Dynamic structure factor of a Bose-Hubbard gas

Milena Imamović-Tomasović, Allan Griffin

Viktor Borisovich Bobrov, Yu.P. Vlasov, С. А. Тригер +1 more

Ch. C. Moustakidis

Guillaume Roux, Anna Minguzzi, Tommaso Roscilde

We study the dynamic structure factor of a one-dimensional Bose gas confined in an optical lattice and modeled by the Bose–Hubbard Hamiltonian, using a variety of numerical and analytical approaches. The dynamic structure factor, experimentally measurable by Bragg spectroscopy, is studied in three relevant cases: in the clean regime, featuring either a superfluid or a Mott phase; and in the presence of two types of (quasi-)disordered external potentials: a quasi-periodic potential obtained from a bichromatic superlattice and a random box disorder—both featuring a Bose-glass phase. In the clean case, we show the emergence of a gapped doublon mode (corresponding to a repulsively bound state) for incommensurate filling, well separated from the low-energy acoustic mode. In the disordered case, we show that the dynamic structure factor provides direct insight into the spatial structure of the excitations, unveiling their localized nature, which represents a fundamental signature of the Bose-glass phase. Furthermore, it provides a clear fingerprint of the very nature of the localization mechanism which differs for the two kinds of disorder potentials we consider. In special cases, the dynamic structure factor may provide an estimate of the position of the localization transition from superfluid to Bose glass, in a complementary manner to the information deduced from the momentum distribution.

Z. Oztas, Ruveyde Ergun

In this paper, we investigate the dynamical emergence of spatial correlations in a driven triple-well Bose–Hubbard system with asymmetric well energies and time-dependent tunneling. The system has a time-periodic Hamiltonian, and its dynamics synchronize with the driving frequency. The observed oscillations in the structure factor are a direct manifestation of this Floquet driving. Focusing on the time evolution of the structure factor, we show that correlation-based observables reveal dynamical regimes. We demonstrate that increasing the inter-well asymmetry and atomic interactions results in regular oscillations in well occupations, accompanied by a qualitative change in the structure factor, indicating a transition from a dynamically disordered to an ordered regime. Therefore, our results establish the time-dependent structure factor as a sensitive probe of dynamical ordering in few-site-driven Bose–Hubbard systems, providing insight into the correlation buildup beyond effective Hamiltonian descriptions. The findings will shed light on future experimental and theoretical research on Floquet engineering, instability regimes and dynamic phase transitions.

Robert Roth, Keith R. Burnett

We investigate the dynamic structure factor of atomic Bose and Fermi gases in one-dimensional optical lattices at zero temperature. The focus is on the generic behaviour of S ( k , ω) as a function of filling and interaction strength with the aim of identifying possible experimental signatures for the different quantum phase transitions. We employ the Hubbard or Bose–Hubbard model and solve the eigenvalue problem of the Hamiltonian exactly for moderate lattice sizes. This allows us to determine the dynamic structure factor and other observables directly in the phase transition regime, where approximation schemes are generally not applicable. We discuss the characteristic signatures of the various quantum phases appearing in the dynamic structure factor and illustrate that the centroid of the strength distribution can be used to estimate the relevant excitation gaps. Employing sum rules, these quantities can be evaluated using ground-state expectation values only. Important differences between bosonic and fermionic systems are observed, e.g., regarding the origin of the excitation gap in the Mott-insulator phase.