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Register a new userInterspecies entanglement with impurity atoms in a lattice gas
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The dynamics of impurity atoms introduced into bosonic gases in an optical lattice have generated a lot of recent interest, both in theory and experiment. We investigate to what extent measurements on either the impurity species or the majority species in these systems are affected by their interspecies entanglement. This arises naturally in the dynamics and plays an important role when we measure only one species. We explore the corresponding effects in strongly interacting regimes, using a combination of few-particle analytical calculations and Density Matrix Renormalisation group methods in one dimension. We identify how the resulting effects on impurities can be used to probe the many-body states of the majority species, and separately ask how to enter regimes where this entanglement is small, so that the impurities can be used as probes that do not significantly affect the majority species. The results are accessible in current experiments, and provide important considerations for the measurement of complex systems with using few probe atoms.
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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.
We present a proposal for the realization of entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. Our approach is based on the notion that the entanglement spectrum of such systems can be realized with a physical Hamiltonian containing a set of position-dependent couplings. We focus on reproducing the universal ratios of the entanglement spectrum for systems in two different geometries: a harmonic trap, which corresponds to a partition embedded in an infinite system, and a linear potential, which reproduces the properties of a half-partition with open boundary conditions. Our results demonstrate the possibility of measuring the entanglement spectra of the Heisenberg and XX models in a realistic cold-atom experimental setting by simply using gravity and standard trapping techniques.
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 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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