Quantum quenches and off-equilibrium dynamical transition in the
  infinite-dimensional Bose-Hubbard model

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Abstract

We study the off-equilibrium dynamics of the infinite dimensional Bose Hubbard Model after a quantum quench. The dynamics can be analyzed exactly by mapping it to an effective Newtonian evolution. For integer filling, we find a dynamical transition separating regimes of small and large quantum quenches starting from the superfluid state. This transition is very similar to the one found for the fermionic Hubbard model by mean field approximations.

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Most cited references 11

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Boson localization and the superfluid-insulator transition

Matthew Fisher, Peter Weichman, G. Grinstein … (1989)

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Thermalization and its mechanism for generic isolated quantum systems

Vanja Dunjko, Maxim Olshanii, Marcos Rigol (2007)

Time dynamics of isolated many-body quantum systems has long been an elusive subject. Very recently, however, meaningful experimental studies of the problem have finally become possible, stimulating theoretical interest as well. Progress in this field is perhaps most urgently needed in the foundations of quantum statistical mechanics. This is so because in generic isolated systems, one expects nonequilibrium dynamics on its own to result in thermalization: a relaxation to states where the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of statistical mechanics. However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible, in a sense analogous to that in which dynamical chaos makes classical thermalization possible. For example, dynamical chaos itself cannot occur in an isolated quantum system, where time evolution is linear and the spectrum is discrete. Underscoring that new rules could apply in this case, some recent studies even suggested that statistical mechanics may give wrong predictions for the outcomes of relaxation in such systems. Here we demonstrate that an isolated generic quantum many-body system does in fact relax to a state well-described by the standard statistical mechanical prescription. Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation and that thermalization happens instead at the level of individual eigenstates, as first proposed by J.M. Deutsch and M. Srednicki. A striking consequence of this eigenstate thermalization scenario is that the knowledge of a single many-body eigenstate suffices to compute thermal averages-any eigenstate in the microcanonical energy window will do, as they all give the same result.

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A Mott insulator of fermionic atoms in an optical lattice

, , … (2010)

In a solid material strong interactions between the electrons can lead to surprising properties. A prime example is the Mott insulator, where the suppression of conductivity is a result of interactions and not the consequence of a filled Bloch band. The proximity to the Mott insulating phase in fermionic systems is the origin for many intriguing phenomena in condensed matter physics, most notably high-temperature superconductivity. Therefore it is highly desirable to use the novel experimental tools developed in atomic physics to access this regime. Indeed, the Hubbard model, which encompasses the essential physics of the Mott insulator, also applies to quantum gases trapped in an optical lattice. However, the Mott insulating regime has so far been reached only with a gas of bosons, lacking the rich and peculiar nature of fermions. Here we report on the formation of a Mott insulator of a repulsively interacting two-component Fermi gas in an optical lattice. It is signalled by three features: a drastic suppression of doubly occupied lattice sites, a strong reduction of the compressibility inferred from the response of double occupancy to atom number increase, and the appearance of a gapped mode in the excitation spectrum. Direct control of the interaction strength allows us to compare the Mott insulating and the non-interacting regime without changing tunnel-coupling or confinement. Our results pave the way for further studies of the Mott insulator, including spin ordering and ultimately the question of d-wave superfluidity.