We study, analytically and numerically, the dynamics of interband transitions in two-dimensional hexagonal periodic photonic lattices. We develop an analytical approach employing the Bragg resonances of different types and derive the effective multi-level models of the Landau-Zener-Majorana type. For two-dimensional periodic potentials without a tilt, we demonstrate the possibility of the Rabi ...

We derive and apply an optical Bloch equation (OBE) model for describing collisions of ground and excited laser cooled alkali atoms in the presence of near-resonant light. Typically these collisions lead to loss of atoms from traps. We compare the results obtained with a quantum mechanical complex potential treatment, semiclassical Landau-Zener models with decay, and a quantum timedependent Mon...

We show by direct calculation starting from a microscopic model that the two-state system with timedependent energy levels in the presence of fast quantum noise obeys the master equation. The solution of master equation is found analytically and analyzed in a broad range of parameters. The fast transverse noise affects the transition probability during much longer time the accumulation time tha...

A qubit may undergo Landau–Zener transitions due to its coupling to one or several quantum harmonic oscillators. We show that for a qubit coupled to one oscillator, Landau–Zener transitions can be used for single-photon generation and for the controllable creation of qubit–oscillator entanglement, with state-of-the-art circuit QED as a promising realization. Moreover, for a qubit coupled to two...

A transition between energy levels at an avoided crossing is known as a Landau–Zener transition. When a two-level system (TLS) is subject to periodic driving with sufficiently large amplitude, a sequence of transitions occurs. The phase accumulated between transitions (commonly known as the Stückelberg phase) may result in constructive or destructive interference. Accordingly, the physical obse...

We discuss the interband light tunneling in a two-dimensional periodic photonic structure, as studied recently in experiments for optically induced photonic lattices [Trompeter, Phys. Rev. Lett. 96, 053903 (2006)]. We identify the Zener tunneling regime at the crossing of two Bloch bands, which occurs in the generic case of a Bragg reflection when the Bloch index crosses the edge of the irreduc...

A simple algorithm is presented based on a type of partial reverse engineering that generates an unlimited number of exact analytical solutions to the Schrödinger equation for a general time-dependent two-level Hamiltonian. I demonstrate this method by deriving exact solutions corresponding to fast control pulses that contain arbitrarily many tunable parameters. It is shown that the formalism i...

We formulate and approximately solve a specific many body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving rates. The structure of the theory suggests that this finding reflects a more general phenomenon in the physics of adiabatically driven many particle systems....

Temperature-independent magnetic viscosity in ferritin has been observed from ∼ 2 K down to 100 mK, proving that quantum tunneling plays the main role in these particles at low temperature. Magnetic relaxation has also been studied using the Landau-Zener method making the system crossing zero resonant field at different rates, α = dH/dt, ranging from 10 −5 to 10 −3 T/s, and at different tempera...