Optical lattices

Bragg diffraction on crystalline colloidal arrays Photonic crystal material is composed of a crystalline colloidal array that diffracts light at wavelengths determined by the optical lattice spacing, which is affected by the presence of analyte 5,14,15... 

Site-to-Site Population Transfer of a BEC in an Optical Lattice Using a Harmonic Potential... 

An interesting application of the fast-forward protocol is site-to-site population transfer of particles in a BEC confined on an optical lattice. As shown below, the features of that protocol differ somewhat between continuous and lattice systems. We consider a BEC subjected to an external potential that is a superposition of a lattice potential and a harmonic potential, with the representation... 

S. Masuda, K. Nakamura, and A. del Campo. High-fidelity rapid ground-state loading of an ultta-cold gas into an optical lattice. Phys. Rev. Lett., 113(6) 063003-063007(2014). 

AM of the coupling arises, for example, for radiative-decay modulation due to atomic motion through a high-Q cavity or a photonic crystal [68,69], or for atomic tunneling in optical lattices with time-varying lattice acceleration [59,70], Let the coupling be turned on and off periodically, for the time and tq -, respectively,... 

Since the Hamiltonian for atoms in accelerated optical lattices is similar to the Legett Hamiltonian for current-biased Josephson junctions [37], the present theory has been extended to describe effects of current modulations on the rate of macroscopic quanmm tunneling in Josephson junctions in Ref. [11]. 

Figure 7.19 Schematic of the Rydberg induced many-body interaction among ultracold Rb atoms in an optical lattice. Reproduced from Ref. [51] with permission from Springer.

If molecules are cooled to a very low temperature, their translational motion may be restricted by an application of an optical lattice. An optical lattice is an interference of counter-propagating laser beams, producing a standing wave of electric field. Molecules in the ground state placed in an optical lattice will be pushed toward regions of the field strength maxima. An optical lattice can... 

Figure 8.6 Collisions of ultracold molecules in a quasi-2D geometry. Presented are the rates of the loss of molecules from an optical lattice trap occurring due to chemical reactions. The squares represent the reactions of molecules prepared in the same (translational and internal) quantum states the circles are for collisions of molecules in different translational states but the same internal states the triangles are for molecules in different internal states. Adapted with permission from Ref. [1].

IThe name optic mode comes from the behavior of ionic crystals such as Na+Cl . When Na and Cl in a given cell move out of phase with each other, there is an oscillating electric dipole. Optical absorption will occur for light having frequency equal to that of the optic lattice mode. 

The second term is —3JN/16, when Tj is a two-dimensional classical spin, and is —3JN/% in the quantum-spin case. A total number of sites is N. This model is proposed as a orbital state for the layered iron oxide, [5, 6, 26], and is also recently proposed in study of the optical lattice [27-29]. A similar orbital model in a honeycomb lattice termed the Kitaev model is recently well examined. [30,31] Let us introduce the Fourier transformation for the orbital pseudo-spin operator. The Hamiltonian (15) is represented in the momentum space, [5,27]... 

POSITION AND MOMENTUM ENTANGLEMENT OF DIPOLE-DIPOLE INTERACTING ATOMS IN OPTICAL LATTICES... 

Abstract We consider a possible realization of the position- and momentum-correlated atomic pairs that are confined to adjacent sites of two mutually shifted optical lattices and are entangled via laser-induced dipole-dipole interactions. The Einstein-Podolsky-Rosen (EPR) "paradox" [Einstein 1935] with translational variables is then modified by lattice-diffraction effects. We study a possible mechanism of creating such diatom entangled states by varying the effective mass of the atoms. 

Keywords Entanglement, optical lattice, dipole-dipole interaction, effective mass. 

Figure 2 Proposed scheme of two kinds of mutually shifted overlapping optical lattices used to create the translational EPR state. The lattices are displaced from each other in the y direction by l. They are sparsely occupied by two different kinds of atoms. Each kind of atoms interacts with a different lattice. The oval regions depict the energy minima (potential wells) of the lattices.

Our aim here is to demonstrate the feasibility of preparing a momentum- and position-entangled state of atom pairs in optical lattices, which would be a vari-... 

Let us focus on the subensemble of tube-pairs in which each tube is occupied by exactly one atom. In the ID optical lattice, the single-atom Hamiltonian in x representation is... 

Figure 10. Simulation of the EPR state preparation in an optical lattice with 25 sites, at three consecutive times. First row shows the joint probability distribution in x representation, the second one in p representation, (ol) and (a2) initially (t = 0), the atoms are cooled down to the external harmonic potential ground state, whereas the LIDDI is off. (61) and (62) at t = 1.4 x 10-4 s LIDDI and the repulsive linear potential (with the slope 0.04 Erec per lattice site) are on, whereas the harmonic potential is off. The diatoms are moving through the lattice very slowly in comparison to the single atoms, (cl) and (c2) at t = 2.16 x 10 4 s single atoms are ejected out of the lattice and discarded and the diatoms are separated out.

One may envision extensions of the present approach to matter teleportation [Opatrny 2001] and quantum computation based on continuous variables [Braunstein 1998 (a) Lloyd 1998 Lloyd 1999], Such extensions may involve the coupling of entangled atomic ensembles in optical lattices by photons carrying quantum information. 

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