Josephson-junction-embedded transmission-line resonators: From Kerr medium to in-line transmon

By J. Bourassa, Felix Beaudoin, Jay M. Gambetta, Alexandre Blais. 2012

145 citations recorded by the source corpus.

We provide a general method to find the Hamiltonian of a linear circuit in the presence of a nonlinearity. Focusing on the case of a Josephson junction embedded in a transmission-line resonator, we solve for the normal modes of the system by taking into account exactly the effect of the quadratic (i.e., inductive) part of the Josephson potential. The nonlinearity is then found to lead to self and cross-Kerr effects, as well as beam-splitter-type interactions between modes. By adjusting the parameters of the circuit, the Kerr coefficient $K$ can be made to reach values that are weak ($Kl\ensuremath{\kappa}$), strong ($Kg\ensuremath{\kappa}$), or even very strong ($K\ensuremath{\gg}\ensuremath{\kappa}$) with respect to the photon-loss rate $\ensuremath{\kappa}$. In the latter case, the $\mathrm{resonator}+\mathrm{junction}$ circuit corresponds to an in-line version of the transmon. By replacing the single junction by a SQUID, the Kerr coefficient can be tuned in situ, allowing, for example, the fast generation of Schr\"odinger cat states of microwave light. Finally, we explore the maximal strength of qubit-resonator coupling that can be reached in this setting.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/b43e1e9e607c00618a8461b1630d8cd8bc86f233

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Topological photonics (2018, background): “…of the interactions between Rydberg polaritons (Bienias et al., 2014; Jachymski, Bienias, and Büchler, 2016) and of the Josephson dynamics in circuit-QED devices (Bourassa et al., 2012), the simplest form (54) of the interaction Hamiltonian is typically sufficient to capture the main physics.”
Rapid High-fidelity Multiplexed Readout of Superconducting Qubits (2018, methodology): “Thus, the mode function for the flux variable φ(x, t) (time-integral of the voltage) of each resonator is given by [55]”
Microwave photonics with superconducting quantum circuits (2017, methodology): “The proposals include using a flux qubit with a rapidly controllable gap [406], a switchable coupling [407], a multimode coupling with a lefthanded transmission line [408], a transmon made part of a transmission line [409], and a transmon coupled to an array of Josephson junctions [410].”
Quantum simulation with interacting photons (2016, background): “The approach can also be interpreted as the SQUIDs and resonators being ultra-strongly coupled [30, 31, 62, 158] so that the splitting between the two normal modes in each resonator becomes”