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Alexej I. Streltsov

Publications and source records attributed to Alexej I. Streltsov.

51 records · Page 3Linked to original sources
arXiv2008

Many-body theory for systems with particle conversion: Extending the multiconfigurational time-dependent Hartree method

We derive a multiconfigurational time-dependent Hartree theory for systems with particle conversion. In such systems particles of one kind can convert to another kind and the total number of particles varies in time. The theory thus extends the scope of the available and successful multiconfigurational time-dependent Hartree methods -- which were solely formulated for and applied to systems with a fixed number of particles -- to new physical systems and problems. As a guiding example we treat explicitly a system where bosonic atoms can combine to form bosonic molecules and vise versa. In the theory for particle conversion, the time-dependent many-particle wavefunction is written as a sum of configurations made of a different number of particles, and assembled from sets of atomic and molecular orbitals. Both the expansion coefficients and the orbitals forming the configurations are time-dependent quantities that are fully determined according to the Dirac-Frenkel time-dependent variational principle. Particular attention is paid to the reduced density matrices of the many-particle wavefunction that appear in the theory and enter the equations of motion. There are two kinds of reduced density matrices: particle-conserving reduced density matrices which directly only couple configurations with the same number of atoms and molecules, and particle non-conserving reduced density matrices which couple configurations with a different number of atoms and molecules. Closed-form and compact equations of motion are derived for contact as well as general two-body interactions, and their properties are analyzed and discussed.

quant-ph↗
arXiv2008

Reduced density matrices and coherence of trapped interacting bosons

The first- and second-order correlation functions of trapped, interacting Bose-Einstein condensates are investigated numerically on a many-body level from first principles. Correlations in real space and momentum space are treated. The coherence properties are analyzed. The results are obtained by solving the many-body Schrödinger equation. It is shown in an example how many-body effects can be induced by the trap geometry. A generic fragmentation scenario of a condensate is considered. The correlation functions are discussed along a pathway from a single condensate to a fragmented condensate. It is shown that strong correlations can arise from the geometry of the trap, even at weak interaction strengths. The natural orbitals and natural geminals of the system are obtained and discussed. It is shown how the fragmentation of the condensate can be understood in terms of its natural geminals. The many-body results are compared to those of mean-field theory. The best solution within mean-field theory is obtained. The limits in which mean-field theories are valid are determined. In these limits the behavior of the correlation functions is explained within an analytical model.

cond-mat.other↗
arXiv2007

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.

cond-mat.other↗
arXiv2007

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 Schrödinger 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.

cond-mat.other↗
arXiv2006

Role of excited states in the splitting dynamics of interacting Bose-Einstein condensates when ramping-up a barrier

An essentially-exact approach to compute the wavefunction in the time-dependent many-boson Schrödinger equation is derived and employed to study accurately the process of splitting a trapped condensate when ramping-up a barrier such that a double-well is formed. We follow the role played by many-body excited states during the splitting process. Among others, a 'counter-intuitive' regime is found in which the evolution of the condensate when the barrier is ramped-up sufficiently slow {\it is not} to the ground-state which is a fragmented condensate, but to a low-lying excited-state which is a coherent condensate. Experimental implications are discussed.

cond-mat.other↗
arXiv2006

Cold atoms in real-space optical lattices

Cold atoms in optical lattices are described in {\it real space} by multi-orbital mean-field Ansätze. 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.

cond-mat.other↗
arXiv2006

General variational many-body theory with complete self-consistency for trapped bosonic systems

In this work we develop a complete variational many-body theory for a system of $N$ trapped bosons interacting via a general two-body potential. In this theory both the many-body basis functions {\em and} the respective expansion coefficients are treated as variational parameters. The optimal variational parameters are obtained {\em self-consistently} by solving a coupled system of non-eigenvalue -- generally integro-differential -- equations to get the one-particle functions and by diagonalizing the secular matrix problem to find the expansion coefficients. We call this theory multi-configurational Hartree for bosons or MCHB(M), where M specifies explicitly the number of one-particle functions used to construct the configurations. General rules for evaluating the matrix elements of one- and two-particle operators are derived and applied to construct the secular Hamiltonian matrix. We discuss properties of the derived equations. It is demonstrated that for any practical computation where the configurational space is restricted, the description of trapped bosonic systems strongly depends on the choice of the many-body basis set used, i.e., self-consistency is of great relevance. As illustrative examples we consider bosonic systems trapped in one- and two-dimensional symmetric and asymmetric double-well potentials. We demonstrate that self-consistency has great impact on the predicted physical properties of the ground and excited states and show that the lack of self-consistency may lead to physically wrong predictions. The convergence of the general MCHB(M) scheme with a growing number M is validated in a specific case of two bosons trapped in a symmetric double-well.

cond-mat.other↗
arXiv2005

Coupled-Cluster Theory for Systems of Bosons in External Traps

A coupled-cluster approach for systems of $N$ bosons in external traps is developed. In the coupled-cluster approach the exact many-body wavefunction is obtained by applying an exponential operator $\exp{T}$ to the ground configuration $|ϕ_0>$. The natural ground configuration for bosons is, of course, when all reside in a single orbital. Because of this simple structure of $|ϕ_0>$, the appearance of excitation operators $T=\sum_{n=1}^N T_n$ for bosons is much simpler than for fermions. We can treat very large numbers of bosons with coupled-cluster expansions. In a substantial part of this work, we address the issue of size consistency for bosons and enquire whether truncated coupled-cluster expansions are size consistent. We show that, in contrast to the familiar situation for fermions for which coupled-cluster expansions are size consistent, for bosons the answer to this question {\it depends} on the choice of ground configuration. Utilizing the natural ground configuration, working equations for the truncated coupled-cluster with $T=T_1+T_2$, i.e., coupled-cluster singles doubles (CCSD) are explicitly derived. Finally, an illustrative numerical example for a condensate with up to N=10000 bosons in an harmonic trap is provided and analyzed. The results are highly promising.

cond-mat.other↗
arXiv2005

Exact ground state of finite Bose-Einstein condensates on a ring

The exact ground state of the many-body Schrödinger equation for $N$ bosons on a one-dimensional ring interacting via pairwise $δ$-function interaction is presented for up to fifty particles. The solutions are obtained by solving Lieb and Liniger's system of coupled transcendental equations for finite $N$. The ground state energies for repulsive and attractive interaction are shown to be smoothly connected at the point of zero interaction strength, implying that the \emph{Bethe-ansatz} can be used also for attractive interaction for all cases studied. For repulsive interaction the exact energies are compared to (i) Lieb and Liniger's thermodynamic limit solution and (ii) the Tonks-Girardeau gas limit. It is found that the energy of the thermodynamic limit solution can differ substantially from that of the exact solution for finite $N$ when the interaction is weak or when $N$ is small. A simple relation between the Tonks-Girardeau gas limit and the solution for finite interaction strength is revealed. For attractive interaction we find that the true ground state energy is given to a good approximation by the energy of the system of $N$ attractive bosons on an infinite line, provided the interaction is stronger than the critical interaction strength of mean-field theory.

cond-mat.other↗
arXiv2004

Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices

Quantum phases and phase transitions of weakly- to strongly-interacting bosonic atoms in deep to shallow optical lattices are described by a {\it single multi-orbital mean-field approach in real space}. For weakly-interacting bosons in 1D, the critical value of the superfluid to Mott insulator (MI) transition found is in excellent agreement with {\it many-body} treatments of the Bose-Hubbard model. For strongly-interacting bosons, (i) additional MI phases appear, for which two (or more) atoms residing in {\it each site} undergo a Tonks-Girardeau-like transition and localize and (ii) on-site excitation becomes the excitation lowest in energy. Experimental implications are discussed.

cond-mat.other↗
arXiv2004

Properties of fragmented repulsive condensates

Repulsive Bose-Einstein condensates immersed into a double-well trap potential are studied within the framework of the recently introduced mean-field approach which allows for bosons to reside in several different orthonormal orbitals. In the case of a one-orbital mean-field theory (Gross-Pitaevskii) the ground state of the system reveals a bifurcation scenario at some critical values of the interparticle interaction and/or the number of particles. At about the same values of the parameters the two-orbital mean-field predicts that the system becomes two-fold fragmented. By applying the three-orbital mean field we verify numerically that for the double-well external potential studied here the overall best mean-field is achieved with two orbitals. The variational principle minimizes the energy at a vanishing population of the third orbital. To discuss the energies needed to remove a boson from and the energies gained by adding a boson to the condensate, we introduce boson ionization potentials and boson affinities and relate them to the chemical potentials. The impact of the finite number of bosons in the condensate on these quantities is analyzed. We recall that within the framework of the multi-orbital mean-field theory each fragment is characterized by its own chemical potential. Finally, the stability of fragmented states is discussed in terms of the boson transfer energy which is the energy needed to transfer a boson from one fragment to another.

cond-mat.other↗
arXiv2004

Ground state fragmentation of repulsive BEC in double-trap potentials

The fragmentation of the ground state of a repulsive condensate immersed into a double-trap potential is found to be a general and critical phenomenon. It takes place for a given number of bosons if their scattering length is larger than some critical value or for a given value of the scattering length if the number of bosons is above some critical number. We demonstrate that the geometry of the inner trap determines these critical parameters while the number of the fragments and the fraction of bosons in the various fragments can be manipulated by the outer trap. There is also a maximal number of bosons for which the ground state is fragmented. If this number is exceeded, the fragmented state becomes a very low-lying excited state of the condensate. This maximal number of bosons can be substantially manipulated by varying the inner and outer traps. To study three-fold fragmentation we have chosen a potential well with two barriers as the inner trap and embedded by two types of outer ones. A many-fold fragmentation is also addressed.

cond-mat.other↗
arXiv2004

On interacting fermions and bosons with definite total momentum

Any {\it exact} eigenstate with a definite momentum of a many-body Hamiltonian can be written as an integral over a {\it symmetry-broken} function $Φ$. For two particles, we solve the problem {\it exactly} for all energy levels and any inter-particle interaction. Especially for the ground-state, $Φ$ is given by the simple Hartree-Fock/Hartree ansatz for fermions/bosons. Implications for several and many particles as well as a numerical example are provided.

quant-ph↗
arXiv2004

Continuous configuration-interaction for condensates in a ring

A continuous configuration-interaction approach for condensates in a ring is introduced. In its simplest form this approach utilizes for attractive condensates the Gross-Pitaevskii symmetry-broken solution and arrives at a ground-state of correct symmetry. Furthermore, the energy found is {\it lower} than the Gross-Pitaevskii one and, with increasing number of particles and/or strength of inter-particle interaction, is even {\it lower} than that accessed by tractable diagonalization of the many-body Hamiltonian. Implications also to excited states are briefly discussed.

cond-mat.other↗