Quantum magnetism is a fundamental phenomenon of nature. As of late, it has garnered a lot of interest because experiments with ultracold atomic gases in optical lattices can be used as a simulator for phenomena of magnetic systems. A paradigmatic example is the time-evolution of a domain-wall state of a spin-1/2 Heisenberg chain, the so-called domain-wall melting. The model can be implemented by having two species of bosonic atoms with unity filling and strong on-site repulsion U in an optical lattice. In this paper, we study the domain-wall melting in such a setup on the basis of the time-dependent density matrix renormalization group (tDMRG). We are particularly interested in the effects of defects that originate from an imperfect preparation of the initial state. Typical defects are holes (empty sites) and flipped spins. We show that the dominating effects of holes on observables like the spatially resolved magnetization can be taken account of by a linear combination of spatially shifted observables from the clean case. For sufficiently large $U$, further effects due to holes become negligible. In contrast, the effects of spin flips are more severe as their dynamics occur on the same time-scale as that of the domain-wall melting itself. It is hence advisable to avoid preparation schemes that are based on spin-flips.
Quantum magnetism is a fundamental phenomenon of nature. As of late, it has garnered a lot of interest because experiments with ultracold atomic gases in optical lattices can be used as a simulator for phenomena of magnetic systems. A paradigmatic example is the time-evolution of a domain-wall state of a spin-1/2 Heisenberg chain, the so-called domain-wall melting. The model can be implemented by having two species of bosonic atoms with unity filling and strong on-site repulsion U in an optical lattice. In this paper, we study the domain-wall melting in such a setup on the basis of the time-dependent density matrix renormalization group (tDMRG). We are particularly interested in the effects of defects that originate from an imperfect preparation of the initial state. Typical defects are holes (empty sites) and flipped spins. We show that the dominating effects of holes on observables like the spatially resolved magnetization can be taken account of by a linear combination of spatially shifted observables from the clean case. For sufficiently large U, further effects due to holes become negligible. In contrast, the effects of spin flips are more severe as their dynamics occur on the same time-scale as that of the domain-wall melting itself. It is hence advisable to avoid preparation schemes that are based on spin-flips.
Quantum magnetism is a fundamental phenomenon of nature. As of late, it has garnered a lot of interest because experiments with ultracold atomic gases in optical lattices could be used as a simulator for phenomena of magnetic systems. A paradigmatic example is the time evolution of a domain-wall state of a spin-1/2 Heisenberg chain, the so-called domain-wall melting. The model can be implemented by having two species of bosonic atoms with unity filling and strong on-site repulsion U in an optical lattice. In this paper, we study the domain-wall melting in such a setup on the basis of the time-dependent density matrix renormalization group (tDMRG). We are particularly interested in the effects of defects that originate from an imperfect preparation of the initial state. Typical defects are holes (empty sites) and flipped spins. We show that the dominating effects of holes on observables like the spatially resolved magnetization can be taken account of by a linear combination of spatially shifted observables from the clean case. For sufficiently large U, further effects due to holes become negligible. In contrast, the effects of spin flips are more severe as their dynamics occur on the same time scale as that of the domain-wall melting itself. It is hence advisable to avoid preparation schemes that are based on spin flips.
In spin chains with local unitary evolution preserving the magnetization Sz, the domain-wall state $\left|\ensuremath{\cdots}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\cdots}\right\ensuremath{\rangle}$ typically ``melts.'' At large times, a nontrivial magnetization profile develops in an expanding region around the initial position of the domain wall. For nonintegrable dynamics, the melting is diffusive, with entropy production within a melted region of size t. In contrast, when the evolution is integrable, ballistic transport dominates and results in a melted region growing linearly in time, with no extensive entropy production: The spin chain remains locally in states of zero entropy at any time. Here we show that, for the integrable spin-1/2 XXZ chain, low-energy quantum fluctuations in the melted region give rise to an emergent Luttinger liquid which, remarkably, differs from the equilibrium one. The striking feature of this emergent Luttinger liquid is its quasiparticle charge (or Luttinger parameter K), which acquires a fractal dependence on the XXZ chain anisotropy parameter $\mathrm{\ensuremath{\Delta}}$.
Nanoscale topological spin textures in magnetic systems are emerging as promising candidates for scalable quantum architectures. Despite their potential as qubits, previous studies have been limited to semiclassical approaches, leaving a critical gap: the lack of a fully quantum demonstration. Here, we address this challenge by employing the density matrix renormalization group (DMRG) method to establish domain wall (DW) qubits in coupled quantum spin-1/2 chains. We calculate the ground-state energies and excitation gaps of the system and find that DWs with opposite chiralities form a well-defined low-energy sector, distinctly isolated from higher excited states in the presence of anisotropies. This renders the chirality states suitable for encoding quantum information, serving as robust qubits. Interestingly, when a magnetic field is applied, we observe tunneling between quantum DW states with opposite chiralities. Through quantum simulations, we construct an effective qubit Hamiltonian that exhibits strongly anisotropic g factors, offering a way to implement single-qubit gates. Furthermore, we obtain an effective interacting Hamiltonian for two mobile DWs in coupled quantum spin chains from DMRG simulations, enabling the implementation of two-qubit gates. Single-qubit and two-qubit gates are also demonstrated in real-time simulations using the time-dependent variational principle. Our work represents a critical step from semiclassical constructions to a fully quantum demonstration of the potential of DW textures for scalable quantum computing, establishing a solid foundation for future quantum architectures based on topological magnetic textures.
The three experiments described in this thesis investigate fundamental properties of ultracold atoms. Using laser cooling and evaporative cooling, a dilute gas of sodium atoms is cooled to ~100 nK. Under these circumstances a Bose-Einstein condensate (BEC) forms, where millions of atoms collapse into the lowest energy state of the system and share a macroscopic wavefunction. The experiments are done in an ultrahigh vacuum and the atoms are manipulated remotely using laser beams, magnetic fields, and RF-fields. Using ultracold atoms allows unprecedented control over the internal and external degrees of freedom of the system, making it very suitable for precision measurements. Ultracold atoms also serve as a model system for more complicated or remote fields such as solid-state physics and cosmology. In the first experiment the refractive index of an ultracold bosonic gas is studied. The atomic clouds are analyzed for temperature and number of particles using nearly non-destructive phase-contrast imaging. After each pulse of probe light a small fraction of the atoms is lost, while the cloud is simultaneously slightly heated. This makes it possible to study the scattering rate as a function of temperature using only a single sample. It is observed that the scattering rate increases below the critical temperature for BEC by more than a factor of 3 compared to the classical value. This enhancement is in good agreement with the predictions by theoretical work that takes two-body correlation and the Lorentz-Lorenz correction into account. The method is also used to perform calorimetry on the Bose gas and directly measure the heat capacity of the BEC. The second chapter deals with magnetism in ultracold gases. When cooling an ultracold gas containing different spin components below the critical temperature for BEC, stable magnetic domains form. The appearance of these domains and the dynamics of the domain walls are studied. The spin mixture is prepared by performing an RF-sweep on ground state atoms in the presence of a magnetic field. Spin dynamics are induced by applying magnetic gradients. Spin drag, which is the transport coefficient responsible for damping spin currents, was measured in a two-component system. Furthermore a new method for spin resolved phase contrast imaging is presented, which is used to study time evolution in situ non-destructively. The last experiment focuses on spontaneous symmetry breaking. When passing a continuous phase transition, spontaneous symmetry breaking causes the development of domains with an independently chosen order parameter. The domains are separated by boundary defects. In this experiment the spontaneous creation of solitons was observed, which are boundary defects in the phase of the condensate, as well as magnetic domain walls, which are the boundary defects in the magnetization. Through the Kibble-Zurek mechanism it is possible to determine the critical exponents that characterize the phase transition. The critical exponents are predicted to be universal, i.e. do not depend on the microphysics of the system, so the results from our ultracold atoms lab can help answer universal questions for example from cosmology and from the early universe.
We numerically investigate the expansion of clouds of hard-core bosons in the two-dimensional square lattice using a matrix-product-state--based method. This nonequilibrium setup is induced by quenching the trapping potential to zero and our work is specifically motivated by a recent experiment with interacting bosons in an optical lattice [Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013)]. As the anisotropy of the amplitudes Jx and Jy for hopping in different spatial directions is varied from the one- to the two-dimensional case, we observe a crossover from a fast ballistic expansion in the one-dimensional limit ${J}_{x}\ensuremath{\gg}{J}_{y}$ to much slower dynamics in the isotropic two-dimensional limit Jx=Jy. We further study the dynamics on multileg ladders and long cylinders. For these geometries we compare the expansion of a cloud to the melting of a domain wall, which helps us to identify several different regimes of the expansion as a function of time. By studying the dependence of expansion velocities on both the anisotropy Jy/Jx and the number of legs, we observe that the expansion on two-leg ladders, while similar to the two-dimensional case, is slower than on wider ladders. We provide a qualitative explanation for this observation based on an analysis of the rung spectrum.
Ultracold bosonic gases in optical lattices are strongly correlated quantum systems similar to solids. The strong correlation between the electrons in a solid on the one hand, and the bosonic atoms in optical lattice on the other, exhibit various quantum phenomena like insulation, conductivity, localization of electrons and atoms, respectively. Controlled by the intensity of the lattice laser, the ultracold bosonic gas can be transferred from a regime with superfluid character for shallow lattices into a regime of strong correlations, the Mott insulator. As an additional external parameter besides the lattice depth, one can generate spatial inhomogeneities by superimposing an additional standing wave (so-called two-color superlattices), which gives rise to localization effects or the formation of a Bose-glass phase. In the present work, numerical simulations are employed in order to investigate characteristic signatures of the quantum phases in the low-energy excitation spectrum of one-dimensional systems. We simulate temporal small amplitude modulations of the optical lattice in analogy to experiments, and evaluate the response of the system from the time-evolved initial state. The lattice systems are described in the framework of the Bose-Hubbard model. For the evaluation of the time-evolved state, we employ several numerical methods. We analyze systems of small size (6 particles on 6 sites) using an exact time-evolution by integration of the time-dependent Schrödinger equation. The formulation of an importance truncation scheme enables us to retain only the relevant components of the model space in the strongly correlated regime and, thus, allows for the investigation of systems with 10 particles on 10 sites using exact time-evolution. Based on this method, we present results of the Mott-insulating regime as well as for the Bose-glass phase. Furthermore, we employ particle-hole methods, which allow for the treatment of systems with experimental lattice sizes and particle numbers. Starting from the equation of motion method we adapt the Tamm-Dancoff approximation as well as the random-phase approximation for the occupation number representation of the Bose-Hubbard model. We present results of simulations of up to 50 particles on 50 sites and discuss the impact of the lattice depth on the low-energy excitations (U-resonance). Moreover, the impact of a two-color superlattice and the variation of its amplitude is investigated.