Observation of a dissipative phase transition in a one-dimensional circuit QED lattice

Abstract: Condensed matter physics has been driven forward by significant experimental and theoretical progress in the study and understanding of equilibrium phase transitions based on symmetry and topology. However, nonequilibrium phase transitions have remained a challenge, in part due to their complexity in theoretical descriptions and the additional experimental difficulties in systematically controlling systems out of equilibrium. Here, we study a one-dimensional chain of 72 microwave cavities, each coupled to a superconducting qubit, and coherently drive the system into a nonequilibrium steady state. We find experimental evidence for a dissipative phase transition in the system in which the steady state changes dramatically as the mean photon number is increased. Near the boundary between the two observed phases, the system demonstrates bistability, with characteristic switching times as long as 60 ms -- far longer than any of the intrinsic rates known for the system. This experiment demonstrates the power of circuit QED systems for studying nonequilibrium condensed matter physics and paves the way for future experiments exploring nonequilbrium physics with many-body quantum optics.

• The paper presents clear experimental evidence of a dissipative phase transition in a one-dimensional circuit QED lattice with a sudden change in steady-state behavior.
• It details a setup using 72 microwave cavities coupled to superconducting qubits, observing hysteresis and long switching times up to 60 ms.
• The study employs a Lindblad master equation and mean-field approximation to bridge theoretical predictions with experimental observations, advancing nonequilibrium physics.

Observation of a Dissipative Phase Transition in a One-Dimensional Circuit QED Lattice

The paper entitled "Observation of a dissipative phase transition in a one-dimensional circuit QED lattice" presents a detailed experimental investigation into nonequilibrium phase transitions within a circuit quantum electrodynamics (QED) lattice. Nonequilibrium phase transitions, distinct from their equilibrium counterparts, have historically posed both theoretical and experimental challenges due to their inherent complexity. This study leverages a circuit QED lattice, a promising platform due to its inherent dissipation characteristics, which serves as both a challenge in traditional quantum information processing and a feature for studying these transitions.

Experimental Setup and Methodology

The experimental system is a one-dimensional chain consisting of 72 microwave cavities, each strongly coupled to a superconducting qubit. The system is driven to a nonequilibrium steady state by varying the mean photon number, observing for changes that might signal a phase transition. The device operates in a regime characterized by strong coupling and significant dissipation, making it an ideal candidate for observing dissipative phase transitions. In particular, the experiment focuses on detecting bistability—a hallmark of these transitions—measured through exceptional long-duration switching times between distinct steady states, ranging up to 60 ms.

Key Findings

The results indicate clear experimental evidence for a dissipative phase transition within the one-dimensional QED lattice. The transition is marked by a sudden change in the steady state of the lattice as the mean photon number increases. Near the transition boundary separating the two phases, the system reveals substantial bistability, demonstrated by significant hysteresis and stochastic switching between two metastable states, denoted as $\rho_1$ and $\rho_2$.

A central feature of the experiment is the analysis of the switching dynamics and corresponding asymptotic decay rates (ADR). The experiment reveals that the ADR becomes exceptionally slow, reaching values as low as 10 Hz, which is several orders of magnitude slower than intrinsic system timescales. Such deceleration supports the hypothesis of an impending phase transition, analogous to the closing of the spectral gap in equilibrium phase transitions.

Theoretical Model and Implications

Theoretical modeling uses a Lindblad master equation to describe the system dynamics, with a mean-field approximation approach to understand the transition qualitatively. The transition is signaled by the closing of the spectral gap in the Liouvillian superoperator—an indication of the system's move to a new steady state, as captured by the mean-field equations.

The significance of this research lies in its implications for nonequilibrium condensed matter physics. The results open pathways for exploring complex quantum many-body phenomena in environments where dissipative processes play a critical role. Furthermore, the study demonstrates the utility of circuit QED lattices as a versatile platform for simulating Hamiltonians and studying nonequilibrium physics, potentially guiding future investigations into dissipative phase transitions.

Future Directions

Looking forward, this work lays a foundation for more comprehensive explorations of dissipative phase transitions in larger and higher-dimensional circuit QED lattices and other nonequilibrium systems. Future research might explore alterations in system configurations, examining how varying the lattice structure or introducing additional interaction terms impacts the transition dynamics and steady-state properties. Additionally, studies into how disorder and system size influence the critical behavior could yield further insights into universality classes of nonequilibrium phase transitions. The outcomes gleaned could bridge gaps in understanding between classical theories of phase transitions and quantum systems, offering rich avenues for theoretical and experimental advancements in quantum optics and materials science.