arXiv subjects

Holger Cartarius

Publications and source records attributed to Holger Cartarius.

At least 37 records · Page 2Linked to original sources

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

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

Purity oscillations in Bose-Einstein condensates with balanced gain and loss

In this work we present a new generic feature of PT-symmetric Bose-Einstein condensates by studying the many-particle description of a two-mode condensate with balanced gain and loss. This is achieved using a master equation in Lindblad form whose mean-field limit is a PT-symmetric Gross-Pitaevskii equation. It is shown that the purity of the condensate periodically drops to small values but then is nearly completely restored. This has a direct impact on the average contrast in interference experiments which cannot be covered by the mean-field approximation, in which a completely pure condensate is assumed.

quant-ph↗

arXiv2016

$\mathcal{PT}$-symmetric currents of a Bose-Einstein condensate in a triple well

We study the case of $\mathcal{PT}$-symmetric perturbations of Hermitian Hamiltonians with degenerate eigenvalues using the example of a triple-well system. The degeneracy complicates the question, whether or not a stationary current through such a system can be established, i.e.\ whether or not the $\mathcal{PT}$-symmetric states are stable. It is shown that this is only the case for perturbations that do not couple to any of the degenerate states. The physical explanation for the inhibition of stable currents is discussed. However, introducing an on-site interaction restores the capability to support stable currents.

quant-ph↗

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

Structural information about the $\text{Ar}_6$ cluster with the frozen Gaussian imaginary time propagator

A numerically cheap way to obtain structural information about clusters of rare gas atoms at low temperatures is developed. The semiclassical frozen Gaussian imaginary time propagator is extended such that it can account for the mean values of all inter-atomic distances in the cluster and their variances. To reduce the required numerical effort an approximation for the mean values is developed which preserves the quality of the results offered by the semiclassical ansatz. The method is applied to the $\text{Ar}_6$ cluster. It is found that the cluster dissociates almost in one step to six free atoms when the temperature is increased. Precursors of the dissociation are only observable in the distances of the atoms via the appearance of a second isomer. The process is almost classical. However, the method is able to resolve small differences in the temperatures at which the dissociation takes place and in the mean distances of the bound configuration.

physics.atm-clus↗

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

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

Supersymmetric model of a Bose-Einstein condensate in a $\mathcal{PT}$-symmetric double-delta trap

The most important properties of a Bose-Einstein condensate subject to balanced gain and loss can be modelled by a Gross-Pitaevskii equation with an external $\mathcal{PT}$-symmetric double-delta potential. We study its linear variant with a supersymmetric extension. It is shown that both in the $\mathcal{PT}$-symmetric as well as in the $\mathcal{PT}$-broken phase arbitrary stationary states can be removed in a supersymmetric partner potential without changing the energy eigenvalues of the other state. The characteristic structure of the singular delta potential in the supersymmetry formalism is discussed, and the applicability of the formalism to the nonlinear Gross-Pitaevskii equation is analysed. In the latter case the formalism could be used to remove $\mathcal{PT}$-broken states introducing an instability to the stationary $\mathcal{PT}$-symmetric states.

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

Quantum master equation with balanced gain and loss

We present a quantum master equation describing a Bose-Einstein condensate with particle loss on one lattice site and particle gain on the other lattice site whose mean-field limit is a non-Hermitian PT-symmetric Gross-Pitaevskii equation. It is shown that the characteristic properties of PT-symmetric systems, such as the existence of stationary states and the phase shift of pulses between two lattice sites, are also found in the many-particle system. Visualizing the dynamics on a Bloch sphere allows us to compare the complete dynamics of the master equation with that of the Gross-Pitaevskii equation. We find that even for a relatively small number of particles the dynamics are in excellent agreement and the master equation with balanced gain and loss is indeed an appropriate many-particle description of a PT-symmetric Bose-Einstein condensate.

quant-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↗

arXiv2014

Dipolar Bose-Einstein condensates in a PT-symmetric double-well potential

We investigate dipolar Bose-Einstein condensates in a complex external double-well potential that features a combined parity and time-reversal symmetry. On the basis of the Gross-Pitaevskii equation we study the effects of the long-ranged anisotropic dipole-dipole interaction on ground and excited states by the use of a time-dependent variational approach. We show that the property of a similar non-dipolar condensate to possess real energy eigenvalues in certain parameter ranges is preserved despite the inclusion of this nonlinear interaction. Furthermore, we present states that break the PT symmetry and investigate the stability of the distinct stationary solutions. In our dynamical simulations we reveal a complex stabilization mechanism for PT-symmetric, as well as for PT-broken states which are, in principle, unstable with respect to small perturbations.

quant-ph↗