Quench Spectroscopy Distinguishes Insulator and Superfluid Phases in Confined Bosonic Systems.

The behaviour of interacting bosons—particles that collectively occupy the lowest quantum state—within confining potentials represents a fundamental problem in condensed matter physics. Jiachen Yu, Yuanzhe Hu, et al. investigate this behaviour using a technique called quench spectroscopy, a method for determining the energy levels of a quantum system by rapidly changing a parameter governing its interactions. Their research, conducted with one-dimensional bosonic atoms trapped within a harmonic potential—a force that increases with displacement from an equilibrium point—demonstrates the practical application of quench spectroscopy in more realistic, experimentally achievable conditions. The team’s findings, validated through comparison with density matrix renormalization group simulations—a numerical method for solving quantum many-body problems—reveal how harmonic confinement alters the observed energy spectrum, particularly within the Mott insulator phase, a state characterised by localised particles. This work provides crucial insights into optimising quench spectroscopy for probing quantum phases in trapped systems.

Quench spectroscopy is emerging as a technique for probing the energy spectrum of quantum phases in systems undergoing non-equilibrium dynamics. Practical implementations often involve confining potentials, such as harmonic traps, which complicate analysis, although previously demonstrated theoretically for homogeneous systems. This work presents an experimental investigation of quench spectroscopy applied to one-dimensional bosons in optical lattices with harmonic confinement, comparing results to density matrix renormalization group (DMRG) simulations.

Researchers induced quenches – sudden changes in system parameters – and measured the resulting momentum distribution evolution. Applying a Fourier transform yielded the quench spectral function, S(k, ω), which reveals detailed information about the system’s energy spectrum. For the Mott insulator (MI) phase, the study found a broadened band signal and a momentum cutoff at the half first Brillouin zone. This modification is attributed to additional excitations induced by the harmonic confinement. Despite this modification, a clear distinction between the MI and superfluid (SF) phases remains, with the MI phase exhibiting a gap in the spectrum.

Larger amplitude quenches yield the clearest spectral signal. Qualitative agreement between experimental results and DMRG simulations validates the methodology in the presence of confinement. The findings elucidate the physical mechanisms modifying the quench spectral function (QSF) in confined systems and propose optimal conditions for applying quench spectroscopy in such scenarios. Statistical analysis also identified optimal parameters for maximising gap visibility in these measurements.

The research provides valuable insight into performing quench spectroscopy in realistic experimental conditions, bridging the gap between theoretical predictions and practical implementation. Future work could focus on extending these techniques to explore more complex systems, such as disordered potentials or higher-dimensional lattices, and refining the quantitative agreement between simulations and experiments to fully characterise the influence of confinement on excitation spectra.