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Bulletin of the American Physical Society

Engineering artificial Hamiltonians with parametric superconducting circuits

Yao Lu, Srivatsan Chakram, Nelson L. C. Leung, Ravi Naik, Nathan Earnest, Peter Groszkowski, Jens Koch, Eliot Kapit, David Schuster

Published Mar 14, 2016• 0 citations
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In this thesis, we study two topics on superconducting circuits. \nThe first topic is the tunable coupler for resonators. \nThis coupler is implemented with a superconducting circuit coupling with resonators in the dispersive regime. \nIt possesses a high on/off ratio and the coupling between two degenerate resonators can be turned off by tuning the frequency of the coupler via the biasing flux. \nWe present the design, the simulation, \nand the fabrication of the chip implementing this coupler. \nWe derive the Hamiltonian of the chip via formal circuit quantization. \nWe also present numerical results of the eigenenergies and the eigenstates of the chip. \nFrom the numerical results, \nwe show that the tunable coupling and the turn-off point can be realized on the chip. \n \nThe second topic is impedance engineering for enhancing the bandwidth of a Josephson parametric amplifier. \nBy transforming the input impedance seen by the Josephson parametric amplifier, \nthe frequency dependence of the gain function can be decreased and the bandwidth of the Josephson parametric amplifier can be enhanced. \nWe study impedance engineering for two different types of flux pumping Josephson parametric amplifier. \nFor each type of amplifier, \nwe develop a corresponding method of impedance engineering, \nand study implementing the method with transmission lines.
In this talk, I will start by briefly introducing the Josephson-junction, which is the non-linear circuit element used to engineer the artificial atoms. Then I will discuss two qualitatively different methods using this non-linear element for generating entangled photon pairs in superconducting circuits. One approach builds on parametric down-conversion of a coherent ac drive (see fig. 1)[2] while the other relies on the ac Josephson effect, requiring only a dc voltage bias (see fig. 2) [3]. Finally, I will discuss a few recent experimental implementations [4-8].
With the assistance of a cyclic three-level artificial atom of a superconducting flux quantum circuit interacting with a two-mode superconducting transmission-line resonator, we study theoretically the degenerate microwave parametric down-conversion (PDC) in a circuit-QED system. By adiabatically eliminating the excited states of the three-level artificial atom, we obtain an effective microwave PDC Hamiltonian for the two resonator modes (i.e., the fundamental and second-harmonic modes). The corresponding PDC efficiency in our model can be much larger than that in the similar circuit-QED system based on a single two-level superconducting qubit [K. Moon and S. M. Girvin, Phys. Rev. Lett. 95, 140504 (2005)]. Furthermore, we investigate the squeezing and bunching behavior of the fundamental resonator mode resulting from the coherent driving to the second-harmonic one.