We first calculated the diffraction intensity distributions of the Dammann gratings illuminated by Gaussian light wave. The empirical equations were deduced by numerical calculations to calculate the parameters, such as the spatial period, the maximum intensity, and the maximum intensity gradient, of the optical trap array composed by a set of Dammann gratings and a focus lens. Thus, a novel type of optical trap array for trapping cold atoms (or molecules) was proposed and its features were discussed. The results showed the optical trap array with very short period could be generated. High optical dipole potential could be presented so as to have strong attractive force to the atoms to form atomic optical lattices of high lattice density. Compared with the optical lattices formed by standing wave interferences of CO2 laser, there are many unique advantages of which are formed by Dammann gratings. 1. Introduction In early 1970s, the concept of “Dammann grating” was first proposed by Dammann and G？rtler [1] when they studied the copy of multiple imaging. The Dammann grating is a kind of phase-type grating with several groups of phase jump points in each period. The positions of the phase jump points can be computed by optimal designing. When the Dammann grating is illuminated by a coherent monochromatic light wave, many beams of diffraction light wave with equal intensity can be generated without the nonuniformity of beam intensity caused by sinc functions in common gratings. Many types [2–5] of Dammann gratings with high efficiency and large splitting ratio are developed in several decades to satisfy their applications. The orthogonal binary-phase gratings completing 64 × 64 splitting ratio have been successfully fabricated. Due to their advantages, such as the simplicity to be designed [6], the mature production process, and the easy calibration, they have been widely paid attentions to. In 1980s, Dammann grating was applied to the field of optical computing and optical interconnection. In 1990s, Tooley realized the image process of optical cells by using Dammann grating [7]. In recent years, a series of important developments and fruitful results have been obtained both in theory and in experiment on the cooling, trapping, and manipulating the neutral atoms (or molecules). As the deeply developing of the quantum information process and optical lattices [8–10], the surface microtrap array for trapping the cold atoms (or molecules) has become the research frontier in the field of atomic, molecular, and optical physics. Schemes of generating surface
References
[1]
H. Dammann and K. G？rtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Optics Communications, vol. 3, no. 5, pp. 312–315, 1971.
[2]
A. Vasara, M. R. Taghizadeh, J. Turunen, et al., “Binary surface-relief gratings for array illumination in digital optics,” Applied Optics, vol. 31, no. 17, pp. 3320–3336, 1992.
[3]
S. Zhao and P. S. Chung, “Design of a circular Dammann grating,” Optics Letters, vol. 31, no. 16, pp. 2387–2389, 2006.
[4]
B. Luo, C. Wang, J. Du, C. Ma, Y. Guo, and J. Yao, “Design and analysis of phase gratings for laser beams coherent combination,” Microelectronic Engineering, vol. 83, no. 4–9, pp. 1368–1371, 2006.
[5]
S. Zhao, J. F. Wen, and P. S. Chung, “Simple focal-length measurement technique with a circular Dammann grating,” Applied Optics, vol. 46, no. 1, pp. 44–49, 2007.
[6]
P. Xi, C. H. Zhou, S. Zhao, H. S. Wang, and L. R. Liu, “Design and fabrication of 64×64× spot array Dammann grating,” Chinese Journal of Lasers, vol. 28, no. 4, pp. 369–371, 2001.
[7]
F. A. P. Tooley, S. Wakelin, and M. R. Taghizadeh, “Interconnects for a symmetric-self-electro-optic-effect-device cellular-logic image processor,” Applied Optics, vol. 33, no. 8, pp. 1398–1404, 1994.
[8]
X. He, P. Xu, J. Wang, and M. Zhan, “Rotating single atoms in a ring lattice generated by a spatial light modulator,” Optics Express, vol. 17, no. 23, pp. 21014–21021, 2009.
[9]
A. Ji, W. M. Liu, J. L. Song, and F. Zhou, “Dynamical creation of fractionalized vortices and vortex lattices,” Physical Review Letters, vol. 101, no. 1, Article ID 010402, 2008.
[10]
G.-P. Zheng, J.-Q. Liang, and W. M. Liu, “Phase diagram of two-species Bose-Einstein condensates in an optical lattice,” Physical Review A, vol. 71, no. 5, Article ID 053608, 2005.
[11]
M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, “One-dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip,” Journal of Physics B, vol. 41, no. 6, Article ID 065301, 2008.
[12]
G. N. Lewis, Z. Moktadir, C. Gollasch et al., “Fabrication of magnetooptical atom traps on a chip,” Journal of Microelectromechanical Systems, vol. 18, no. 2, pp. 347–353, 2009.
[13]
C. D. J. Sinclair, E. A. Curtis, I. L. Garcia et al., “Bose-Einstein condensation on a permanent-magnet atom chip,” Physical Review A, vol. 72, no. 3, Article ID 031603, 2005.
[14]
G. Birkl, F. B. J. Buchkremer, R. Dumke, and W. Ertmer, “Atom optics with microfabricated optical elements,” Optics Communications, vol. 191, no. 1-2, pp. 67–81, 2001.
[15]
R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, “Micro-optical realization of arrays of selectively addressable dipole traps: a scalable configuration for quantum computation with atomic qubits,” Physical Review Letters, vol. 89, no. 9, Article ID 097903, 2002.
[16]
J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics, John Wiley & Sons, New York, NY, USA, 1978.
[17]
C. Zhou and L. Li, “Numerical study of Dammann array illuminators,” Applied Optics, vol. 34, pp. 5961–5969, 1995.
[18]
T. Rom, T. Best, D. Van Oosten et al., “Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice,” Nature, vol. 444, no. 7120, pp. 733–736, 2006.
[19]
R. Gerritsma, S. Whitlock, T. Fernholz et al., “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Physical Review A, vol. 76, no. 3, Article ID 033408, 2007.
[20]
J. K. Asbóth, H. Ritsch, and P. Domokos, “Optomechanical coupling in a one-dimensional optical lattice,” Physical Review A, vol. 77, no. 6, Article ID 063424, 2008.
[21]
K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nature Physics, vol. 3, no. 8, pp. 556–560, 2007.
[22]
P. Kakashvili, S. G. Bhongale, H. Pu, and C. J. Bolech, “Realizing Luttinger liquids in trapped ultra-cold atomic Fermi gases using 2D optical lattices,” Physica B, vol. 404, no. 19, pp. 3320–3323, 2009.
[23]
C. Reichhardt and C. J. O. Reichhardt, “Pattern switching and polarizability for colloids in optical-trap arrays,” Physical Review E, vol. 80, Article ID 022401, 2009.
[24]
Y. Shin, C. Sanner, G. B. Jo et al., “Interference of Bose-Einstein condensates split with an atom chip,” Physical Review A, vol. 72, no. 2, Article ID 021604, pp. 1–4, 2005.
[25]
J. Mun, P. Medley, G. K. Campbell, L. G. Marcassa, D. E. Pritchard, and W. Ketterle, “Phase diagram for a bose-einstein condensate moving in an optical lattice,” Physical Review Letters, vol. 99, no. 15, Article ID 150604, 2007.
[26]
I. Bloch, “Quantum coherence and entanglement with ultracold atoms in optical lattices,” Nature, vol. 453, no. 7198, pp. 1016–1022, 2008.
[27]
K. B. Davis, M. O. Mewes, M. R. Andrews et al., “Bose-Einstein condensation in a gas of sodium atoms,” Physical Review Letters, vol. 75, no. 22, pp. 3969–3973, 1995.
[28]
S. Friebel, R. Scheunemann, J. Walz, T. W. H？nsch, and M. Weitz, “Laser cooling in a CO2-laser optical lattice,” Applied Physics B, vol. 67, no. 6, pp. 699–704, 1998.
[29]
S. Friebel, C. D'Andrea, J. Walz, M. Weitz, and T. W. H？nsch, “CO2-laser optical lattice with cold rubidium atoms,” Physical Review A, vol. 57, no. 1, pp. R20–R23, 1998.
