Thermalization and dephasing in an isolated system of coupled qubits

This paper investigates the internal thermalization dynamics of an isolated, all-to-all coupled ensemble of qubits. While open quantum systems thermalize through interaction with an external heat bath, the authors explore whether a closed system—where one qubit acts as a subsystem and the remaining qubits serve as an effective bath—can reach a thermal state through internal interactions alone.

The authors model an ensemble of $N$ qubits, considering both weakly anharmonic oscillators (WAOs) and ideal two-level systems. They derive a self-consistent weak-coupling master equation to track the evolution of the density matrix for a single qubit. The study compares two distinct coupling mechanisms: linear coupling, which conserves the number of excitations, and non-linear three-wave mixing, which allows for energy exchange between non-degenerate qubits. The authors use numerical simulations to track the long-time behavior of populations and off-diagonal elements (dephasing) and compare these results to analytical predictions based on energy conservation.

The study demonstrates that non-linear three-wave mixing is sufficient to drive an isolated system toward a thermal (Gibbs) distribution. In this regime, the system effectively acts as its own heat bath, and the final temperature is uniquely determined by the initial energy of the system. The authors show that the off-diagonal elements of the density matrix decay exponentially, indicating dephasing. Conversely, linear coupling restricts interactions to degenerate qubits, preventing the system from reaching a global thermal state. The authors also propose a superconducting quantum circuit design using asymmetric SQUIDs as a potential experimental platform to observe these phenomena.

Understanding internal thermalization in isolated quantum systems is critical for quantum technology. As quantum processors scale, managing the transition from unitary evolution to thermalization is essential for maintaining quantum advantage. This work provides a theoretical framework and an experimental blueprint for controlling these dynamics in solid-state platforms, offering insights into how non-linearity can be leveraged to manage decoherence and thermalization in closed quantum architectures.