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Physica Scripta

Tunable offset locking in a Ξ system: an experimental study on the rubidium atom

Md Sabir Ali, Ayan Ray, Alok Chakrabarti

Published Nov 7, 2013• 3 citations
Publisher

Abstract

In this report, we present an experimental investigation on atomic frequency offset locking (AFOL) of a laser under ladder ( ) level coupling scheme.The 5S 1/2 → 5P 3/2 → 5D 5/2 two-photon transition manifold of the rubidium (Rb) atom is chosen to demonstrate the performance of stabilization scheme in terms of frequency stability and tunability.The coherent pump-probe spectroscopy performed on the 5S → 5P → 5D levels results in signatures of two-photon absorption (TPA) and electromagnetically induced transparency (EIT).Here the pump laser is locked to the fringe of a scanning Fabry-Perot interferometer with the help of frequency modulation spectroscopy.The probe laser is subsequently stabilized on the resulting EIT (TPA) signals.It is found that the probe laser attains relative frequency stability σ (2, τ ) ∼ 1.4 × 10 -12 (2.0 × 10 -12 ) as a square root of Allan variance calculated from the frequency noise power density S ν ( f ) under closed-loop condition.Further, the current locking scheme has wide tuning range {Doppler width of 5S 1/2 (F = 2 → 5P 3/2 (F ) transition manifold.This particular tunable AFOL (TAFOL) scheme can provide large tuning range without compromising the frequency stability and such implementation of TAFOL may open new opportunities in research areas like metrology, ultra precision coherent spectroscopy, etc.

DOI
10.1088/0031-8949/88/06/065301

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In this report, we present an experimental investigation on atomic frequency offset locking (AFOL) of a laser under ladder ( ) level coupling scheme.The 5S 1/2 → 5P 3/2 → 5D 5/2 two-photon transition manifold of the rubidium (Rb) atom is chosen to demonstrate the performance of stabilization scheme in terms of frequency stability and tunability.The coherent pump-probe spectroscopy performed on the 5S → 5P → 5D levels results in signatures of two-photon absorption (TPA) and electromagnetically induced transparency (EIT).Here the pump laser is locked to the fringe of a scanning Fabry-Perot interferometer with the help of frequency modulation spectroscopy.The probe laser is subsequently stabilized on the resulting EIT (TPA) signals.It is found that the probe laser attains relative frequency stability σ (2, τ ) ∼ 1.4 × 10 -12 (2.0 × 10 -12 ) as a square root of Allan variance calculated from the frequency noise power density S ν ( f ) under closed-loop condition.Further, the current locking scheme has wide tuning range {Doppler width of 5S 1/2 (F = 2 → 5P 3/2 (F ) transition manifold.This particular tunable AFOL (TAFOL) scheme can provide large tuning range without compromising the frequency stability and such implementation of TAFOL may open new opportunities in research areas like metrology, ultra precision coherent spectroscopy, etc.
We investigate the coherent pump?probe spectroscopy of a three-level ? system, , in the hyperfine manifold of D2 transition (852?nm) of cesium with particular reference to the sub-Doppler linewidth resonance arising from Aulter?Townes (AT) splitting and the possibility of using it for realizing a scheme for tunable atomic frequency offset locking (AFOL). We discuss here the theoretical framework for a ? system interacting with a coherent pump and probe and use it to describe the process of modulation transfer in the AT and electromagnetically induced transparency regimes. We further employ an experimental scheme consisting of a strong pump and a pair of weak probes to resolve the sub-Doppler linewidth (~8?MHz) AT resonance and study its dependence on pump intensity and detuning. In order to explore the possibility of using such a sub-Doppler linewidth resonance for AFOL, we use its first derivative signal as a frequency discriminator to stabilize the probe laser. The frequency stability of the probe is characterized by means of error signal analysis. This study reveals that while the frequency stability of the AT locked laser is limited by the pump laser, the tuning range of the offset frequency lock can cover the entire Doppler profile and its immediate neighbourhood, thereby providing a simple and cost effective alternative to the external modulator. The study described in this paper contributes to the discussion on the subtle link between dressed state spectroscopy and AFOL, which is relevant for developing a master?slave-type laser system in the domain of coherent photon?atom interaction.
In this work, we address the issue of the suitability of blue fluorescent light as a frequency offset reference during the ladder-level excitation 5S1/2→5P3/2→5D3/2 of Rb85 atoms. A simple pump–probe spectroscopy experiment is performed to generate non-degenerate blue light emission produced by the spontaneous decay route 5D3/2→6P3/2→5S1/2. By varying the relative intensity of the pump–probe combination, we can hover between regimes dominated by mechanisms such as double resonance optical pumping (DROP) and Autler–Townes splitting. The efficacy of the blue fluorescence (420 nm) as a frequency offset reference is pronounced under the DROP regime due to its narrow (∼natural) linewidth. To provide further insight into the stability performance, the pump laser connecting the 5P3/2→5D3/2 transition is stabilized to the peak of the blue light with the help of a probe stabilized to the saturation absorption signal of the 5S1/2→5P3/2 transition. For this purpose, we used the coherence-induced modulation transfer technique. The error frequency noise power spectra and the subsequent Allan variance calculation clearly show that probe fluctuations are transferred to the pump laser because of an existing two-photon coherent coupling.
We established a theoretical model for the ladder-type EIT laser frequency stabilization method based on the analysis of the system response. By using the method of deriving the density matrix equations, we obtained the density matrix elements of the three-level system and subsequently derived the system’s response function. Based on this, we revealed the complex interference mechanism of the modulated probe light in the atomic medium. Through quantitative analysis of this process, we obtained the output signal, which carries information about the frequency offset of the coupling light, after the probe light passes through the atomic medium. The error signal obtained after demodulation can then serve as the reference signal for the closed-loop feedback system. To make the error signal more intuitively reflect its variation with the coupling light frequency offset, we introduced the equivalent transfer of the modulation frequency based on the locking relationship between the probe light detuning and the coupling light detuning. This paper provides a deep analysis of the impact of the probe light modulation frequency on the error signal and experimentally validates our theoretical analysis results. Finally, we select a modulation frequency of 10 MHz to lock the coupling light and compare the Allan variance before and after locking. The minimum value of σ ( τ ) was reduced from 4.62×10 −10 before locking to 1.70×10 −10 after locking.
We studied non-resonant two photon absorption (NRTPA) 5S1/2→5D5/2 of hot Rb atom using a laser emitting at 778nm. The decay channel 5D5/2→6P3/2→5S1/2 is monitored to record the blue fluorescence. Two important aspects of blue fluorescence are explored: (i) photon number statistics under counter-propagating beam geometry, (ii) extraction of a workable discriminator signal by using modulation transfer for offset locking. The blue photon statistics histogram closely follows super–Poissonian distribution revealing the partially coherent or chaotic character under the limit of large photon counts. On the other hand modulation amplitude vs. peak height of 1-st derivative signal reveals that too small or too large modulation is detrimental for extracting discriminator signal. Under weak modulation, the offset stabilized laser attains square root of Allan variance σ(τ) ∼ 1.5 × 10−10 at integration time τ>10s. We propose generation of an offset stabilized chaotic blue light source by coupling (i) and (ii).
We have experimentally and theoretically studied resonant two-photon absorption (TPA) and electromagnetically induced transparency (EIT) in the open ladder-type atomic system of the 5S(1/2) (F = 1)-5P(3/2) (F' = 0, 1, 2)-5D(5/2) (F″ = 1, 2, 3) transitions in (87)Rb atoms. As the coupling laser intensity was increased, the resonant TPA was transformed to EIT for the 5S(1/2) (F = 1)-5P(3/2) (F' = 2)-5D(5/2) (F″ = 3) transition. The transformation of resonant TPA into EIT was numerically calculated for various coupling laser intensities, considering all the degenerate magnetic sublevels of the 5S(1/2)-5P(3/2)-5D(5/2) transition. From the numerical results, the crossover from TPA to EIT could be understood by the decomposition of the spectrum into an EIT component owing to the pure two-photon coherence and a TPA component caused by the mixed term.
We have experimentally and theoretically studied resonant two-photon absorption (TPA) and electromagnetically induced transparency (EIT) in the open ladder-type atomic system of the 5S(1/2) (F = 1)-5P(3/2) (F' = 0, 1, 2)-5D(5/2) (F″ = 1, 2, 3) transitions in (87)Rb atoms. As the coupling laser intensity was increased, the resonant TPA was transformed to EIT for the 5S(1/2) (F = 1)-5P(3/2) (F' = 2)-5D(5/2) (F″ = 3) transition. The transformation of resonant TPA into EIT was numerically calculated for various coupling laser intensities, considering all the degenerate magnetic sublevels of the 5S(1/2)-5P(3/2)-5D(5/2) transition. From the numerical results, the crossover from TPA to EIT could be understood by the decomposition of the spectrum into an EIT component owing to the pure two-photon coherence and a TPA component caused by the mixed term.