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arXiv:0803.4048

Macroscopic quantum self-trapping in a Bose-Josephson junction with fermions

Santiago F. Caballero-Benítez, Elena A. Ostrovskaya, M. Gulácsi, Yuri S. Kivshar

Published Mar 28, 2008• 0 citations
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Abstract

We study the macroscopic quantum self-trapping effect in a mixture of Bose-Einstein condensate and a large number of quantum degenerate fermions, trapped in a double-well potential with a variable separation between the wells. The large number of fermions localized in each well form quasi-static impurities that affect the dynamics of the bosonic cloud. Our semi-analytical analysis based on a mean-field model shows that main features of macroscopic quantum self trapping in a pure bosonic system are radically modified by the influence of fermions, with both the onset of self-trapping and properties of the self-trapped state depending on the fermion concentration as well as on the type of inter-species interaction. Remarkably, repulsive inter-species interaction leads to population inversion of the bosonic energy levels in the trapping potential and hence to the inversion of symmetry of the macroscopic wavefunction. Realistic physical estimates are given based on experimental parameters for a $^{40}$K-$^{87}$Rb system.

DOI
10.48550/arxiv.0803.4048

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We study the macroscopic quantum self-trapping effect in a mixture of Bose-Einstein condensate and a large number of quantum degenerate fermions, trapped in a double-well potential with a variable separation between the wells. The large number of fermions localized in each well form quasi-static impurities that affect the dynamics of the bosonic cloud. Our semi-analytical analysis based on a mean-field model shows that main features of macroscopic quantum self trapping in a pure bosonic system are radically modified by the influence of fermions, with both the onset of self-trapping and properties of the self-trapped state depending on the fermion concentration as well as on the type of inter-species interaction. Remarkably, repulsive inter-species interaction leads to population inversion of the bosonic energy levels in the trapping potential and hence to the inversion of symmetry of the macroscopic wavefunction. Realistic physical estimates are given based on experimental parameters for a 40^{40}40K-87^{87}87Rb system.
We study the macroscopic quantum self-trapping effect in a mixture of Bose–Einstein condensate (BEC) and quantum degenerate fermions, confined in a double-well potential with a variable separation between the wells. The fermions form a finite-size cloud that affects the static and dynamical properties of the BEC. In particular, our quasi-analytical and numerical analysis based on a mean-field model shows that the main features of macroscopic quantum self-trapping in a pure bosonic system are modified by the influence of fermions. Both the onset of self-trapping and the properties of the self-trapped state depend on the amount of fermions in the system as well as on the type of inter-species interaction. The properties of the quantum degenerate mixture are explored using realistic parameters for a 40 K– 87 Rb system.
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In a double-well potential, a Bose-Einstein condensate exhibits Josephson oscillations or self-trapping, depending on its initial preparation and on the ratio of interparticle interaction to interwell tunneling. Here, we elucidate the role of the exchange symmetry for the dynamics with a mixture of two distinguishable species with identical physical properties, that is, which are governed by an isospecific interaction and external potential. In the mean-field limit, the spatial population imbalance of the mixture can be described by the dynamics of a single species in an effective potential with modified properties or, equivalently, with an effective total particle number. The oscillation behavior can be tuned by populating the second species while maintaining the spatial population imbalance and all other parameters constant. In the corresponding many-body approach, the single-species description approximates the full counting statistics well also outside the realm of spin-coherent states. The method is extended to general Bose-Hubbard systems and to their classical mean-field limits, which suggests an effective single-species description of multicomponent Bose gases with weakly an-isospecific interactions.
We consider the tunneling properties of a single fermionic impurity immersed in a Bose-Einstein condensate in a double-well potential. For strong boson-fermion interaction, we show the existence of a tunnel resonance where a large number of bosons and the fermion tunnel simultaneously. We give analytical expressions for the line shape of the resonance using degenerate Brillouin-Wigner theory. We finally compute the time-dependent dynamics of the mixture. Using the fermionic tunnel resonances as a beam splitter for wave functions, we construct a Mach-Zehnder interferometer that allows complete population transfer from one well to the other by tilting the double-well potential and only taking into account the fermion's tunnel properties.
We investigate the fully quantum evolution of the population imbalance in a perfectly symmetric Bose-Josephson junction modeled by a two-mode Bose-Hubbard Hamiltonian, focusing on the validity of macroscopic quantum self-trapping beyond the mean-field theory. We show that for any finite number of particles, the exact quantum dynamics leads to the breakdown of macroscopic quantum self-trapping after a finite time, regardless of the initial state. Using the symmetries of the Bose-Hubbard Hamiltonian, we provide a mathematical demonstration of this result and analyze the spectral properties governing the dynamics. We identify a branching behavior in the eigenvalue differences and a nontrivial structure of the population-imbalance amplitudes. These features allow us to distinguish two clearly different dynamical regimes and to elucidate the mechanism leading to the emergence of a quasi–macroscopic quantum self-trapping regime for large particle numbers. These findings bridge the gap between mean-field predictions and exact quantum dynamics and provide insight into the emergence of classical nonlinear behavior from finite quantum many-body systems.
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