Shachar Klaiman

Visualization of Branch Points in PT-Symmetric Waveguides

The visualization of an exceptional point in a PT-symmetric directional coupler (DC) is demonstrated. In such a system the exceptional point can be probed by varying only a single parameter. Using the Rayleigh-Schrödinger perturbation theory we prove that the spectrum of a PT-symmetric Hamiltonian is real as long as the radius of convergence has not been reached. We also show how one can use a PT-symmetric directional coupler to measure the radius of convergence for non-PT-symmetric structures. For such systems the physical meaning of the rather mathematical term radius of convergence is exemplified.

The absolute position of a resonance peak

It is common practice in scattering theory to correlate the position of a resonance peak in the cross section to the real part of a complex energy of a pole of the scattering amplitude. In this work, we show that the resonance peak position appears at the absolute value of the poles complex energy rather than its real part. We further demonstrate that a local theory of resonances can still be used even in the cases previously thought to be impossible.

On Resonance: A First Glance into the Behavior of Unstable States

Abstract Dynamical processes in nature often involve unstable states. Analyzing systems with a finite lifetime can be challenging for a practitioner of quantum mechanics. To study such processes in a quantum system, one must venture into the continuum where the use of a continuous superposition of states, i.e., a wave packet, is required. Most of our quantum education focuses on quantized bound states rather than on the behavior of wave packets. Here, we aim to give a pedagogic introduction to the behavior and analysis of unstable states. To achieve this, we introduce two complementary viewpoints by which such states can be analyzed. We further discuss the physical mechanisms through which quantum unstable states are formed.

The exact wavefunction factorization of a vibronic coupling system

We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation.

Ab initio calculation of ICD widths in photoexcited HeNe

Excitation of HeNe by synchrotron light just below the frequency of the 1s → 3p transition of isolated He has been recently shown to be followed by resonant interatomic Coulombic decay (ICD). The vibrationally resolved widths of the ICD states were extracted with high precision from the photoion spectra. In this paper, we report the results of ab initio calculations of these widths. We show that interaction between electronic states at about the equilibrium distance of HeNe makes dark states of He accessible for the photoexcitation and subsequent electronic decay. Moreover, the values of the calculated widths are shown to be strongly sensitive to the presence of the non-adiabatic coupling between the electronic states participating in the decay. Therefore, only by considering the complete manifold of interacting decaying electronic states a good agreement between the measured and computed ICD widths can be achieved.

Two trapped particles interacting by a finite-range two-body potential in two spatial dimensions

We examine the problem of two particles confined in an isotropic harmonic trap, which interact via a finite-ranged Gaussian-shaped potential in two spatial dimensions. We derive an approximative transcendental equation for the energy and study the resulting spectrum as a function of the interparticle interaction strength. Both the attractive and repulsive systems are analyzed. We study the impact of the potentials range on the ground-state energy. Complementary, we also explicitly verify by a variational treatment that in the zero-range limit the positive delta potential in two dimensions only reproduces the non-interacting results, if the Hilbert space in not truncated. Finally, we establish and discuss the connection between our finite-range treatment and regularized zero-range results from the literature.

The best orbital and pair function for describing ionic and excited states on top of the exact ground state

Many-body processes inevitably lead to the transition from one many-body wavefunction to another. Due to the complexity of the initial and final states many-body wavefunctions, one often wishes to try and describe such transitions using only a single-particle function. While there are numerous types of orbitals and densities which are commonly used, the question remains which one is optimal and in which sense. Here we present the optimal one and two body functions whose anti-symmetrized product with the initial state yields the maximal overlap with the final state. A definition of the above optimal condition and its rigorous proof are given. The resulting optimal functions shed additional light on the well-known Dyson orbital and reduced transition matrix, demonstrating further their physical meaning as independent functions.

Controlling the velocities and the number of emitted particles in the tunneling to open space dynamics

A scheme to control the many-boson tunneling process to open space is derived and demonstrated. The number of ejected particles and their velocities can be controlled by two parameters, the threshold of the potential and the interparticle interaction. Since these p arameters are fully under experimental control, this is also the case for the number of ejected particles and their emission spectrum. The process of tunneling to open space can hence be used, for example, for the quantum simulation of complicated tunneling ionization processes and atom lasers. To understand the many-body tunneling process, a generalization of the model introduced in [Proc. Natl. Acad. Sci. USA, 109, 13521 (2012)] for tunneling in the absence of a threshold is put forward and proven to apply for systems with a non-zero threshold value. It is demonstrated that the model is applicable for general interparticle interact ion strengths, particle numbers and threshold values. The model constructs the many-body process from single-particle emission processes. The rates and emission momenta of the single-particle processes are determined by the chemical potentials and energy differences to the threshold value of the potential for syst ems with different particle numbers. The chemical potentials and these energy differences depend on the interparticle interaction. Both the number of confined particles and their rate of emission thus allow for a con trol by the manipulation of the interparticle interaction and the threshold. Numerically exact results f or two, three and one hundred bosons are shown and discussed. The devised control scheme for the many-body tunneling process performs very well for the dynamics of the momentum density, the correlations, the coherence and of the final state, i.e., the number of particles that remain confined in the potential.

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system`s ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed using a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs.

Resonance theory for discrete models: methodology and isolated resonances.

We here consider open quantum systems defined on discretized space, motivated by experimental and theoretical interest in the electronic conduction through nanoscale devices such as molecular junctions and quantum dots. We particularly focus on effects of resonances on the conductance through the systems. We develop a method of calculating the conductance with the use of Greens function expansion with respect to the eigenstates of the effective Hamiltonian for the open quantum systems. Unlike previous methodologies where one can treat only narrow resonances far from the band edges in a satisfactory manner with a Lorentzian profile, our method provides a novel resonance profile which can be used to describe any isolated resonance in the spectrum even close to the band edges.