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 manybody methods are found to deviate substantially from the exact dynamics. The system exhibits rich many-body dynamics like enhanced tunneling and a novel equilibration phenomenon of the junction depending on the interaction, attributed to a quick loss of coherence.

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 interparticle interaction have a time dependency, the numerically exact solutions of the corresponding time-dependent many-boson Schrödinger 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. 99, 030402 (2007); Phys. Rev. A 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 nonequilibrium dynamic for driven scenarios where both the trap-and interparticle-interaction potentials are 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 a 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 ultracold Bose-Einstein condensed systems are addressed.

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 Schr\"odinger 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.Comment: 40 pages, 6 figure

Single experimental shots of ultracold quantum gases sample the many-particle probability distribution. In a few cases such single shots could be successfully simulated from a given many-body wavefunction 1-4 , but for realistic time-dependent many-body dynamics this has been di cult to achieve. Here, we show how single shots can be simulated from numerical solutions of the time-dependent many-body Schrödinger equation. Using this approach, we provide first-principle explanations for fluctuations in the collision of attractive Bose-Einstein condensates (BECs), for the appearance of randomly fluctuating vortices and for the centre-of-mass fluctuations of attractive BECs in a harmonic trap. We also show how such simulations provide full counting distributions and correlation functions of any order. Such calculations have not been previously possible and our method is broadly applicable to many-body systems whose phenomenology is driven by information beyond what is typically available in low-order correlation functions.A postulate of quantum mechanics states that the positions r 1 , . . . , r N of N particles measured in an experiment are distributed according to the N -particle probability density P(r 1 , . . . , r N ) = |Ψ (r 1 , . . . , r N )| 2 , where Ψ (r 1 , . . . , r N ) is the manybody wavefunction of the system. In many experiments the positions of individual particles cannot be measured directly. Ultracold atom experiments provide a rare exception to this rule, which is why we focus on ultracold atoms in the following, but the concept is completely general. If Ψ (r 1 , . . . , r N ) is known, single experimental shots can be simulated by drawing the positions of all particles from P(r 1 , . . . , r N ), which results in a vector of positions (r 1 , . . . , r N ) that we refer to as a single shot. This has been realized for time-invariant many-body systems 1-4 . However, for time-dependent many-body systems it has remained a challenge. The difficulty stems from the fact that the functional form of the wavefunction is generally not known in many-body dynamics.Attempts at simulating single shots have been reported in the context of semiclassical dynamics: several authors have interpreted classical trajectories obtained within the truncated Wigner approximation as individual realizations of experiments 5,6 . Under the strict condition that the Wigner function is non-negative, some authors consider this interpretation plausible 7 or have fewer objections to it 8 . Here we show that this interpretation must also be dismissed for positive Wigner functions (see Supplementary Information). Although quantum Monte Carlo algorithms 9 sample the N -particle probability to obtain lower ground state energies, for time-dependent many-body systems not even the nodal structure of the wavefunction is known in advance, and hence quantum Monte Carlo methods are less suited. For further details see Supplementary Information.For sampling P(r 1 , . . . , r N ) it helps to realize that P(r 1 , . . . , r N ) = P(r 1 )P(r 2 |r 1...