Electromagnetic waves propagation through an array of superconducting qubits: manifestations of non-equilibrium steady states of qubits

Abstract

We report a theoretical study of the electromagnetic waves (EWs) propagation through an array of superconducting qubits, i.e. coherent two-level systems, embedded in a low-dissipative transmission line. We focus on the near-resonant case as the frequency of EWs $\omega \simeq {\omega }_q$, where ${\omega }_q$ is the qubit frequency. In this limit we derive the effective dynamic nonlinear wave equation allowing one to obtain the frequency dependent transmission coefficient of EWs, $D(\omega )$. In the linear regime and a relatively wide frequency region we obtain a strong resonant suppression of $D(\omega )$ in both cases of a single qubit and chains composed of a large number of densely arranged qubits. However, in narrow frequency regions a chain of qubits allows the resonant transmission of EWs with greatly enhanced $D(\omega )$. In the nonlinear regime realized for a moderate power of applied microwave radiation, we predict and analyze various transitions between states characterized by high and low values of $D(\omega )$. These transitions are manifestations of nonequilibrium steady states of an array of qubits achieved in this regime.

arXiv comment7 pages and 6 figures

References in corpus (25)

• Coupling Superconducting Qubits via a Cavity Bus
• Coherent dynamics of a flux qubit coupled to a harmonic oscillator
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Quantum oscillations in two coupled charge qubits
• Resonance Fluorescence of a Single Artificial Atom
• Nonlinear properties of left-handed metamaterials
• Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime
• The Single-Photon Router
• Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED
• Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms
• The Physics and Applications of Superconducting Metamaterials
• Josephson junction-embedded transmission-line resonators: from Kerr medium to in-line transmon
• Superconducting Metamaterials
• Quantum metamaterials: Electromagnetic waves in a Josephson qubit line
• Implementation of a Quantum Metamaterial
• Life after charge noise: recent results with transmon qubits
• Chimeras in SQUID Metamaterials
• A multi-stable switchable metamaterial
• Scattering of coherent states on a single artificial atom
• Quantum Networks in Divergence-free Circuit QED
• Breathers in Josephson junction ladders: resonances and electromagnetic waves spectroscopy
• Qubit lattice coherence induced by electromagnetic pulses in superconducting metamaterials
• Collective quantum coherent oscillations in a globally coupled array of qubits
• Effects of lasing in a one-dimensional quantum metamaterial
• Double resonance response of a superconducting quantum metamaterial: manifestation of non-classical states of photons

Cited by in corpus (1)

• Photon transport in a Bose-Hubbard chain of superconducting artificial atoms