Spectral signatures of many-body localization with interacting photons (1709.07108v2)

Abstract: Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization, but, can interacting systems always equilibrate regardless of parameter values\,? The energy spectrum of a system can answer this question and reveal the nature of the underlying phases. However, most experimental techniques only indirectly probe the many-body energy spectrum. Using a chain of nine superconducting qubits, we implement a novel technique for directly resolving the energy levels of interacting photons. We benchmark this method by capturing the intricate energy spectrum predicted for 2D electrons in a magnetic field, the Hofstadter butterfly. By increasing disorder, the spatial extent of energy eigenstates at the edge of the energy band shrink, suggesting the formation of a mobility edge. At strong disorder, the energy levels cease to repel one another and their statistics approaches a Poisson distribution - the haLLMark of transition from the thermalized to the many-body localized phase. Our work introduces a new many-body spectroscopy technique to study quantum phases of matter.

• The paper introduces a novel time-domain spectroscopy method to directly resolve many-body eigen-energies in a superconducting qubit chain.
• It reveals the transition from Gaussian Orthogonal Ensemble to Poisson statistics, indicating a breakdown of ergodicity in interacting systems.
• The study demonstrates precise Hamiltonian control by simulating Bloch electrons and measuring deviations in energy levels to capture quantum localization.

Spectral Signatures of Many-Body Localization with Interacting Photons

The paper "Spectral signatures of many-body localization with interacting photons" presents a novel experimental approach for probing the many-body energy spectrum, specifically focusing on the phenomena of many-body localization (MBL) in a system of interacting photons. Utilizing a chain of nine superconducting qubits, the authors introduce a technique to directly resolve the energy levels, providing a valuable tool for studying quantum phases of matter.

Many-body localization poses intriguing questions in statistical mechanics. Traditional understanding posits that systems reach thermal equilibrium through interactions, yet MBL represents a scenario where certain interacting systems fail to thermalize. Unlike conventional phase transitions that focus on ground-state changes, the thermal and MBL phases exhibit differences in their dynamical behaviors and properties of all many-body eigenstates, necessitating a comprehensive examination of the energy spectrum.

In this paper, the authors employ a time-domain spectroscopy method to measure the eigen-energies of a Hamiltonian system. This approach pivots on preparing qubits in various initial states and analyzing their evolution through the lens of quantum mechanics. By examining the Fourier transform of this evolution, the energy levels are identified, showcasing the Fourier transform's ability to reveal system eigen-energies and associated wavefunctions.

A significant application of this method is demonstrated through the simulation of Bloch electrons on a two-dimensional lattice subject to a magnetic field, experimentally capturing features associated with Hofstadter's butterfly. The capability to accurately set Hamiltonian terms and resolve corresponding eigen-energies is highlighted, with average deviation measurements indicating precise control over quantum systems.

The paper extends to two-photon scenarios to probe interacting systems. It discusses energy level statistics, emphasizing the transition from Gaussian Orthogonal Ensemble (GOE) to Poisson statistics as disorder strength increases, reflecting MBL's haLLMark of vanishing level repulsion and increased independence between energy levels. The results suggest a breakdown of ergodicity as eigenstates become more localized.

Further examination of spatial and energy extension of eigenstates through participation ratio showcases the transition from extended to localized states. This is indicative of the formation of a mobility edge, where localization begins at the energy band's edges and expands with increasing disorder. Such findings align with Anderson localization concepts but invite further exploration, particularly concerning the theoretical existence of a mobility edge in MBL phases.

Theoretical implications of the paper suggest potential technological advancements, especially in quantum computation, as systems approach limits of classical simulability. The technique's scalability, though constrained by decoherence and frequency broadening in larger systems, leads to promising insights into quantum system dynamics and could contribute significantly to the ongoing paper of quantum thermodynamics and statistical mechanics.

Overall, this paper not only contributes a powerful experimental method for exploring MBL and quantum phases but also suggests pathways for future research, potentially redefining our understanding of system dynamics in the quantum field.