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Physica Scripta

Coherent spectroscopy of a Λ atomic system and its prospective application to tunable frequency offset locking

Y. B. Kale, Ayan Ray, Q. V. Lawande, B. N. Jagatap

Published Aug 9, 2011• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/84/03/035401

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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 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 coherent pump–probe spectroscopy of a medium of atoms in Λ configuration with a closely placed adjacent excited level. The presence of the additional level results in two simultaneous Λ resonances excited by the same pair of pump and probe fields. A master equation framework is used to discuss the probe absorption spectrum and dispersion in the absence/presence of inhomogeneous broadening, and the results are illustrated by using a model four-level system in the D2 transition of 85Rb. The system is observed to exhibit additional interference effects arising from two competing Λ resonances. These effects manifest in terms of linewidths of the triplet dressed state spectrum and suppression of the subnatural peak for the stationary atoms. The effect on electromagnetically induced transparency is discussed in the light of its shape, position and linewidth. The discussion is further augmented by the study of a six-level model as applicable to the D2 transition of 85Rb. The analysis presented here provides a realistic theoretical description of the pump–probe spectroscopy of hyperfine transitions of alkali atoms.
In this Letter, we present a widely tunable laser frequency offset locking technique based on four-wave mixing (FWM). The Raman-amplified probe light and newly generated conjugate light exhibit high signal amplitude and ultra-narrow spectral characteristics, which contribute to robust laser frequency stabilization. The laser frequency can be selectively locked to the Stokes or anti-Stokes frequency of the four-wave mixing spectrum, maintaining a fixed frequency difference relative to the pump light that corresponds to the atomic ground state hyperfine splitting. By adjusting the detuning of the pump light frequency, a wide tuning range of several GHz can be achieved. Compared to the frequency modulation spectroscopy method, the modulation transfer technique in a double-lambda atomic system provides an atomic coherence-enhanced error signal with a larger peak-to-peak amplitude and a steeper zero-crossing gradient, resulting in significantly improved laser frequency stabilization performance. This method can enhance the performance of atomic sensors, such as improving the stability of the Raman light for atomic interferometers and increasing the laser stability of highly sensitive atomic magnetometers.
We make a detailed comparison of frequency modulation spectroscopy (FMS) and modulation transfer spectroscopy (MTS) and of their applications in stabilizing laser frequency. In both FMS and MTS, intensity modulations of probe beam are observed in saturated absorption spectroscopy of 87Rb atoms. However, the two modulation profiles appear different due to their distinct origins. Demodulation gives rise to frequency discrimination spectra, which can serve as error signals for frequency locking. The optimal error signal of FMS has a larger linear slope but also a slanted baseline, in contrast to that of MTS. We apply FMS and MTS to stabilize two 780 nm external cavity diode lasers to D2 lines of 87Rb atoms. We measure laser linewidth and stability using beat notes of two independently locked lasers. A laser linewidth as narrow as 12.9 kHz is achieved in FMS locking, compared to 70.8 kHz in MTS locking. A laser stability at the level of 10−12 is reached in both schemes. Nevertheless, FMS locking offers a better short-term stability, whereas MTS locking yields a smaller long-term drift. Our investigation of FMS and MTS would be valuable for making a choice of these spectroscopy techniques for laser stabilization as well as other relevant applications.
The stabilizing and shifting of laser frequency are very important for the interaction between the laser and atoms. The modulation transfer spectroscopy for the 87 Rb atom with D2 line transition F = 2 → F′ = 3 is used for stabilizing and shifting the frequency of the external cavity grating feedback diode laser. The resonant phase modulator with electro—optical effect is used to generate frequency sideband to lock the laser frequency. In the locking scheme, circularly polarized pump- and probe-beams are used. By optimizing the temperature of the vapor, the pump- and probe-beam intensity, the laser linewidth of 280 kHz is obtained. Furthermore, the magnetic field generated by a solenoid is added into the system. Therefore the system can achieve the frequency locking at any point in a range of hundreds of megahertz frequency shifting with very low power loss.
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.