A quantum model for rf-SQUIDs based metamaterials enabling 3WM and 4WM Travelling Wave Parametric Amplification
arXiv:2009.01002 · doi:10.1103/PhysRevB.104.184517
Abstract
A quantum model for Josephson-based metamaterials working in the Three-Wave Mixing (3WM) and Four-Wave Mixing (4WM) regimes at the single-photon level is presented. The transmission line taken into account, namely Traveling Wave Josephson Parametric Amplifier (TWJPA), is a bipole composed by a chain of rf-SQUIDs which can be biased by a DC current or a magnetic field in order to activate the 3WM or 4WM nonlinearities. The model exploits a Hamiltonian approach to analytically determine the time evolution of the system both in the Heisenberg and interaction pictures. The former returns the analytic form of the gain of the amplifier, while the latter allows recovering the probability distributions vs. time of the photonic populations, for multimodal Fock and coherent input states. The dependence of the metamaterial's nonlinearities is presented in terms of circuit parameters in a lumped model framework while evaluating the effects of the experimental conditions on the model validity.
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Cited by in corpus (6)
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- Ultra low noise readout with travelling wave parametric amplifiers: the DARTWARS project
- Nonlinear Behavior of Josephson Traveling Wave Parametric Amplifiers
- On Parametric Amplification In Discrete Josephson Transmission Line
- Coherence-Mediated Quantum Thermometry in a Hybrid Circuit-QED Architecture