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arXiv:1602.01367 · Physical Review A

Superconducting quantum metamaterials as an active lasing medium: Effects of disorder

Martin Koppenhöfer, Michael Marthaler, Gerd Schön

Published Jun 8, 2016• 7 citations
arXivHTMLPDF

Abstract

A metamaterial formed by superconducting circuits or quantum dots can serve as an active lasing medium when coupled to a microwave resonator. For these artificial atoms, in contrast to real atoms, variations in their parameters cannot be avoided. In this paper, we examine the influence of disorder on such a multiatom lasing setup. We find that the lasing process evolves into a self-organized stationary state that is quite robust against disorder. The reason is that photons created by those atoms which are in or close to resonance with the resonator stimulate the emission also of more detuned atoms. Not only the number of photons grows with the number of atoms but also the width of the resonance as a function of the detuning. Similar properties are found for other types of disorder such as variations in the individual coupling. We present relations on how the allowed disorder scales with the number of atoms and confirm it by a numerical analysis. We also provide estimates for the sample-to-sample variations to be expected for setups with moderate numbers of atoms.

DOI
10.1103/physreva.93.063808

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A metamaterial formed by superconducting circuits or quantum dots can serve as an active lasing medium when coupled to a microwave resonator. For these artificial atoms, in contrast to real atoms, variations in their parameters cannot be avoided. In this paper, we examine the influence of disorder on such a multiatom lasing setup. We find that the lasing process evolves into a self-organized stationary state that is quite robust against disorder. The reason is that photons created by those atoms which are in or close to resonance with the resonator stimulate the emission also of more detuned atoms. Not only the number of photons grows with the number of atoms but also the width of the resonance as a function of the detuning. Similar properties are found for other types of disorder such as variations in the individual coupling. We present relations on how the allowed disorder scales with the number of atoms and confirm it by a numerical analysis. We also provide estimates for the sample-to-sample variations to be expected for setups with moderate numbers of atoms.
We consider a disordered quantum metamaterial formed by an array of superconducting flux qubits coupled to microwave photons in a cavity. We map the system on the Tavis-Cummings model accounting for the disorder in frequencies of the qubits. The complex transmittance is calculated with the parameters taken from state-of-the-art experiments. We demonstrate that photon phase shift measurements allow to distinguish individual resonances in the metamaterial with up to 100 qubits, in spite of the decoherence spectral width being remarkably larger than the effective coupling constant. Our simulations are in agreement with the results of the recently reported experiment.
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Electromagnetic pulse propagation in a quantum metamaterial, an artificial, globally quantum coherent optical medium, is numerically simulated. We show that a one-dimensional quantum metamaterial based on superconducting quantum bits, initialized in an easily reachable factorized excited state, demonstrates lasing in the microwave range, accompanied by the chaotization of qubit states and generation of higher harmonics. These effects may provide a tool for characterization and optimization of quantum metamaterial prototypes.
We explore experimentally a quantum metamaterial based on a superconducting chip with 25 frequency-tunable transmon qubits coupled to a common coplanar resonator. The collective bright and dark modes are probed via the microwave response, i.e., by measuring the transmission amplitude of an external microwave signal. All qubits have individual control and readout lines. Their frequency tunability allows the number NNN of resonantly coupled qubits to change and a disorder in their excitation frequencies to be introduced with preassigned distributions. While increasing NNN, we demonstrate the expected N1/2{N}^{1/2}N1/2 scaling law for the energy gap (Rabi splitting) between bright modes around the cavity frequency. By introducing a controllable disorder and averaging the transmission amplitude over a large number of realizations, we demonstrate a decay of mesoscopic fluctuations which mimics an approach towards the thermodynamic limit. The collective bright states survive in the presence of disorder when the strength of individual qubit coupling to the cavity dominates over the disorder strength.
The use of artificial atoms as an active lasing medium opens a way to construct novel sources of nonclassical radiation. An example is the creation of photon-number squeezed light. Here, we present a design of a laser consisting of multiple Cooper-pair transistors coupled to a microwave resonator. Over a broad range of experimentally realizable parameters, this laser creates photon-number squeezed microwave radiation, characterized by a Fano factor $F\ensuremath{\ll}1$, at a very high resonator photon number. We investigate the impact of gate-charge disorder in a Cooper-pair transistor and show that the system can create squeezed strong microwave fields even in the presence of maximum disorder.