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arXiv:1109.3906 · New Journal of Physics

Quantum criticality and population trapping of fermions by non-equilibrium lattice modulations

Regine Frank

Published Dec 17, 2013• 20 citations
arXivHTMLPDF

Abstract

An ultracold gas of interacting fermionic atoms in a three-dimensional optical lattice is considered, where the lattice potential strength is periodically modulated. This non-equilibrium system is non-perturbatively described by means of a Keldysh–Floquet–Green's function approach for Mott–Hubbard systems employing a generalized dynamical mean field theory (DMFT). Strong repulsive interactions between different atoms lead to a Mott insulator state for the equilibrium system, but the additional external driving at zero temperature yields a non-equilibrium quantum critical behavior, where an infinite number of Floquet states arise and a transition to the liquid and conducting phase is given.

DOI
10.1088/1367-2630/15/12/123030

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An ultracold gas of interacting fermionic atoms in a three-dimensional optical lattice is considered, where the lattice potential strength is periodically modulated. This non-equilibrium system is non-perturbatively described by means of a Keldysh–Floquet–Green's function approach for Mott–Hubbard systems employing a generalized dynamical mean field theory (DMFT). Strong repulsive interactions between different atoms lead to a Mott insulator state for the equilibrium system, but the additional external driving at zero temperature yields a non-equilibrium quantum critical behavior, where an infinite number of Floquet states arise and a transition to the liquid and conducting phase is given.
An ultracold gas of interacting fermionic atoms in a three-dimensional optical lattice is considered, where the lattice potential strength is periodically modulated. This non-equilibrium system is non-perturbatively described by means of a Keldysh-Floquet-Green's function approach for Mott-Hubbard systems employing a generalized dynamical mean field theory (DMFT). Strong repulsive interactions between different atoms lead to a Mott insulator state for the equilibrium system, but the additional external driving at zero temperature yields a non-equilibrium quantum critical behavior, where an infinite number of Floquet states arise and a transition to the liquid and conducting phase is given.
The fermionic Hubbard model plays a fundamental role in the description of strongly correlated materials. We have realized this Hamiltonian in a repulsively interacting spin mixture of ultracold (40)K atoms in a three-dimensional (3D) optical lattice. Using in situ imaging and independent control of external confinement and lattice depth, we were able to directly measure the compressibility of the quantum gas in the trap. Together with a comparison to ab initio dynamical mean field theory calculations, we show how the system evolves for increasing confinement from a compressible dilute metal over a strongly interacting Fermi liquid into a band-insulating state. For strong interactions, we find evidence for an emergent incompressible Mott insulating phase. This demonstrates the potential to model interacting condensed-matter systems using ultracold fermionic atoms.
We have studied a system of ultracold fermionic potassium ( 40 K) atoms in a three-dimensional (3D) optical lattice in the vicinity of an s-wave Feshbach resonance. Close to resonance, the system is described by a multi-band Bose–Fermi Hubbard Hamiltonian. We derive an effective lowest-band Hamiltonian in which the effect of higher bands is incorporated by a self-consistent mean-field approximation. The resulting model is solved by means of generalized dynamical mean-field theory. In addition to the BEC–BCS crossover, we find a phase transition to a fermionic Mott insulator at half-filling, induced by the repulsive fermionic background scattering length. We also calculate the critical temperature of the BEC/BCS state and find it to be minimal at resonance.
We study the quantum (zero-temperature) critical behaviors of confined particle systems described by the one-dimensional (1D) Bose-Hubbard model in the presence of a confining potential, at the Mott insulator to superfluid transitions, and within the gapless superfluid phase. Specifically, we consider the hard-core limit of the model, which allows us to study the effects of the confining potential by exact and very accurate numerical results. We analyze the quantum critical behaviors in the large trap-size limit within the framework of the trap-size scaling (TSS) theory, which introduces a new trap exponent $\ensuremath{\theta}$ to describe the dependence on the trap size. This study is relevant for experiments of confined quasi-1D cold atom systems in optical lattices. At the low-density Mott transition, TSS can be shown analytically within the spinless fermion representation of the hard-core limit. The trap-size dependence turns out to be more subtle in the other critical regions, when the corresponding homogeneous system has a nonzero filling fff, showing an infinite number of level crossings of the lowest states when increasing the trap size. At the n=1n=1n=1 Mott transition, this gives rise to a modulated TSS: The TSS is still controlled by the trap-size exponent $\ensuremath{\theta}$, but it gets modulated by periodic functions of the trap size. Modulations of the asymptotic power-law behavior is also found in the gapless superfluid region, with additional multiscaling behaviors.
We study theoretically the Mott metal-insulator transition for a system of fermionic atoms confined in a three-dimensional optical lattice and a harmonic trap. We describe an inhomogeneous system of several thousand sites using an adaptation of dynamical mean-field theory solved efficiently with the numerical renormalization group method. Above a critical value of the on-site interaction, a Mott-insulating phase appears in the system. We investigate signatures of the Mott phase in the density profile and in time-of-flight experiments.
Non-equilibrium quantum phenomena are ubiquitous in nature. Yet, theoretical predictions on the real-time dynamics of many-body quantum systems remain formidably challenging, especially for high dimensions, strong interactions or disordered samples. Here we consider a notable paradigm of strongly correlated Fermi systems, the Mott phase of the Hubbard model, in a setup resembling ultracold-gases experiments. We study the three-dimensional expansion of a cloud into an optical lattice after removing the confining potential. We use time-dependent density-functional theory combined with dynamical mean-field theory, considering interactions below and above the Mott threshold, as well as disorder effects. At strong coupling, we observe multiple timescales in the melting of the Mott wedding-cake structure, as the Mott plateau persist orders of magnitude longer than the band insulating core. We also show that disorder destabilises the Mott plateau and that, compared to a clean setup, localisation can decrease, creating an interesting dynamic crossover during the expansion.