Haruna Katayama

Stability and quasi-normal ringing in analogue black-white holes in SNAIL-based traveling-wave parametric amplifiers

  1. Daisuke Yamauchi,
  2. Haruna Katayama,
  3. and Norihiro Tanahashi
The circuit dynamics constructed by traveling-wave parametric amplifiers (TWPA), using superconducting nonlinear asymmetric elements (SNAILs), are known to be approximately described
by the Korteweg-de Vries (KdV) or modified KdV equations in the continuum limit and admit soliton solutions. The soliton spatially modulates the effective propagation velocity of the weak probe field, which leads to the effective realization of the causal structure of the analogue event horizons in the SNAIL-TWPA circuit system. In this paper, we derive the master equation for the weak probe field where the background soliton acts as an effective potential. We show the absence of normalizable negative modes in the SNAIL-TWPA circuit system by using the language of supersymmetric quantum mechanics. We also present the first study of quasi-normal modes (QNM) of the SNAIL-TWPA analogue black-white hole system by semi-analytic and numerical methods. Based on the resultant QNM frequency, we clarify the timescale at which nonlinear dispersion becomes effective in the SNAIL-TWPA circuit system and demonstrate how ringdown is excited.
arxiv pdf

Analogue black-white hole solitons in travelling wave parametric amplifiers with superconducting nonlinear asymmetric inductive elements

  1. Haruna Katayama,
  2. Noriyuki Hatakenaka,
  3. Toshiyuki Fujii,
  4. and Miles P. Blencowe
We propose an analogue black-white hole soliton realization using existing travelling wave parametric amplifier (TWPA) setups comprising superconducting nonlinear asymmetric inductive
elements (SNAILs). We show that the dynamics in terms of the phase difference coordinate across a SNAIL is described by the Korteweg-de Vries (KdV) or modified Korteweg-de Vries (mKdV) equations in the continuum approximation, depending on the external magnetic flux bias, which admit solitary wave solutions. We also validate the KdV-derived solitons by numerically solving the original, discrete element circuit equations. Soliton solutions to the (m)KdV equation spatially modulate the velocity for probe microwaves propagating in the TWPA, resulting in the effective realization of analogue black hole-white hole event horizon pairs.
arxiv pdf