# Excitation of an inertial Unruh detector in the Minkowski vacuum: a numerical calculation using spherical modes

## TL;DR

This paper numerically investigates the excitation probability of an inertial Unruh detector in Minkowski vacuum using spherical modes, revealing time-dependent multipole components and effects of switching protocols.

## Contribution

It introduces a numerical method to analyze the excitation of an inertial detector in Minkowski space with spherical modes, highlighting the impact of switching functions on excitation probabilities.

## Key findings

- Multipole components of excitation probability are time-dependent.
- Sudden switch-on yields twice the excitation probability of adiabatic switch-on.
- Method can extend to radial trajectories in curved spacetimes.

## Abstract

We consider the excitation of a finite-length inertial Unruh detector in the Minkowski vacuum with an adiabatic switch on of the interaction in the infinite past and a sudden switch off at finite times, and obtain the excitation probability via a numerical calculation using the expansion of the quantum field in spherical modes. We evaluate first the excitation probabilities for the final states of the field with one particle per mode, and then we sum over the modes. An interesting feature is that, despite of the inertial trajectory and of the vacuum state of the field, the multipole components of the excitation probability are time-dependent quantities. We make clear how the multipole sum yields the time-independent probability characteristic to an inertial trajectory. In passing, we point out that the excitation probability for a sudden switch on of the interaction in the infinite past is precisely twice as large as that for an adiabatic switch on. The procedure can be easily extended to obtain the response of the detector along radial trajectories in spherically symmetric spacetimes.