Cold atoms in real-space optical lattices

Cold atoms in optical lattices are described in {\it real space} by multi-orbital mean-field Ans\"atze. In this work we consider four typical systems: (i) spinless identical bosons, (ii) spinor identical bosons (iii), Bose-Bose mixtures, and (iv) Bose-Fermi mixtures and derive in each case the corresponding multi-orbital mean-field energy-functional and working equations. The notions of {\it dressed} Wannier functions and Wannier spinors are introduced and the equations defining them are presented and discussed. The dressed Wannier functions are the set of orthogonal, translationally-equivalent orbitals which minimizes the energy of the Hamiltonian including boson-boson (particle-particle) interactions. Illustrative examples of dressed Wannier functions are provided for spinless bosonic atoms and mixtures in one-dimensional optical lattices.Comment: 27 pages, 4 figures; [version minus figures published

On-top fragmentation stabilizes atom-rich attractive Bose-Einstein condensates

It is well known that attractive condensates do not posses a stable ground state in three dimensions. The widely used Gross-Pitaevskii theory predicts the existence of metastable states up to some critical number $N_{\mathrm{cr}}^{\mathrm{GP}}$ of atoms. It is demonstrated here that fragmented metastable states exist for atom numbers well above $N_{\mathrm{cr}}^{\mathrm{GP}}$. The fragments are strongly overlapping in space. The results are obtained and analyzed analytically as well as numerically. The implications are discussed.Comment: 12 pages, 4 figure

Solitary waves and yrast states in Bose-Einstein condensed gases of atoms

Considering a Bose-Einstein condensed gas confined in one dimension with periodic boundary conditions, we demonstrate that, very generally, solitary-wave and rotational excitations coincide. This exact equivalence allows us to establish connections between a number of effects that are present in these two problems, many of which have been studied using the mean-field approximation.Comment: Revised version, where the generality of our arguments is presented more clearl

The multi-configurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems

The evolution of Bose-Einstein condensates is amply described by the time-dependent Gross-Pitaevskii mean-field theory which assumes all bosons to reside in a single time-dependent one-particle state throughout the propagation process. In this work, we go beyond mean-field and develop an essentially-exact many-body theory for the propagation of the time-dependent Schr\"odinger equation of $N$ interacting identical bosons. In our theory, the time-dependent many-boson wavefunction is written as a sum of permanents assembled from orthogonal one-particle functions, or orbitals, where {\it both} the expansion coefficients {\it and} the permanents (orbitals) themselves are {\it time-dependent} and fully determined according to a standard time-dependent variational principle. By employing either the usual Lagrangian formulation or the Dirac-Frenkel variational principle we arrive at two sets of coupled equations-of-motion, one for the orbitals and one for the expansion coefficients. The first set comprises of first-order differential equations in time and non-linear integro-differential equations in position space, whereas the second set consists of first-order differential equations with time-dependent coefficients. We call our theory multi-configurational time-dependent Hartree for bosons, or MCTDHB($M$), where $M$ specifies the number of time-dependent orbitals used to construct the permanents. Numerical implementation of the theory is reported and illustrative numerical examples of many-body dynamics of trapped Bose-Einstein condensates are provided and discussed.Comment: 30 pages, 2 figure

Artificial intelligence and robots inindividuals’ lives: how to aligntechnological possibilities andethical issues

Purpose: This paper reports the panel discussion on the topic of artificial intelligence (AI) and robots in our lives. This discussion was held at the Digitization of the Individual (DOTI) workshop at the International Conference on Information Systems in 2019. Three scholars (in alphabetical order: Ting-Peng Liang, Lionel Robert, and Suprateek Sarker) who have done AI- and robot-related research (to varying degrees) were invited to participate in the panel discussion. The panel was moderated by Manuel Trenz. Design/methodology/approach: This paper introduces the topic, chronicles the responses of the three panelists to the questions the workshop chairs posed, and summarizes their responses, such that readers can have an overview of research on AI and robots in individuals’ lives, and insights about future research directions. Findings: The panelists discussed four questions with regards to their research experiences on AI- and robot-related topics. They expressed their viewpoints on the underlying nature, potential, and effects of AI in work and personal life domains. They also commented on the ethical dilemmas for research and practice, and provided their outlook for future research in these emerging fields. Originality/values: This paper aggregates the panelists’ viewpoints, as expressed at the DOTI workshop. Crucial ethical and theoretical issues related to AI and robots in both work and personal life domains are addressed. Promising research directions to these cutting-edge research fields are also proposed

On the intensity interferometry and the second-order correlation function g(2)g^{(2)} in astrophysics

Most observational techniques in astronomy can be understood as exploiting the various forms of the first-order correlation function g^(1). As however demonstrated by the Narrabri Stellar Intensity Interferometer back in the 1960's by Hanbury Brown & Twiss, and which is the first experiment to measure the second-order correlation function g^(2), light can carry more information than simply its intensity, spectrum and polarization. Since this experiment, theoretical and laboratory studies of non-classical properties of light have become a very active field of research, namely quantum optics. Despite the variety of results in this field, astrophysics remained focused essentially on first-order coherence. In this paper, we study the possibility that quantum properties of light could be observed in cosmic sources. We provide the basic mathematical ingredients about the first and the second order correlation functions, applied to the modern context of astronomical observations. The exploitation of g^(2) is certainly richer than what a modern intensity interferometer could bring and is particularly interesting for sources of non-thermal light. We conclude by briefly presenting why microquasars in our galaxy and their extragalactic parents can represent an excellent first target in the optical/near-infrared where to observe non-thermal light, and test the use of g^(2) in astrophysical sources.Comment: 10 pages, accepted for publication in A&A. Vastly rewritten. Much more precise and (hopefully) accurat

Searching For Transiting Circumbinary Planets in CoRoT and Ground-Based Data Using CB-BLS

Aims. We search for transiting circumbinary (CB) planets around eclipsing binaries (EBs). Methods. CB-BLS is a recently-introduced algorithm for the detection of transiting CB planets around EBs.We describe progress in search sensitivity, generality and capability of CB-BLS, and detection tests of CB-BLS on simulated data. We also describe an analytical approach for the determination of CB-BLS detection limits, and a method for the correct detrending of intrinsically-variable stars. Results. We present some blind-tests with simulated planets injected to real CoRoT data. The presented upgrades to CB-BLS allowed it to detect all the blind tests successfully, and these detections were in line with the detection limits analysis. We also correctly detrend bright eclipsing binaries from observations by the TrES planet search, and present some of the first results of applying CB-BLS to multiple real light curves from a wide-field survey. Conclusions. CB-BLS is now mature enough for its application to real data, and the presented processing scheme will serve as the template for our future applications of CB-BLS to data from wide-field surveys such as CoRoT. Being able to put constraints even on non-detection will help to determine the correct frequency of CB planets, contributing to the understanding of planet formation in general. Still, searching for transiting CB planets is still a learning experience, similarly to the state of transiting planets around single stars only a few years ago. The recent rapid progress in this front, coupled with the exquisite quality of space-based photometry, allows to realistically expect that if transiting CB planets exist - then they will soon be found.Comment: A&A accepted. Presented at the 1st CoRoT symposium. Note table 3 is too wide in this version, but omitted data is of minor significance. 10 pages, 10 figures, 3 table

Exact quantum dynamics of bosons with finite-range time-dependent interactions of harmonic type

The exactly solvable quantum many-particle model with harmonic one- and two-particle interaction terms is extended to include time-dependency. We show that when the external trap potential and finite-range interparticle interaction have a time-dependency the exact solutions of the corresponding time-dependent many-boson Schr\"odinger equation are still available. We use these exact solutions to benchmark the recently developed multiconfigurational time-dependent Hartree method for bosons (MCTDHB) [Phys. Rev. Lett. {\bf 99}, 030402 (2007), Phys. Rev. A {\bf 77}, 033613 (2008)]. In particular, we benchmark the MCTDHB method for: (i) the ground state; (ii) the breathing many-body dynamics activated by a quench scenario where the interparticle interaction strength is suddenly turned on to a finite value; (iii) the non-equilibrium dynamic for driven scenarios where both the trap- and interparticle-interaction potentials are {\it time-dependent}. Excellent convergence of the ground state and dynamics is demonstrated. The great relevance of the self-consistency and time-adaptivity, which are the intrinsic features of the MCTDHB method, is demonstrated by contrasting the MCTDHB predictions and those obtained within the standard full configuration interaction method spanning the Fock space of the same size, but utilizing as one-particle basis set the fixed-shape eigenstates of the one-particle potential. Connections of the model's results to ultra-cold Bose-Einstein condensed systems are addressed.Comment: 31 pages, 5 figure