Differentially detected coherent population trapping resonances excited by orthogonally polarized laser fields

Michael Rosenbluh; Vishal Shah; Svenja Knappe; John Kitching

doi:10.1364/OE.14.006588

Optics Express
Vol. 14,
Issue 15,
pp. 6588-6594
(2006)
•https://doi.org/10.1364/OE.14.006588

Differentially detected coherent population trapping resonances excited by orthogonally polarized laser fields

Michael Rosenbluh, Vishal Shah, Svenja Knappe, and John Kitching

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Michael Rosenbluh, Vishal Shah, Svenja Knappe, and John Kitching, "Differentially detected coherent population trapping resonances excited by orthogonally polarized laser fields," Opt. Express 14, 6588-6594 (2006)

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Abstract

We demonstrate the excitation and low-noise differential detection of a coherent population trapping (CPT) resonance with two modulated optical fields with orthogonal circular polarizations. When a microwave phase delay of λ/4 is introduced in the optical path of one of the fields, the difference in the power transmitted through the cell in each polarization shows a narrow, dispersive resonance. The differential detection allows a high degree of suppression of laser-induced noise and will enable nearly shot-noise-limited operation of atomic frequency references and magnetometers based on CPT.

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Fig. 1. (a) Experimental configuration for differential detection of CPT resonances. (b) Atomic level diagram showing detunings and polarizations of the incident optical fields. Here Ω_ij is the Rabi frequency connecting levels i and j, Γ/2 is the population decay rate from the excited states to each hyperfine state and γ is the decay rate of the hyperfine coherence. The optical fields are assumed to be on resonance and δ_r is the Raman detuning.

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Fig. 2. Lineshapes of atomic-coherence-induced resonances for phase-shifted, two-beam excitation. (a) One beam blocked, conventional CPT resonance, (b) both beams present, signals from balanced photodetectors subtracted, (c) both beams present, phase-advanced signal only, (d) both beams present, phase-delayed signal only.

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Fig. 3. Noise spectra taken with the local oscillator tuned to resonance with the center of the CPT transition (δ_r = 0). Trace A is the sum of the balanced detector channels, Traces B and C are the phase advanced and delayed detector channel respectively, Trace D is the difference of the channels and Trace E is the electronic noise floor (both beams blocked). The inset shows a smaller frequency range and the white noise component of the spectrum around 200 Hz. The dashed line indicates the approximate shot noise level for the sum and difference configurations, as estimated from the DC detector photocurrents.

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Fig. 4. Calculated resonance lineshapes for the model in Fig. 1(b) for ψ/γ = 1. Fractional absorption for the (a) phase-delayed and (b) phase-advanced field as a function of Raman detuning. Trace A: ϕ = 0; Trace B: ϕ = π/4; Trace C: ϕ = 3π/8; Trace D: ϕ = π/2. These results for ϕ = π/4 correspond closely to the experimental data shown in Fig. 2(c) and (d).

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Equations (6)

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ρ_{12} = - \frac{Ψ \cos (ϕ)}{γ + 2 Ψ + i δ_{r}}

Im [Ω_{i 4}^{*} ρ_{i 4}] = Ψ - \frac{2 (γ + 2 Ψ) Ψ^{2} \cos^{2} (ϕ)}{δ_{r}^{2} + {(γ + 2 Ψ)}^{2}} - \frac{δ_{r} Ψ^{2} \sin (2 ϕ)}{δ_{r}^{2} + {(γ + 2 Ψ)}^{2}}

Im [Ω_{i 3}^{*} ρ_{i 3}] = Ψ - \frac{2 (γ + 2 Ψ) Ψ^{2} \cos^{2} (ϕ)}{δ_{r}^{2} + {(γ + 2 Ψ)}^{2}} + \frac{δ_{r} Ψ^{2} \sin (2 ϕ)}{δ_{r}^{2} + {(γ + 2 Ψ)}^{2}}

β = \frac{Ω^{2}}{2 (γ Γ + Ω^{2})} \frac{ΔΩ}{Ω} γ .

〈 Im [F_{1}^{*} ρ] 〉 = \frac{2 γ (\frac{Ω^{2}}{2 ω_{12}}) \cos^{2} (ϕ)}{δ^{2} + γ^{2}} + \frac{δ (\frac{Ω^{2}}{2 ω_{12}}) \sin (2 ϕ)}{δ^{2} + γ^{2}}

〈 Im [F_{2}^{*} ρ] 〉 = \frac{2 γ (\frac{Ω^{2}}{2 ω_{12}}) \cos^{2} (ϕ)}{δ^{2} + γ^{2}} + \frac{δ (\frac{Ω^{2}}{2 ω_{12}}) \sin (2 ϕ)}{δ^{2} + γ^{2}}

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Equations (6)

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