Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Atomic (or molecular) guiding using a blue-detuned doughnut mode in a hollow metallic waveguide

Zhengling Wang, Meng Dai, Jianping Yin, and Zhengling Wang

Open Access Open Access

Abstract

We propose a new scheme to guide cold atoms (or molecules) using a blue-detuned TE01 doughnut mode in a hollow metallic waveguide (HMW), and analyze the electromagnetic field distributions of various modes in the HMW. We calculate the optical potentials of the TE01 doughnut mode for three-level atoms using dressed-atom approach, and find that the optical potential of the TE01 mode is high enough to guide cold atoms released from a standard magneto-optical trap. Our study shows that when the input laser power is 0.5W and its detuning is 3GHz, the guiding efficiency of cold atoms in the straight HMW with a hollow radius of 15 μm can reach 98%, and this guiding efficiency will be almost unchanged with the change of curvature radius R of the bent HMW as R > 2cm, which is a desirable scheme to do some atom-optics experiments or realize a computer-controlled atom lithography with an arbitrary pattern. We also analyze the losses of the guided atoms in the HMW due to the spontaneous emission and background thermal collisions and briefly discuss some potential applications of our guiding scheme in atom and molecule optics.

©2005 Optical Society of America

Full Article  |  PDF Article
More Like This
Atomic quantum motion and single-mode waveguiding in a hollow metallic waveguide

Zhengling Wang and Jianping Yin
J. Opt. Soc. Am. B 25(6) 1051-1058 (2008)

Cold atom guidance in a capillary using blue-detuned, hollow optical modes

Joseph A. Pechkis and Fredrik K. Fatemi
Opt. Express 20(12) 13409-13418 (2012)

Optical potential for atom guidance in a dark hollow laser beam

Jianping Yin, Yifu Zhu, Wenbao Wang, Yuzhu Wang, and Wonho Jhe
J. Opt. Soc. Am. B 15(1) 25-33 (1998)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)
Fig. 1.
Fig. 1. (a) The structure of the HMW; (b) schematic diagram of atomic guiding. HMW, BDGB, MOT and 2π PP stand for hollow metallic waveguide, blue-detuned Gaussian beam, magneto-optic trap and 2π -phase plate.

Download Full Size | PDF

Fig. 2.
Fig. 2. Normalized electric field distribution: (a) against the radial position r for the TE01 mode; (b) against the propagation distance z.

Download Full Size | PDF

Fig. 3.
Fig. 3. Dependences of the optical potentials: (a) on the detuning; (b) on the radial position r.

Download Full Size | PDF

Fig. 4.
Fig. 4. Dependences of the spontaneous emission rates: (a) on the detuning δ/2π ; (b) on the intensity.

Download Full Size | PDF

Fig. 5.
Fig. 5. Dependences of the guiding efficiency on the input laser power: (a) for the straight HMW; (b) for the bent HMW.

Download Full Size | PDF

Equations (49)

Equations on this page are rendered with MathJax. Learn more.

E r = − 1 k i 2 ( iγ ∂ E s ∂ r + m r μ 0 ωH z ) ,
E ϕ = − 1 k i 2 ( − iμ 0 ω ∂ H z ∂ r + m r γE z ) ,
H r = − 1 k i 2 ( iγ ∂ H z ∂ r − m r ε 0 ωE z ) ,
H ϕ = − 1 k i 2 ( iε 0 ω ∂ E z ∂ r + m r γH z ) ,
E z ( r ) = C 1 J m ( k i r ) + C 2 N m ( k i r ) ,
H z ( r ) = C 3 J m ( k i r ) + C 4 N m ( k i r ) ,
E r = − 1 k i 2 [ − i γ 0 C 1 J m ' ( k i r ) + m r μ 0 ω C 3 J m ( k i r ) ] ,
E ϕ = − 1 k i 2 [ − i μ 0 ω C 3 J m ' ( k i r ) + m r γC 1 J m ( k i r ) ] .
E r = 0 ,
E ϕ ( r ) = − iμ 0 ωC 3 k i 2 J 1 ( u 01 r a ) .
E FHB ( r ) = ( 4 k 1 P in π ) 1 2 × r w 0 2 × exp ( − r 2 w 0 2 ) ,
A = ∣ ∫ 0 a E FHB ( r ) E ϕ ( r ) r dr ∣ 2 ∫ 0 ∞ ∣ E FHB ( r ) ∣ 2 r dr ∫ 0 a ∣ E ϕ ( r ) ∣ 2 r dr .
I ( r ) = P J 1 2 ( u 01 r a ) 2 π ∫ 0 a J 1 2 ( u 01 r a ) r dr = P J 1 2 ( u 01 r a ) − a 2 π J 0 ( μ 01 ) J 2 ( μ 01 ) .
ħ ( n + 1 ) ω L + δ hfs 0 G 2 ( n + 1 ) 1 2 0 ( n + 1 ) ω L G 1 ( n + 1 ) 1 2 G 2 ( n + 1 ) 1 2 G 1 ( n + 1 ) 1 2 nω L + ω 0 A i B i C i = E Dr i A i B i C i ,
U 1 = − ħδ 4 ∓ ħ Ω 1 ' 4 ± ħ [ ( ± Ω 1 ' 2 + δ 2 ) 2 + Ω 1 2 ] 1 2 2 ,
U 2 = − ħ δ 4 ∓ ħ Ω 1 ' 4 − ħδ hfs 2 + sgn × ħ [ ( ± Ω 1 ' 2 + δ 2 + δ hfs ) 2 + Ω 2 2 ] 1 2 2 ,
U 3 = ħ δ 4 ± ħ Ω 1 ' 4 + ħδ hfs 2 ∓ ħ [ ( ± Ω 1 ' 2 + δ 2 ) 2 + Ω 1 2 ] 1 2 2 − sgn × ħ [ ( ± Ω 1 ' 2 + δ 2 + δ hfs ) 2 + Ω 2 2 ] 1 2 2 ,
∣ i , n 〉 = A i ∣ g 2 , n + 1 〉 + B i ∣ g 2 , n + 1 〉 + C i ∣ e , n 〉 ,
A i = ∣ a i 2 ∣ ( 1 + a i 1 2 + a i 2 2 ) 1 2 , B i = ∣ a i 1 ∣ ( 1 + a i 1 2 + a i 2 2 ) 1 2 , C i = 1 ( 1 + a i 1 2 + a i 2 2 ) 1 2 ,
a 11 = Ω 1 − δ 2 ∓ Ω 1 ' 2 ± [ ( ± Ω 1 ' 2 + δ 2 ) 2 + Ω 1 2 ] 1 2 ,
a 12 = Ω 2 − δ 2 ∓ Ω 1 ' 2 ± [ ( ± Ω 1 ' 2 + δ 2 ) 2 + Ω 1 2 ] 1 2 − 2 δ hfs ,
a 21 = − Ω 1 δ 2 ± Ω 1 ' 2 − δ hfs − sgn × [ ( ± Ω 1 ' 2 + δ 2 + δ hfs ) 2 + Ω 2 2 ] 1 2 ,
a 22 = − Ω 2 δ 2 ± Ω 1 ' 2 + δ hfs − sgn × [ ( ± Ω 1 ' 2 + δ 2 + δ hfs ) 2 + Ω 2 2 ] 1 2 ,
a 31 = − Ω 1 δ ∓ Ω 1 ' − δ hfs ± [ ( ± Ω 1 ' 2 + δ 2 ) 2 + Ω 1 2 ] 1 2 + sgn × [ ( ± Ω 1 ' 2 + δ 2 + δ hfs ) 2 + Ω 2 2 ] 1 2 ,
a 32 = − Ω 2 δ ∓ Ω 1 ' + δ hfs ± [ ( ± Ω 1 ' 2 + δ 2 ) 2 + Ω 1 2 ] 1 2 + sgn × [ ( ± Ω 1 ' 2 + δ 2 + δ hfs ) 2 + Ω 2 2 ] 1 2 .
Γ ij = B i 2 C j 2 Γ 1 + A i 2 C j 2 Γ 2 ,
Γ i 1 = B i 2 C 1 2 Γ 1 + A i 2 C 1 2 Γ 2 .
f ( v x , v y , v z ) = ( M 2 πk B T ) 3 2 exp [ − M 2 k B T ( v x 2 + v y 2 + v z 2 ) ] ,
J i = ∫∫ x 2 + y 2 < r 0 2 1 V dxdy ∫∫∫∫ v z > 0 v z f ( v x , v y , v z ) dv x dv y dv z = ( π 2 ) 1 2 ( k B T M ) 1 2 r 0 2 V ,
J 0 ( δ , P in ) = ∫∫ r < r 0 1 V rdrd ϕ ∫∫∫ S , v z > 0 v z f ( v x , v ϕ , v z ) dv r dv ϕ dv z ,
S = { r , v r , v ϕ : 1 2 Mv r 2 + 1 2 Mv ϕ 2 + U ( r ) < 1 2 M r 2 r 0 2 v ϕ 2 + U ( r 0 ) } ,
r = ρr 0 , v r = u r ( 2 k B T M ) 1 2 , v ϕ = u ϕ ( 2 k B T M ) 1 2 , v z = u z ( 2 k B T M ) 1 2 .
J 0 ( δ , P in ) = r 0 2 V ( 2 k B T M ) 1 2 ∫ 0 1 ρ { ∫∫ S ' ( ρ ) exp [ − ( u r 2 + u ϕ 2 ) ] du r du ϕ } dρ ,
S ' ( ρ ) = { ρ , u r , u ϕ : u r 2 + k B T ( 1 − ρ 2 ) u ϕ 2 < U ( r 0 ) − U ( r 0 ρ ) } .
η = π 2 ∫ 0 1 ρ { ∫∫ S ' ( ρ ) exp [ − ( u r 2 + u ϕ 2 ) ] du r du ϕ } dρ .
x = x ' ,
y = R ⌊ 1 − cos ( z ' R ) ⌋ + y ' cos ( z ' R ) ,
z = ( R − y ' ) sin ( z ' R ) .
e x = e x ' ,
e y = e y ' cos ( z ' R ) + e z ' sin ( z ' R )
e z = − e y ' sin ( z ' R ) + e z ' cos ( z ' R ) .
a = a x ' e x ' + [ a y ' + v z ' 2 R ( 1 − y ' R ) ] e y ' + [ a z ' ( 1 − y ' R ) − 2 v y ' v z ' R ] e z ' .
1 2 Mv x ' 2 + 1 2 Mv y ' 2 + M v z ' 2 R ( y ' + r 0 ) + U ( x ' , y ' , z ' ) ≤ U ( r 0 , z ' ) .
U x ' y ' z ' = { 0 , ∣ x ' ∣ < r 0 and ∣ y ' ∣ < r 0 , U r 0 z ' , ∣ x ' ∣ = r 0 or ∣ y ' ∣ = r 0 ,
1 2 Mv x ' 2 ≤ U r 0 z '
1 2 Mv y ' 2 + M v z ' 2 R ( y ' + r 0 ) ≤ U r 0 z ' .
η = ( erf { [ U ( r 0 , z ' ) k B T ] 1 2 } ) 2 − 1 2 erf { [ U r 0 z ' k B T ] 1 2 }
× ∫ − 1 1 exp [ − U r 0 z ' k B T R 2 r 0 ( 1 + l ) ] [ R 2 r 0 ( 1 + l ) − 1 ] 1 2 × erfi ( { U r 0 z ' k B T [ R 2 r 0 ( 1 + l ) − 1 ] } 1 2 ) dl ,
γ ac = 1 τ ac ≈ 100 n σ Rb ( 3 k B T ther M ) ,
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use