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arXiv:1306.2711 · Physical Review A

Robustness of fragmented condensate many-body states for continuous distribution amplitudes in Fock space

Uwe R. Fischer, Bo Xiong

Published Nov 4, 2013• 11 citations
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Abstract

We consider a two-mode model describing scalar bosons with two-body interactions in a single trap, taking into account coherent pair exchange between the modes. It is demonstrated that the resulting fragmented many-body states with continuous (nonsingular) Fock-space distribution amplitudes are robust against perturbations due to occupation number and relative phase fluctuations, Josephson-type tunneling between the modes, and weakly broken parity of orbitals, as well as against perturbations due to interaction with a third mode.

DOI
10.1103/physreva.88.053602

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We consider a two-mode model describing scalar bosons with two-body interactions in a single trap, taking into account coherent pair exchange between the modes. It is demonstrated that the resulting fragmented many-body states with continuous (nonsingular) Fock-space distribution amplitudes are robust against perturbations due to occupation number and relative phase fluctuations, Josephson-type tunneling between the modes, and weakly broken parity of orbitals, as well as against perturbations due to interaction with a third mode.
We investigate whether the many-body ground states of bosons in a generalized two-mode model with localized inhomogeneous single-particle orbitals and anisotropic long-range interactions (e.g., dipole-dipole interactions) are coherent or fragmented. It is demonstrated that fragmentation can take place in a single trap for positive values of the interaction couplings, implying that the system is potentially stable. Furthermore, the degree of fragmentation is shown to be insensitive to small perturbations on the single-particle level.
We construct a two-state theoretical model describing attractively interacting bosons in a cylindrical harmonic potential of varied anisotropy. These systems exhibit true many-body ground-state energy minima stable against variations in single-particle state radial and axial widths and occupation number. The many-body ground state undergoes a phase transition from pure to fragmented as the aspect ratio increases above an anisotropy threshold dependent on the interaction energy per particle. This fragmentation is robust and does not require careful tuning of experimental parameters.
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.
We develop the Fock-space many-body quantum approach for large number of bosons, when the bosons occupy significantly only few modes. The approach is based on an analogy with the dynamics of a single particle of either positive or negative mass in a quantum potential, where the inverse number of bosons plays the role of Planck constant. As application of the method we consider the Bose-Einstein condensate in a double-well trap. The ground state of positive mass particle corresponds to the mean-field fixed point of lower energy, while that of negative mass to the excited fixed point. In the case of attractive BEC above the threshold for symmetry breaking, the ground state is a cat state and we relate this fact to the double-well shape of the quantum potential for the positive mass quantum particle. The tunneling energy splitting between the local Fock states of the cat state is shown to be extremely small for the nonlinearity parameter just above the critical value and exponentially decreasing with the number of atoms. In the repulsive case, the phase locked (πππ-phase) macroscopic quantum self-trapping of BEC is related to the double-well structure of the potential for the negative mass quantum particle. We also analyze the running phase macroscopic quantum self-trapping state and show that it is subject to quantum collapses and revivals. Moreover, the quantum dynamics just before the first collapse of the running phase shows exponential growth of dispersion of the quantum phase distribution which may explain the growth of the phase fluctuations seen in the experiment on the macroscopic quantum self-trapping.
We theoretically investigate the possibility of performing high precision estimation of an externally imposed acceleration using scalar bosons in a single-well trap. We work at the level of a two-mode truncation, valid for weak to intermediate two-body interaction couplings. The splitting process into two modes is in our model entirely caused by the interaction between the constituent bosons and is hence neither due to an externally imposed double-well potential nor due to populating a spinor degree of freedom. The precision enhancement gained by using various initial quantum states using a two-mode bosonic system is well established. Here we therefore instead focus on the effect of the intrinsic dynamics on the precision, where, in a single well, the Hamiltonian assumes a form different from that of the typical double-well case. We demonstrate how interactions can significantly increase the quantum Fisher information maximized over initial states as well as the quantum Fisher information for a fragmented or a coherent state, the two many-body states that can commonly represent the ground state of our system.
We present a theory of measurement-induced interference for weakly interacting Bose-Einstein-condensed gases. The many-body state resulting from the evolution of an initial fragmented (Fock) state can be approximated as a continuous superposition of Gross-Pitaevskii (GP) states; the measurement breaks the initial phase symmetry, producing a distribution pattern corresponding to only one of the GP solutions. We discuss also analytically solvable models, such as two-mode on-chip adiabatic recombination and soliton generation in quasi-one-dimensional condensates.