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Magnetic-enhanced modulation transfer spectroscopy and laser locking for 87Rb repump transition

Jin-Bao Long, Sheng-Jun Yang, Shuai Chen, and Jian-Wei Pan

Open Access Open Access

Abstract

Locking of a laser frequency to an atomic or molecular resonance line is a key technique in applications of laser spectroscopy and atomic metrology. Modulation transfer spectroscopy (MTS) provides an accurate and stable laser locking method which has been widely used. Normally, the frequency of the MTS signal would drift due to Zeeman shift of the atomic levels and rigorous shielding of stray magnetic field around the vapor cell is required for the accuracy and stability of laser locking. Here on the contrary, by applying a transverse bias magnetic field, we report for the first time observation of a magnetic-enhanced MTS signal on the transition of 87Rb D2-line Fg = 1→ Fe = 0 (close to the repump transition of Fg = 1→ Fe = 2), with signal to noise ratio larger than 100:1. The error signal is immune to the external magnetic fluctuation. Compared to the ordinary MTS scheme, it provides a robust and accurate laser locking approach with more stable long-term performance. This technique can be conveniently applied in areas of laser frequency stabilization, laser manipulation of atoms and precision measurement.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Figures (7)
Fig. 1
Fig. 1 Energy level diagrams for the two-level MTS (a), and the tripod-level MTSs of two orthogonal linearly-polarized configurations corresponding to the 87Rb D2 line transition Fg = 1 → Fe = 0 (b, c). Left and right of (b, c) are considering the degenerate and non-degenerate ground states respectively. |g1,2,3〉 and |e〉, the ground and excited states; ωp(c), the probe (pump) beam, ωc = ωp = ω; Ω, the modulation frequency; ωc(p)±Ω, the 1st-order sidebands of the pump/probe beam; and δ, energy splitting of the adjacent ground states due to a bias magnetic field shown in Fig. 2.

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Fig. 2
Fig. 2 Schematic for the magnetic-enhanced MTS and laser frequency stabilization. The bias field is along z-direction, perpendicular to the optical table. λ/2: half-wave plate, λ/4: quarter-wave plate, PBS: polarization beam splitter, coupler: laser collimator, EOM: electro-optic modulator, BS: 50/50% beam splitter, f: lens, PD: photodiode detector, Amp: preamplifier, PID: proportion-integration-differentiation servo.

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Fig. 3
Fig. 3 Error signal comparison when the laser-diode frequency is scanned over the 87Rb D2-line transition of Fg = 1 → Fe = {0, 1, 2}. Inset is enlarged of the gray part. MTS-a, the magnetic-enhanced MTS with orthogonal linear polarization setting; MTS-b, the ordinary MTS with orthogonal linear polarization setting; MTS-c, the ordinary MTS with parallel linear polarization setting; and FMS, the frequency modulation spectroscopy. The zero point in x-axis corresponds to the resonant transition of Fg = 1 → Fe = 0. CO01 is the crossover transition of Fe = 0 & 1. The modulation frequency is 4 MHz. A 10-point moving average has been applied to all the data.

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Fig. 4
Fig. 4 (a) Residual error signal fluctuation of three spectroscopy methods after laser lock; and (b) the corresponding statistical distribution of it. MTS [2, 3] (black square): the ordinary MTS lock on the transition of Fg = 2 → Fe = 3; MTS [1, 0] (red circle): the magnetic-enhanced MTS lock on the transition of Fg = 1 → Fe = 0; and FMS [1, CO01] (blue triangle): the FMS lock on the crossover transition of Fg = 1 → Fe = 0 & 1. Sample interval in (a) is 100 μs and the total duration is 0.25 s; the y-axis in (b) is normalized to the peak value of the Gaussian fit. The FWHMs (full width at half maximum) of them are 82(1), 85(2) and 229(6) kHz respectively.

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Fig. 5
Fig. 5 Measurement of laser linewidth and long-term stability by light beat of two independent laser diodes after lock. (a) Beat signal of the magnetic-enhanced MTS locking, fitting with a Lorentz-Gaussian function. Linewidth (FWHM) of the laser is about 209 kHz. All the data is 10-times averaged. (b) Beat frequency variation of the two independent laser diodes after lock for 10 hours. Three spectroscopy methods as discussed in Fig. 4 are carried out here. The gate time of the frequency measurement is 0.5 s. (c) Allan variance of the beat frequency.

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Fig. 6
Fig. 6 The peak-to-peak amplitude of the magnetic-enhanced MTS signal for various parameter settings, including (a) light polarization, (b) modulation frequency Ω and (c) modulation index β when changing the bias magnetic strength B. Polarizations within parentheses in (a) corresponds to the probe and pump beams respectively. H/V, horizontal/vertical-linearly polarization; R/L, right/left-circularly polarization. Polarization configuration in (b) and (c) is (V, H). The x-axis is Zeeman splitting between the ground states of Fg = 1, m F g =±1.

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Fig. 7
Fig. 7 The signal to noise ratio (left, black circle) and the zero-crossing gradient (right, blue square) of the MTS signal on the transition of Fg = 1 → Fe = 0 while changing the modulation frequency. Modulation index β is fixed at 1.43.

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Equations (4)

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E c = E 0 sin ( ( ω 0 + Δ ) t + β sin Ω t ) = E 0 ∑ n = − ∞ ∞ J n ( β ) sin ( ω 0 + Δ + n Ω ) t ,
S ( Ω ) = C [ Γ 2 + Ω 2 ] 1 / 2 ∑ n = − ∞ ∞ J n ( β ) J n − 1 ( β ) [ ( L ( n + 1 ) / 2 + L ( n − 2 ) / 2 ) cos ( Ω t + ϕ )     + ( D ( n + 1 ) / 2 − D ( n − 2 ) / 2 ) sin ( Ω t + ϕ ) ] ,
S ( Ω ) = C [ Γ 2 + Ω 2 ] 1 / 2 J 0 ( β ) J 1 ( β ) [ ( − L − 1 + L − 1 / 2 − L 1 / 2 + L 1 ) cos ( Ω t + ϕ )     + ( D − 1 − D − 1 / 2 − D 1 / 2 + D 1 ) sin ( Ω t + ϕ ) ] .
S ( Ω ) = X cos ( Ω t + ϕ ) + Y sin ( Ω t + ϕ ) .
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