arXiv subjects

Jörg Main

Publications and source records attributed to Jörg Main.

At least 73 records · Page 4Linked to original sources

arXiv2016

Magnetoexcitons in cuprous oxide

Two of the most striking experimental findings when investigating exciton spectra in cuprous oxide using high-resolution spectroscopy are the observability and the fine structure splitting of $F$ excitons reported by J. Thewes et al. [Phys. Rev. Lett. 115, 027402 (2015)]. These findings show that it is indispensable to account for the complex valence band structure and the cubic symmetry of the solid in the theory of excitons. This is all the more important for magnetoexcitons, where the external magnetic field reduces the symmetry of the system even further. We present the theory of excitons in $\mathrm{Cu_{2}O}$ in an external magnetic field and especially discuss the dependence of the spectra on the direction of the external magnetic field, which cannot be understood from a simple hydrogen-like model. Using high-resolution spectroscopy, we also present the corresponding experimental spectra for cuprous oxide in Faraday configuration. The theoretical results and experimental spectra are in excellent agreement as regards not only the energies but also the relative oscillator strengths. Furthermore, this comparison allows for the determination of the fourth Luttinger parameter $κ$ of this semiconductor.

cond-mat.mtrl-sci↗

arXiv2016

Bose-Einstein condensates with balanced gain and loss beyond mean-field theory

Most of the work done in the field of Bose-Einstein condensates with balanced gain and loss has been performed in the mean-field approximation using the PT-symmetric Gross-Pitaevskii equation. In this work we study the many-particle dynamics of a two-mode condensate with balanced gain and loss described by a master equation in Lindblad form whose purity periodically drops to small values but then is nearly completely restored. This effect cannot be covered by the mean-field approximation, in which a completely pure condensate is assumed. We present analytic solutions for the dynamics in the non-interacting limit and use the Bogoliubov backreaction method to discuss the influence of the on-site interaction. Our main result is that the strength of the purity revivals is almost exclusively determined by the strength of the gain and loss and is independent of the amount of particles in the system and the interaction strength. For larger particle numbers, however, strong revivals are shifted towards longer times, but by increasing the interaction strength these strong revivals again occur earlier.

quant-ph↗

arXiv2016

Dynamics of Solitons in the One-Dimensional Nonlinear Schrödinger Equation

We investigate bright solitons in the one-dimensional Schrödinger equation in the framework of an extended variational approach. We apply the latter to the stationary ground state of the system as well as to coherent collisions between two or more solitons. Using coupled Gaussian trial wave functions, we demonstrate that the variational approach is a powerful method to calculate the soliton dynamics. This method has the advantage that it is computationally faster compared to numerically exact grid calculations. In addition, it goes far beyond the capability of analytical ground state solutions, because the variational approach provides the ability to treat excited solitons as well as dynamical interactions between different wave packets. To demonstrate the power of the variational approach, we calculate the stationary ground state of the soliton and compare it with the analytical solution showing the convergence to the exact solution. Furthermore, we extend our calculations to nonstationary solitons by investigating the breathing oscillations of excited solitons and the coherent collisions of several wave packets in both the low- and high-energy regime. Comparisons of the variational approach with numerically exact simulations on grids reveal excellent agreement in the high-energy regime while deviations can be observed for low energies.

quant-ph↗

arXiv2016

$K$ dependent exchange interaction of the $1S$ ortho exciton in Cu$_2$O

When treating the exchange interaction of Wannier excitons, usually only the leading terms of the analytic and the nonanalytic exchange interaction are considered. However, higher order terms can lead to a splitting of exciton states, for which reason a splitting of the $1S$~exciton in cuprous oxide $\left(\mathrm{Cu_{2}O}\right)$ depending on its total momentum $\hbar K$ has been attributed to a $K$ dependent analytic exchange interaction by Dasbach et al [Phys. Rev. Lett. 91, 107401 (2003)]. Going beyond the common treatment of the exchange interaction, we derive the correct expressions for these $K$ dependent higher order terms using $\boldsymbol{k}\cdot\boldsymbol{p}$ perturbation theory. We prove that the appearance of a $K$ dependent exchange interaction is inseparably connected with a $K$ independent exchange interaction of $P$ and $D$ excitons. We estimate the magnitude of these terms for $\mathrm{Cu_{2}O}$ from microscopic calculations and show that they are far too small to explain the observed $K$ dependent splitting. Instead, this splitting has to be treated in terms of the dispersion of the excitons. Furthermore, we prove the occurence of a coupling between longitudinal and transverse excitons in $\mathrm{Cu_{2}O}$ due to the $K$ dependent nonanalytic exchange interaction.

cond-mat.mtrl-sci↗

arXiv2016

Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate

We investigate the bifurcation structure of stationary states in a dipolar Bose-Einstein condensate located in an external PT-symmetric potential. The imaginary part of this external potential allows for the effective description of in- and out-coupling of particles. To unveil the complete bifurcation structure and the properties of the exceptional points we perform an analytical continuation of the Gross-Pitaevskii equation, which is used to describe the system. We use an elegant and numerically efficient method for the analytical continuation of the Gross-Pitaevskii equation with dipolar interactions containing bicomplex numbers. The Bose-Einstein condensate with dipole interaction shows a much richer bifurcation scenario than a condensate without long-range interactions. The inclusion of analytically continued states can also explain property changes of bifurcation points which were hidden before, and allows for the examination of the properties of the exceptional points associated with the branch points. With the new analytically continued states we are able to prove the existence of an exceptional point of fifth order.

quant-ph↗

arXiv2016

Rydberg systems in parallel electric and magnetic fields: an improved method for finding exceptional points

Exceptional points are special parameter points in spectra of open quantum systems, at which resonance energies degenerate and the associated eigenvectors coalesce. Typical examples are Rydberg systems in parallel electric and magnetic fields, for which we solve the Schrödinger equation in a complete basis to calculate the resonances and eigenvectors. Starting from an avoided crossing within the parameter-dependent spectra and using a two-dimensional matrix model, we develop an iterative algorithm to calculate the field strengths and resonance energies of exceptional points and to verify their basic properties. Additionally, we are able to visualise the wave functions of the degenerate states. We report the existence of various exceptional points. For the hydrogen atom these points are in an experimentally inaccessible regime of field strengths. However, excitons in cuprous oxide in parallel electric and magnetic fields, i. e., the corresponding hydrogen analogue in a solid state body, provide a suitable system, where the high-field regime can be reached at much smaller external fields and for which we propose an experiment to detect exceptional points.

quant-ph↗

arXiv2016

Impact of the valence band structure of Cu$_{2}$O on excitonic spectra

We present a method to calculate the exciton spectra of all direct semiconductors with a complex valence band structure. The Schrödinger equation is solved using a complete basis set with Coulomb Sturmian functions. This method also allows for the computation of oscillator strengths. Here we apply this method to investigate the impact of the valence band structure of cuprous oxide $\left(\mathrm{Cu_{2}O}\right)$ on the yellow exciton spectrum. Results differ from those in [Phys. Rev. Lett. 115, 027402 (2015)]; the differences are discussed and explained. The difference between the second and third Luttinger parameter can be determined by comparisons with experiments, however, the evaluation of all three Luttinger parameters is not uniquely possible. Our results are consistent with band structure calculations. Considering also a finite momentum $\hbar K$ of the center of mass, we show that the large $K$-dependent line splitting observed for the $1S$ exciton state [Phys. Rev. Lett. 91, 107401 (2003)] is not related to an exchange interaction but rather to the complex valence band structure of $\mathrm{Cu_{2}O}$.

cond-mat.mtrl-sci↗

arXiv2016

Linewidths in excitonic absorption spectra of cuprous oxide

We present a theoretical calculation of the absorption spectrum of cuprous oxide $\left(\mathrm{Cu_{2}O}\right)$ based on the general theory developed by Y. Toyozawa. An inclusion not only of acoustic phonons but also of optical phonons and of specific properties of the excitons in $\mathrm{Cu_{2}O}$ like the central-cell corrections for the $1S$-exciton allows us to calculate the experimentally observed line widths in experiments by T. Kazimierczuk et al [Nature 514, 343, (2014)] within the same order of magnitude, which demonstrates a clear improvement in comparison to earlier work on this topic. We also discuss a variety of further effects, which explain the still observable discrepancy between theory and experiment but can hardly be included in theoretical calculations.

cond-mat.mtrl-sci↗

arXiv2015

Tilted optical lattices with defects as realizations of PT symmetry in Bose-Einstein condensates

A PT-symmetric Bose-Einstein condensate can theoretically be described using a complex optical potential, however, the experimental realization of such an optical potential describing the coherent in- and outcoupling of particles is a nontrivial task. We propose an experiment for a quantum mechanical realization of a PT-symmetric system, where the PT-symmetric currents are implemented by an accelerating Bose-Einstein condensate in a titled optical lattice. A defect consisting of two wells at the same energy level then acts as a PT-symmetric double-well if the tilt in the energy offsets of all further wells in the lattice is varied in time. We map the time-dependence of the amplitudes of a frozen Gaussian variational ansatz to a matrix model and increase the system size step by step starting with a six-well setup. In terms of this simple matrix model we derive conditions under which two wells of the Hermitian multi-well system behave exactly as the two wells of the PT-symmetric system.

quant-ph↗

arXiv2015

State Flip at Exceptional Points in Atomic Spectra

We study the behavior of the non-adiabatic population transfer between resonances at an exceptional point in the spectrum of the hydrogen atom. It is known that, when the exceptional point is encircled, the system always ends up in the same state, independent of the initial occupation within the two-dimensional subspace spanned by the states coalescing at the exceptional point. We verify this behavior for a realistic quantum system, viz. the hydrogen atom in crossed electric and magnetic fields. It is also shown that the non-adiabatic hypothesis can be violated when resonances in the vicinity are taken into account. In addition, we study the non-adiabatic population transfer in the case of a third-order exceptional point, in which three resonances are involved.

quant-ph↗

arXiv2015

Realizing PT-symmetric BEC subsystems in closed hermitian systems

In open double-well Bose-Einstein condensate systems which balance in- and outfluxes of atoms and which are effectively described by a non-hermitian PT-symmetric Hamiltonian PT-symmetric states have been shown to exist. PT-symmetric states obey parity and time reversal symmetry. We tackle the question of how the in- and outfluxes can be realized and introduce a hermitian system in which two PT-symmetric subsystems are embedded. This system no longer requires an in- and outcoupling to and from the environment. We show that the subsystems still have PT-symmetric states. In addition we examine what degree of detail is necessary to correctly model the PT-symmetric properties and the bifurcation structure of such a system. We examine a four-mode matrix model and a system described by the full Gross-Pitaevskii equation in one dimension. We see that a simple matrix model correctly describes the qualitative properties of the system. For sufficiently isolated wells there is also quantitative agreement with the more advanced system descriptions. We also investigate which properties the wave functions of a system must fulfil to allow for PT-symmetric states. In particular the requirements for the phase difference between different parts of the system are examined.

quant-ph↗

arXiv2015

Fano resonances in scattering: an alternative perspective

In a previous paper it has been shown that the interference of the first and second order pole of the Green's function at an exceptional point, as well as the interference of the first order poles in the vicinity of the exceptional point, gives rise to asymmetric scattering cross section profiles. In the present paper we demonstrate that these line profiles are indeed well described by the Beutler-Fano formula, and thus are genuine Fano resonances. Also further away from the exceptional points excellent agreement can be found by introducing energy dependent Fano parameters.

quant-ph↗

arXiv2015

Normal form expansions and thermal decay rates of Bose-Einstein condensates with short- and long-range interaction

The thermally induced coherent collapse of Bose-Einstein condensates at finite temperature is the dominant decay mechanism near the critical scattering length in condensates with at least partially attractive interaction. The collapse dynamics out of the ground state is mediated by a transition state whose properties determine the corresponding decay rate or lifetime of the condensate. In this paper, we perform normal form expansions of the ground and the transition state of condensates with short-range scattering interaction as well as with anisotropic and long-range dipolar interaction in a variational framework. This method allows one to determine the local properties of these states, i.e. their mean-field energy, their normal modes, the coupling between different modes, and the structure of the reaction channel to any desired order. We discuss the physical interpretation of the transition state as a certain density distribution of the atomic cloud and the behavior of the single normal form contributions in dependence on the s-wave scattering length. Moreover, we investigate the convergence of the local normal form when using extended Gaussian variational approaches, and present the condensate's decay rate.

cond-mat.quant-gas↗

arXiv2015

Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates

A Bose-Einstein condensate in a double-well potential features stationary solutions even for attractive contact interaction as long as the particle number and therefore the interaction strength do not exceed a certain limit. Introducing balanced gain and loss into such a system drastically changes the bifurcation scenario at which these states are created. Instead of two tangent bifurcations at which the symmetric and antisymmetric states emerge, one tangent bifurcation between two formerly independent branches arises [D. Haag et al., Phys. Rev. A 89, 023601 (2014)]. We study this transition in detail using a bicomplex formulation of the time-dependent variational principle and find that in fact there are three tangent bifurcations for very small gain-loss contributions which coalesce in a cusp bifurcation.

quant-ph↗

arXiv2014

Classical dynamics and localization of resonances in the high energy region of the hydrogen atom in crossed fields

When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom a saddle point appears, which is called the Stark saddle point. For energies slightly above the saddle point energy one can find classical orbits, which are located in the vicinity of this point. We follow those so-called quasi-Penning orbits to high energies and field strengths observing structural changes and uncovering their bifurcation behavior. By plotting the stability behavior of those orbits against energy and field strength the appearance of a stability apex is reported. A cusp bifurcation, located in the vicinity of the apex, will be investigated in detail. In this cusp bifurcation another orbit of similar shape is found, which becomes completely stable in the observed region of positive energy, i.e., in a region of parameter space, where the Kepler-like orbits located around the nucleus are already unstable. By quantum-mechanically exact calculations we prove the existence of signatures in quantum spectra belonging to those orbits. Husimi distributions are used to compare quantum-Poincaré sections with the extension of the classical torus structure around the orbits. Since periodic orbit theory predicts that each classical periodic orbit contributes an oscillating term to photoabsorption spectra, we finally give an estimation for future experiments, which could verify the existence of the stable orbits.

physics.atom-ph↗

arXiv2014

Verification of exceptional points in the collapse dynamics of Bose-Einstein condensates

In Bose-Einstein condensates with an attractive contact interaction the stable ground state and an unstable excited state emerge in a tangent bifurcation at a critical value of the scattering length. At the bifurcation point both the energies and the wave functions of the two states coalesce, which is the characteristic of an exceptional point. In numerical simulations signatures of the exceptional point can be observed by encircling the bifurcation point in the complex extended space of the scattering length, however, this method cannot be applied in an experiment. Here we show in which way the exceptional point effects the collapse dynamics of the Bose-Einstein condensate. The harmonic inversion analysis of the time signal given as the spatial extension of the collapsing condensate wave function can provide clear evidence for the existence of an exceptional point. This method can be used for an experimental verification of exceptional points in Bose-Einstein condensates.

cond-mat.quant-gas↗

arXiv2014

Coupling approach for the realization of a $\mathcal{PT}$-symmetric potential for a Bose-Einstein condensate in a double well

We show how non-Hermitian potentials used to describe probability gain and loss in effective theories of open quantum systems can be achieved by a coupling of the system to an environment. We do this by coupling a Bose-Einstein condensate (BEC) trapped in an attractive double-delta potential to a condensate fraction outside the double well. We investigate which requirements have to be imposed on possible environments with a linear coupling to the system. This information is used to determine an environment required for stationary states of the BEC. To investigate the stability of the system we use fully numerical simulations of the dynamics. It turns out that the approach is viable and possible setups for the realization of a $\mathcal{PT}$-symmetric potential for a BEC are accessible. Vulnerabilities of the whole system to small perturbations can be adhered to the singular character of the simplified delta-shaped potential used in our model.

quant-ph↗

arXiv2014

Realizing PT-symmetric non-Hermiticity with ultra-cold atoms and Hermitian multi-well potentials

We discuss the possibility of realizing a non-Hermitian, i.e. an open two-well system of ultra-cold atoms by enclosing it with additional time-dependent wells that serve as particle reservoirs. With the appropriate design of the additional wells PT-symmetric currents can be induced to and from the inner wells, which support stable solutions. We show that interaction in the mean-field limit does not destroy this property. As a first method we use a simplified variational ansatz leading to a discrete nonlinear Schrödinger equation. A more accurate and more general variational ansatz is then used to confirm the results.

quant-ph↗