Session E19: Precision Many Body Physics IV

Quantum Transport in Strongly Interacting Fermi Gases

Transport is the defining property of states of matter, but often the most difficult to understand. Strongly interacting Fermi gases are especially challenging, despite their ubiquitous presence across many fields of physics. Experiments on ultracold fermionic atoms allow the direct measurement of transport properties in ideal model systems where the hamiltonian is precisely known while transport properties are difficult to calculate theoretically.
In this talk I will present transport measurements on two strongly interacting Fermi systems, the unitary Fermi gas and the Fermi-Hubbard gas, both realized in uniform box potentials. In the unitary gas, we excite first and, in the superfluid regime, also second sound waves and demonstrate a quantum limited sound diffusivity given by hbar over the particle mass. The first and second sound diffusivities give direct access to the thermal conductivity and the viscosity of the gas. For the Fermi-Hubbard gas, realized under a quantum gas microscope, we measure spin diffusion and spin conductivity in the Mott insulator at half filling. For strong interactions, spin diffusion is driven by super-exchange and doublon-hole-assisted tunneling, and strongly violates the quantum limit of charge diffusion. The technique developed in this work can be extended to finite doping, which can shed light on the complex interplay between spin and charge in the Hubbard model.   

Spectra of heavy polarons and molecules coupled to a Fermi sea

We study the spectrum of an impurity coupled to a Fermi sea (e.g., minority atom in an ultracold gas, exciton in a solid) by attraction strong enough to form a molecule/trion. We introduce a diagrammatic scheme which allows treating a finite mass impurity while reproducing the Fermi edge singularity in the immobile limit. For large binding energies the spectrum is characterized by a semi-coherent repulsive polaron and an incoherent molecule, which is the lowest-energy feature in the single-particle spectrum. The previously predicted attractive polaron seems not to exist for strong binding.   

Energy and short-range correlations of Bose Polarons in the strong coupling regime

The concept of the Bose polaron quasiparticle originates in Landau’s description of a crystal’s conduction electron which deforms the surrounding ionic lattice. Despite the conceptual simplicity of the Bose polaron – i.e. an impurity dressed by a surrounding bosonic bath – this quasiparticle poses remarkable challenges for both theoretical and experimental physicists. These challenges arise at strong interaction strengths where a multitude of bosons can simultaneously interact with the impurity thereby forming a complicated many-body state. We here report on the first creation of an ensemble of Bose polarons – comprised of fermionic ⁴⁰K impurities immersed in a ²³Na Bose Einstein condensate – in local equilibrium and in the strongly interacting regime. Using radio frequency ejection spectroscopy, we measure the Bose polaron ground-state energy and short-range correlations as a function of temperature across a variety of interaction strengths by tuning an interspecies magnetic Feshbach resonance. We further study collective oscillations between the BEC and the impurities, demonstrating strong dissipation of the impurities’ momentum at the transition from collisionless to hydrodynamic regime.   

Polaron mobility in the ``beyond quasiparticles" regime

In a number of physical situations, from polarons, to non-Fermi liquids, to Dirac liquids,
one often faces a problem of computing particle mobility/conductivity when conditions for
applicability of the kinetic equation approach are violated. The corresponding
``beyond quasiparticles" (or ``overdamped") regime is formally identified as a state in which
an inelastic scattering time (computed formally within the standard perturbative approach)
is exceeding the typical thermal energy of quasiparticles. We employ the Diagrammatic Monte
Carlo method to study mobility of Frohlich polarons in the overdamped regime and find
two effects: a substantial delay in developing an exponential law at temperatures below
the optical mode frequency, and a mobility minimum at T close to optical ode frequency.
Both effects should be taken into account in interpreting mobility data in materials with strong
electron-phonon coupling.   

The contact of the Fermi gas at unitarity

The unitary Fermi gas is a strongly correlated system with a short-range interaction that saturates the upper bound on the modulus of the two-particle s-wave scattering amplitude. It is characterized by an infinite scattering length and sits in the middle of the BCS-BEC crossover. The contact of this system is a quantity that describes short-range pairing correlations and appears in the high momentum tail of the momentum distribution and the static structure factor, as well as in the high-frequency tail of the shear viscosity spectral function. There have been a number of recent calculations and important experimental advances towards determining the contact for the unitary Fermi gas. We present results for the temperature dependence of the contact at unitarity using finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods on the lattice. Our calculations are carried out within the canonical ensemble with multiple filling factors and extrapolated to the continuum limit. We compare our results with other theoretical calculations and with experiment.   

Spin Transport in a Mott Insulator of Ultracold Fermions

Understanding transport in strongly interacting Fermi systems is among the most pressing but difficult tasks of many-body physics. The Fermi-Hubbard model serves as a prototypical example of a strongly correlated fermionic quantum system, and is believed to hold the key to high-temperature superconductivity. However, the transport properties in the various regions of its phase diagram are far from understood. We realize the Fermi-Hubbard model using a gas of fermionic atoms in an optical lattice, confined in a homogeneous box trap. In this setting, we study spin and charge transport using a quantum gas microscope, able to resolve individual atoms. In particular, at half filling, the charge degree of freedom is frozen, while spins are still able to move. Spin transport is induced by applying a spin-dependent magnetic field gradient. We observe spin dynamics which are diffusive in nature, and obtain the spin conductivity and spin diffusivity. These findings can be compared to existing theoretical approaches, such as the numerical-linked-cluster expansion (NLCE).   

Excitation spectrum of dipolar Bose gases

We investigate the excitation spectrum of a dipolar Bose gas in the low temperature limit across the superfluid-supersolid-crystal transition. At sufficiently low temperatures, a system of aligned dipolar bosons will undergo a quantum phase transition by tuning the range of the repulsive two-body potential. In one limit, the phase of the system is that of a classical crystal of filaments. At the other limit, the system experiences quantum melting into a superfluid phase. In the intermediate regime, the system exists in a supersolid state. We use Quantum Monte Carlo techniques to compute imaginary time correlation functions at the different regions of the phase diagram, and we use the method of Maximum Entropy to extract the dynamical structure factor, which is then used to obtain the excitation spectrum and its evolution throughout the phase diagram.   

Bose liquid in checkerboard antiferromagnet

The frustrated J₁-J₂ antiferromagnet model on the checkerboard lattice, known as the two-dimensional analog of the pyrochlore lattice, provides a perfect platform for dimensional crossover effect due to competition between the two exchange constants J₁ and J₂. Using recently developed tensor network algorithm based on Projected Entangled Simplex States (PESS), we obtain a line degenerate bose liquid state without magnetic order on the whole range of J₂ > J₁ for both XY and Heisenberg antiferromagnetic limit. The degenerate liquid state is stable even when small anisotropy on J₁ bond is introduced and the interaction enhance the robustness of the bose liquid behavior.   

Impenetrable SU(N) fermions in one-dimensional lattices

We study SU(N) fermions in the limit of infinite on-site repulsion between all species. We focus on states in which every pair of consecutive fermions carries a different spin flavor. Since the particle order cannot be changed (because of the infinite on-site repulsion) and contiguous fermions have a different spin flavor, we refer to the corresponding constrained model as the model of distinguishable quantum particles. We introduce an exact numerical method to calculate equilibrium one-body correlations of distinguishable quantum particles based on a mapping onto noninteracting spinless fermions. In contrast to most many-body systems in one dimension, which usually exhibit either power-law or exponential decay of off-diagonal one-body correlations with distance, distinguishable quantum particles exhibit a Gaussian decay of one-body correlations in the ground state, while finite-temperature correlations are well described by stretched exponential decay. We also study the dynamics of distinguishable quantum particles after geometric quantum quenches.   

Efficient exact diagonalization of the n-body reduced density matrix

The n-body reduced density matrix provides an alternate description of a quantum-many body system that can offer considerable compression over the wavefunction while providing access to observables and correlation functions. In this talk, we present an efficient algorithm for its construction and exact diagonalization in a system of N interacting particles. In one spatial dimension, we simplify computations by exploiting translational, reflection and particle-hole symmetries. We illustrate the method by calculating the maximal particle entanglement entropy constructed from the N/2-particle reduced density matrix in the ground state of up to 13 interacting fermions on 26 sites.
  

Prethermalization and Thermalization in Generic Isolated Quantum Systems

Prethermalization has been extensively studied in systems close to integrability. We propose a more general, yet simpler, setup for this phenomenon. We consider a -possibly nonintegrable- reference dynamics, weakly perturbed so that the perturbation violates at least one conservation law of the reference dynamics. We argue then that the evolution of the system proceeds via intermediate (generalized) equilibrium states of the reference dynamics. The motion on the manifold of equilibrium states is governed by an autonomous equation, flowing towards global equilibrium in a time of order g², with g the perturbation strength. We also describe the leading corrections to the time-dependent reference equilibrium state, in general of order g. The theory is well-confirmed by numerical calculations relying on the numerical linked cluster expansion.   

Evolution of two-time correlations in strongly correlated dissipative systems: aging and hierarchical dynamics

In recent years, considerable experimental efforts have been devoted
to dynamically generate complex states and monitor their evolution. Despite
remarkable advances, the theoretical principles behind the
non-equilibrium dynamics of strongly correlated quantum matter are
still far from being fully understood. In particular, very few studies
have sought to clarify the influence of environmental couplings on the
propagation of correlations. We attempt here to fill this gap. To do so, we extend quasi-exact time-dependent matrix product state techniques
to simulate the evolution of two-time correlations in the XXZ spin-1/2 model in
contact with an environment causing local dephasing on all sites.
We find this system to display hierarchical and aging dynamics. The latter dynamical regime is
characterized by a breakdown of time-translation invariance, a slow
non-exponential relaxation of two-time correlations and the presence
of dynamical scaling.