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Register a new userQuantum chaos in a Bose-Hubbard dimer with modulated tunnelling
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In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically evolving state that are correlated with the presence of chaos in the classical limit. We propose the statistical distance between initially similar number distributions as a reliable measure to distinguish regular from chaotic behaviour in the quantum dynamics. Besides being experimentally accessible, number distributions can be efficiently reconstructed numerically from binned phase-space trajectories in a truncated Wigner approximation. Although the evolving Wigner function becomes very irregular in the chaotic regions, the truncated Wigner method is nevertheless able to capture accurately the beyond mean-field dynamics.
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We theoretically explore quantum correlation properties of a dissipative Bose-Hubbard dimer in presence of a coherent drive. In particular, we focus on the regime where the semiclassical theory predicts a bifurcation with a spontaneous spatial symmetry breaking. The critical behavior in a well defined thermodynamical limit of large excitation numbers is considered and analyzed within a Gaussian approach. The case of a finite boson density is also examined by numerically integrating the Lindblad master equation for the density matrix. We predict the critical behavior around the bifurcation points accompanied with large quantum correlations of the mixed steady-state, in particular exhibiting a peak in the logarithmic entanglement negativity.
We consider a Bose-Hubbard trimer, i.e. an ultracold Bose gas populating three quantum states. The latter can be either different sites of a triple-well potential or three internal states of the atoms. The bosons can tunnel between different states with variable tunnelling strength between two of them. This will allow us to study; i) different geometrical configurations, i.e. from a closed triangle to three aligned wells and ii) a triangular configuration with a $pi$-phase, i.e. by setting one of the tunnellings negative. By solving the corresponding three-site Bose-Hubbard Hamiltonian we obtain the ground state of the system as a function of the trap topology. We characterise the different ground states by means of the coherence and entanglement properties. For small repulsive interactions, fragmented condensates are found for the $pi$-phase case. These are found to be robust against small variations of the tunnelling in the small interaction regime. A low-energy effective many-body Hamiltonian restricted to the degenerate manifold provides a compelling description of the $pi$-phase degeneration and explains the low-energy spectrum as excitations of discrete semifluxon states.
We analyze a modified Bose-Hubbard model, where two cavities having on-site Kerr interactions are subject to two-photon driving and correlated dissipation. We derive an exact solution for the steady state of this interacting driven-dissipative system, and use it show that the system permits the preparation and stabilization of pure entangled non-Gaussian states, so-called entangled cat states. Unlike previous proposals for dissipative stabilization of such states, our approach requires only a linear coupling to a single engineered reservoir (as opposed to nonlinear couplings to two or more reservoirs). Our scheme is within the reach of state-of-the-art experiments in circuit QED.
Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the system carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register and can introduce errors during error correction. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott Insulator phase transition. It was shown that by adding an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime.
Entanglement preparation and signal accumulation are essential for quantum parameter estimation, which pose significant challenges to both theories and experiments. Here, we propose how to utilize chaotic dynamics in a periodically driven Bose-Josephson system for achieving a high-precision measurement beyond the standard quantum limit (SQL). Starting from an initial non-entangled state, the chaotic dynamics generates quantum entanglement and simultaneously encodes the parameter to be estimated. By using suitable chaotic dynamics, the ultimate measurement precision of the estimated parameter can beat the SQL. The sub-SQL measurement precision scaling can also be obtained via specific observables, such as population measurements, which can be realized with state-of-art techniques. Our study not only provides new insights for understanding quantum chaos and quantum-classical correspondence, but also is of promising applications in entanglement-enhanced quantum metrology.
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