Abstract The geometry of optical lattices can be engineered, allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question feasible to atomic systems is related to the speed of matter-wave propagation as a function of the lattice geometry. To address this issue, we investigated, theoretically, the quantum transport of noninteracting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, and the cross-linked square lattice has an even faster propagation velocity. The increase results from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity due to its localized atoms. Possible realizations of those dynamical phenomena are discussed.
Abstract The geometry of optical lattices can be engineered, allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question feasible to atomic systems is related to the speed of matter-wave propagation as a function of the lattice geometry. To address this issue, we investigated, theoretically, the quantum transport of noninteracting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, and the cross-linked square lattice has an even faster propagation velocity. The increase results from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity due to its localized atoms. Possible realizations of those dynamical phenomena are discussed.
The geometry of optical lattices can be engineered allowing the study of\natomic transport along paths arranged in patterns that are otherwise difficult\nto probe in the solid state. A question readily accessible to atomic systems is\nrelated to the speed of propagation of matter-waves as a function of the\nlattice geometry. To address this issue, we have investigated theoretically the\nquantum transport of non-interacting and weakly-interacting ultracold fermionic\natoms in several 2D optical lattice geometries. We find that the triangular\nlattice has a higher propagation velocity compared to the square lattice,\ndespite supporting longer paths. The body-centered square lattice has even\nlonger paths, nonetheless the propagation velocity is yet faster. This apparent\nparadox arises from the mixing of the momentum states which leads to different\ngroup velocities in quantum systems. Standard band theory provides an\nexplanation and allows for a systematic way to search and design systems with\ncontrollable matter-wave propagation. Moreover, the presence of a flat band\nsuch as in a two-leg ladder geometry leads to a dynamical density\ndiscontinuity, which contrasts the behavior of mobile and localized atoms in\nquantum transport. Our predictions are realizable with present experimental\ncapability.
Motivated by recent advances in the realization of complex two-dimensional optical lattices, we investigate theoretically the quantum transport of ultracold fermions in an optical kagome lattice. In particular, we focus on its extensively degenerate localized states (flat band). By loading fermions in a partial region of the lattice and depleting the mobile atoms at the far boundary of the initially unoccupied region, we find a dynamically generated flat-band insulator, which is also a population-inverted state. We further show that inclusion of weak repulsion leads to a dynamical stripe phase for two-component fermions in a similar setup. Finally, by preparing a topological insulating state in a partially occupied kagome lattice, we find that the topological chiral current decays but exhibits an interesting oscillating dynamics during the nonequilibrium transport. Given the broad variety of lattice geometries supporting localized or topological states, our work suggests new possibilities for using geometrical effects and their dynamics in atomtronic devices.
Ultracold atoms in a moving optical lattice with high controllability are a feasible platform to research the transport phenomenon. Here, we study the transport process of ultracold atoms at the D band in a one-dimensional optical lattice and manipulate the transport of superposition states with different superposition weights of S-band and D-band atoms. In the experiment, we first load ultracold atoms into an optical lattice using the shortcut method and then accelerate the optical lattice by scanning the phase of lattice beams. The atomic transport at the D band and S band is demonstrated, respectively. The group velocity of atoms at the D band is opposite to that at the S band. By preparing superposition states with different superposition weights of the D-band and S-band atoms, we realize the manipulation of atomic group velocity from positive to negative, and observe the quantum interference between atoms at different bands. The influence of the lattice depth and acceleration on the transport process is also studied. Moreover, the multiorbital simulations are coincident with the experimental results. Our paper sheds light on the transport process of ultracold atoms at higher bands in optical lattices and provides a useful method to manipulate the transport of atomic superposition states.
Transport properties and nonequilibrium dynamics in strongly correlated materials are \ntypically difficult to calculate. This holds true even for minimalistic model Hamiltonians \nof these systems, such as the fermionic Hubbard model. \nUltracold atoms in optical lattices enable an alternative realization of the Hubbard \nmodel and have the advantage of being free of additional complications such as phonons, \nlattice defects or impurities. This way, cold atoms can be used as quantum simulators of \nstrongly interacting materials. Being thermally isolated systems, however, we show that \ncold atoms in optical lattices can also behave very differently from solids and can show a \nplethora of novel dynamic effects. \nIn this thesis, several out-of equilibrium processes involving interacting fermionic atoms \nin optical lattices are presented. We first analyze the expansion dynamics of an initially \nconfined atomic cloud in the lowest band of an optical lattice. While non-interacting atoms \nexpand ballistically, the cloud expands with a dramatically reduced velocity in the presence \nof interactions. Most prominently, the expansion velocity is independent of the attractive \nor repulsive character of the interactions, highlighting a novel dynamic symmetry of the \nHubbard model. \nIn a second project, we discuss the possibility of realizing negative absolute temperatures in optical lattices. Negative absolute temperatures characterize equilibrium states \nwith an inverted occupation of energy levels. Here, we propose a dynamical process to realize equilibrated Fermions at negative temperatures and analyze the time scales of global \nrelaxation to equilibrium, which are associated with a redistribution of energy and particles \nby slow diffusive processes. \nWe show that energy conservation has a major impact on the dynamics of an interacting \ncloud in an optical lattice, which is exposed to an additional weak linear (gravitational) \npotential. Instead of ‘falling downwards‘, the cloud diffuses symmetrically upwards and \ndownwards in the gravitational potential. Furthermore, we show analytically that the \nradius R grows with the time t according to R ∼ t^1/3, consistent with numerical simulations \nof the Boltzmann equation. \nFinally, we analyze the damping of Bloch oscillations by interactions. For a homogeneous system, we discuss the possibility of mapping the dynamics of the particle current to \na classical damped harmonic oscillator equation, thereby giving an analytic explanation for \nthe transition from weakly damped to over-damped Bloch oscillations. We show that the \ndynamics of a strongly Bloch oscillating and weakly interacting atomic cloud can be discribed in terms of a novel effective “stroboscopic” diffusion equation. In this approximation, \nthe cloud’s radius R grows asymptotically in time t according to R ∼ t^1/5 .
Quantum gases in optical lattices allow for fundamental studies in atomic and condensed-matter physics and the exploration of novel effects. After a brief introduction to the fundamentals of quantum gas experiments in optical lattices, we discuss two recent experiments focusing on driven matter waves in a one-dimensional optical lattice. The first experiment uses a tilted bichromatic optical lattice to investigate the interplay of disorder and collisional interactions in the accelerated transport of a Bose-Einstein condensate. Here, a screening effect is observed, in which the interactions effectively cancel the damping of Bloch oscillations induced by a (quasi-)disordered potential. This effect can be understood through a modification of the underlying band structure by the interactions. The second experiment studies the dynamics of a weakly trapped condensate resonantly coupled to the orbitals of a strongly confining state-selective lattice. We observe momentum distributions that correspond to matter wave diffraction from a periodic structure; however, the diffractive dynamics remain strongly linked to the internal-state Rabi oscillations. In the regime investigated, which we call the nonadiabatic regime, no diffracting potential can be defined. We show how only for much stronger coupling, the internal and external dynamics decouple, transitioning from nonadiabatic diffraction to the well-studied Kapitza-Dirac diffraction. We further investigate prospects for realizing dissipative spin models in our ultracold atomic gas experiment. To this end, we develop and test in the laboratory several possible implementations of effective spins with differential coupling to a superfluid background and examine their viability for a realization of the spin-boson model. | 94 pages
Recent work in atom optics has led to enormous progress in the study of quantum chaos and has addressed a broad range of problems in quantum transport, traditionally studied in the context of condensed matter physics. This issue brings together the various researchers working in the border domain between atom optics and solid state physics and focuses on atomic motion in light fields in a regime that is dominated by quantum effects. The topics discussed in this issue include: • quantum effects of atomic motion in light fields; • quantum chaos in time dependent lattices; • tunnelling in stationary or time-dependent lattices; • Wannier-Stark ladder and Bloch oscillations; • atomic band structures; • many-body effects on transport in optical lattices; • effects of decoherence on quantum transport; • weak and dynamical localization. At this point we take the opportunity to express our gratitude to the authors of the papers of this issue and the reviewers for their efforts in preparing and ensuring the high quality of the state of the art presentation.