Ofir E. Alon

Exact Quantum Dynamics of a Bosonic Josephson Junction

The quantum dynamics of a one-dimensional bosonic Josephson junction is studied by solving the time-dependent many-boson Schrödinger equation numerically exactly. Already for weak interparticle interactions and on short time scales, the commonly employed mean-field and many-body methods are found to deviate substantially from the exact dynamics. The system exhibits rich many-body dynamics such as enhanced tunneling and a novel equilibration phenomenon of the junction depending on the interaction, which is attributed to a quick loss of coherence.

Unified view on multiconfigurational time propagation for systems consisting of identical particles

We show that the successful and formally exact multiconfigurational time-dependent Hartree method (MCTDH) takes on a unified and compact form when specified for systems of identical particles (MCTDHF for fermions MCTDHB for bosons). In particular the equations of motion for the orbitals depend explicitly and solely on the reduced one- and two-body density matrices of the systems many-particle wave function. We point out that this appealing representation of the equations of motion opens up further possibilities for approximate propagation schemes.

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

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

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

trapped bosons interacting via a general two-body potential. The many-body solution of this system is expanded over orthogonal many-body basis functions (configurations). In this theory both the many-body basis functions and the respective expansion coefficients are treated as variational parameters. The optimal variational parameters are obtained self-consistently by solving a coupled system of noneigenvalue\char22{}generally integro-differential\char22{}equations to get the one-particle functions and by diagonalizing the secular matrix problem to find the expansion coefficients. We call this theory multiconfigurational Hartree theory for bosons or

Pathway from condensation via fragmentation to fermionization of cold bosonic systems.

\mathrm{MCHB}(M)

How an interacting many-body system tunnels through a potential barrier to open space.

, where

The solution of the time‐dependent Schrödinger equation by the (t,t’) method: Multiphoton ionization/dissociation probabilities in different gauges of the electromagnetic potentials

M

General mapping for bosonic and fermionic operators in Fock space

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. We show that in the limiting cases of one configuration the theory boils down to the well-known Gross-Pitaevskii and the recently developed multi-orbital mean fields. The invariance of the complete solution with respect to unitary transformations of the one-particle functions is utilized to find the solution with the minimal number of contributing configurations. In the second part of our work we implement and apply the developed theory. 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

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

\mathrm{MCHB}(M)