Abstract The nonequilibrium quantum dynamics of few boson ensembles which experience a spatially modulated interaction strength and are confined in finite optical lattices is investigated. We utilize a cosinusoidal spatially modulated effective interaction strength which is characterized by its wavevector, inhomogeneity amplitude, interaction offset and a phase. Performing quenches either on the wavevector or the phase of the interaction profile an enhanced imbalance of the interatomic repulsion between distinct spatial regions of the lattice is induced. Following both quench protocols triggers various tunneling channels and a rich excitation dynamics consisting of a breathing and a cradle mode. All modes are shown to be amplified for increasing inhomogeneity amplitude of the interaction strength. Especially the phase quench induces a directional transport enabling us to discern energetically, otherwise, degenerate tunneling pathways. Moreover, a periodic population transfer between distinct momenta for quenches of increasing wavevector is observed, while a directed occupation of higher momenta can be achieved following a phase quench. Finally, during the evolution regions of partial coherence are revealed between the predominantly occupied wells.
Ultracold atoms in optical lattices constitute a versatile many-body platform with highly tunable parameters, allowing us to emulate a multitude of complex quantum systems, in the laboratory, even those eluding analytical treatment. In particular, the nonequilibrium dynamics of strongly correlated many-body systems represents one of the most challenging problems of modern quantum physics, with applications ranging from thermalization dynamics and transport properties to the management of correlations and the control of the dynamics. Understanding nonequilibrium phenomena of strongly correlated systems is a formidable task. A very promising route to gain insight into such systems is to examine few-body setups which contain only a few relevant degrees of freedom, yet incorporating the quantum correlations between the particles.
The present dissertation contributes to the understanding of the nonequilibrium dynamics of strongly-correlated quantum many-body systems by exploring systems of few-bosons
− of one or two species
− trapped in optical lattices. The systems are driven out-of-equilibrium either by performing a quench of a Hamiltonian parameter or by considering a time-periodic modulation of the external confinement. In the course of several consecutive works, we showcase different ways to couple the nonequilibrium modes, while unveiling their correlated nature and microscopic origin. To simulate the nonequilibrium dynamics, a sophisticated, highly flexible ab-initio method for numerically solving the time-dependent many-body Schrodinger equation is utilized, namely the Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Atomic Mixtures (ML-MCTDHX).
Within the first part we study in six consecutive works the correlated nonequilibrium dynamics of few-boson systems in one-dimensional finite lattices. Starting from weak interactions, it is shown that a sudden increase of the interaction strength generates a global density-wave tunneling dynamics as well as intrawell breathing and cradle-like excited-band processes. The cradle process is a dipole-like process generated by the quench-induced over-barrier transport and it is one of the central results of the present thesis. Remarkably enough, the interaction quenches couple the density-wave and cradle modes, inducing resonance phenomena between the inter and intrawell dynamics. We further show that the cradle mode is inherently related to the initial delocalization and, following a quench from strong-to-weak interactions, can be excited only for incommensurate setups with filling larger than unity. Alternatively, a sudden ramping down of the lattice depth which favors the spatial delocalization is employed to access the cradle mode for setups with filling smaller than unity. Following a multiple interaction quench protocol, we observe the rise of several lowest-band tunneling modes as well as the cradle and the breathing mode. Besides the cradle mode, all other excited modes are highly tunable possessing different frequencies during and in between the quenches. In the excitation dynamics a monotonic behavior with increasing quench amplitude and a non-linear dependence on the duration of the application of the quenched interaction strength is revealed. Additionally, a periodic population transfer between momenta for quenches of increasing interaction is observed, with a power-law frequency dependence on the quench amplitude. Linear interaction quenches from a superfluid to a Mott-insulator state excite various inter- and intraband tunneling modes. The competition between the quench rate and the interparticle repulsion leads to a resonant dynamical response, at moderate ramp times, being related to avoided-crossings in the many-body eigenspectrum.
The resultant higher-band excitation dynamics is shown to obey an exponential decay possessing two distinct time scales with varying ramp time. Inspecting the crossover from shallow to deep lattices we find that for a diabatic quench the excited-band fraction decreases, while approaching the adiabatic limit it exhibits a nonlinear behavior for increasing height of the potential barrier. Quenching from strong-to-weak interactions leads to a melting of the Mott-insulator and negligible higher-band excitations.
Performing quenches either on the wavevector or the phase of a spatially dependent interaction profile triggers various tunneling channels and a rich excitation dynamics which is amplified for increasing inhomogeneity amplitude. Most importantly, the phase quench is shown to induce a directional transport enabling us to discern, otherwise, energetically degenerate tunneling pathways.
Finally, a periodic population transfer between distinct momenta for quenches of increasing wavevector and a directed occupation of higher momenta following a phase quench is observed. Employing a quench of an additional harmonic trap from strong-to-weak confinement, we find that the competition between the initial localization and the repulsive interaction leads to a resonant response of the system related to avoided-crossings in the many-body eigenspectrum with varying final trap frequency. Furthermore, we show that these avoided-crossings can be utilized to prepare the system in a desired state.
The second part comprises two efforts and is devoted to the study of the nonequilibrium dynamics of finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices. For a shaken lattice, a wide range of driving frequencies is covered and a resonant behavior of the intrawell dynamics is revealed and found to be related to a rich intraband excitation spectrum.
Moreover, it is shown that for increasing repulsion a strong suppression of the interwell tunneling and an enhanced excitation dynamics occurs. For a vibrating lattice, an additional interaction quench gives rise to admixtures of different excitations in the outer wells, an enhanced breathing in the center and an amplification of the emerging tunneling dynamics. The occurence of multiple resonances between the inter- and intrawell dynamics at different quench amplitudes is revealed, with the position of the resonances being tunable via the driving frequency and thus allowing for further control of the mode coupling in optical lattices.
In the third and final part of this thesis we unravel the quench dynamics of a Bose-Bose and a Bose-Fermi mixture. Utilizing an interspecies interaction quench we cross the miscibility-immiscibility threshold in a harmonically confined Bose-Bose mixture. We show that increasing the interspecies repulsion coefficient results in a filamentation of the density of each species, with the spontaneously generated filaments being strongly correlated and exhibiting domain-wall structures. Strikingly, by following the reverse quench protocol, i.e., upon decreasing the interspecies interaction strength, the formation of multiple dark-antidark solitary waves is observed. These solitary wave structures are found to decay into the many-body environment, soon after their generation in sharp contrast to the predictions of the mean-field approximation. To relate our findings with possible experimental realizations, we simulate, for the first time for binary mixtures, single-shot images showcasing that the growth rate of the variance of a sample of single-shots probes the degree of entanglement inherent in the system. As a next step we investigate the expansion dynamics of a mass balanced Bose-Fermi mixture confined in a one-dimensional optical lattice upon quenching an imposed harmonic trap from strong-to-weak confinement. Tuning the interspecies interaction strength we realize the immiscible and miscible correlated ground state phases. We further show that the system's dynamical response crucially depends on the initial phase and consists of an expansion of each cloud and an interwell tunneling dynamics. Varying the quench amplitude and referring to a fixed phase a multitude of response regimes is unveiled, being richer within the immiscible phase, which are described by distinct expansion strengths and tunneling channels. Finally, in the expansion dynamics a two-body anti-correlated behavior between the predominantly occupied wells is unveiled.
The correlated non-equilibrium dynamics of few-boson systems in one-dimensional finite lattices is investigated. Starting from weak interactions we perform a sudden interaction quench and employ the numerically exact multi-layer multi-configuration time-dependent Hartree method for bosons to obtain the resulting quantum dynamics. Focusing on the low-lying modes of the finite lattice we observe the emergence of density-wave tunneling, breathing and cradle-like processes. In particular, the tunneling induced by the quench leads to a 'global' density-wave oscillation. The resulting breathing and cradle modes are inherent to the local intrawell dynamics and connected to excited-band states. Moreover, the interaction quenches couple the density-wave and the cradle modes allowing for resonance phenomena. These are associated with an avoided-crossing in the respective frequency spectrum and lead to a beating dynamics for the cradle. Finally, complementing the numerical studies, an effective Hamiltonian in terms of the relevant Fock states is derived for the description of the spectral properties and the related resonant dynamics.
The out-of-equilibrium dynamics of interaction quenched finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices is investigated. It is shown that periodic driving enforces the bosons in the outer wells of the finite lattice to exhibit out-of-phase dipolelike modes, while in the central well the atomic cloud experiences a local breathing mode. The dynamical behavior is investigated with varying driving frequencies, revealing resonantlike behavior of the intrawell dynamics. An interaction quench in the periodically driven lattice gives rise to admixtures of different excitations in the outer wells, enhanced breathing in the center, and amplification of the tunneling dynamics. We then observe multiple resonances between the inter- and the intrawell dynamics at different quench amplitudes, with the position of the resonances being tunable via the driving frequency. Our results pave the way for future investigations of the use of combined driving protocols in order to excite different inter- and intrawell modes and to subsequently control them.
We explore the nonequilibrium dynamics of a density-ordered dipolar Bose gas in a finite one-dimensional optical lattice following a negative interaction quench, using the numerically exact multiconfigurational time-dependent Hartree method for bosons. The interaction sign reversal, effectively driving a crossover from long-range to short-range interactions, generates rich intra- and interwell tunneling dynamics spanning superfluid, Mott-insulating, and fragmented regimes. A striking finding is the robustness of the underlying crystal-state correlations against the quench, despite the strong dynamical response. We identify emergent excitation modes, including local breathing and dipole-like oscillations, via real- and momentum-space observables, and quantify tunneling through site-resolved position variance. One- and two-body Glauber correlation functions further uncover a direct connection between tunneling and correlation dynamics. Moreover, we show that combining interaction quenches with lattice-depth ramping enables controllable dynamical engineering, establishing dipolar lattice systems as a promising platform for nonequilibrium quantum simulation.
The nonequilibrium dynamics following a quench of strongly repulsive bosonic ensembles in one-dimensional finite lattices is investigated by employing interaction quenches and/or a ramp of the lattice potential. Both sudden and time-dependent quenches are analyzed in detail. For the case of interaction quenches we address the transition from the strong repulsive to the weakly interacting regime, suppressing in this manner the heating of the system. The excitation modes such as the cradle process and the local breathing mode are examined via local density observables. In particular, the cradle mode is inherently related to the initial delocalization and, following a negative interaction quench, can be excited only for incommensurate setups with filling larger than unity. Alternatively, a negative quench of the lattice depth which favors the spatial delocalization is used to access the cradle mode for setups with filling smaller than unity. Our results shed light on possible schemes to control the cradle and the breathing modes. Finally, employing the notion of fidelity we study the dynamical response of the system after a diabatic or adiabatic parameter modulation for short and long evolution times. The evolution of the system is obtained numerically using the ab initio multilayer multiconfiguration time-dependent Hartree method for bosons, which permits us to follow nonequilibrium dynamics including the corresponding investigation of higher-band effects.