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arXiv:1211.7085 · Physical Review A

Controlling transport of ultracold atoms in one-dimensional optical lattices with artificial gauge fields

Chih-Chun Chien, Massimiliano Di Ventra

Published Feb 8, 2013• 22 citations
arXivHTMLPDF

Abstract

We show that the recently developed optical lattices with Peierls substitution---which can be modeled as a lattice with a complex tunneling coefficient---may be used to induce controllable quantum transport of ultracold atoms. In particular, we show that by ramping up the phase of the complex tunneling coefficient in a spatially uniform fashion, a finite quasi-steady-state current (QSSC) ensues from the exact dynamics of noninteracting fermions. The direction and magnitude of the current can be controlled by the overall phase difference but not the details of the ramp. The entanglement entropy does not increase when the QSSC lasts. Due to different spin statistics, condensed noninteracting bosons do not support a finite QSSC under the same setup. We also find that an approximate form of the QSSC survives when perturbative effects from interactions, weak harmonic background traps, and finite temperature are present, which suggests that our findings should be observable with available experimental capabilities.

DOI
10.1103/physreva.87.023609

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We show that the recently developed optical lattices with Peierls substitution---which can be modeled as a lattice with a complex tunneling coefficient---may be used to induce controllable quantum transport of ultracold atoms. In particular, we show that by ramping up the phase of the complex tunneling coefficient in a spatially uniform fashion, a finite quasi-steady-state current (QSSC) ensues from the exact dynamics of noninteracting fermions. The direction and magnitude of the current can be controlled by the overall phase difference but not the details of the ramp. The entanglement entropy does not increase when the QSSC lasts. Due to different spin statistics, condensed noninteracting bosons do not support a finite QSSC under the same setup. We also find that an approximate form of the QSSC survives when perturbative effects from interactions, weak harmonic background traps, and finite temperature are present, which suggests that our findings should be observable with available experimental capabilities.
Using the microcanonical picture of transport---a framework ideally suited to describe the dynamics of closed quantum systems such as ultracold atom experiments---we show that the exact dynamics of noninteracting fermions and bosons exhibits very different transport properties when the system is set out of equilibrium by removing the particles from half of the lattice. We find that fermions rapidly develop a finite quasisteady-state current reminiscent of electronic transport in nanoscale systems. This result is robust---it occurs with or without a harmonic confining potential and at zero or finite temperature. The zero-temperature bosonic current instead exhibits strong oscillatory behavior that decays into a steady-state of zero current only in the thermodynamic limit. These differences appear most strikingly in the different particle number fluctuations on half of the lattice as a consequence of the spin statistics. These predictions can be readily verified experimentally.
Artificial gauge fields open the possibility to realize quantum many-body systems with ultracold atoms, by engineering Hamiltonians usually associated with electronic systems. In the presence of a periodic potential, artificial gauge fields may bring ultracold atoms closer to the quantum Hall regime. Here, we describe a one-dimensional lattice derived purely from effective Zeeman shifts resulting from a combination of Raman coupling and radio-frequency magnetic fields. In this lattice, the tunneling matrix element is generally complex. We control both the amplitude and the phase of this tunneling parameter, experimentally realizing the Peierls substitution for ultracold neutral atoms.
The study of time-dependent, many-body transport phenomena is increasingly within reach of ultra-cold atom experiments. We show that the introduction of spatially inhomogeneous interactions, e.g., generated by optically controlled collisions, induce negative differential conductance in the transport of atoms in one-dimensional optical lattices. Specifically, we simulate the dynamics of interacting fermionic atoms via a micro-canonical transport formalism within both a mean-field and a higher-order approximation, as well as with a time-dependent density-matrix renormalization group (DMRG). For weakly repulsive interactions, a quasi-steady-state atomic current develops that is similar to the situation occurring for electronic systems subject to an external voltage bias. At the mean-field level, we find that this atomic current is robust against the details of how the interaction is switched on. Further, a conducting–non-conducting transition exists when the interaction imbalance exceeds some threshold from both our approximate and time-dependent DMRG simulations. This transition is preceded by the atomic equivalent of negative differential conductivity observed in transport across solid-state structures.
Bosons and fermions, in the presence of frustration or background gauge fields, can form manybody ground states which support equilibrium 'charge' or 'spin' currents. Motivated by the experimental creation of frustration or artificial gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge invariant route to visualizing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge currents in gapped topological states, such as quantum Hall or quantum spin Hall insulators.
We explore the transport properties of an interacting Fermi gas in a three-dimensional optical lattice. The center of mass dynamics of the atoms after a sudden displacement of the trap minimum is monitored for different interaction strengths and lattice fillings. With increasingly strong attractive interactions the weakly damped oscillation, observed for the noninteracting case, turns into a slow relaxational drift. Tuning the interaction strength during the evolution allows us to dynamically control the transport behavior. Strong attraction between the atoms leads to the formation of local pairs with a reduced tunneling rate. The interpretation in terms of pair formation is supported by a measurement of the number of doubly occupied lattice sites. This quantity also allows us to determine the temperature of the noninteracting gas in the lattice to be as low as (27+/-2)% of the Fermi temperature.
A new millennia ushered in novel experimental capabilities to investigate engineered quantum systems. Gases consisting of charge neutral atoms are cooled to the ground state and by exploiting the dipole interaction can be trapped by laser light. In ultracold atomic systems the tunneling and interactions are controllable, and the system is absent of disorder. Disorder and interactions in solid-state systems inhibits a complete understanding of transport phenomena. Theoretical investigations into non-equilibrium and equilibrium dynamics of fermions in discretized potentials and in continuum are presented. The affect of controllable, external system parameters is evaluated and exploited to reveal new properties of fermion dynamics. My thesis will begin with an overview of the physics associated with many-body fermion and the models used to obtain results, followed by my thesis research on how matter-waves can be manipulated by lattice geometry and tunneling strengths. Next, I present how dissipation affects current in a continuous ring, demonstrating rate-dependent hysteresis as the particles are driven by an artificial gauge field. After presenting the continuous ring, I will then focus on persistent current and corresponding quantum current fluctuations in a discretized ring. Lissajous curves are found in the system whose area strongly depends on the presence and absence of interactions. Lastly, I will discuss dynamical detection methods for one-dimensional topological insulators using ultracold fermions. All of the results are supported with discussion on how they can be realized using current experimental technology.