Quantum Manifestation of the Classical Bifurcation in the Driven Dissipative Bose-Hubbard Dimer.

We analyze the classical and quantum dynamics of the driven dissipative Bose-Hubbard dimer. Under variation of the driving frequency, the classical system is shown to exhibit a bifurcation to the limit cycle, where its steady-state solution corresponds to periodic oscillation with the frequency unrelated to the driving frequency. This bifurcation is shown to lead to a peculiarity in the single-particle density matrix of the quantum system.

Bistability and chaos-assisted tunneling in dissipative quantum systems.

We revisit the problem of quantum bi- and multistability by considering the dissipative double resonance model. For a large driving frequency, this system has a simpler phase structure than the driven dissipative nonlinear oscillator, the paradigm model for classical and quantum bistability. This allows us to obtain an analytical estimate for the lifetime of quantum limit cycles.

Quantum entanglement and the Born-Markov approximation for an open quantum system.

We revisit the Born-Markov approximation for an open quantum system by considering a microscopic model of the bath, namely, the Bose-Hubbard chain in the parameter region where it is chaotic in the sense of quantum chaos. It is shown that strong ergodic properties of the bath justify all approximations required for deriving the Markovian master equation from the first principles.

Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional lattice. II. Arbitrary electric field directions.

We study the quantum dynamics of a charged particle in a two-dimensional lattice, subject to constant and homogeneous electric and magnetic fields. We find that different regimes characterize these motions, depending on a combination of conditions, corresponding to weak and strong electric field intensities, rational or irrational directions of the electric field with respect to the lattice, and small or large values of the magnetic (Peierls) phase.

Nucleation in finite topological systems during continuous metastable quantum phase transitions.

Finite topological quantum systems can undergo continuous metastable quantum phase transitions to change their topological nature. Here we show how to nucleate the transition between ring currents and dark soliton states in a toroidally trapped Bose-Einstein condensate. An adiabatic passage to wind and unwind its phase is achieved by explicit global breaking of the rotational symmetry.

Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional lattice.

This paper studies the quantum dynamics of a charged particle in a two-dimensional square lattice, under the influence of electric and magnetic fields, the former being aligned with one of the lattice axes and the latter perpendicular to the lattice plane. While in free space these dynamics consist of uniform motions in the direction orthogonal to the electric field vector, we find that, in a lattice, this directed drift takes place only for specific initial conditions and for electric field magnitudes smaller than a critical value. Otherwise, the quantum wave packet spreads ballistically in both directions orthogonal to the electric field.

Semiclassical analysis of the Bogoliubov spectrum in the Bose-Hubbard model.

We analyze the Bogoliubov spectrum of the Bose-Hubbard model with a finite number of sites and Bose particles by using a semiclassical approach. This approach allows us to take into account the finite-size effects responsible for evolution of the Bogoliubov spectrum into an irregular (chaotic) spectrum at higher energies. A manifestation of this transition for the excitation dynamics of the Bose-Hubbard system is discussed as well.

Semiclassical quantization of the Bogoliubov spectrum.

We analyze the Bogoliubov spectrum of the three-site Bose-Hubbard model with a finite number of Bose particles by using a semiclassical approach. The Bogoliubov spectrum is shown to be associated with the low-energy regular component of the classical Hubbard model. We identify the full set of the integrals of motion of this regular component and, quantizing them, obtain the energy levels of the quantum system.

Atomic current across an optical lattice.

We devise a microscopic model for the emergence of a collision-induced, fermionic atomic current across a tilted optical lattice. Tuning the--experimentally controllable--parameters of the microscopic dynamics allows us to switch from Ohmic to negative differential conductance.

Interaction-induced decoherence of atomic BLOCH oscillations.

We show that the energy spectrum of the Bose-Hubbard model amended by a static field exhibits Wigner-Dyson level statistics. In itself a characteristic signature of quantum chaos, this induces the irreversible decay of Bloch oscillations of cold, interacting atoms loaded into an optical lattice, and provides a Hamiltonian model for interaction-induced decoherence.

Floquet-Bloch operator for the Bose-Hubbard model with static field.

This paper deals with the spectral properties of the one-dimensional Bose-Hubbard Hamiltonian amended by an external static field-a model for cold spinless atoms loaded in a quasi-one-dimensional optical lattice and subject to an additional static (for example, gravitational) force. The analysis is performed in terms of the Floquet-Bloch operator, defined as the evolution operator of the system over one Bloch period. Depending on the particular choice of parameters, the spectrum is found to be either regular or chaotic.

New bloch period for interacting cold atoms in 1D optical lattices.

This paper studies Bloch oscillations of ultracold atoms in an optical lattice, in the presence of atom-atom interactions. A new, interaction-induced Bloch period is identified. Analytical results are corroborated by realistic numerical calculations.

Quantum coherence, evolution of the Wigner function, and transition from quantum to classical dynamics for a chaotic system.

The paper deals with dynamics of a quantum chaotic system under influence of an environment. The effect of an environment is known to destroy the quantum coherence and can convert the quantum dynamics of a system to classical. We use a semiclassical technique for studying the process of decoherence.