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arXiv:1701.01845 · Physical Review A

Impurity and soliton dynamics in a Fermi gas with nearest-neighbor interactions

Anne-Maria Visuri, Päivi Törmä, Thierry Giamarchi

Published Jun 7, 2017• 1 citation
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Abstract

We study spinless fermions with repulsive nearest-neighbor interactions perturbed by an impurity particle or a local potential quench. Using the numerical time-evolving block decimation method and a simplified analytic model, we show that the perturbations create a soliton-antisoliton pair. If solitons are already present in the bath, the two excitations have a drastically different dynamics: The antisoliton does not annihilate with the solitons and is therefore confined close to its origin while the soliton excitation propagates. We discuss the consequences for experiments with ultracold gases.

DOI
10.1103/physreva.95.063605

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We study spinless fermions with repulsive nearest-neighbor interactions perturbed by an impurity particle or a local potential quench. Using the numerical time-evolving block decimation method and a simplified analytic model, we show that the perturbations create a soliton-antisoliton pair. If solitons are already present in the bath, the two excitations have a drastically different dynamics: The antisoliton does not annihilate with the solitons and is therefore confined close to its origin while the soliton excitation propagates. We discuss the consequences for experiments with ultracold gases.
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.
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.
Ultracold quantum gases in the superfluid regime exhibit solitons, localized excitations that require nonlinearity of the underlying field equation in order to preserve their shape as they propagate. Here, we investigate the behavior of solitons at an inhomogeneity: an interface that separates two different interaction regimes of a superfluid Fermi gas. It is known that the soliton properties depend on the interaction regime, but what happens as a soliton impinges on such an interface is not clear. Using an effective field theory to describe the superfluid Fermi gas, we reveal the nontrivial dynamics of such a collision. Whether the original soliton makes it through the interface depends on the amplitude of the soliton. Regardless of whether the original soliton is transmitted or not, there will always be a shock wave with a phonon train created behind the interface and reflected secondary solitons. The details of this dynamics depends strongly on the equation of state corresponding to underlying microscopic theory describing the superfluid Fermi gas, and we argue that these collisions are realistic experimental probes to test microscopic theories of pairing in ultracold Fermi gases.
We investigate the possibilities for the generation of solitons and vortices in a degenerate gas of neutral fermionic atoms. In analogy with the already experimentally demonstrated technique applied to a gaseous Bose-Einstein condensate we propose the phase engineering of a Fermi gas as a practical route to excited states with solitons and vortices. We stress that solitons and vortices appear even in a non-interacting fermionic gas. For solitons, in a system with a sufficiently large number of fermions and appropriate trap configuration, the Pauli blocking acts as the interaction between particles.
We simulate a balanced attractively interacting two-component Fermi gas in a one-dimensional lattice perturbed with a moving potential well or barrier. Using the time-evolving block decimation (TEBD) method, we study different velocities of the perturbation and distinguish two velocity regimes based on clear differences in the time evolution of particle densities and the pair correlation function. We show that, in the slow regime, the densities deform as particles are either attracted by the potential well or repelled by the barrier, and a wave front of hole or particle excitations propagates at the maximum group velocity. Simultaneously, the initial pair correlations are broken and coherence over different sites is lost. In contrast, in the fast regime, the densities are not considerably deformed and the pair correlations are preserved.
We consider the dynamics of an impurity atom immersed in an ideal Fermi gas at zero temperature. We focus on the coherent quantum evolution of the impurity following a quench to strong impurity-fermion interactions, where the interactions are assumed to be short range like in cold-atom experiments. To approximately model the many-body time evolution, we use a truncated basis method, where at most two particle-hole excitations of the Fermi sea are included. When the system is initially noninteracting, we show that our method exactly captures the short-time dynamics following the quench, and we find that the overlap between initial and final states displays a universal nonanalytic dependence on time in this limit. We further demonstrate how our method can be used to compute the impurity spectral function, as well as describe many-body phenomena involving coupled impurity spin states, such as Rabi oscillations in a medium or highly engineered quantum quenches.