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Quantum magnetism describes the properties of many materials such as transition metal oxides and cuprate superconductors. One of its elementary processes is the propagation of spin excitations. Here we study the quantum dynamics of a deterministically created spin-impurity atom, as it propagates in a one-dimensional lattice system. We probe the full spatial probability distribution of the impurity at different times using single-site-resolved imaging of bosonic atoms in an optical lattice. In the Mott-insulating regime, a post-selection of the data allows to reduce the effect of temperature, giving access to a space- and time-resolved measurement of the quantum-coherent propagation of a magnetic excitation in the Heisenberg model. Extending the study to the baths superfluid regime, we determine quantitatively how the bath strongly affects the motion of the impurity. The experimental data shows a remarkable agreement with theoretical predictions allowing us to determine the effect of temperature on the coherence and velocity of impurity motion. Our results pave the way for a new approach to study quantum magnetism, mobile impurities in quantum fluids, and polarons in lattice systems.
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We investigate the Fermi polaron problem in a spin-1/2 Fermi gas in an optical lattice for the limit of both strong repulsive contact interactions and one dimension. In this limit, a polaronic-like behaviour is not expected, and the physics is that of a magnon or impurity. While the charge degrees of freedom of the system are frozen, the resulting tight-binding Hamiltonian for the impuritys spin exhibits an intriguing structure that strongly depends on the filling factor of the lattice potential. This filling dependency also transfers to the nature of the interactions for the case of two magnons and the important spin balanced case. At low filling, and up until near unit filling, the single impurity Hamiltonian faithfully reproduces a single-band, quasi-homogeneous tight-binding problem. As the filling is increased and the second band of the single particle spectrum of the periodic potential is progressively filled, the impurity Hamiltonian, at low energies, describes a single particle trapped in a multi-well potential. Interestingly, once the first two bands are fully filled, the impurity Hamiltonian is a near-perfect realisation of the Su-Schrieffer-Heeger model. Our studies, which go well beyond the single-band approximation, that is, the Hubbard model, pave the way for the realisation of interacting one-dimensional models of condensed matter physics.
Using near-exact numerical simulations we study the propagation of an impurity through a one-dimensional Bose lattice gas for varying bosonic interaction strengths and filling factors at zero temperature. The impurity is coupled to the Bose gas and confined to a separate tilted lattice. The precise nature of the transport of the impurity is specific to the excitation spectrum of the Bose gas which allows one to measure properties of the Bose gas non-destructively, in principle, by observing the impurity; here we focus on the spatial and momentum distributions of the impurity as well as its reduced density matrix. For instance we show it is possible to determine whether the Bose gas is commensurately filled as well as the bandwidth and gap in its excitation spectrum. Moreover, we show that the impurity acts as a witness to the cross-over of its environment from the weakly to the strongly interacting regime, i.e., from a superfluid to a Mott insulator or Tonks-Girardeau lattice gas and the effects on the impurity in both of these strongly-interacting regimes are clearly distinguishable. Finally, we find that the spatial coherence of the impurity is related to its propagation through the Bose gas, giving an experimentally controllable example of noise-enhanced quantum transport.
We present a general variational principle for the dynamics of impurity particles immersed in a quantum-mechanical medium. By working within the Heisenberg picture and constructing approximate time-dependent impurity operators, we can take the medium to be in any mixed state, such as a thermal state. Our variational method is consistent with all conservation laws and, in certain cases, it is equivalent to a finite-temperature Greens function approach. As a demonstration of our method, we consider the dynamics of heavy impurities that have suddenly been introduced into a Fermi gas at finite temperature. Using approximate time-dependent impurity operators involving only one particle-hole excitation of the Fermi sea, we find that we can successfully model the results of recent Ramsey interference experiments on $^{40}$K atoms in a $^6$Li Fermi gas [M.~Cetina et al., Science textbf{354}, 96 (2016)]. We also show that our approximation agrees well with the exact solution for the Ramsey response of a fixed impurity at finite temperature. Our approach paves the way for the investigation of impurities with dynamical degrees of freedom in arbitrary quantum-mechanical mediums.
We explore the quantum dynamics of a one-dimensional trapped ultracold ensemble of bosonic atoms triggered by the sudden creation of a single ion. The numerical simulations are performed by means of the ab initio multiconfiguration time-dependent Hartree method for bosons which takes into account all correlations. The dynamics is analyzed via a cluster expansion approach, adapted to bosonic systems of fixed particle number, which provides a comprehensive understanding of the occurring many-body processes. After a transient during which the atomic ensemble separates into fractions which are unbound and bound with respect to the ion, we observe an oscillation in the atomic density which we attribute to the additional length and energy scale induced by the attractive long-range atom-ion interaction. This oscillation is shown to be the main source of spatial coherence and population transfer between the bound and the unbound atomic fraction. Moreover, the dynamics exhibits collapse and revival behavior caused by the dynamical build-up of two-particle correlations demonstrating that a beyond mean-field description is indispensable.
We discuss the local density approximation approach to calculating the ground state energy of a one-dimensional Fermi gas containing a single impurity, and compare the results with exact numerical values that we have for up to 11 particles for general interaction strengths and up to 30 particles in the strongly interacting case. We also calculate the contact coefficient in the strongly interacting regime. The different theoretical predictions are compared to recent experimental results with few-atom systems. Firstly, we find that the local density approximation suffers from great ambiguity in the few-atom regime, yet it works surprisingly well for some models. Secondly, we find that the strong interaction theories quickly break down when the number of particles increase or the interaction strength decreases.
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