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Chinese Optics Letters
Vol. 14, Issue 7, 070202 (2016)

Cold atoms passing through a thin laser beam: a Fourier optics approach

Shuyu Zhou^1、2、*, Jun Qian¹, Shanchao Zhang², and Yuzhu Wang^1、**

Author Affiliations

¹Key Laboratory for Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

²Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, 999077, China

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DOI: 10.3788/COL201614.070202 Cite this Article Set citation alerts

Shuyu Zhou, Jun Qian, Shanchao Zhang, Yuzhu Wang. Cold atoms passing through a thin laser beam: a Fourier optics approach[J]. Chinese Optics Letters, 2016, 14(7): 070202 Copy Citation Text

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Abstract

A Fourier optics approach can be a concise and powerful tool to solve problems in atom optics. In this report, we adopt it to investigate the kinetic behavior of cold atoms passing through a far red-detuned Gaussian beam. We demonstrate that the aberration has significant influence on the evolution of the atomic cloud, which is rooted in the deviation of the Gaussian profile from the quadratic form. In particular, we observe an intriguing effect analogous to Fresnel’s double prism with cold atoms. The experimental results are in good agreement with the numerical simulation.

k⃗ (r⃗) = \frac{2 π n (r⃗)}{λ_{0}} k⃗,

(1)

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k⃗ (r⃗) = \sqrt{\frac{2 M [E - V (r⃗)]}{�^{2}}} {k⃗}_{0},

(2)

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n (r⃗) = \sqrt{1 - V (r⃗) / E} .

(3)

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n (r⃗) \approx 1 - \frac{V (r⃗)}{2 E} .

(4)

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V (x, z) = \frac{κ}{2} x^{2},

(5)

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n - 1 = - \frac{κ x^{2}}{4 E} .

(6)

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\int_{0}^{h} (n - 1) d z = - \frac{κ x^{2} h}{4 E} .

(7)

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φ = - \frac{x^{2} k}{2 f},

(8)

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f = \frac{2 E}{κ h} .

(9)

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U (x, z) = U_{0} e^{- \frac{x^{2}}{2 σ_{x}^{2}} - \frac{z^{2}}{2 σ_{z}^{2}}},

(10)

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U_{0} = U (0, 0) \approx \frac{ℏ Ω^{2} (0, 0)}{4 δ},

(11)

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Ω = Γ \sqrt{\frac{I}{2 I_{s}}},

(12)

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n \approx 1 - \frac{U}{2 E} = 1 - \frac{ℏ Ω^{2} (0, 0) e^{- \frac{x^{2}}{2 σ_{x}^{2}} - \frac{z^{2}}{2 σ_{z}^{2}}}}{8 E δ},

(13)

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\int n d z \approx A + B e^{- \frac{x^{2}}{2 σ_{x}^{2}}},

(14)

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B = \frac{\sqrt{2 π} ℏ Ω^{2} (0, 0) σ_{z}}{8 E | δ |} .

(15)

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e^{- \frac{x^{2}}{2 σ_{x}^{2}}} \approx 1 - \frac{x^{2}}{2 σ_{x}^{2}} .

(16)

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{\tilde{t}}_{atom} (x) = \exp (- i k \frac{x^{2} B}{2 σ_{x}^{2}}) .

(17)

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{\tilde{t}}_{lens} (x) = \exp (- i k \frac{x^{2}}{2 F}),

(18)

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F = \frac{σ_{x}^{2}}{B} = \frac{4 m v^{2} | δ | σ_{x}^{2}}{\sqrt{2 π} ℏ Ω^{2} (0, 0) σ_{z}} .

(19)

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U (p_{0}) = \iint_{\sum} h (p_{0}, p_{1}) U (p_{1}) d S,

(20)

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h (p_{0}, p_{1}) = \frac{1}{i λ} \frac{e^{i k r_{01}}}{r_{01}} \cos (n⃗, {r⃗}_{01}),

(21)

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References (25)

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Shuyu Zhou, Jun Qian, Shanchao Zhang, Yuzhu Wang. Cold atoms passing through a thin laser beam: a Fourier optics approach[J]. Chinese Optics Letters, 2016, 14(7): 070202

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