Enhancement of optical pumping efficiency by frequency-modulated lasers

Pierre Tremblay; Jean Beaubien; Alain Michaud; Éric Cauchon

doi:10.1364/JOSAB.9.001537

Journal of the Optical Society of America B
Vol. 9,
Issue 9,
pp. 1537-1542
(1992)
•https://doi.org/10.1364/JOSAB.9.001537

Enhancement of optical pumping efficiency by frequency-modulated lasers

Pierre Tremblay, Jean Beaubien, Alain Michaud, and Éric Cauchon

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Pierre Tremblay, Jean Beaubien, Alain Michaud, and Éric Cauchon, "Enhancement of optical pumping efficiency by frequency-modulated lasers," J. Opt. Soc. Am. B 9, 1537-1542 (1992)

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Abstract

Optical pumping of an atomic vapor with low-power lasers often results in low pumping efficiency because of the narrow laser linewidth. Broadening of the laser spectrum by frequency modulation (FM) ensures the contribution of atoms from all velocity classes. We numerically evaluate the difference between the population enhancement for a vapor pumped with a modulated laser and that with a nonmodulated laser. The most efficient modulation scheme among those considered is FM with narrow-band Gaussian noise. The achieved optical pumping enhancement depends on laser linewidth and available power.

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Modulation Type	Power Spectral Density, S_ζm(f)
Triangle wave FM	$\frac{1}{2 π Δ f} arctan [\frac{4 π^{2} Δ f Δ ν}{{(π Δ ν)}^{2} + 4 π^{2} (Δ f^{2} - f^{2})}]$
Sine wave FM	$\sqrt{2} \frac{{({(π Δ ν)}^{2} + 4 π^{2} (Δ f^{2} - f^{2}) + {[{(π Δ ν)}^{2} + 4 π^{2} {(Δ f - f)}^{2}] [{(π Δ ν)}^{2} + 4 π^{2} {(Δ f + f)}^{2}]}^{1 / 2})}^{1 / 2}}{{[{(π Δ ν)}^{2} + 4 π^{2} {(Δ f - f)}^{2}] [{(π Δ ν)}^{2} + 4 π^{2} {(Δ f + f)}^{2}]}^{1 / 2}}$
Square wave FM	$π Δ ν [\frac{1}{{(π Δ ν)}^{2} + 4 π^{2} {(Δ f + f)}^{2}} + \frac{1}{{(π Δ ν)}^{2} + 4 π^{2} {(Δ f - f)}^{2}}]$
Narrow-band Gaussian noise FM	$\frac{2 π Δ ν}{{(π Δ ν)}^{2} + 4 π^{2} f^{2}} * \frac{1}{σ \sqrt{2 π}} exp (- f^{2} / 2 σ^{2}) (Voigt profile)$
Wideband Gaussian noise FM	$\frac{2 π Δ ν + 4 π^{2} N_{0}}{{(π Δ ν + 2 π^{2} N_{0})}^{2} + 4 π^{2} f^{2}}$
Square pulses AM	$\frac{2 π Δ ν}{{(π Δ ν)}^{2} + 4 π^{2} f^{2}} + \frac{2}{Δ T} \frac{[{(π Δ ν)}^{2} - 4 π^{2} f^{2}] [exp (- π Δ ν Δ T) cos (2 π f Δ T) - 1] - 4 π^{2} f Δ ν exp (- π Δ ν Δ T) sin (2 π f Δ T)}{{[{(π Δ ν)}^{2} + 4 π^{2} f^{2}]}^{2}}$

Parameter	Value
λ_ef≈λ_eg	780 nm
1/Γ	27.0 ns
A_eg = A_ef	Γ/2
ν_fg	6.835 GHz
γ₁	200 s⁻¹
Δ ν_D	500 MHz
Δ ν	25 MHz

Modulation Type	Power Spectral Density, S_ζm(f)
Triangle wave FM	$\frac{1}{2 π Δ f} arctan [\frac{4 π^{2} Δ f Δ ν}{{(π Δ ν)}^{2} + 4 π^{2} (Δ f^{2} - f^{2})}]$
Sine wave FM	$\sqrt{2} \frac{{({(π Δ ν)}^{2} + 4 π^{2} (Δ f^{2} - f^{2}) + {[{(π Δ ν)}^{2} + 4 π^{2} {(Δ f - f)}^{2}] [{(π Δ ν)}^{2} + 4 π^{2} {(Δ f + f)}^{2}]}^{1 / 2})}^{1 / 2}}{{[{(π Δ ν)}^{2} + 4 π^{2} {(Δ f - f)}^{2}] [{(π Δ ν)}^{2} + 4 π^{2} {(Δ f + f)}^{2}]}^{1 / 2}}$
Square wave FM	$π Δ ν [\frac{1}{{(π Δ ν)}^{2} + 4 π^{2} {(Δ f + f)}^{2}} + \frac{1}{{(π Δ ν)}^{2} + 4 π^{2} {(Δ f - f)}^{2}}]$
Narrow-band Gaussian noise FM	$\frac{2 π Δ ν}{{(π Δ ν)}^{2} + 4 π^{2} f^{2}} * \frac{1}{σ \sqrt{2 π}} exp (- f^{2} / 2 σ^{2}) (Voigt profile)$
Wideband Gaussian noise FM	$\frac{2 π Δ ν + 4 π^{2} N_{0}}{{(π Δ ν + 2 π^{2} N_{0})}^{2} + 4 π^{2} f^{2}}$
Square pulses AM	$\frac{2 π Δ ν}{{(π Δ ν)}^{2} + 4 π^{2} f^{2}} + \frac{2}{Δ T} \frac{[{(π Δ ν)}^{2} - 4 π^{2} f^{2}] [exp (- π Δ ν Δ T) cos (2 π f Δ T) - 1] - 4 π^{2} f Δ ν exp (- π Δ ν Δ T) sin (2 π f Δ T)}{{[{(π Δ ν)}^{2} + 4 π^{2} f^{2}]}^{2}}$

Parameter	Value
λ_ef≈λ_eg	780 nm
1/Γ	27.0 ns
A_eg = A_ef	Γ/2
ν_fg	6.835 GHz
γ₁	200 s⁻¹
Δ ν_D	500 MHz
Δ ν	25 MHz

Abstract

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Figures (7)

Tables (2)

Equations (30)

Journal of the Optical Society of America B