Detecting the Unruh Effect via an Engineered Low-Mass Field in a Superconducting Qubit

TL;DR

This paper derives the exponential suppression of detecting the Unruh effect with massive fields, shows the impracticality of high accelerations, and proposes a superconducting circuit method to engineer an effective small mass for detection.

Contribution

It provides a quantitative derivation of the suppression factor and introduces a superconducting circuit implementation to overcome detection challenges.

Findings

Exponential suppression of massive field excitation in Unruh effect detection.

Detection requires unfeasibly high accelerations for massive fields.

Engineered small effective mass in superconducting circuits can enable detection.

Abstract

Detecting the Unruh effect is a major challenge in fundamental physics. It is known that exciting massive fields with the Unruh thermal bath is heavily suppressed when the field's rest energy is much larger than the acceleration energy scale, $Mc^2 \gg\hbar a/c$. However, the standard literature lacks an explicit quantitative derivation of this suppression. In this work, we first fill this gap by deriving the exponential suppression, $\sim \exp(-\text{constant}\times Mc^2/(\hbar a/c))$, in two different frameworks: a (3+1)-dimensional Unruh-DeWitt detector and a (1+1)-dimensional cavity QED setup. This shows the suppression is universal and sets an insurmountable barrier for any detection method that relies on exciting massive fields. For an electron-mass field at achievable accelerations ($a \sim 10^{20}$ m/s$^2$), the suppression exceeds $10^9$ orders of magnitude. To avoid this suppression, the field's rest energy must be less than or of the order of the acceleration energy scale, $M c^2 \lesssim \hbar a / c$. Achieving this condition, however, requires astronomically high accelerations. For example, detecting the effect for an electron-mass field would require accelerations of $a \gtrsim 4.6\times 10^{29}$ m/s$^2$, which is far beyond experimental reach. While using a massless field avoids this suppression, we show the best strategy is not to avoid mass, but to engineer a small effective mass that satisfies the optimal condition $\hbar a / c \gg M_{\text{eff}} c^2$. We propose a concrete implementation using a superconducting circuit with a Josephson persistent-current qubit (the analog of a UDW detector) coupled to a microwave resonator (the analog of the scalar field). For this system, the optimal condition is $2I_p\Delta\Phi \gg \Delta$, where $I_p$ is the persistent current, $\Delta\Phi$ is the magnetic flux swing, and $\Delta$ is the qubit's tunneling energy gap....