Bloch oscillations and Zener tunneling in two-dimensional photonic lattices

We report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square lattice superimposed on a refractive index ramp. We observe oscillations of the beam inside the first Brilloin zone and tunneling of light from the first to the higher-order bands of the lattice band gap spectrum.     

Light propagation and oscillations in two-dimensional graded square photonic lattices

We have studied the optical oscillations and transitions in two-dimensional graded square photonic lattices (GSPL) formed by evanescently coupled optical waveguide arrays with parabolic confinements in all transverse directions. When we retain only the orthogonal couplings, decoupled one-dimensional models can be used to obtain the various normal modes, which correspond to a variety of optical oscillations. Six different combinations of Bloch oscillation (BO), dipole oscillation (DO), and reflections from the boundaries of finite lattice are classified on the phase diagram. If we include the diagonal couplings, transitions among various oscillations are obtained with the Hamiltonian optics approach and confirmed by the field-evolution analysis. We studied in detail a typical example in which a switching occurs from the constituent BO and DO to both DOs in the two orthogonal directions. The method to analyze the complex field evolution in GSPL can be extended to similar systems with different types of lattices and/or confinements.     

Simulating cyclotron-Bloch dynamics of a charged particle in a 2D lattice by means of cold atoms in driven quasi-1D optical lattices

Quantum dynamics of a charged particle in a two-dimensional (2D) lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations (the case of vanishing electric field) and Bloch oscillations (zero magnetic field), details of which has not yet been completely understood. In the present work we suggest to study this problem by using cold atoms in optical lattices. We introduce a one-dimensional (1D) model which can be easily realized in laboratory experiments with quasi-1D optical lattices and show that this model captures many features of the cyclotron-Bloch dynamics of the quantum particle in 2D square lattices.     

Atomic Bloch-Zener oscillations and Stückelberg interferometry in optical lattices

We report on experiments investigating quantum transport and band interferometry of an atomic Bose-Einstein condensate in an optical lattice with a two-band miniband structure, realized with a Fourier-synthesized optical lattice potential. Bloch-Zener oscillations, the coherent superposition of Bloch oscillations and Landau-Zener tunneling between the two bands, are observed. When the relative phase between paths in different bands is varied, an interference signal is observed, demonstrating the coherence of the dynamics in the miniband system. Measured fringe patterns of this Stückelberg interferometer allow us to interferometrically map out the band structure of the optical lattice over the full Brillouin zone.     

Beam dynamics in PT symmetric optical lattices

The possibility of parity-time (PT) symmetric periodic potentials is investigated within the context of optics. Beam dynamics in this new type of optical structures is examined in detail for both one- and two-dimensional lattice geometries. It is shown that PT periodic structures can exhibit unique characteristics stemming from the nonorthogonality of the associated Floquet-Bloch modes. Some of these features include double refraction, power oscillations, and eigenfunction unfolding as well as nonreciprocal diffraction patterns.     

Dipole and Bloch oscillations of cold atoms in a parabolic lattice

The paper studies the dynamics of a Bose-Einstein condensate loaded in a 1D parabolic optical lattice and excited by a sudden shifting of the lattice center. Depending on the initial shift, this dynamics is either the dipole or Bloch oscillations of the atoms. The effects of the dephasing and atom-atom interactions on the above atomic oscillations are discussed.     

Oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap

In this work, we study parametric excitations in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric excitations (oscillations of the BEC width). Regular oscillations disappear when one of the competing factors, i.e. the strength of harmonic trap or the strength of optical lattice, dominates. Parametric instabilities (chaotic dynamics) arise for large variations in the strength of the optical lattice.     

Feedback control of atomic motion in an optical lattice

We demonstrate a real-time feedback scheme to manipulate wave-packet oscillations of atoms in an optical lattice. The average position of the atoms in the lattice wells is measured continuously and nondestructively. A feedback loop processes the position signal and translates the lattice potential. Depending on the feedback loop characteristics, we find amplification, damping, or an entire alteration of the wave-packet oscillations. Our results are well supported by simulations.     

Properties of nano-scale soliton-like excitations in two-dimensional lattice layers

Nano-scale soliton-like supersonic, intrinsic localized excitations in two-dimensional atomic anharmonic lattice layers are here considered. We study the propagation, the velocity and other soliton-like features at head-on collisions of such lattice excitations created by using suitable initial mechanical and thermal conditions. Noteworthy is that narrow, highly-energetic solitons moving along one lattice row are very robust, accompanied by weak anti-phase oscillations in the lateral direction.     

Two-dimensional imaging of gauge fields in optical lattices

We propose a scheme to generate an arbitrary Abelian vector potential for atoms trapped in a two-dimensional optical lattice. By making the optical lattice potential dependent on the atomic state, we transform the problem into that of a two-dimensional imaging. It is shown that an arbitrarily fine pattern of the gauge field in the lattice can be realized without need of diffraction-limited imaging.     

Collective properties of a relativistic electron beam injected into a high intensity optical lattice

Behaviour of a relativistic electron bunch, injected and trapped in a high intensity optical lattice resulting from the interference of two laser beams is studied. The optical lattice modifies the phase space distribution of the electron bunch due to the trapping and compression of the electrons by a ponderomotive force. High-frequency longitudinal beam eigenmodes of the trapped electron bunch are described in the framework of fluid and kinetic models. Such beam oscillations are expected to play a pivotal role in a stimulated Raman scattering of laser beams on the electrons.     

Matter-wave gap solitons in atomic band-gap structures

We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic crystal for light waves. We study in detail the case of a two-dimensional square optical lattice and show that this atomic band-gap structure allows nonlinear localization of atomic Bloch waves in the form of two-dimensional matter-wave gap solitons.     

光晶格势阱中二元凝聚体的矢量孤子的振荡和分裂

考虑外部囚禁势阱为光晶格势阱,研究了二元玻色-爱因斯坦凝聚体中亮-亮孤子的动力学行为.结果表明,亮-亮孤子的运动方向和振荡行为可以分别通过调节光晶格势阱的晶格常数和势阱深度来控制.进一步地,亮-亮孤子还可以被局域在光晶格势阱中,并且随着势阱深度的增加,局域孤子会产生分裂行为.     

Semiclassical and quantum transport in the two-dimensional electron gas in a hard-wall antidot lattice

Commensurate peaks of magnetoresistance and Shubnikov-de Haas and Aharonov-Bohm oscillations in the two-dimensional electron gas (2DEG) in a lattice of antidots with hard potential walls have been experimentally studied. The behavior of both classical magnetoresistance peaks and quantum oscillations has been shown to fundamentally depend on the lattice period and the antidot size, as well as on the smoothness of the potential at the 2DEG-antidot interface. This result indicates the necessity of revising the interpretation of all numerous experiments with antidot lattices, since this effect has been explicitly or implicitly neglected in them.     

Pinning of vortices in a Bose-Einstein condensate by an optical lattice

We consider the ground state of vortices in a Bose-Einstein condensate. We show that turning on a weak optical periodic potential leads to a transition from the triangular Abrikosov vortex lattice to phases where the vortices are pinned by the optical potential. We discuss the phase diagram of the system for a two-dimensional optical periodic potential with one vortex per optical lattice cell. We also discuss the influence of a one-dimensional optical periodic potential on the vortex ground state. The latter situation has no analog in other condensed-matter systems.     

Some dynamical properties of a two-dimensional Wigner crystal

Results for the static part of the ground state energy of the square and hexagonal two-dimensional Wigner lattices are given. The hexagonal lattice has the lower energy. Phonon dispersion curves and the vibrational zeropoint energy are calculated for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal χ_αβ(q) has been determined in the long wavelength limit in the presence of a static magnetic field perpendicular to the crystal, and explicit expressions have been obtained for the hexagonal lattice. Applying the analysis developed by Chiu and Quinn, the results for the susceptibility have been used to obtain the dispersion relation for the plasma oscillations in the electron crystal on the assumption that the crystal is embedded in a dielectric medium. The dispersion curves have been calculated for differing magnitudes of the applied magnetic field.     

Minibands of p-type δ-doping superlattices in GaAs

A microscopic theory is presented for high-field miniband transport in a two-dimensional superlattice. The energy transfer to the lateral electron motion is taken into account as well as scattering on polar optical phonons. Oscillatory current anomalies appear when the optical phonon frequency is a multiple of the Bloch frequency. The current oscillations, which are due to Wannier–Stark localization, are much more pronounced in a two-dimensional than in a three-dimensional system with a superlattice structure in one direction.     

Two-dimensional optical lattice solitons

We study various families of two-dimensional discrete or lattice solitons, and show that they are possible only when their power level exceeds a critical threshold. In addition, we show that gap-lattice solitons exist only when the lattice possesses a complete 2D band gap. Our results suggest that these conditions are universally valid, irrespective of the nature of the nonlinearity or the specific structure of the index lattice. The analysis explains fundamental aspects of behavior of two-dimensional discrete solitons that have been very recently observed in photosensitive optical crystals.     

Driving defect modes of Bose-Einstein condensates in optical lattices

We present an approximate analytical theory and direct numerical computation of defect modes of a Bose-Einstein condensate loaded in an optical lattice and subject to an additional localized (defect) potential. Some of the modes are found to be remarkably stable and can be driven along the lattice by means of a defect moving following a steplike function defined by the period of Josephson oscillations and the macroscopic stability of the atoms.     

Bose-Einstein Condensates in Optical Lattices with Higher-Order Interactions

The higher-order interactions of Bose-Einstein condensate in multi-dimensional optical lattices are discussed both analytically and numerically.It is demonstrated that the effects of the higher-order atomic interactions on the sound speed and the stabilities of Bloch waves strongly depend on the lattice strength.In the presence of higher-order effects,tighter and high-dimensional lattices are confirmed to be two positive factors for maintaining the system's energetic stability,and the dynamical instability of Bloch waves can take place simultaneously with the energetic instability.In addition,we find that the higher-order interactions exhibit a long-range behavior and the long-lived coherent Bloch oscillations in a tilted optical lattice exist.Our results provide an effective way to probe the higher-order interactions in optical lattices.