Entangling strings of neutral atoms in 1D atomic pipeline structures

Quantum quench and coherent-incoherent dynamics of Ising chains interacting with dissipative baths

The modular path integral methodology is used to extend the well-known spin-boson dynamics to finite-length quantum Ising chains, where each spin is coupled to a dissipative harmonic bath. The chain is initially prepared in the ferromagnetic phase where all spins are aligned, and the magnetization is calculated with spin-spin coupling parameters corresponding to the paramagnetic phase, mimicking a quantum quench experiment. The observed dynamics is found to depend significantly on the location of the tagged spin. In the absence of a dissipative bath, the time evolution displays irregular patterns that arise from multiple frequencies associated with the eigenvalues of the chain Hamiltonian. Coupling of each spin to a harmonic bath leads to smoother dynamics, with damping effects that are stronger compared to those observed in the spin-boson model and more prominent in interior spins, a consequence of additional damping from the spin environment. Interior spins exhibit a transition from underdamped oscillatory to overdamped monotonic dynamics as the temperature, spin-bath, or spin-spin coupling is increased. In addition to these behaviors, a new dynamical pattern emerges in the evolution of edge spins with strong spin-spin coupling at low and intermediate temperatures, where the magnetization oscillates either above or below the equilibrium value.

Thermal bosons in 3d optical lattices via tensor networks

Ultracold atoms in optical lattices are one of the most promising experimental setups to simulate strongly correlated systems. However, efficient numerical algorithms able to benchmark experiments at low-temperatures in interesting 3d lattices are lacking. To this aim, here we introduce an efficient tensor network algorithm to accurately simulate thermal states of local Hamiltonians in any infinite lattice, and in any dimension. We apply the method to simulate thermal bosons in optical lattices. In particular, we study the physics of the (soft-core and hard-core) Bose–Hubbard model on the infinite pyrochlore and cubic lattices with unprecedented accuracy. Our technique is therefore an ideal tool to benchmark realistic and interesting optical-lattice experiments.

Relative criterion for validity of a semiclassical approach to the dynamics near quantum critical points

Based on an analysis of Feynman's path integral formulation of the propagator, a relative criterion is proposed for validity of a semiclassical approach to the dynamics near critical points in a class of systems undergoing quantum phase transitions. It is given by an effective Planck constant, in the relative sense that a smaller effective Planck constant implies better performance of the semiclassical approach. Numerical tests of this relative criterion are given in the XY model and in the Dicke model.

Assisted finite-rate adiabatic passage across a quantum critical point: exact solution for the quantum Ising model

The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point, allowing one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.

Semiclassical approach to survival probability at quantum phase transitions

We study the decay of survival probability at quantum phase transitions with infinitely degenerate ground levels at critical points. For relatively long times, the semiclassical theory predicts power-law decay of the survival probability in systems with d=1 and exponential decay in systems with sufficiently large d, where d is the degrees of freedom of the classical counterpart of the system. The predictions are checked numerically in four models.

Phase transition in space: how far does a symmetry bend before it breaks?

We extend the theory of symmetry-breaking dynamics in non-equilibrium second-order phase transitions known as the Kibble-Zurek mechanism (KZM) to transitions where the change of phase occurs not in time but in space. This can be due to a time-independent spatial variation of a field that imposes a phase with one symmetry to the left of where it attains critical value, while allowing spontaneous symmetry breaking to the right of that critical borderline. Topological defects need not form in such a situation. We show, however, that the size, in space, of the 'scar' over which the order parameter adjusts as it 'bends' interpolating between the phases with different symmetries follows from a KZM-like approach. As we illustrate on the example of a transverse quantum Ising model, in quantum phase transitions this spatial scale--the size of the scar--is directly reflected in the energy spectrum of the system: in particular, it determines the size of the energy gap.

Sweeping from the superfluid to the Mott phase in the Bose-Hubbard model

We study the sweep through the quantum phase transition from the superfluid to the Mott state for the Bose-Hubbard model with a time-dependent tunneling rate J(t). In the experimentally relevant case of exponential decay J(t) proportional variant e -gamma t, an adapted mean-field expansion for large fillings n yields a scaling solution for the fluctuations. This enables us to analytically calculate the evolution of the number and phase variations (on-site) and correlations (off-site) for slow (gamma<<mu), intermediate, and fast (nonadiabatic gamma>>mu) sweeps, where mu is the chemical potential. Finally, we derive the dynamical decay of the off-diagonal long-range order as well as the temporal shrinkage of the superfluid fraction in a persistent ring-current setup.

Dynamics of a quantum phase transition

We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.

Toward Atom Chips

As a novel approach for turning the peculiar features of quantum mechanics into practical devices, researchers are investigating the use of ultracold atomic clouds above microchips. Such "atom chips" may find use as sensitive probes for gravity, acceleration, rotation, and tiny magnetic forces. In their Perspective, Fortagh and Zimmermann discuss recent advances toward creating atom chips, in which current-carrying conductors in the chips create magnetic microtraps that confine the atomic clouds. Despite some intrinsic limits to the performance of atom chips, existing technologies are capable of producing atom chips, and many possibilities for their construction remain to be explored.

Multipartite entanglement detection in bosons

We propose a simple quantum network to detect multipartite entangled states of bosons and show how to implement this network for neutral atoms stored in an optical lattice. We investigate the special properties of cluster states, multipartite entangled states, and superpositions of distinct macroscopic quantum states that can be identified by the network.

Quantum computation with a one-dimensional optical lattice

We present an economical dynamical control scheme to perform quantum computation on a one-dimensional optical lattice, where each atom encodes one qubit. The model is based on atom tunneling transitions between neighboring sites of the lattice. They can be activated by external laser beams resulting in a two-qubit phase gate or in an exchange interaction. A realization of the Toffoli gate is presented, which requires only a single laser pulse and no individual atom addressing.