Josephson tunable metamaterials for quantum devices

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Presently there is a growing interest in development of quantum devices (qubits, detectors, etc.) that, due to their nature, operate at low and ultra low temperatures and at frequencies of several (tens of) GHz. Therefore, the design of functional metamaterials (filters, amplifies, and so on) that operate at the same temperatures and frequencies and allow to control, process and readout of the information as well as amplify weak quantum signals is very relevant. Superconductivity brings unique advantages to metamaterials such as low loss, compact dimensions of meta-atoms, while the Josephson effect provides the possibility to tune metamaterial properties in-situ.In the framework of this joint project we are going to design, fabricate and investigate both theoretically (numerically) and experimentally several metamaterials based on arrays of meta-atoms, such as Josephson junctions (JJs) or SQUIDs, embedded into coplanar transmission line. The Tübingen group will focus on the development of novel Josephson MetaMaterials (JMMs) with unique and tunable properties. In the linear regime the aim is to design a JMM with the tunable dispersion that allows to create, \eg, JMM that works as a tunable band-pass or band-rejection filter or, \eg, JMMs with zero group velocity, where the propagating electromagnetic waves can be stopped.The main focus of the Moscow group is more application oriented. It is the development and experimental tests of the Josephson Traveling Wave Parametric Amplifier (JTWPA) --- a JMM working in a non-linear regime, where non-linear mixing of a weak input signal (to be amplified) at the signal frequency with the strong pump signal at pump frequency results in an amplified signal at the signal frequency at the output of the JTWPA. The theory predicts that a JTWPA consisting of 300 SQUIDs should provide a uniform gain of 20 dB over the bandwidth of about 5 GHz at the pump frequency of 12 GHz. The noise temperature is expected to reach 0.2 K at 5 GHz at a temperature of 4.2K. At the later stage of the project the JTWPA will be redesigned for temperatures below 1K.The Tübingen group will also investigate JMMs experimentally by means of Low Temperature Scanning Electron (or Laser) Microscopy (LTSEM/LTSLM) -- a unique technique available in Tübingen. After upgrade, it will allow to visualize the operation of the JMMs such as JTWPA and find the problem areas if any. In this context an important point is to understand how the deviation of parameters of (a) one single meta-atom (important for LTSEM/LTSLM imaging) or (b) all meta-atoms (technological spread) affect the operation and figures of merit of JMM. The group in Tübingen will investigate this question by making full scale non-linear numerical simulations of JMM dynamics.Finally, novel JMMs designed by the Tübingen group will be fabricated in Moscow and experimentally investigated by both groups.