Understanding quantum tunneling in many-body systems is crucial for advancing quantum technologies and nanoscale device design. Despite extensive studies of quantum tunneling, the role of interactions in determining directional transport through asymmetric barriers in discrete quantum systems remains unclear. Here we show that noninteracting fermions exhibit symmetric tunneling probabilities regardless of barrier orientation, while inter-particle interactions break this symmetry and create pronounced asymmetric tunneling behavior. We explore the dependence of tunneling behavior on the initial spin configurations of two spin-1/2 fermions: spin-triplet states preserve tunneling symmetry, while spin-singlet states show strong asymmetry. We identify regimes where interactions mediate tunneling through under-barrier resonant trapping and enhance tunneling via many-body resonant tunneling - a phenomenon arising solely from inter-particle interactions and being fundamentally different from traditional single-particle resonant tunneling. Our results may be applied to the design of nanoscale devices with tailored transport properties, such as diodes and memristors.
Understanding quantum tunneling in many-body systems is crucial for advancing quantum technologies and nanoscale device design. Despite extensive studies of quantum tunneling, the role of interactions in determining directional transport through asymmetric barriers in discrete quantum systems remains unclear. Here we show that noninteracting fermions exhibit symmetric tunneling probabilities regardless of barrier orientation, while inter-particle interactions break this symmetry and create pronounced asymmetric tunneling behavior. We explore the dependence of tunneling behavior on the initial spin configurations of two spin-1/2 fermions: spin-triplet states preserve tunneling symmetry, while spin-singlet states show strong asymmetry. We identify regimes where interactions mediate tunneling through under-barrier resonant trapping and enhance tunneling via many-body resonant tunneling - a phenomenon arising solely from inter-particle interactions and being fundamentally different from traditional single-particle resonant tunneling. Our results may be applied to the design of nanoscale devices with tailored transport properties, such as diodes and memristors.
In this thesis, the tunneling dynamics of a few boson system in a double-well is investigated from an ab-initio prospective using the numerically exact Multi-Configuration Time-Dependent Hartree method. We first study a system consisting of single species of bosons with a spatially modulated interaction. The main emphasis is on the role of inhomogeneity and its effect on the tunneling. The dynamics changes from Rabi oscillations in the non-interacting case to a highly suppressed tunneling for intermediate interaction strengths followed by a reappearance of tunneling near the fermionization limit. With extreme interaction inhomogeneity in the regime of strong correlations we observe tunneling between the higher bands. A richer behavior is found for systems with higher particle number. For systems with more than two bosons, the inhomogeneity of the interaction can be tuned to generate tunneling resonances. These observations are explained on the basis of the few-body spectrum and stationary eigenstates. A tilted double-well and its interplay with the interaction asymmetry is discussed next. We demonstrate that the effects of the interaction can be compensated by the tilt leading to tunneling resonances. We then explore tunneling dynamics of binary bosonic mixtures. The focus is on the role of the inter- and intra-species interactions and their interplay. The dynamics is studied for three initial configurations: complete and partial population imbalance and a phase separated state. Increasing the inter-species interaction leads to a strong increase of the tunneling time period analogous to the quantum self-trapping for condensates. The intra-species repulsion can suppress or enhance the tunneling period depending on the strength of the inter-species correlations as well as the initial configuration. Completely correlated tunneling between the two species and within the same species as well as mechanisms of species separation and counterflow are revealed. These effects are explained by studying the many-body energy spectra as well as the properties of the contributing stationary states.
Abstract The emission of two correlated fermions from a nuclear, or, in general, quantum meta-stable system is a poorly known, but fundamental problem: the interaction between the fermions can significantly affect the tunneling process. The behaviour of spin-singlet or spin-triplet emission has not been fully studied. In this article, the one-dimensional tunneling process of two fermions of the same kind is investigated. We solve the time-dependent Schrödinger equation for the two-fermion (2F) state, which is initially confined inside the square-well-plus-barrier potential. The interaction between the two fermions is schematically described by a short-range square-well attractive potential. A noticeable difference between the spin-singlet and triplet emissions is shown. Their tunneling probability, which is evaluated from the time-dependent survival probability, depends on the total spin, even if the effective-barrier height is fixed to be equivalent. Also, a spatial correlation of two fermions appears (vanishes) in the spin-singlet (triplet) case. The total-spin dependence of 2F emission can be attributed to the anti-symmetrization condition: it allows (prohibits) degenerate pairing, where two fermions can occupy the same spatial orbit, in the spin-singlet (triplet) case. This degenerate pairing makes the spin-singlet 2F state more long-lived than the spin-triplet one, even under the equivalent conditions. Only in the spin-singlet channel, the short-range 2F attraction enhances the degenerate-pair component, providing the difference between correlated and uncorrelated emissions. On the other hand, the spin-triplet emission cannot profit from the 2F interaction, due to the Pauli principle. These conclusions are independent of the physical scales.
Spin transport typically relies on direct manipulation of the spin degree of freedom via magnetic fields, spin-orbit coupling, or engineered spin-dependent potentials. We show theoretically that directional spin currents can arise in a relatively simple setting - a one-dimensional interacting fermionic ring with static, spin-independent asymmetric barriers. By introducing asymmetric potential barrier geometry, spin-resolved circulating currents emerge on a closed chain even for symmetric initial configurations. The effect can be enhanced or reversed by appropriate initial state preparation and tuning the barrier asymmetry to resonant conditions.
Abstract In his celebrated textbook, Quantum Mechanics: Nonrelativistic Theory, Landau argued that, for single particle systems in 1D, tunneling probability remains the same for a particle incident from the left or the right of a barrier. This left–right symmetry of tunneling probability holds regardless of the shape of the potential barrier. However, there are a variety of known cases that break this symmetry, e.g. when observing composite particles. We computationally (and analytically, in the simplest case) show this breaking of the left–right tunneling symmetry for Bose–Einstein condensates (BECs) in 1D, modeled by the Gross–Pitaevskii equation. By varying g, the parameter of inter-particle interaction in the BEC, we demonstrate that the transition from symmetric (g = 0) to asymmetric tunneling is a threshold phenomenon. Our computations employ experimentally feasible parameters such that these results may be experimentally demonstrated in the near future. We conclude by suggesting applications of the phenomena to design atomtronic diodes, synthetic gauge fields, Maxwell’s demons, and black-hole analogues.
Few- and many-fermion systems on the verge of stability, and consisting of strongly interacting particles, appear in many areas of physics. The theoretical modeling of such systems is a very difficult problem. In this work we present a theoretical framework that is based on the rigged Hilbert space formulation. The few-body problem is solved by exact diagonalization using a basis in which bound, resonant, and non-resonant scattering states are included on an equal footing. Current experiments with ultracold atoms offer a fascinating opportunity to study universal properties of few-body systems with a high degree of control over parameters such as the external trap geometry, the number of particles, and even the interaction strength. In particular, particles can be allowed to tunnel out of the trap by applying a magnetic-field gradient that effectively lowers the potential barrier. The result is a tunable open quantum system that allows detailed studies of the tunneling mechanism. In this Paper we introduce our method and present results for the decay rate of two distinguishable fermions in a one-dimensional trap as a function of the interaction strength. In particular, we present for the first time several technical and numerical details of our approach, recently published in Lundmark et al. (Phys Rev A 91:041601, 2015). We also show results from a careful analysis of the numerical convergence.
We study many-body quantum coherence and interaction blockade in two Josephson-linked Bose-Einstein condensates. We introduce universal operators for characterizing many-body coherence without limitations on the system symmetry and total particle number N . We reproduce the results for both coherence fluctuations and number squeezing in symmetric systems of large N , and reveal several peculiar phenomena that may occur in asymmetric systems and systems of small N . For asymmetric systems, we show that, due to an interplay between asymmetry and inter-particle interaction, the coherence fluctuations are suppressed dramatically when | E C / E J |≪1, and both resonant tunneling and interaction blockade take place for large values of | E C / E J |, where E C and E J are the interaction and tunneling energies, respectively. We emphasize that the resonant tunneling and interaction blockade may allow creating single-atom devices with promising technology applications. We demonstrate that for the systems at finite temperatures the formation of self-trapped states causes an anomalous behavior.