A driven resonator coupled to a josephson junction: An exploration of the quantum and classical dynamics

I. N. Askerzade, Ali Bozbey, Mehmet Cantürk

Vijay Pal Singh, Juan Polo, Ludwig Mathey +1 more

We study driven atomic Josephson junctions realized by coupling two two-dimensional atomic clouds with a tunneling barrier. By moving the barrier at a constant velocity, dc and ac Josephson regimes are characterized by a zero and nonzero atomic density difference across the junction, respectively. Here, we monitor the dynamics resulting in the system when, in addition to the above constant velocity protocol, the position of the barrier is periodically driven. We demonstrate that the time-averaged particle imbalance features a plateau behavior that is the analog of Shapiro steps observed in driven superconducting Josephson junctions. The underlying dynamics reveals an intriguing interplay of the vortex and phonon excitations, where Shapiro steps are induced via suppression of vortex growth. We study the system with a classical-field dynamics method, and benchmark our findings with a driven circuit dynamics.

Andrew D. Armour, M. P. Blencowe, Erind Brahimi +1 more

We analyze the quantum dynamics of a superconducting cavity coupled to a voltage-biased Josephson junction. The cavity is strongly excited at resonances where the voltage energy lost by a Cooper pair traversing the circuit is a multiple of the cavity photon energy. We find that the resonances are accompanied by substantial squeezing of the quantum fluctuations of the cavity over a broad range of parameters and are able to identify regimes where the fluctuations in the system take on universal values.

Chiara Bottero

Physikalisch-Technische Bundesanstalt

Tim van de Veen

A single photon interacting with a single atom is the most fundamental form of light interacting with matter and has been extensively studied in the field of Cavity Quantum Electrodynamics (cavity QED). Here, a non-linearity like an atom is coupled to a single mode of the electromagnetic field in a cavity. Another field which explores the quantum mechanical nature of photons is Circuit Quantum Electrodynamics (cQED) where photons are the quantized excitations of a superconducting microwave resonator and non-linearity is introduced by the Josephson junction. Like this, setups analog to that of in cavity QED can be copied to cQED, with a number of differences. For example, the photons propagating in a transmission line are more confined and the circuits are made with conventional lithography techniques, allowing for more freedom in engineering the system parameters. In the first part of the thesis, we build a numerical model in order to examine the feasibility of quenching the ground state of a coplanar waveguide (CPW) interrupted by a tunable coupling element. Next, by means of experiments and simulations we considered the feasibility of observing experimentally a synchronization effect in a driven CPW with its central conductor interrupted by equally spaced capacitively shunted Josephson junctions (Josephson crystal) based on a recent proposal. Finally, we made a first step in understanding the synchronization from a classical perspective by modelling a Josephson crystal of two junctions as two degenerate non-linearly coupled Duffng oscillators. Concerning the quenching experiment, we found that the plasma frequency must be tuned faster than 1/f with f the resonance frequency of the CPW, which is in the sub-nanosecond regime and therefore unfeasible with current state the art electronics. We also found that, in contrast to what was claimed in the proposal, the synchronization effect cannot be observed for the parameters common in cQED. One way would be to push the limits of the capacitances to several picofarads. Finally, we found that the non-linear coupling causes the two degenerate non-linearly coupled Duffng oscillator to synchronize, which is a first step in understanding the proposed synchronization effect in a fully classical way.