantum states, we show that such a system demonstrates interesting new effects, such as a “breathing” photonic crystal with an oscillating bandgap. Similar behaviour is expected from a transmission line formed by flux qubits. The key ingredient of these effects is that the optical properties of the Josephson transmission line are controlled by the quantum coherent state of the qubits (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We consider the propagation of a classical electromagnetic wave through a transmission line, formed by identical superconducting charge qubits inside a superconducting resonator. Since the qubits can be in a coherent superposition of quantum states, we show that such a system demonstrates interesting effects, such as a ``breathing'' photonic crystal with an oscillating band gap and a ``quantum Archimedean screw'' that transports, at an arbitrary controlled velocity, Josephson plasma waves through a transmission line. The key ingredient of these effects is that the optical properties of the Josephson transmission line are controlled by the quantum coherent state of the qubits.
We study the coherent control of microwave photons propagating in a superconducting waveguide consisting of coupled transmission line resonators, each of which is connected to a tunable charge qubit. While these coupled line resonators form an artificial photonic crystal with an engineered photonic band structure, the charge qubits collectively behave as spin waves in the low excitation limit, which modify the band-gap structure to slow and stop the microwave propagation. The conceptual exploration here suggests an electromagnetically controlled quantum device based on the on-chip circuit QED for the coherent manipulation of photons, such as the dynamic creation of laserlike output from the waveguide by pumping the artificial atoms for population inversion.
Quantum metamaterials consist of quantum coherent structures made up of artificial atoms connected by a transmission medium. In this work we investigate the effects of decoherence in both the transmission medium and the artificial atom using a fully quantum mechanical model. We consider a prototypical solid state 1D quantum metamaterial, i.e. a superconducting flux qubit coupled to a transmission line section on resonance. An initially excited qubit is found to effectively pump a propagating coherent pulse and increase the average output power of the transmission line. Evidence of entanglement between the qubit and the transmission line with a propagating coherent pulse is also demonstrated. This signature behaviour is found to still be evident when a level of decoherence in line with that found in typical experiments is introduced into the transmission line section as well as the qubit. Increasing levels of decoherence, particularly in the qubit, are shown to be dangerous as they destroy the quantum correlations between the qubit and the propagating field.
Quantum theory is expected to govern the electromagnetic properties of a quantum metamaterial, an artificially fabricated medium composed of many quantum objects acting as artificial atoms. Propagation of electromagnetic waves through such a medium is accompanied by excitations of intrinsic quantum transitions within individual meta-atoms and modes corresponding to the interactions between them. Here we demonstrate an experiment in which an array of double-loop type superconducting flux qubits is embedded into a microwave transmission line. We observe that in a broad frequency range the transmission coefficient through the metamaterial periodically depends on externally applied magnetic field. Field-controlled switching of the ground state of the meta-atoms induces a large suppression of the transmission. Moreover, the excitation of meta-atoms in the array leads to a large resonant enhancement of the transmission. We anticipate possible applications of the observed frequency-tunable transparency in superconducting quantum networks.
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.
Abstract We study the entanglement creation between two flux qubits interacting with electromagnetic field modes. No direct interaction between the qubits exists. Entanglement is reached using the entanglement swapping method by an interference measurement performed on photons. We discuss the influence of off‐resonance and multi‐photon initial states on the qubit–qubit entanglement. The presented scheme is able to drive an initially separable state of two qubits into an highly entangled state suitable for quantum information processing (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)