Dominik Muth

Wigner crystallization of single photons in cold Rydberg ensembles.

The coupling of weak light fields to Rydberg states of atoms under conditions of electromagnetically induced transparency leads to the formation of Rydberg polaritons which are quasiparticles with tunable effective mass and nonlocal interactions. Confined to one spatial dimension their low energy physics is that of a moving-frame Luttinger liquid which, due to the nonlocal character of the repulsive interaction, can form a Wigner crystal of individual photons. We calculate the Luttinger K parameter using density-matrix renormalization group simulations and find that under typical slow-light conditions kinetic energy contributions are too strong for crystal formation. However, adiabatically increasing the polariton mass by turning a light pulse into stationary spin excitations allows us to generate true crystalline order over a finite length. The dynamics of this process and asymptotic correlations are analyzed in terms of a time-dependent Luttinger theory.

Steady-state crystallization of Rydberg excitations in an optically driven lattice gas

We study the conditions for attaining crystalline order in the stationary state of a continuously driven, open many-body system. Specifically, we consider resonant optical excitations of atoms in a one-dimensional lattice to the Rydberg states interacting via the van der Waals potential. Strong blockade of excitations at neighboring lattice sites steers the system toward a crystalline state while competing with the fluctuations associated with relaxation. We analyze the stationary state of the many-body system and the dynamics of its buildup employing numerically exact time-dependent density-matrix renormalization-group simulations for two- and three-level excitation schemes. We also present an approximate rate equation model which provides qualitative conditions for attaining crystalline order.

Fermionization dynamics of a strongly interacting one-dimensional Bose gas after an interaction quench

We study the dynamics of a one-dimensional Bose gas after a sudden change of the interaction strength from zero to a finite value using the numerical time-evolving block decimation (TEBD) algorithm. It is shown that despite the integrability of the system, local quantities such as the two-particle correlation g(2)(x, x) attain steady-state values in a short characteristic time inversely proportional to the Tonks parameter γ and the square of the density. The asymptotic values are very close to those of a finite temperature grand canonical ensemble, with a local temperature corresponding to the initial energy and density. Non-local density–density correlations, however, approach a steady state on a much larger time scale determined by the finite propagation velocity of oscillatory correlation waves.

Dynamics of pair correlations in the attractive Lieb-Liniger gas.

We investigate the dynamics of a one-dimensional Bose gas after a quench from the Tonks-Girardeau regime to the regime of strong attractive interactions applying analytical techniques and numerical simulations. After the quench the system is found to be predominantly in an excited gaslike state, the so-called super-Tonks gas, however with a small coherent admixture of two-particle bound states. Despite its small amplitude, the latter leads to a pronounced oscillation of the local density correlation with a frequency corresponding to the binding energy of the pair. Contributions from bound states with larger particle numbers are found to be negligible.

Spatiotemporal fermionization of strongly interacting one-dimensional bosons

Building on the recent experimental achievements obtained with scanning electron microscopy on ultracold atoms, we study one-dimensional Bose gases in the crossover between the weakly (quasi-condensate) and the strongly interacting (Tonks-Girardeau) regime. We measure the temporal two-particle correlation function and compare it with calculations performed using the Time Evolving Block Decimation algorithm. More pronounced antibunching is observed when entering the more strongly interacting regime. Even though this mimics the onset of a fermionic behavior, we highlight that the exact and simple duality between 1D bosons and fermions does not hold when such dynamical response is probed. The onset of fermionization is also reflected in the density distribution, which we measure \emph{in situ} to extract the relevant parameters and to identify the different regimes. Our results show agreement between experiment and theory and give new insight into the dynamics of strongly correlated many-body systems.

Transport-induced melting of crystals of Rydberg dressed atoms in a one-dimensional lattice

We discuss the many-body physics of an ensemble of Rydberg dressed atoms with van der Waals dipole-dipole interactions in a one- dimensional lattice. Using a strong coupling expansion and numerical density- matrix renormalization group simulations, we calculate the many-body phase diagram. A devils staircase structure emerges with Mott-insulating phases at any rational filling fraction. Closed analytic expressions are given for the phase boundaries in second order of the tunneling amplitude and are shown to agree very well with the numerical results. The transition point where the incompressible phases melt due to the kinetic energy term depends strongly on the denominator of the filling fraction and varies over many orders of magnitude between different phases.

Dynamical simulation of integrable and nonintegrable models in the Heisenberg picture.

The numerical simulation of quantum many-body dynamics is typically limited by the linear growth of entanglement with time. Recently numerical studies have shown that for 1D Bethe-integrable models the simulation of local operators in the Heisenberg picture can be efficient. Using the spin-1/2 XX chain as generic example of an integrable model that can be mapped to free fermions, we provide a simple explanation for this. We show furthermore that the same reduction of complexity applies to operators that have a high-temperature autocorrelation function which decays slower than exponential, i.e., with a power law. Thus efficient simulability may already be implied by a single conservation law as we will illustrate numerically for the spin-1 XXZ model.

Ultracold bosons in disordered superlattices: Mott insulators induced by tunneling

We analyse the phase diagram of ultra-cold bosons in a one-dimensional superlattice potential with disorder using the time evolving block decimation algorithm for infinite sized systems (iTEBD). For degenerate potential energies within the unit cell of the superlattice loophole-shaped insulating phases with non-integer filling emerge with a particle-hole gap proportional to the boson hopping. Adding a small amount of disorder destroys this gap. For not too large disorder the loophole Mott regions detach from the axis of vanishing hopping giving rise to insulating islands. Thus the system shows a transition from a compressible Bose-glass to a Mott-insulating phase with increasing hopping amplitude. We present a straight forward effective model for the dynamics within a unit cell which provides a simple explanation for the emergence of Mott-insulating islands. In particular it gives rather accurate predictions for the inner critical point of the Bose-glass to Mott-insulator transition.

Discretized versus continuous models of p-wave interacting fermions in one dimension

We present a general mapping between continuous and lattice models of Bose and Fermi gases in one dimension, interacting via local two-body interactions. For s-wave interacting bosons we arrive at the Bose-Hubbard model in the weakly interacting, low-density regime. The dual problem of p-wave interacting fermions is mapped to the spin-1/2 XXZ model close to the critical point in the highly polarized regime. The mappings are shown to be optimal in the sense that they produce the least error possible for a given discretization length. As an application we examine the ground state of an interacting Fermi gas in a harmonic trap, calculating numerically real-space and momentum-space distributions as well as two-particle correlations. In the analytically known limits the convergence of the results of the lattice model with the continuous one is shown.

Short-time versus long-time dynamics of entanglement in quantum lattice models

We study the short-time evolution of the bipartite entanglement in quantum lattice systems with local interactions in terms of the purity of the reduced density matrix. A lower bound for the purity is derived in terms of the eigenvalue spread of the interaction Hamiltonian between the partitions. Starting from an initially separable state the purity decreases as