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Register a new userTwo Fermions in a double well: Exploring a fundamental building block of the Hubbard model
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We have prepared two ultracold fermionic atoms in an isolated double-well potential and obtained full control over the quantum state of this system. In particular, we can independently control the interaction strength between the particles, their tunneling rate between the wells and the tilt of the potential. By introducing repulsive (attractive) interparticle interactions we have realized the two-particle analog of a Mott-insulating (charge-density-wave) state. We have also spectroscopically observed how second-order tunneling affects the energy of the system. This work realizes the first step of a bottom-up approach to deterministically create a single-site addressable realization of a ground-state Fermi-Hubbard system.
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We investigate the origin of a disagreement between the two-mode model and the exact Gross-Pitaevskii dynamics applied to double-well systems. In general this model, even in its improved version, predicts a faster dynamics and underestimates the critical population imbalance separating Josephson and self-trapping regimes. We show that the source of this mismatch in the dynamics lies in the value of the on-site interaction energy parameter. Using simplified Thomas-Fermi densities, we find that the on-site energy parameter exhibits a linear dependence on the population imbalance, which is also confirmed by Gross-Pitaevskii simulations. When introducing this dependence in the two-mode equations of motion, we obtain a reduced interaction energy parameter which depends on the dimensionality of the system. The use of this new parameter significantly heals the disagreement in the dynamics and also produces better estimates of the critical imbalance.
We present a two-band Bose-Hubbard model which is shown to be minimal in the necessary coupling terms at resonant tunneling conditions. The dynamics of the many-body problem is studied by sweeping the system across an avoided level crossing. The linear sweep generalizes Landau-Zener transitions from single-particle to many-body realizations. The temporal evolution of single- and two-body observables along the sweeps is investigated in order to characterize the non-equilibrium dynamics in our complex quantum system.
We compare and contrast the mean-field and many-body properties of a Bose-Einstein condensate trapped in a double well potential with a single impurity atom. The mean-field solutions display a rich structure of bifurcations as parameters such as the boson-impurity interaction strength and the tilt between the two wells are varied. In particular, we study a pitchfork bifurcation in the lowest mean-field stationary solution which occurs when the boson-impurity interaction exceeds a critical magnitude. This bifurcation, which is present for both repulsive and attractive boson-impurity interactions, corresponds to the spontaneous formation of an imbalance in the number of particles between the two wells. If the boson-impurity interaction is large, the bifurcation is associated with the onset of a Schroedinger cat state in the many-body ground state. We calculate the coherence and number fluctuations between the two wells, and also the entanglement entropy between the bosons and the impurity. We find that the coherence can be greatly enhanced at the bifurcation.
Based on the analytic model of Feshbach resonances in harmonic traps described in Phys. Rev. A 83, 030701 (2011) a Bose-Hubbard model is introduced that provides an accurate description of two atoms in an optical lattice at a Feshbach resonance with only a small number of Bloch bands. The approach circumvents the problem that the eigenenergies in the presence of a delta-like coupling do not converge to the correct energies, if an uncorrelated basis is used. The predictions of the Bose-Hubbard model are compared to non-perturbative calculations for both the stationary states and the time-dependent wavefunction during an acceleration of the lattice potential. For this purpose, a square-well interaction potential is introduced, which allows for a realistic description of Feshbach resonances within non-perturbative single-channel calculations.
We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double well potential. We consider in particular the case when one of the double wells confines excited states. Similarly to the known ground state oscillations, the states can tunnel between the wells experiencing the physics known for electrons in a Josephson junction, or be self-trapped. As the existence of dark solitons in a harmonic trap are continuations of such non-ground state excitations, one can view the Josephson-like oscillations as tunnelings of dark solitons. Numerical existence and stability analysis based on the full equation is performed, where it is shown that such tunneling can be stable. Through a numerical path following method, unstable tunneling is also obtained in different parameter regions. A coupled-mode system is derived and compared to the numerical observations. Regions of (in)stability of Josephson tunneling are discussed and highlighted. Finally, we outline an experimental scheme designed to explore such dark soliton dynamics in the laboratory.
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