# Can the dynamical Lamb effect be observed in a superconducting circuit?

## TL;DR

This paper proposes a method to observe the dynamical Lamb effect in superconducting circuits by periodically switching the qubit-resonator coupling between longitudinal and transverse modes via magnetic flux modulation, and analyzes the resulting quantum dynamics.

## Contribution

It introduces a superconducting circuit design enabling switching between coupling types to observe the dynamical Lamb effect, with theoretical analysis of the quantum state evolution.

## Key findings

- Maximum excitation probability occurs at specific modulation frequencies.
- Switching coupling types enhances the observability of the effect.
- Theoretical calculations show significant photon creation due to the effect.

## Abstract

The dynamical Lamb effect is predicted to arise in superconducting circuits when the coupling of a superconducting qubit with a resonator is periodically switched "on" and "off" nonadiabatically. We show that by using a superconducting circuit which allows to switch between longitudinal and transverse coupling of a qubit to a resonator, it is possible of to observe the dynamical Lamb effect. {The switching between longitudinal and transverse coupling can be achieved by modulating the magnetic flux through the circuit loops.} By solving the Schr\"{o}dinger equation for a qubit coupled to a resonator, we calculate the time evolution of the probability of excitation of the qubit and the creation of $n$ photons in the resonator due to the dynamical Lamb effect. The probability is maximum when the coupling is periodically switched between longitudinal and transverse using a square-wave or sinusoidal modulation of the magnetic flux with frequency equal to the sum of the average qubit and photon transition frequencies.