Tunneling Amplitude Research Articles

Super periodic potential

In this paper we introduce the concept of super periodic potential (SPP) of arbitrary order n, n∈I+, in one dimension. General theory of wave propagation through SPP of order n is presented and the reflection and transmission coefficients are derived in their closed analytical form by transfer matrix formulation. We present scattering features of super periodic rectangular potential and super periodic delta potential as special cases of SPP. It is found that the symmetric self-similarity is the special case of super periodicity. Thus by identifying a symmetric fractal potential as special cases of SPP, one can obtain the tunnelling amplitude for a particle from such fractal potential. By using the formalism of SPP we obtain the close form expression of tunnelling amplitude of a particle for general Cantor and Smith–Volterra–Cantor potentials.

Coupled dynamics of interacting spin-1 bosons in a double-well potential

We present a detailed analysis of dynamical processes involving two or three particles in a double-well potential. Motivated by experimental realizations of such a system with optically trapped cold atoms, we focus on spin-1 bosons with special attention on the effects of a spin-dependent interaction in addition to the usual Hubbard-like repulsive one. For a sufficiently weak tunneling amplitude in comparison to the dominant Hubbard coupling, particle motion is strongly correlated, occurring only under fine-tuned relationships between well-depth asymmetry and interactions. We highlight processes involving tunneling of coupled particle pairs and triads, emphasizing the role of the spin-dependent interaction in resonance conditions.

Extremal tunneling and Anti-de Sitter instantons

We rederive and extend the amplitude for charged spherical shells tunneling through the outer horizon of charged black holes. In particular, we explicitly confirm that an effective action approach with natural initial conditions for a spherical shell, including backreaction, reduces to the tunneling integral. Consequently, we establish a universal expression for the probability of emission in terms of the change in the horizon entropy. Notably, the result for the charged black hole also captures the superradiant regime of charged particle decay at low energies. We then explore an appropriately regulated extremal and near-horizon limit, relating the tunneling amplitude to a family of gravitational instantons in the near-horizon Anti-de Sitter geometry, reducing to the known result for AdS2 domain walls to leading order in the probe limit. We comment on the relation to the Weak Gravity Conjecture and the conjectured instability of (non-supersymmetric) Anti-de Sitter vacua.

Two Topologically Distinct Dirac-Line Semimetal Phases and Topological Phase Transitions in Rhombohedrally Stacked Honeycomb Lattices

Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines which form closed loops inside the Brillouin zone. In particular, an energy gap can be opened only by first merging the Dirac lines going through the Brillouin zone in a pairwise manner so that they turn into closed loops inside the Brillouin zone, and then by shrinking these loops into points. We show that this kind of topological phase transition can occur in rhombohedrally stacked honeycomb lattices by tuning the ratio of the tunneling amplitudes in the directions perpendicular and parallel to the layers. We also discuss the properties of the surface states in the different phases of the model.

Phase transitions of the coherently coupled two-component Bose gas in a square optical lattice

We investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean field theory as well as bosonic dynamical mean field theory. We find that the interplay of strong inter-species repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.

Charge pumping in strongly coupled molecular quantum dots

The interaction between electrons and the vibrational degrees of freedom of a molecular quantum dot can lead to an exponential suppression of the conductance, an effect which is commonly termed Franck-Condon blockade. Here, we investigate this effect in a quantum dot driven by time-periodic gate voltages and tunneling amplitudes using nonequilibrium Green's functions and a Floquet expansion. Building on previous results showing that driving can lift the Franck-Condon blockade, we investigate driving protocols which can be used to pump charge across the quantum dot. In particular, we show that due to the strongly coupled nature of the system, the pump current at resonance is an exponential function of the drive strength.

Semiclassical construction of Green's functions for multidimensional systems with barrier tunneling

We develop a treatment that divides phase space into regions bounded by surfaces and forms the energy-dependent semiclassical Green's function from short classical trajectory segments confined to the individual regions. We use this to generalize Bogomolny's quantization method to systems with barrier tunneling. Combined with an appropriate treatment of tunneling amplitudes, this yields a unified semiclassical framework that uses ordinary, real trajectories in classically allowed regions and imaginary-time trajectories in forbidden regions to obtain energies, decay rates, and wave functions for arbitrary states of multidimensional systems undergoing tunneling. Because the trajectory segments in the allowed region are short, components in the Green's function expression can be numerically evaluated using semiclassical initial value methods, yielding a promising approach for practical calculations.

Tight-binding tunneling amplitude of an optical lattice

The particle in a periodic potential is an important topic in an undergraduate quantum mechanics curriculum and a stepping stone on the way to more advanced topics, such as courses on interacting electrons in crystalline solids, and graduate-level research in solid-state and condensed matter physics. The interacting many-body phenomena are usually described in terms of the second quantized lattice Hamiltonians which treat single-particle physics on the level of tight-binding approximation and add interactions on top of it. The aim of this paper is to show how the tight-binding tunneling amplitude can be related to the strength of the periodic potential for the case of a cosine potential used in the burgeoning field of ultracold atoms. We show how to approach the problem of computing the tunneling amplitude of a deep lattice using the JWKB (Jeffreys–Wentzel–Kramers–Brillouin, also known as semiclassical) approximation. We also point out that care should be taken when applying the method of the linear combination of atomic orbitals (LCAO) in an optical lattice context. A summary of the exact solution in terms of Mathieu functions is also given.

Stabilizing strongly correlated photon fluids with non-Markovian reservoirs

We introduce a novel frequency-dependent incoherent pump scheme with a square-shaped spectrum as a way to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a non-equilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-Insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or non-integer densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic non-equilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero temperature many-body physics is highlighted.

On the decoupling theorem for vacuum metastability

In this paper, we numerically study the impact heavy field degrees of freedom have on vacuum metastability in a toy model, with the aim of better understanding how the decoupling theorem extends to semiclassical processes. We observe that decoupling applies to partial amplitudes associated with fixed final state field configurations emerging from the tunneling processes, characterized by a scale such as the inverse radius of a spherically symmetric bubble, and not directly on the total lifetime (as determined by the “bounce”). More specifically, tunneling amplitudes for bubbles with inverse radii smaller than the scale of the heavier fields are largely insensitive to their presence, while those for bubbles with inverse radii larger than that scale may be significantly modified.

Persistent current in 2D topological superconductors

A junction between two boundaries of a topological superconductor (TSC), mediated by localized edge modes of Majorana fermions, is investigated. The tunneling of fermions across the junction depends on the magnetic flux. It breaks the time-reversal symmetry at the boundary of the sample. The persistent current is determined by the emergence of Majorana edge modes. The structure of the edge modes depends on the magnitude of the tunneling amplitude across the junction. It is shown that there are two different regimes, which correspond to strong and weak tunneling of Majorana fermions, distinctive in the persistent current behavior. In a strong tunneling regime, the fermion parity of edge modes is not conserved and the persistent current is a 2π-periodic function of the magnetic flux. When the tunneling is weak the chiral Majorana states, which are propagating along the edges have the same fermion parity. They form a 4π-phase periodic persistent current along the boundaries. The regions in the space of parameters, which correspond to the emergence of 2π- and of 4π-harmonics, are numerically determined. The peculiarities in the persistent current behavior are studied.

Spin-dependent coupling between quantum dots and topological quantum wires

Considering Rashba quantum wires with a proximity-induced superconducting gap as physical realizations of Majorana bound states and quantum dots, we calculate the overlap of the Majorana wave functions with the local wave functions on the dot. We determine the spin-dependent tunneling amplitudes between these two localized states and show that we can tune into a fully spin polarized tunneling regime by changing the distance between dot and Majorana bound state. Upon directly applying this to the tunneling model Hamiltonian, we calculate the effective magnetic field on the quantum dot flanked by two Majorana bound states. The direction of the induced magnetic field on the dot depends on the occupation of the nonlocal fermion formed from the two Majorana end states which can be used as a readout for such a Majorana qubit.

Thermometry of bosonic mixtures in Optical Lattices via Demixing

Motivated by recent experiments and theoretical investigations on binary mixtures, we investigate the miscible-immiscible transition at finite temperature by means of Quantum Monte Carlo. Based on the observation that the segregated phase is strongly affected by temperature, we propose to use the degree of demixing for thermometry of a binary bosonic mixture trapped in an optical lattice. We show that the proposed method is especially sensitive at low temperatures, of the order of the tunnelling amplitude, and therefore is particularly suitable in the regime where quantum magnetism is expected.

Quantum perfect crossed Andreev reflection in top-gated quantum anomalous Hall insulator–superconductor junctions

We investigate the quantum tunneling and Andreev reflection in a top-gated quantum anomalous Hall insulator proximity coupled with a superconductor junction. A quantized perfect crossed Andreev reflection with its coefficient being integer 1 is obtained and all other scattering processes (the normal reflection, normal tunneling, and local Andreev reflection) are completely suppressed when the topological superconductor phase with Chern number $\mathcal{N}=1$ is realized. This perfect crossed Andreev reflection originates from the tunneling of the chiral Majorana edge states, and the phase of tunneling amplitude only being 0 and $\ensuremath{\pi}$ plays a decisive role. Furthermore, because of the chiral characteristic of the Majorana edge states, the perfect crossed Andreev reflection is robust against the disorder and can work in a wide range of system parameters.

Noncommutative duality and fermionic quasinormal modes of the BTZ black hole

We analyze the fermionic quasinormal modes of the BTZ black hole in the presence of space-time noncommutativity. Our analysis exploits a duality between a spinless and spinning BTZ black hole, the spin being proportional to the noncommutative deformation parameter. Using the AdS/CFT correspondence we show that the horizon temperatures in the dual CFT are modified due to noncommutative contributions. We demonstrate the equivalence between the quasinormal and non-quasinormal modes for the noncommutative fermionic probes, which provides further evidence of holography in the noncommutative setting. Finally we present an analysis of the emission of Dirac fermions and the corresponding tunneling amplitude within this noncommutative framework.

Spatial non-adiabatic passage using geometric phases

Quantum technologies based on adiabatic techniques can be highly effective, but often at the cost of being very slow. Here we introduce a set of experimentally realistic, non-adiabatic protocols for spatial state preparation, which yield the same fidelity as their adiabatic counterparts, but on fast timescales. In particular, we consider a charged particle in a system of three tunnel-coupled quantum wells, where the presence of a magnetic field can induce a geometric phase during the tunnelling processes. We show that this leads to the appearance of complex tunnelling amplitudes and allows for the implementation of spatial non-adiabatic passage. We demonstrate the ability of such a system to transport a particle between two different wells and to generate a delocalised superposition between the three traps with high fidelity in short times.

Noisy quantum walks of two indistinguishable interacting particles

We investigate the dynamics of continuous-time two-particle quantum walks on a one-dimensional noisy lattice. Depending on the initial condition, we show how the interplay between particle indistinguishability and interaction determines distinct propagation regimes. A realistic model for the environment is considered by introducing non-Gaussian noise as time-dependent fluctuations of the tunneling amplitudes between adjacent sites. We observe that the combined effect of particle interaction and fast noise (weak coupling with the environment) provides a faster propagation compared to the noiseless case. This effect can be understood in terms of the band structure of the Hubbard model, and a detailed analysis as a function of both noise and system parameters is presented.

Transmission and tunneling probability in two-band metals: Influence of magnetic breakdown on the Onsager phase of quantum oscillations

Tunneling amplitude through magnetic breakdown (MB) gap is considered for two-bands Fermi surfaces illustrated in many organic metals. In particular, the S-matrix associated to the wave function transmission through the MB gap for the relevant class of differential equations is the main object allowing the determination of tunneling probabilities and phases. The calculated transmission coefficients include a field-dependent Onsager phase. As a result, quantum oscillations are not periodic in 1/B for finite magnetic breakdown gap. Exact and approximate methods are proposed for computing ratio amplitudes of the wave function in interacting two-band models.

Realizing type-II Weyl points in an optical lattice

The recent discovery of the Lorentz symmetry-violating 'Type II' Weyl semimetal phase has renewed interest in the study of Weyl physics in condensed matter systems. However, tuning the exceptional properties of this novel state has remained a challenge. Optical lattices, created using standing laser beams, provide a convenient platform to tune tunnelling parameters continuously in time. In this paper, we propose a generalised two level system exhibiting type II Weyl points that can be realised using ultra-cold atoms in an optical lattice. The system is engineered using a three-dimensional lattice with complex $\pi$ phase tunnelling amplitudes. Various unique properties of the type II Weyl semimetal such as open Fermi surface, anomalous chirality and topological Fermi arcs can be probed using the proposed optical lattice scheme.

Spin-polarized tunneling into helical edge states: Asymmetry and conductances

We consider tunneling from the spin-polarized tip into the Luttinger liquid edge state of quantum spin Hall system. This problem arose in the context of the spin and charge fractionalization of an injected electron. Renormalization of the dc conductances of the system is calculated in the fermionic approach and scattering states formalism. In the lowest order of the tunneling amplitude we confirm previous results for the scaling dependence of conductances. Going beyond the lowest order we show that the interaction affects not only the total tunneling rate, but also the asymmetry of the injected current. The helical edge state forbids the backscattering, which leads to the possibility of two stable fixed points in the renormalization group sense, in contrast to the Y-junction between the usual quantum wires.