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Register a new userSubdiffusion and heat transport in a tilted 2D Fermi-Hubbard system
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Added by
Elmer Guardado-Sanchez
Publication date
2019
fields
Physics
and research's language is
English
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Using quantum gas microscopy we study the late-time effective hydrodynamics of an isolated cold-atom Fermi-Hubbard system subject to an external linear potential (a tilt). The tilt is along one of the principal directions of the two-dimensional (2D) square lattice and couples mass transport to local heating through energy conservation. We study transport and thermalization in our system by observing the decay of prepared initial density waves as a function of wavelength $lambda$ and tilt strength and find that the associated decay time $tau$ crosses over as the tilt strength is increased from characteristically diffusive to subdiffusive with $tauproptolambda^4$. In order to explain the underlying physics we develop a hydrodynamic model that exhibits this crossover. For strong tilts, the subdiffusive transport rate is set by a thermal diffusivity, which we are thus able to measure as a function of tilt in this regime. We further support our understanding by probing the local inverse temperature of the system at strong tilts, finding good agreement with our theoretical predictions. Finally, we discuss the relation of the strongly tilted limit of our system to recently studied 1D models which may exhibit nonergodic dynamics.
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Quantum many-body systems may defy thermalization even without disorder. Intriguingly, non-ergodicity may be caused by a fragmentation of the many-body Hilbert-space into dynamically disconnected subspaces. The tilted one-dimensional Fermi-Hubbard model was proposed as a platform to realize fragmented models perturbatively in the limit of large tilt. Here, we demonstrate the validity of this effective description for the transient dynamics using ultracold fermions. The effective analytic model allows for a detailed understanding of the emergent microscopic processes, which in our case exhibit a pronounced doublon-number dependence. We study this experimentally by tuning the doublon fraction in the initial state.
The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.
We use quantum kinetic theory to calculate the thermoelectric transport properties of the 2D single band Fermi-Hubbard model in the weak coupling limit. For generic filling, we find that the high-temperature limiting behaviors of the electrical ($sim T$) and thermal ($sim T^2$) resistivities persist down to temperatures of order the hopping matrix element $Tsim t$, almost an order of magnitude below the bandwidth. At half filling, perfect nesting leads to anomalous low temperature scattering and nearly $T$-linear electrical resistivity at all temperatures. We hypothesize that the $T$-linear resistivity observed in recent cold atom experiments is continuously connected to this weak coupling physics and suggest avenues for experimental verification. We find a number of other novel thermoelectric results, such as a low-temperature Wiedemann-Franz law with Lorenz coefficient $5pi^2/36$.
Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system -- leading to long-lived prethermal regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization, and provide insight into the characterization of heating for driven bosonic systems.
Charge transport is a revealing probe of the quantum properties of materials. Strong interactions can blur charge carriers resulting in a poorly understood quantum soup. Here we study the conductivity of the Fermi-Hubbard model, a testing ground for strong interaction physics, in a clean quantum system - ultracold $^6$Li in a 2D optical lattice. We determine the charge diffusion constant in our system by measuring the relaxation of an imposed density modulation and modeling its decay hydrodynamically. The diffusion constant is converted to a resistivity, which exhibits a linear temperature dependence and exceeds the Mott-Ioffe-Regel limit, two characteristic signatures of a bad metal. The techniques we develop here may be applied to measurements of other transport quantities, including the optical conductivity and thermopower.
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