Scalable collective Lamb shift of a 1D superconducting qubit array in front of a mirror

TL;DR

This paper theoretically explores the collective Lamb shift in a 1D superconducting qubit array near a mirror, revealing how virtual photon interactions cause energy shifts and collective phenomena, with implications for scalable quantum systems.

Contribution

It introduces a model for the collective Lamb shift in a 1D superconducting qubit array with a mirror, including a master equation and analysis of superradiance and subradiance effects.

Findings

Large energy splitting when a qubit is at a node of the standing wave.

Demonstration of the collective Lamb shift due to virtual photon exchange.

Scaling behavior of the Lamb shift with increasing qubit number.

Abstract

We theoretically investigate resonant dipole-dipole interaction (RDDI) between artificial atoms in a 1D geometry, implemented by N transmon qubits coupled through a transmission line. Similarly to the atomic cases, RDDI comes from exchange of virtual photons of the unexcited modes, and causes the so-called collective Lamb shift (CLS). To probe the shift, we effectively set one end of the transmission line as a mirror, and examine the reflection spectrum of the probe field from the other end. Our calculation shows that when a qubit is placed at the node of the standing wave formed by the incident and reflected waves, even though it is considered to be decoupled from the field, it results in large energy splitting in the spectral profile of a resonant qubit located elsewhere. This directly signals the interplay of virtual photon processes and explicitly demonstrates the CLS. We further derive a master equation to describe the system, which can take into account mismatch of participating qubits and dephasing effects. Our calculation also demonstrates the superradiant and subradiant nature of the atomic states, and how the CLS scales when more qubits are involved.