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 DC 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.In the past several years, following the seminal paper by Bender and Boettcher [1], non-hermitian PTsymmetric Hamiltonians have caught a lot of attention (see [2] and references therein). Under certain conditions PT -symmetric Hamiltonians can have a completely real spectrum and thus can serve, under the appropriate inner products, as the Hamiltonians for unitary quantum systems [3].Recently, the realization of PT -symmetric "Hamiltonians" has been studied using optical waveguides with complex refractive indices [4,5]. The equivalence of the Maxwell and Schrödinger equations in certain regimes provides a physical system in which the properties of PT -symmetric operators can be studied and exemplified.An extremely interesting property of PT -symmetric operators stems from the anti-linearity of the time symmetry operator. Consider a PT -symmetric operatorĤ, i.e., [PT ,Ĥ] = 0. Due to the non-linearity of T one cannot in general choose simultaneous eigenfunctions of the operators PT andĤ. However, if an eigenvalue of thê H is real then it's corresponding eigenfunction is a also an eigenfunction of the PT operator. This property has come to be known as exact/spontaneously-broken PTsymmetry. Exact PT -symmetry refers to the case when every eigenfunction of the PT symmetric operator is also an eigenfunction of the PT operator. In any other case the PT -symmetry is said to be broken.Usually, the transition between exact and spontaneously-broken PT symmetry can be controlled by a parameter in the Hamiltonian. This parameter serves as a measure of the non-hermiticity. An important class of PT -symmetric Hamiltonians are of the form: H(λ) = H 0 + iλV . Where H 0 (and V ) are real and symmetric(anti-symmetric) with respect to parity so that [PT ,Ĥ] = 0. When λ = 0 the Hamiltonian is hermitian and the entire spectrum is real. The spectrum remains real even when λ = 0 as long as λ < λ c . At this critical value and beyond, pairs of eigenvalues collide and become complex, see for example [6]. Bender et al. [7] showed that the reality of the spectrum is explained by the real secular equations one can write for PT -symmetric matrices. These secular equations will depend on the non-hermiticity parameter and, consequently, yield either real or complex solutions. Delabaere et al. [8] showed for the one-parameter family of complex cubic oscillators that pairs of eigenvalues cross each other at Bender and Wu branch points. Dorey et al. [9] after proving ...

Bose-Einstein condensates made of ultracold trapped bosonic atoms have become a central venue in which interacting many-body quantum systems are studied. The ground state of a trapped Bose-Einstein condensate has been proven to be 100% condensed in the limit of infinite particle number and constant interaction parameter [Lieb and Seiringer, Phys. Rev. Lett. 88, 170409 (2002)].The meaning of this result is that properties of the condensate, noticeably its energy and density, converge to those obtained by minimizing the Gross-Pitaevskii energy functional. This naturally raises the question whether correlations are of any importance in this limit. Here, we demonstrate both analytically and numerically that even in the infinite particle limit many-body correlations can lead to a substantial modification of the variance of any operator compared to that expected from the Gross-Pitaevskii result. The strong deviation of the variance stems from its explicit dependence on terms of the reduced two-body density matrix which otherwise do not contribute to the energy and density in this limit. This makes the variance a sensitive probe of many-body correlations even when the energy and density of the system have already converged to the Gross-Pitaevskii result. We use the center-of-mass position operator to exemplify this persistence of correlations.Implications of this many-body effect are discussed.

In the present work we show, analytically and numerically, that the variance of many-particle operators and their uncertainty product for an out-of-equilibrium Bose-Einstein condensate (BEC) can deviate from the outcome of the time-dependent Gross-Pitaevskii dynamics, even in the limit of infinite number of particles and at constant interaction parameter when the system becomes 100% condensed. We demonstrate our finding on the dynamics of the center-of-mass positionmomentum uncertainty product of a freely expanding as well as of a trapped BEC. This timedependent many-body phenomenon is explained by the existence of time-dependent correlations which manifest themselves in the system's reduced two-body density matrix used to evaluate the uncertainty product. Our work demonstrates that one has to use a many-body propagation theory to describe an out-of-equilibrium BEC, even in the infinite particle limit.

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 potential's 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.

In this work, we study the out-of-equilibrium many-body tunneling dynamics of a Bose-Einstein condensate in a two-dimensional radial double well. We investigate the impact of interparticle repulsion and compare the influence of angular momentum on the many-body tunneling dynamics.Accurate many-body dynamics are obtained by solving the full many-body Schrödinger equation.We demonstrate that macroscopic vortex states of definite total angular momentum indeed tunnel and that, even in the regime of weak repulsions, a many-body treatment is necessary to capture the correct tunneling dynamics. As a general rule, many-body effects set in at weaker interactions when the tunneling system carries angular momentum.

We report on large-scale coupled cluster calculations of the electron affinities of the C60 fullerene. The full spectrum of bound states of the anion is investigated. Thereby, a new state bound by correlation is discovered. The binding of this state is highly dependent on the correct description of the polarization and the electron correlation in the fullerene. We present the natural orbital occupied by the excess electron for each of the anionic states and show how the bound spectrum can be divided into two different groups according to their binding mechanism. We discuss in depth how approximating the correlation with perturbation theory leads in the case of the C60 – anion to unreliable predictions of the electron affinities in contrast to other large clusters and molecules. Some possible implications of the new weakly bound state are discussed.

Much like the neutral C60 fullerene, the C60(-) anion possesses certain unique properties which have attracted a great deal of research. One of these special properties, only recently fully uncovered, is that the C60(-) anion supports a substantial number of electronically stable excited states in contrast to other molecular anions with comparable electron affinity. In this work, we clarify how the C60(-) anion can support so many stable states by analyzing the radial and angular distributions of the excess electron bound to the anion. The analysis is based on ab initio calculations which are by far the most accurate on the C60(-) anion to date. Surprisingly, the radial distributions are highly similar for states of very different binding energies and the analysis stresses the importance of angular correlation in binding the excess electron. We further analyze the effect of the single excess electron on the electrons of the underlying neutral molecule. We demonstrate how this substantially modifies the actual distribution of the excess charge by shifting the underlying electron density. Implications of these findings are discussed.

It has been proven theoretically for bosons with two-body repulsive interaction potentials in the dilute limit that the Gross-Pitaevskii equation provides the exact energy and density per particle as does the basic many-particle Schrödinger equation [Lieb and Seiringer, Phys. Rev. Lett. 88, 170409 (2002)]. Here, we investigate the overlap of the Gross-Pitaevskii and exact ground state wavefunctions. It is found that this overlap is always smaller than unity and may even vanish in spite of the fact that both wavefunctions provide the same energy and density per particle. Consequences are discussed. PACS numbers: 03.65.-wSince the experimental discovery of Bose-Einstein condensates (BECs) consisting of dilute atomic gases two decades ago [1-3], there has been vast interest in their properties [4][5][6]. In the respective theoretical studies, the Gross-Pitaevskii equation which is obtained by minimizing the Gross-Pitaevskii energy functional [7] has played a particularly leading role. The simplicity of this mean field equation adds much to its popularity as it can be solved rather straightforwardly and exhibits many interesting and appealing properties. Importantly, it has been rigorously proven by Lieb and Seiringer (LS theorem) [8] that in the dilute limit the Gross-Pitaevskii (GP) equation provides the exact energy and density per particle as does the full many-particle Schrödinger equation. One immediate and highly relevant consequence of this proof is that BECs are 100% condensed in the limit of infinite particle number.In the dilute limit, also called GP limit, the interaction parameter Λ = λ 0 (N − 1) appearing in the GP equation, where λ 0 is the two-particle interaction strength, is kept fixed as N → ∞. The LS theorem might raise the impression that the GP theory correctly describes BECs with large particle numbers at zero temperature. Nevertheless, it is well known that corrections beyond the GP theory can be relevant for experiments with typical particle numbers [9]. Does GP theory also provide an accurate wavefunction of BECs in the dilute limit? This is a relevant question as, after all, the wavefunction contains all the physical properties of the system. A first clear indication that boson correlations not included in GP theory can be relevant has been shown very recently by Klaiman and Alon [10,11]. To answer the latter question we have chosen the overlap of the GP and exact ground states as an obvious measure of the quality of the GP wavefunction. The proof by Lieb and Seiringer is restricted to 3 and 2 dimensions and assumes the existence of a finite scattering length, but we would like to go beyond and consider the general case of a many-boson Hamiltonian and its mean field (which we call GP) in the dilute limit.We shall show that the LS theorem applies also for cases not covered by the available proof.As a first step we introduce a many-body perturbation theory (MBPT) where the unperturbed Hamiltonian is the GP one. The situation is similar to the so called Møller-Plesset MBPT widely and successf...