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A Tunable Doppler-Free Dichroic Lock for Laser Frequency Stabilization

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A Tunable Doppler-Free Dichroic Lock for Laser Frequency Stabilization my journal manuscript No. (will be inserted by the editor) A tunable Doppler-free dichroic lock for laser frequency stabilization Vivek Singh, V. B. Tiwari, S. R. Mishra and H. S. Rawat Laser Physics Applications Section, Raja Ramanna Center for Advanced Technology, Indore-452013, India. Received: date / Revised version: date Abstract We propose and demonstrate a laser fre- resolution spectroscopy [2], precision measurements [3] quency stabilization scheme which generates a dispersion- etc. A setup for laser cooling and trapping of atoms re- like tunable Doppler-free dichroic lock (TDFDL) signal. quires several lasers which are actively frequency sta- This signal offers a wide tuning range for lock point bilized and locked at few line-widths detuned from the (i.e. zero-crossing) without compromising on the slope peak of atomic absorption. In the laser cooling experi- of the locking signal. The method involves measurement ments, the active frequency stabilization is achieved by of magnetically induced dichroism in an atomic vapour generating a reference signal which is based on absorp- for a weak probe laser beam in presence of a counter tion profile of atom around the resonance. The refer- propagating strong pump laser beam. A simple model is ence locking signal can be either Doppler-broadened with presented to explain the basic principles of this method wide tuning range or Doppler-free with comparatively to generate the TDFDL signal. The spectral shift in the much steeper slope but with limited tuning range. The locking signal is achieved by tuning the frequency of the most commonly used technique for frequency locking pump beam. The TDFDL signal is shown to be use- involves locking to the side of the Doppler free peak ful for locking the frequency of a cooling laser used for generated from the saturated absorption spectroscopy magneto-optcal trap (MOT) for 87Rb atoms. (SAS) [4, 5]. The locking of the laser frequency to the arXiv:1604.07619v1 [physics.atom-ph] 26 Apr 2016 peak of an atomic reference signal such as in frequency modulated spectroscopy (FMS) [6] provides high signal 1 Introduction to noise ratio (SNR) but needs dithering of laser fre- quency and a phase sensitive detection system. A suit- Laser frequency stabilization is an essential requirement able dispersion-like reference signal for peak locking can for various applications including atom cooling [1], high 2 Vivek Singh et al. be generated using polarizing spectroscopy (PS) [7{11] study on DFDL spectroscopy of D-2 line of 87Rb includes without frequency modulation and phase sensitive detec- coherence for calculation of line-shape of real atomic sys- tion. Along with these techniques, there are also meth- tem [30]. ods for laser frequency stabilization which employ PS Here, we present a technique which generates a narrow with external magnetic field [12, 13]. However, the tech- tunable DFDL (TDFDL) signal without compromising niques involving polarization spectroscopy are sensitive with the slope of the signal. The frequency tuning of this to the surrounding stray magnetic field [14]. An alterna- dispersion like TDFDL signal is achieved by varying the tive technique which can generate narrow dispersion like pump laser frequency using AOMs. We have studied the reference signal exploits circular dichroism of an atomic dependence of this frequency locking signal's amplitude vapour in the presence of a magnetic field. In this tech- and the slope on various experimental parameters such nique, the difference of Zeeman shifted saturated ab- as the pump beam power and the magnetic field. The sorption signals generate the Doppler free dichroic lock locking performance of an extended cavity diode laser (DFDL)signal [15{24]. This technique requires only low (ECDL) system is investigated by measuring change in magnetic field for its operation and is less sensitive to the number of cold atoms in a magneto-optical trap the surrounding stray magnetic field. However, the tun- (MOT). A simple theoretical model to explain the gen- ing range of this technique is limited to few natural eration of TDFDL signal is also presented. linewidths of the transition. The tuning range can be in- creased by electronically adding an offset voltage to the 2 Theoretical analysis signal or by optically changing the quarter wave plate We adopt a simple two-level system involving hyperfine axis relative to the polarisation beam splitter axis [16]. energy levels to explain the generation of TDFDL signal. The locking range can also be extended by either using A linearly polarized weak probe beam is overlapped by Doppler-broadened version of this technique known as a counter-propagating strong pump beam in an atomic dichroic atomic vapor laser lock (DAVLL) [25{28] sig- vapor cell placed in a weak magnetic field. The propa- nal or by locking at positive as well as negative slopes gation of the probe beam is along the axis of magnetic of DFDL signal [16]. Another method involves increas- field. The linearly polarized light can be resolved into ing the magnetic field [29] to extend the locking range of two counter-rotating circular components σ± using quar- the DFDL signal. This frequency tuning is often achieved ter wave plate and polarizing beam splitter. In the ab- by compromising the slope of the signal which is a cru- sence of magnetic field (B=0), different mF 0 states are cial parameter for frequency locking. A recently reported degenerate and hence, σ+ and σ− transitions overlap. A tunable Doppler-free dichroic lock for laser frequency stabilization 3 ( ) p ( ) c Probe Atom Pump mF ' 1 2kvz B F'1 mF ' 0 B mF ' 1 2kvz c ( ) p ( ) c ( ) p ( ) F 0 mF 0 (i) B 0 (ii) B 0 Fig. 1 Schematic diagram showing resonant interaction of σ+ and σ− polarized pump and the probe beams when a weak magnetic field is applied to an atom having lower level F = 0 and upper level F 0 = 1 is in motion. When a small magnetic field (few Gauss) is applied, the of frequency detunings with the pump and the probe degeneracy is lifted and medium becomes dichroic due beams in the presence of magnetic field. The σ± polar- to the displacement of σ+ and σ− transitions. As a re- ized pump and the probe beams can interact resonantly sult, the pair of spectrally shifted saturated absorption with this group of atoms if, spectroscopy (SAS) signals on subtraction generate the !p(σ±) − kvz = !0 ± ∆B (1) Doppler free dispersion like signal [29]. For atoms moving with velocity v, the Doppler shifted laser frequency in 0 !c(σ±) + kvz = !0 ± ∆B (2) the frame of moving atom becomes ! = !0 −k:v. When the laser beam passes through a Rb atomic sample with Using equation (1) and (2), the relation between the a Maxwell-Boltzmann velocity distribution, only those ± probe beam detuning ∆p = !p(σ±) − !0 and the pump atoms which fall within the homogeneous linewidth Γ ± beam detuning ∆c = !c(σ±) − !0 for resonant interac- around the center frequency !0 of Rb atom at rest can tion is given by significantly contribute to the absorption. ± ± ∆c + ∆p = ±2∆B (3) If the pump beam having frequency (!c) and the probe beam having frequency (! ) are in counter propagating p Again using equation (1) and (2), the difference between directions, the atoms having velocity components of v z the pump and the probe beam detunings is given by, along direction of the probe beam see different values ± ± ∆cp = ∆c − ∆p = −2kvz (4) 4 Vivek Singh et al. Using equation (3) and (4), resonance condition for σ± of dips burnt in the distribution by the pump beam and probe beam in presence of counter propagating pump depends on the pump beam intensity used. For our cal- beam and applied magnetic field can be written as culations, we have assumed g = g1 = g2. The population ∆ in the ground state with velocity range vz and vz + dvz ∆± = − cp ± ∆ (5) p 2 B from where probe makes absorption transition is given Therefore, the probe absorption signal will depend upon as the difference between the pump and the probe beams 0 2 N (vz)dvz = Cexp[−(vz=vp) ]dvz (8) detunings and the applied magnetic field. In the case of simple model, F = 0 ! F 0 = 1, the where vp is most probable velocity and C is a constant depending on number of atoms in gas, density etc.. absorption cross-section for σ± probe beam for an atom The absorption coefficient for a weak probe laser beam with velocity component vz is given as [4] in presence of the pump beam is given by ρ (Γ=2)2 ρ (∆±; v ) = 0 (6) ± p z ± 2 2 (∆p ∓ ∆B − kvz) + (Γ=2) Z 1 ± ± ± ± α±(∆p ; ∆c ) = ρ±(∆p ; vz)∆N(∆c ; vz)dvz (9) ± −∞ where ρ0 is maximum absorption cross section at ∆p = 0 The integration in (9) can be performed over velocity ±∆B + kvz, ∆B = µBBgF 0 mF 0 =~ (for F = 0 ! F = 1 and assuming the Doppler width, ∆D >> Γ (where case) is Zeeman splitting of the levels in magnetic field, ∆D = kvp) to obtain α± values. k is the wave vector of laser light. For low optical density of the sample, the TDFDL signal Due to pump laser beam (!c), population density in (represented by DS) can be calculated to be ground state (F = 0 level) decreases within the veloc- Γ ± ± + + − − ity interval dvz = k , while population density in mag- DS(∆p ; ∆c ) = α+(∆p ; ∆c ) − α−(∆p ; ∆c ) (10) netically shifted upper level (F 0 = ±1 level) increases. Using equation (7), (8) and (9), the TDFDL signal is Therefore, population in the lower level after pump has ± ± caused excitation from lower level is given by DS(∆p ; ∆c ) = C[(D+ − D−) − g(D+L+ − D−L−)] (11) ± 0 ∆N(∆c ; vz) = N (vz)[1− 1 2 ± 2 (Γ=2) where D± = p exp [−((∆ ∓ ∆B)=∆D) ] − g π p 1 + 2 2 (∆c − ∆B + kvz) + (Γ=2) Γ 2 L = 2 ± ± ± 2 2 (Γ=2) (∆p + ∆c ∓ 2∆B) + (2Γ=2) − g2 ] (7) (∆− + ∆ + kv )2 + (Γ=2)2 c B z L± can be written in terms of ∆cp using equation (4), 2 0 (Γ=2) where Γ is a natural line width for F = 0 ! F = 1 tran- L = ± ∆ (∆± + cp ∓ ∆ )2 + (Γ=2)2 p 2 B sition, g1 and g2 are coefficients representing the depth A tunable Doppler-free dichroic lock for laser frequency stabilization 5 - 4 0 M H z 4 0 0 M H z ) .
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