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arXiv:1407.6037 · Physical Review Letters

Relaxation Dynamics of a Fermi Gas in an Optical Superlattice

Daniel Pertot, Ameneh Sheikhan, Eugenio Cocchi, Luke A. Miller, Johanna E. Bohn, Marco Koschorreck, Michael Köhl, Corinna Kollath

Published Oct 23, 2014• 36 citations
arXivHTMLPDF

Abstract

This Letter comprises an experimental and theoretical investigation of the time evolution of a Fermi gas following fast and slow quenches of a one-dimensional optical double-well superlattice potential. We investigate both the local tunneling in the connected double wells and the global dynamics towards a steady state, i.e., a time-independent state. The local observables in the steady state resemble those of a thermal equilibrium state, whereas the global properties indicate a strong nonequilibrium situation.

DOI
10.1103/physrevlett.113.170403

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This Letter comprises an experimental and theoretical investigation of the time evolution of a Fermi gas following fast and slow quenches of a one-dimensional optical double-well superlattice potential. We investigate both the local tunneling in the connected double wells and the global dynamics towards a steady state, i.e., a time-independent state. The local observables in the steady state resemble those of a thermal equilibrium state, whereas the global properties indicate a strong nonequilibrium situation.
After a brief review of some known steady state properties of an absorptive bistable system, we discuss in some details new aspects of the transient response that follows a sudden perturbation from steady state. The evolution of the perturbed bistable system towards its new steady state consists of two generally distinct phases: one is the local relaxation within each well of the bimodal potential, the second is the tunneling through the local maximum that separates the metastable and stable steady states. We give an analytic description of both phases of the evolution, and give explicit formulas for the local and global relaxation rates.
We establish a setting-atoms in optical superlattices with period 2-in which one can experimentally probe signatures of the process of local relaxation and apparent thermalization in nonequilibrium dynamics without the need of addressing single sites. This opens up a way to explore the convergence of subsystems to maximum entropy states in quenched quantum many-body systems with present technology. Remarkably, the emergence of thermal states does not follow from a coupling to an environment but is a result of the complex nonequilibrium dynamics in closed systems. We explore ways of measuring the relevant signatures of thermalization in this analogue quantum simulation of a relaxation process, exploiting the possibilities offered by optical superlattices.
In the study of relaxation processes in coherent nonequilibrium dynamics of quenched quantum systems, ultracold atoms in optical superlattices with periodicity 2 provide a very fruitful test ground. We consider the dynamics of a particular, experimentally accessible initial state prepared in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the entire range of interaction strengths, further investigating the issues raised by Cramer et al. [Phys. Rev. Lett. 101, 063001 (2008)]. We investigate the relaxation dynamics analytically in the noninteracting and hard-core bosonic limits, deriving explicit expressions for the dynamics of certain correlation functions, and numerically for finite interaction strengths using the time-dependent density-matrix renormalization (t-DMRG) approach. We can identify signatures of local relaxation that can be accessed experimentally with present technology. While the global system preserves the information about the initial condition, locally the system relaxes to the state having maximum entropy respecting the constraints of the initial condition. For finite interaction strengths and finite times, the relaxation dynamics contains signatures of the relaxation dynamics of both the noninteracting and hard-core bosonic limits.
We study the time-dependent dynamical properties of two-component ultracold fermions in a one-dimensional optical superlattice by applying the adaptive time-dependent density matrix renormalization group to a repulsive Hubbard model with an alternating superlattice potential. We clarify how the time evolution of local quantities occurs when the superlattice potential is suddenly changed to a normal one. For a Mott-type insulating state at quarter filling, the time evolution exhibits a profile similar to that expected for bosonic atoms, where correlation effects are less important. On the other hand, for a band-type insulating state at half filling, the strong repulsive interaction induces an unusual pairing of fermions, resulting in some striking properties in time evolution, such as a paired fermion co-tunneling process and the suppression of local spin moments. We further address the effect of a confining potential, which causes spatial confinement of the paired fermions.
Ultracold atoms in optical lattices provide a versatile platform for studying many-body physics in a defect-free system with tunable parameters. For the analog quantum simulation of the Fermi-Hubbard model, fermionic atoms take on the role of the valence electrons and optical lattices provide the periodic potential in place of the solid-state crystal. The dynamics in the system are described by the tunneling amplitude t between neighboring lattice sites and the interaction energy U of two particles occupying the same lattice site. With the depth of the optical lattices and an external magnetic field, both parameters can be tuned to access a wide range of regimes. Two superimposed lattices with different lattice periods form an optical superlattice, where the most common configuration is a bichromatic superlattice with lattice periods different by a factor of two. Depending on the lattice depths and the relative phase of the lattices, the bichromatic superlattice potential ranges from an array of weakly-coupled double wells to a continuous lattice potential with a staggered energy offset. We developed a calibration technique for measuring the depth of an optical lattice with local resolution. The band structure of the optical lattice is probed by modulating the lattice depth and exciting the atoms to higher bands. However, compared to resolving the band occupations in a time-of-flight measurement, we further excite the atoms to an untrapped band to deplete the optical lattice along equipotential lines where the modulation frequency is resonant with the local band transitions. From the profile of the lattice depth, we obtain the calibration factor for the power regulation, the waist of the underlying lattice beams and the position of the lattice axis. This technique combines several calibration measurements, thereby reducing the measurement time and enabling an automation of the lattice alignment. For the bichromatic superlattice we realized an active stabilization of the superlattice phase that enables long-term measurements with a precise control over the superlattice phase. The instability of the superlattice phase is a result of the different refractive indices for the two lattices in air and the optical elements along the optical path. Using environmental sensors, we monitor the temperature, the pressure, and the relative humidity to apply the expected correction to the superlattice phase. The stabilized superlattice phase enabled the investigation of Floquet-driven double wells by modulating the energy offset through the superlattice phase. We used a near-resonant driving frequency with respect to the interaction energy to enhance the pair-tunneling amplitude in doubly-occupied double wells compared to static double wells and compared to the tunneling amplitude in singly-occupied double wells.
We study how well magnetic models can be implemented with ultracold bosonic atoms of two different hyperfine states in an optical superlattice. The system is captured by a two-species Bose-Hubbard model, but realizes in a certain parameter regime actually the physics of a spin-1/2 Heisenberg magnet, describing the second-order hopping processes. Tuning of the superlattice allows for controlling the effect of fast first-order processes versus the slower second-order ones. Using the density-matrix renormalization-group method, we provide the evolution of typical experimentally available observables. The validity of the description via the Heisenberg model, depending on the parameters of the Hubbard model, is studied numerically and analytically. The analysis is also motivated by recent experiments [S. F\"olling et al., Nature (London) 448, 1029 (2007); S. Trotzky et al., Science 319, 295 (2008)] where coherent two-particle dynamics with ultracold bosonic atoms in isolated double wells were realized. We provide theoretical background for the next step, the observation of coherent many-particle dynamics after coupling the double wells. Contrary to the case of isolated double wells, relaxation of local observables can be observed. The tunability between the Bose-Hubbard model and the Heisenberg model in this setup could be used to study experimentally the differences in equilibration processes for nonintegrable and Bethe ansatz integrable models. We show that the relaxation in the Heisenberg model is connected to a phase averaging effect, which is in contrast to the typical scattering driven thermalization in nonintegrable models. We discuss the preparation of magnetic ground states by adiabatic tuning of the superlattice parameters.