Interstitial hydrogen and deuterium in body-centered-cubic metals constitute archetypal quantum tunneling systems. Their relevance has been renewed by the connection between hydrogenic tunneling in Nb and defect-induced decoherence in superconducting qubits, motivating a predictive microscopic theory. Existing theoretical treatments invoke an adiabatic separation between the light interstitial and the host lattice, an assumption whose validity has not been rigorously established for hydrogenic species. Here, we show that the experimentally measured tunnel splittings of O-trapped H and D in bcc Nb are quantitatively reproduced only within a five-dimensional (5D) Lattice-Renormalized Born-Oppenheimer (LRBO) framework. This approach treats three interstitial modes and two judiciously selected lattice modes, which includes a transition-state mode, on equal quantum footing. By recasting nested Born-Oppenheimer hierarchies within this same formalism and benchmarking against modern \textit{ab initio} potential energy surfaces, we show that adiabatic separation of the light particle from lattice dynamics is satisfied only in the positive-muon ($μ^{+}$) mass limit. In contrast, tunneling for H and D is fundamentally a collective, nonadiabatic process mediated by anharmonic lattice couplings. Finally, we show that the breakdown of adiabaticity can be anticipated from simple energy estimates involving the ground-state light-particle energy evaluated at a small number of fixed lattice configurations, providing a practical criterion for assessing the validity of adiabatic tunneling theories in other systems.
Interstitial hydrogen and deuterium in body-centered-cubic metals constitute archetypal quantum tunneling systems. Their relevance has been renewed by the connection between hydrogenic tunneling in Nb and defect-induced decoherence in superconducting qubits, motivating a predictive microscopic theory. Existing theoretical treatments invoke an adiabatic separation between the light interstitial and the host lattice, an assumption whose validity has not been rigorously established for hydrogenic species. Here, we show that the experimentally measured tunnel splittings of O-trapped H and D in bcc Nb are quantitatively reproduced only within a five-dimensional (5D) Lattice-Renormalized Born-Oppenheimer (LRBO) framework. This approach treats three interstitial modes and two judiciously selected lattice modes, which includes a transition-state mode, on equal quantum footing. By recasting nested Born-Oppenheimer hierarchies within this same formalism and benchmarking against modern \textit{ab initio} potential energy surfaces, we show that adiabatic separation of the light particle from lattice dynamics is satisfied only in the positive-muon (μ+) mass limit. In contrast, tunneling for H and D is fundamentally a collective, nonadiabatic process mediated by anharmonic lattice couplings. Finally, we show that the breakdown of adiabaticity can be anticipated from simple energy estimates involving the ground-state light-particle energy evaluated at a small number of fixed lattice configurations, providing a practical criterion for assessing the validity of adiabatic tunneling theories in other systems.
We present a lattice-renormalized formalism for configurational tunneling two-level systems (TLS) that overcomes limitations of minimum-energy-path and light-particle models. Derived from the nuclear Hamiltonian, our formulation introduces composite phonon coordinates to capture lattice distortions between degenerate potential wells. This approach resolves deficiencies in prior models and enables accurate computation of tunnel splittings and excitation spectra for hydrogen-based TLS in bcc Nb. Our results bound experimental tunnel splittings and reveal strong anharmonic couplings between tunneling atoms and lattice phonons, establishing a direct link between TLS dynamics and phonon-mediated strain interactions. The formalism further generalizes to multi-level systems (MLS), providing insight into defect-induced decoherence in superconducting qubits and guiding strategies for materials design to suppress TLS-related loss.
We perform ab initio calculations of hydrogen-based tunneling defects in alumina to identify deleterious two-level systems (TLS) in superconducting qubits. The defects analyzed include bulk hydrogenated Al vacancies, bulk hydrogen interstitial defects, and a surface OH rotor. The formation energies of the defects are first computed for an Al- and O-rich environment to give the likelihood of defect occurrence during growth. The potential energy surfaces are then computed and the corresponding dipole moments are evaluated to determine the coupling of the defects to an electric field. Finally, the tunneling energy is computed for the hydrogen defect and the analogous deuterium defect, providing an estimate of the TLS energy and the corresponding frequency for photon absorption. We predict that hydrogenated cation vacancy defects will form a significant density of GHz frequency TLSs in alumina.
The Dicke model describes N two-level atoms interacting with a single-mode bosonic field and exhibits a second-order phase transition from the normal to the superradiant phase. The energy levels are not degenerate in the normal phase but have degeneracy in the superradiant phase, where quantum tunneling occurs. By means of the Born-Oppenheimer approximation and the instanton method in quantum field theory, the tunneling splitting, inversely proportional to the tunneling rate for the adiabatic Dicke model, in the superradiant phase can be evaluated explicitly. It is shown that the tunneling splitting vanishes as $\mathrm{exp}(\ensuremath{-}N)$ for large N, whereas for small N it disappears as N∕exp(N). The dependence of the tunneling splitting on the relevant parameters, especially on the atom-field coupling strength, is also discussed.
An idealized model for the quantum tunneling of a particle in interaction with a heat bath is studied by computer simulation. The model may be motivated by consideration of a bound hydrogen–oxygen pair in a metal lattice; the H atom is treated quantum mechanically, the O atom is treated classically, and a double-well potential couples the two. In order to represent the O atom interactions with the rest of the lattice as heat bath, its motion is described by a classical Langevin equation. Computer simulation of the model shows that, with all other parameters held fixed, tunneling through low energy barriers is governed by energy splitting, while for high energy barriers the transmission approach agrees well with simulation results.
Some recent works on the tunneling of light interstitial particles (protons and positive muons) in metals are reviewed. They provide examples of simple quantum systems coupled to “baths” consisting of phonons and conduction electrons. In the limit of strong coupling to such an environment the positive muons move by quantum diffusion, where coherence is lost between each tunneling event, whereas in the weak coupling limit coherence can be maintained and allow a quantum propagation, i.e. a band-like motion. These phenomena can also be seen as examples of wave-function reduction in the presence of dissipative environments and may help to understand the details of such processes.
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.