Abstract We study the nonequilibrium stationary state (NESS) induced by quantum resetting of a system of N noninteracting bosons in a harmonic trap. Our protocol consists of preparing initially the system in the ground state of a harmonic oscillator centered at +a, followed by a rapid quench where the center is shifted to −a and the system is allowed to evolve unitarily up to a random Poissonian time τ distributed via r e − r τ . Then the trap center is reset to +a again and the system is assumed to cool instantaneously to the initial ground state. The system is again allowed to evolve unitarily in the trap centered at −a up to a random time, and the procedure is repeated. Under repeated resetting, the system reaches a NESS where the positions of bosons get strongly correlated due to simultaneous resetting induced by the trap. We fully characterize the steady state by analytically computing several physical observables such as the average density, extreme value statistics, order and gap statistics, and also the distribution of the number of particles in a region [ − L , L ] , known as the full counting statistics (FCS). In particular, we show that in the large N limit, the scaling function describing the FCS exhibits a striking feature: it is supported over a nontrivial finite interval, and moreover is discontinuous at an interior point of the support. Our results are supported by numerical simulations. This is a rare example of a strongly correlated quantum many-body NESS where various observables can be exactly computed.
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.
We investigate finite-size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground states. Both criteria can be computed using ground-state techniques that work for systems larger than full-spectrum diagonalization. As examples, two models are studied: one with free bosons in an harmonic trap whose frequency is quenched and the one-dimensional Bose-Hubbard model that is known to be nonintegrable and for which recent studies have uncovered remarkable nonequilibrium behaviors. The diagonal weights of the time-averaged density matrix are computed, and observables obtained from this diagonal ensemble are compared with the ones from statistical ensembles. It is argued that the ``thermalized'' regime of the Bose-Hubbard model, previously observed in the small quench regime, experiences strong finite-size effects that make a thorough comparison with statistical ensembles difficult. In addition, we show that the nonthermalized regime, emerging on finite-size systems and for large interaction quenches, is not related to the existence of an equilibrium quantum critical point but to the high-energy structure of the energy spectrum in the atomic limit. Its features are reminiscent of the quench from the noninteracting limit to the atomic limit.
Stochastic resetting can generate strong correlations in many-body systems through a shared fluctuating environment. Here, we investigate how such dynamically emergent correlations (DEC) coexist with intrinsic (direct) interactions in a weakly repulsive Bose-Einstein condensate described within the Gross-Pitaevskii framework. The condensate undergoes free expansion from an initial Thomas-Fermi state and is stochastically reset to this initial state at a constant rate. We show that the resetting protocol drives the system into a unique nonequilibrium steady state and obtain its density profile, edge statistics, and full counting statistics analytically. The steady-state density retains an inverted-parabolic form within the core, while developing exponentially decaying tails outside it. We further show that resetting induces nontrivial fluctuations of the condensate edge and particle number, yielding exact scaling forms for the edge distribution and the full counting statistics. Our results provide a tractable setting for exploring the interplay between intrinsic repulsive interactions and attractive DEC generated by a common stochastic environment in quantum many-body systems.
We investigate the nonequilibrium evolution of density correlations in a thermal one-dimensional Bose gas following a trap quench. We focus on the Tonks--Girardeau limit and develop an analytical description based on a finite-temperature extension of Quantum Generalized Hydrodynamics. We benchmark our predictions against exact numerics for a quench from a double well to a harmonic trap and for a trap release, and assess their temperature range of validity. Our results capture the dynamical enhancement of correlations during the expansion stages, namely the crossover from thermally suppressed to power-law bulk correlations. For the trap release, the conformal distance associated with fixed bulk points decreases as
1/t, so the correlations progressively probe a universal regime~
∼1/x2 that is independent of temperature. We thus show that, in the hydrodynamic long-time regime, the bulk density correlations approach their zero-temperature equilibrium form independently of the initial temperature.
We investigate the quantum dynamics of two bosons, trapped in a two-dimensional harmonic trap, upon quenching arbitrarily their interaction strength and thereby covering the entire energy spectrum. Utilizing the exact analytical solution of the stationary system, we derive a closed analytical form of the expansion coefficients of the time-evolved two-body wave function, whose dynamics is determined by an expansion over the postquench eigenstates. The emergent dynamical response of the system is analyzed in detail by inspecting several observables such as the fidelity, the reduced one-body densities, the radial probability density of the relative wave function in both real and momentum space, and the Tan contact, which unveils the existence of short range two-body correlations. When the system is initialized in its bound state, it is perturbed in the most efficient manner as compared to any other initial configuration. Moreover, starting from an interacting ground state, the two-boson response is enhanced for quenches toward the noninteracting limit.