Controllable double-well optical trap for cold atoms or molecules and its one-dimensional and two-dimensional optical lattices

Xianming Ji; Jianping Yin

doi:10.1364/JOSAB.22.001737

Journal of the Optical Society of America B
Vol. 22,
Issue 8,
pp. 1737-1748
(2005)
•https://doi.org/10.1364/JOSAB.22.001737

Controllable double-well optical trap for cold atoms or molecules and its one-dimensional and two-dimensional optical lattices

Xianming Ji and Jianping Yin

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Xianming Ji and Jianping Yin, "Controllable double-well optical trap for cold atoms or molecules and its one-dimensional and two-dimensional optical lattices," J. Opt. Soc. Am. B 22, 1737-1748 (2005)

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Abstract

We propose a novel, to our knowledge, scheme to form a controllable double-well optical dipole trap for cold atoms (or molecules) by using an optical system composed of a binary π-phase plate and a lens illuminated by a plane light wave. We calculate the intensity distribution of the double-well trap and derive the analytical relationships between the characteristic parameters of the double-well trap (including geometric parameters, intensity distributions, and intensity gradients and their curvatures) and the relative aperture β of the lens system. We also extend our controllable double-well trap to its trap array by using a binary π-phase grating combined with an array of spherical microlenses. Our study shows that, if the π-phase plate (or the π-phase grating) is moved along the x direction, our double-well trap (or array of double-well ones) can continuously evolve to a single-well one (or an array of single-well ones) and vice versa, which can be used to study cold collisions between two atomic (or molecular) samples and atom interference with Bose–Einstein condensation (BEC) in a double-well potential; to prepare quantum entanglement between two macroscopic atomic assembles, even to realize an all-optical double-well atomic (molecular) BEC (including an array of all-optical double-well BECs) by using optical-potential evaporative cooling; to form a novel optical lattice with a larger lattice constant; and so on.

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Equations (20)

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$Δ x_{1 / 2} (mm)$	$Δ y_{1 / 2} (mm)$	$Δ z_{1 / 2} (mm)$	$Δ x_{1 / e^{2}} (mm)$
0.399λ/β	0.433λ/β	1.285λ/β²	0.631λ/β
$Δ y_{1 / e^{2}} (mm)$	$Δ z_{1 / e^{2}} (mm)$	$Δ V_{1 / 2} ({mm}^{3})$	$Δ V_{1 / e^{2}} ({mm}^{3})$
$0.700 λ / β$	$2.35 λ / β^{2}$	$0.119 λ^{3} / β^{4}$	$0.494 λ^{3} / β^{4}$


$Δ x_{1 / 2} (μ m)$	$Δ y_{1 / 2} (μ m)$	$Δ z_{1 / 2} (μ m)$	$Δ x_{1 / e^{2}} (μ m)$	$Δ y_{1 / e^{2}} (μ m)$	$Δ z_{1 / e^{2}} (μ m)$	$Δ V_{1 / 2} ({cm}^{3})$
2.11	2.35	34.1	3.34	3.71	56.6	$8.86 \times 10^{- 11}$
$Δ V_{1 / e^{2}} ({cm}^{3})$	${∣ \partial I / \partial x_{0} ∣}_{\max} (W / m^{3})$	${∣ \partial I / \partial y_{0} ∣}_{\max} (W / m^{3})$	${∣ \partial I / \partial z_{0} ∣}_{\max} (W / m^{3})$	${∣ \partial^{2} I / \partial x_{0}^{2} ∣}_{\max} (W / m^{4})$	${∣ \partial^{2} I / \partial y_{0}^{2} ∣}_{\max} (W / m^{4})$	${∣ \partial^{2} I / \partial z_{0}^{2} ∣}_{\max} (W / m^{4})$
$3.68 \times 10^{- 10}$	$5.64 \times 10^{15}$	$4.79 \times 10^{15}$	$2.87 \times 10^{14}$	$1.00 \times 10^{22}$	$7.00 \times 10^{21}$	$2.48 \times 10^{19}$

$λ_{L} (μ m)$	$δ (GHz)$	$I_{\max} (GW / m^{2})$	$\bar{I} (GW / m^{2})$	$U_{\max} (mK)$	$\bar{U} (mK)$	$S_{Sp} (s^{- 1})$	$S_{Rayleigh} (s^{- 1})$	$S_{Ramam} (s^{- 1})$
10.6	$7.1 π \times 10^{5}$	16.8	6.38	0.659	0.251	0.561	$1.99 \times 10^{- 3}$	$3.27 \times 10^{- 9}$
1.06	$6.38 π \times 10^{5}$	7.48	2.84	1.028	0.391	3.07	0.886	$1.45 \times 10^{- 4}$


$Δ x_{1 / 2} (mm)$	$Δ y_{1 / 2} (mm)$	$Δ z_{1 / 2} (mm)$	$Δ x_{1 / e^{2}} (mm)$
0.399λ/β	0.433λ/β	1.285λ/β²	0.631λ/β
$Δ y_{1 / e^{2}} (mm)$	$Δ z_{1 / e^{2}} (mm)$	$Δ V_{1 / 2} ({mm}^{3})$	$Δ V_{1 / e^{2}} ({mm}^{3})$
$0.700 λ / β$	$2.35 λ / β^{2}$	$0.119 λ^{3} / β^{4}$	$0.494 λ^{3} / β^{4}$


$Δ x_{1 / 2} (μ m)$	$Δ y_{1 / 2} (μ m)$	$Δ z_{1 / 2} (μ m)$	$Δ x_{1 / e^{2}} (μ m)$	$Δ y_{1 / e^{2}} (μ m)$	$Δ z_{1 / e^{2}} (μ m)$	$Δ V_{1 / 2} ({cm}^{3})$
2.11	2.35	34.1	3.34	3.71	56.6	$8.86 \times 10^{- 11}$
$Δ V_{1 / e^{2}} ({cm}^{3})$	${∣ \partial I / \partial x_{0} ∣}_{\max} (W / m^{3})$	${∣ \partial I / \partial y_{0} ∣}_{\max} (W / m^{3})$	${∣ \partial I / \partial z_{0} ∣}_{\max} (W / m^{3})$	${∣ \partial^{2} I / \partial x_{0}^{2} ∣}_{\max} (W / m^{4})$	${∣ \partial^{2} I / \partial y_{0}^{2} ∣}_{\max} (W / m^{4})$	${∣ \partial^{2} I / \partial z_{0}^{2} ∣}_{\max} (W / m^{4})$
$3.68 \times 10^{- 10}$	$5.64 \times 10^{15}$	$4.79 \times 10^{15}$	$2.87 \times 10^{14}$	$1.00 \times 10^{22}$	$7.00 \times 10^{21}$	$2.48 \times 10^{19}$

Abstract

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Equations (20)

Journal of the Optical Society of America B