Mikhail V. Fistul

Quantum dynamics of frustrated Josephson junction arrays embedded in a transmission line: an effective XX spin chain with long-range interaction

  1. Benedikt J.P. Pernack,
  2. Mikhail V. Fistul,
  3. and Ilya M. Eremin
We study theoretically a variety of collective quantum phases occurring in frustrated saw-tooth chains of Josephson junctions embedded in a dissipationless transmission line. The basic
element of a system, i.e., the triangular superconducting cell, contains two 0- and one π- Josephson junctions characterized by EJ and αEJ Josephson energies, accordingly. In the frustrated regime the low energy quantum dynamics of a single cell is determined by anticlockwise or clockwise flowing persistent currents (vortex/antivortex). The direct embedding of π-Josephson junctions in a transmission line allows to establish a short/long-range interaction between (anti)vortices of well separated cells. By making use of the variational approach, we map the superconducting circuit Hamiltonian to an effective XX spin model with an exchange spin-spin interaction decaying with the distance x as x−β, and the local σ̂ x,n-terms corresponding to the coherent quantum beats between vortex and antivortex in a single cell. We obtain that in long arrays as N≫ℓ0≃C/C0‾‾‾‾‾√, where C and C0 are capacitances of 0-Josephson junction and transmission line, accordingly, the amplitude of quantum beats is strongly suppressed. By means of exact numerical diagonalization, we study the interplay between the coherent quantum beats and the exchange spin-spin interaction leading to the appearance of various collective quantum phases such as the paramagnetic (P), compressible superfluid (CS) and weakly compressible superfluid (w-CS) states.
arxiv pdf

Schrieffer-Wolff transformation for non-Hermitian systems: application for -symmetric circuit QED

  1. Grigory A. Starkov,
  2. Mikhail V. Fistul,
  3. and Ilya M. Eremin
Combining non-hermiticity and interactions yields novel effects in open quantum many-body systems. Here, we develop the generalized Schrieffer-Wolff transformation and derive the effective
Hamiltonian suitable for various quasi-degenerate \textit{non-Hermitian} systems. We apply our results to an exemplary –symmetric circuit QED composed of two non-Hermitian qubits embedded in a lossless resonator. We consider a resonant quantum circuit as |ωr−Ω|≪ωr, where Ω and ωr are qubits and resonator frequencies, respectively, providing well-defined groups of quasi-degenerate resonant states. For such a system, using direct numerical diagonalization we obtain the dependence of the low-lying eigenspectrum on the interaction strength between a single qubit and the resonator, g, and the gain (loss) parameter γ, and compare that with the eigenvalues obtained analytically using the effective Hamiltonian of resonant states. We identify –symmetry broken and unbroken phases, trace the formation of Exceptional Points of the second and the third order, and provide a complete phase diagram g−γ of low-lying resonant states. We relate the formation of Exceptional Points to the additional -pseudo-Hermitian symmetry of the system and show that non-hermiticity mixes the „dark“ and the „bright“ states, which has a direct experimental consequence.
arxiv pdf