We study the transport, decoherence, and the dissipation of the kinetic energy of a mobile impurity interacting with a bath of free fermions in a one-dimensional lattice. Numerical simulations are made with the time-evolving block decimation method, starting from a state where the impurity and bath are decoupled. We introduce a mass imbalance between the impurity and bath particles and find that the fastest decoherence occurs for a light impurity in a bath of heavy particles. By contrast, the fastest dissipation of energy occurs when the masses are equal. We present a simple model for decoherence in the heavy bath limit, and a linear density response description of the interaction which predicts maximum dissipation for equal masses.
We study the transport, decoherence, and the dissipation of the kinetic energy of a mobile impurity interacting with a bath of free fermions in a one-dimensional lattice. Numerical simulations are made with the time-evolving block decimation method, starting from a state where the impurity and bath are decoupled. We introduce a mass imbalance between the impurity and bath particles and find that the fastest decoherence occurs for a light impurity in a bath of heavy particles. By contrast, the fastest dissipation of energy occurs when the masses are equal. We present a simple model for decoherence in the heavy bath limit, and a linear density response description of the interaction which predicts maximum dissipation for equal masses.
An impurity coupled to a bath is a paradigmatic problem of many-body physics and relevant for various systems. In this work, we study the dynamics due to impurities in one-dimensional lattice systems using the numerical time-evolving block decimation method and analytic calculations. We consider both noninteracting and interacting fermions as the bath, in particular fermions in a singlet superfluid state due to attractive on-site interactions, and baths with a periodic or nearly periodic structure due to nearest-neighbor repulsion. Previous theoretical and experimental research mainly considers homogeneous baths with contact interactions. We find novel phenomena when the bath is probed with energies above its characteristic energyscale. In publication I, a driven perturbation with velocity above the speed of sound of the interacting fermions retains the ground-state power-law decay of singlet superfluid correlations. In publication III, we study the decoherence of an impurity in terms of the purity of its density matrix. The impurity and the bath fermions have different masses, and we find the fastest decoherence for a light impurity in a heavy bath, whereas the fastest dissipation of energy occurs for equal masses. In publications II and IV, we consider a bath of fermions with repulsive nearest-neighbor interactions. In a half-filled lattice, the bath is in the Mott insulator state with a particle every two sites. A filling above one half leads to solitons seen as domain walls in the arrangement of the particles. We find that within a resonance region of interactions, the impurity can create an additional soliton-antisoliton pair in the bath. These two excitations have very different dynamics: The antisoliton can form a bound state with the impurity while the soliton excitation propagates. When the ground state of the bath contains solitons, the antisoliton excitation is confined close to its origin. These phenomena are explained by energy conservation, since processes with an energy change larger than the bandwidth are suppressed. Recent developments in experiments with ultracold gases in optical lattices offer possibilities for testing the theoretical predictions of this work. Long-range interactions in lattice models have been observed in experiments with magnetic atoms and dipolar molecules. Furthermore, single-site addressing techniques allow to create localized impurities and track their motion, and to measure the purity of many-body states.
We study analytically and with the numerical time-evolving block decimation method the dynamics of an impurity in a bath of spinless fermions with nearest-neighbor interactions in a one-dimensional lattice. The bath is in a Mott insulator state with alternating sites occupied and the impurity interacts with the bath by repulsive on-site interactions. We find that when the magnitudes of the on-site and nearest-neighbor interactions are close to each other, the system shows excitations of two qualitatively distinct types. For the first type, a domain wall and an antidomain wall of density propagate into opposite directions, while the impurity stays at the initial position. For the second one, the impurity is bound to the antidomain wall while the domain wall propagates, an excitation where the impurity and bath are closely coupled.
We theoretically investigate the correlated decoherence dynamics of two mobile impurities trapped within a gas of ultracold fermionic atoms. We use a mean-field approximation to self-consistently describe the effect of impurity-gas collisions on impurity motion, while decoherence of the impurities' internal state is computed exactly within a functional determinant approach. At equilibrium, we find that the impurities undergo bath-induced localization as the impurity-gas interaction strength is increased. We then study the nonequilibrium dynamics induced by a sudden change of the impurities' internal state, which can be experimentally probed by Ramsey interferometry. Our theoretical approach allows us to investigate the effect of impurity motion on decoherence dynamics, finding strong deviations from the universal behavior associated with Anderson's orthogonality catastrophe when the mass imbalance between impurity and gas atoms is small. Finally, we show that mobile impurities can be used as thermometers of their environment, and that bath-mediated correlations can be beneficial for thermometric performance at low temperatures, even in the presence of nontrivial impurity motion. Our results showcase the interesting open quantum dynamics of mobile impurities dephasing in a common environment, and they can help to provide more precise temperature estimates of ultracold fermionic mixtures.
We consider two mutually interacting fermionic particle species on a one-dimensional lattice and study how the mass ratio $\ensuremath{\eta}$ between the two species affects the (equilibration) dynamics of the particles. Focusing on the regime of strong interactions and high temperatures, two well-studied points of reference are given by (i) the case of equal masses $\ensuremath{\eta}=1$, i.e., the standard Fermi-Hubbard chain, where initial nonequilibrium density distributions are known to decay, and (ii) the case of one particle species being infinitely heavy, $\ensuremath{\eta}=0$, leading to a localization of the lighter particles in an effective disorder potential. Given these two opposing cases, the dynamics in the case of intermediate mass ratios $0<\ensuremath{\eta}<1$ is of particular interest. To this end, we study the real-time dynamics of pure states featuring a sharp initial nonequilibrium density profile. Relying on the concept of dynamical quantum typicality, the resulting nonequilibrium dynamics can be related to equilibrium correlation functions. Summarizing our main results, we observe that diffusive transport occurs for moderate values of the mass imbalance and manifests itself in a Gaussian spreading of real-space density profiles and an exponential decay of density modes in momentum space. For stronger imbalances, we provide evidence that transport becomes anomalous on intermediate timescales, and in particular, our results are consistent with the absence of strict localization in the long-time limit for any $\ensuremath{\eta}>0$. Based on our numerical analysis, we provide an estimate for the ``lifetime'' of the effective localization as a function of $\ensuremath{\eta}$.
This work examines a mobile impurity interacting with a bath of a few spin- ↑ and spin- ↓ fermions in a small one-dimensional open lattice system. We study ground-state properties using the exact diagonalization method, where the system is modeled by a three-component Fermi Hubbard Hamiltonian. We find that in addition to the standard phase separation between a strongly repulsive impurity and the bath, a strongly attractive impurity also phase separates with the fermionic holes due to the particle-hole symmetry. Furthermore, we find that the impurity can show an oscillatory pattern in its density for intermediate attractive and repulsive bath-impurity interactions, which are induced by Friedel oscillations in the finite-size fermionic bath. This rich behavior of the impurity could be probed with fermionic ultracold mixtures in optical lattices.
We study the non-equilibrium dynamics of an impurity in a harmonic trap that is kicked with a well-defined quasi-momentum, and interacts with a bath of free fermions or interacting bosons in a one-dimensional lattice configuration. Using numerical and analytical techniques we investigate the full dynamics beyond linear response, which allows us to quantitatively characterize states of the impurity in the bath for different parameter regimes. These vary from a tightly bound molecular state in a strongly interacting limit to a polaron (dressed impurity) and a free particle for weak interactions, with composite behaviour in the intermediate regime. These dynamics and different parameter regimes should be readily realizable in systems of cold atoms in optical lattices.