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![Comparison of modulation-based and modulation-free error signals. Results for direct modulation (DM) and modulation transfer (MT) are from [12]. Numbers for MD correspond to the crossover, and all others to the F](publication/232087763/figure/tbl1/AS:601787383967760@1520488701952/Comparison-of-modulation-based-and-modulation-free-error-signals-Results-for-direct.png)
Comparison of modulation-based and modulation-free error signals. Results for direct modulation (DM) and modulation transfer (MT) are from [12]. Numbers for MD correspond to the crossover, and all others to the F
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We study modulation-free methods for producing sub-Doppler, dispersive line shapes for laser stabilization near the potassium D2 transitions at 767 nm. Polarization spectroscopy is performed and a comparison is made between the use of a mirror or beam splitter for aligning the counter-propagating pump and probe beams. Conventional magnetically-indu...
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... [12] we performed modulation spectroscopy either by direct phase modulation of the probe (DM) or by non-linear modulation transfer from the pump (MT). The results are summarized in Table 1. The modulation-free methods presented here compare well with direct modulation, and use only standard optics available in most labs. ...Similar publications
A shearing interferometer is presented that uses polarization control to shear the wavefront and to modulate the interference pattern. The shear is generated by spatial walk-off in a birefringent crystal. By adjusting the orientation of the birefringent crystal, the components of the wavefront gradient can be independently measured to allow determi...
Citations
... Furthermore, combining two spectroscopic methods with a more complex path of spatial optics has been developed as well [10,11]. Irrespective of the atomic spectroscopy methods used to stabilize the frequency of 1083 nm SFFLs, the spectral widths of the error signal are usually wider than the natural linewidth of the atoms owing to power broadening, pressure broadening, and other effects [7][8][9]12,13]. Under the condition that the spectral width of the error signal is wider than the laser linewidth, only a small number of atoms are selected for the interaction with the laser [14]. ...
... Therefore, the absorption linewidth of atoms (W a0 ) is close to zero, and only the laser with a specific frequency (ω 0 ) can be absorbed to excite the SAS [14]. In practice, due to the natural linewidth, power broadening, pressure broadening, and other effects, atoms in a certain velocity range (v 0 ± ∆v) around v 0 can also satisfy the velocity-selected effect [7][8][9]13]. So, the absorption linewidth of atoms is broadened to W a1 , and the frequency of the absorbed laser is also broadened to ω 0 ± ∆ω. In addition, the linewidth of the laser is defined as W L1 . ...
Single-frequency fiber lasers (SFFLs), 1083 nm, have been extensively applied in ⁴He optical pumping magnetometers (OPMs) for magnetic field detection. However, the sensitivity and accuracy of OPMs are constrained by the frequency stability of SFFLs. Focusing on this concern, the frequency-stabilized performance of the 1083 nm SFFLs is successfully improved by externally tailoring the laser linewidth to match the spectral width of the error signal in saturated absorption spectroscopy. Thereinto, a high-intensity error signal of saturated absorption is generated as a large number of ⁴He atoms with a wide range of velocities interacting with the 1083 nm laser. Consequently, the root mean square value of the fluctuating frequency after locking is effectively decreased from 24.6 to 13.6 kHz, which achieves a performance improvement of 44.7%. Such a strategy can provide a technical underpinning for effectuating an absolute frequency stabilization with higher precision based on atomic and molecular absorption spectroscopy techniques.
... Saturated absorption spectra of 39 K obtained with a 5 cm-long cell were experimentally and theoretically analyzed in [1]. The magnetically induced dichroism of 39 K D 2 line in moderate magnetic fields was studied in [2]. Electromagnetically induced transparency (EIT) in a 39 K vapor was realized in [3], where an EIT-resonance with a linewidth significantly smaller than the natural width (∼ 6 MHz) was formed. ...
It is demonstrated that the use of a micrometric thin 39K vapor cell (MTC) and saturated absorption (SA) spectroscopy allows the formation of narrow atomic lines in the transmission spectrum without unwanted cross-over resonances. Another important feature is the small characteristic magnetic field value $B_0 = A_{hf}/\mu_B$ of 39K, significantly smaller than for Rb and Cs. As a consequence, decoupling of J and I can be observed at relatively low magnetic fields ∼300 G, which results in the formation of two groups of four spectrally-resolved and equidistantly-positioned atomic transitions having the same amplitude (each group corresponds to a given circular polarization $\sigma^\pm$) which we record using a simple experimental setup with a linearly polarized tunable diode-laser and a longitudinal magnetic field obtained with two permanent magnets. Fabrication of a MTC is much easier than the fabrication of the 39K nanocells used in our previous works. A simple method to determine the magnitude of a wide range of B-fields with a spatial resolution of 30 µm is presented, which is intrinsically calibrated and does not require a frequency reference.
... Saturated absorption spectra of 39 K obtained with a 5 cm-long cell were experimentally and theoretically analyzed in [1]. The magnetically induced dichroism of 39 K D 2 line in moderate magnetic fields was studied in [2]. Electromagnetically induced transparency (EIT) in a 39 K vapor was realized in [3], where an EIT-resonance with a linewidth significantly smaller than the natural width (∼ 6 MHz) was formed. ...
It is demonstrated that the use of a Micrometric Thin $^{39}$K vapor Cell (MTC) and Saturated Absorption spectroscopy (SA) allows to form narrow atomic lines in transmission spectrum without unwanted Cross-Over (CO) resonances. Another important feature is the small characteristic magnetic field value $B_0 = A_{hf}/\mu_B$ of $^{39}$K, significantly smaller than for Rb and Cs. As a consequence, decoupling of $J$ and $I$ can be observed at relatively low magnetic fields $\sim$300 G, which results in the formation of two groups of four well-spectrally-resolved and equidistantly-positioned atomic transitions having the same amplitude (each group corresponds to a given circular polarization $\sigma^\pm$) which we record using a simple experimental setup with a linearly polarized tunable diode-laser and a longitudinal magnetic field obtained with two permanent magnets. Fabrication of a MTC is much easier than the fabrication of the $^{39}$K nanocells used in our previous works. A simple method to determine the magnitude of a wide range of B-fields with a spatial resolution of 30 $\mu$m is presented, which is intrinsically calibrated and does not require a frequency reference.
... Accurate stabilization of the laser frequency to an atomic or molecular transition line is crucial in atomic and laser spectroscopy. Several spectroscopic methods have been developed so far such as saturated absorption spectroscopy (SAS) [1][2][3], polarization spectroscopy [4,5], dichroic atomic vapor laser lock (DAVLL) [6,7], sub-Doppler DAVLL [8][9][10][11], magnetically assisted rotation spectroscopy [12], magnetically induced dichroism spectroscopy [13], polarization enhanced absorption spectroscopy [14], frequency modulation spectroscopy [15], and modulation transfer spectroscopy (MTS) [16]. Among these spectroscopic techniques, MTS provides a highly stable and robust frequency stabilization because the signal results from a coherent nonlinear four-wave mixing process [16]. ...
We herein present a theoretical and experimental study on magnetic-field enhanced modulation transfer spectroscopy (MTS) for the 5S1/2 (F = 1) → 5P3/2 (F′ = 0, 1, and 2) transitions of ⁸⁷Rb atoms. The density matrix equations are solved numerically to obtain the MTS spectra and an excellent agreement is found between the experimental and calculated results. In particular, the enhancement of the MTS signal for the F = 1 → F′ = 0 transition in the presence of the magnetic field is directly verified based on the comparison of the results calculated by neglecting with those calculated including the Zeeman coherences in the F = 1 ground state. The unexpected behaviors of the F = 1 → F′ = 1 transition are also examined.
... To date, several frequency locking techniques using atomic transitions as frequency reference have been developed. These include saturated absorption spectroscopy (SAS) [1][2][3], polarization spectroscopy (PS) [4][5][6][7][8][9], dichroic atomic vapor laser locking (DAVLL) [10,11], Doppler-free dichroic lock (DFDL) [12][13][14][15][16][17][18][19][20][21][22][23], two photon sub-Doppler spectroscopy [24][25][26][27], dual frequency sub-Doppler spectroscopy [28,29], and subnatural linewidth spectroscopy [30][31][32]. These techniques differ in their method of implementation as well as in their locking performances. ...
... Therefore, a new perspective in the DFDL technique needs to be explored to improve the S/N ratio for the cooling transition. In this context, Pahwa et al. [19] used the same circular polarization for pump and probe beams to enhance the dichroism in the DFDL technique. They demonstrated an enhanced dispersion-like signal in the potassium (K) cell, when two spatially separated and opposite circularly polarized probe beams (each overlapped by counterpropagating pump beam of same polarization) were used to implement the DFDL scheme. ...
... The dependence of the amplitude and slope of the cooling transition F = 2 → F = 3 of 87 Rb atoms in the PET-DFDL technique on pump power and magnetic field is also investigated to find the optimized parameter for the signal. We note that our PET-DFDL technique provides a better S/N ratio for the closed transition as compared to crossover peaks, which is in contrast to the earlier reported work [19]. The frequency stability of a laser locked using PET-DFDL and locked using conventional DFDL signal is compared. ...
We present a technique, called the polarization enhanced tunable Doppler-free dichroic lock (PET-DFDL) technique, for frequency stabilization of a laser system. This technique is based on the magnetically induced circular dichroism for a pair of circularly polarized probe beams overlapped by oppositely circularly polarized counterpropagating pump beams. The amplitude and slope of the signal generated in the PET-DFDL technique at cooling transition ${\rm{F}} = 2 \to {\rm{F}}^\prime = 3$ F = 2 → F ′ = 3 in $^{87}{\rm Rb}$ 87 R b atom are nearly 4 times higher than those of signal generated from conventional Doppler-free dichroic lock (DFDL). The proposed PET-DFDL technique can also provide tunable lock-position. The frequency stability of a laser system locked with the PET-DFDL technique has been improved by factor of 2 as compared to frequency stability obtained by the DFDL technique. The dependence of PET-DFDL signal on pump beam power and magnetic field for the cooling transition of $^{87}{\rm Rb}$ 87 R b atom is also investigated.
... Therefore, K atomic vapor usually receive less interest as compared to Rb or Cs ones and only a small number of papers can be found: the accurate identification of atomic transitions of K was reported in [108,109]; saturated absorption spectra of the D 1 line of potassium atoms have been studied in details both theoretically and experimentally in [63]. Potassium vapors were used for the investigation of nonlinear magneto-optical Faraday rotation in an antirelaxation paraffin-coated cell [110], polarization spectroscopy and magnetically-induced dichroism for magnetic fields in the range of 1 -50 G [111], formation of dark resonance having a sub-natural linewidth [112], electromagnetically induced transparency [113] and four-wave mixing process [114]. A theory describing the transmission of Faraday filters based on sodium and potassium vapors is presented in [115]. ...
This thesis is aimed at studying the resonant interaction of a laser radiation with an atomic alkali vapor layer of wavelength-scale thickness confined in an optical nanocell; and emerging sensing applications.We focus our attention on the selective reflection arising at the interface between a dielectric window and a resonant alkali vapor, and show that the derivative of selective reflection spectra exhibit narrow resonances whose maxima are located exactly at atomic resonance frequencies. These resonances are observed with a spectral linewidth up to fifteen times smaller than the Doppler linewidth of the medium and their amplitudes scale linearly with respect to the transitions ones. Owing to these properties and the possibility to probe thin atomic layers, we investigate atom-surface interaction and measure the C3 coefficient of the van der Waals interaction.We present a theoretical model describing the interaction of near-resonant laser light with alkali vapor-filled nanocell in the presence of an external static magnetic field. We show an excellent agreement between recorded and calculated spectra in a wide range of magnetic fields spanning from Zeeman to Paschen-Back regimes. Following these results, we propose a concept for a nanocell-based optical magnetometer. A proof of feasibility is presented and a performance analysis reveals a coefficient of variation for the magnetic field measurements less than 5% in the range 0.4 - 2 kG.
... Therefore, there is a small number of papers concerning the laser spectroscopy of potassium: the accurate identification of atomic transitions of K was reported in [4,5]; saturated absorption spectra of the D 1 line of potassium atoms have been studied in details both theoretically and experimentally in [6]. Potassium vapours were used for the investigation of nonlinear magneto-optical Faraday rotation in a antirelaxation paraffin-coated cell [7], polarisation spectroscopy and magnetically-induced dichroism for magnetic fields in the range of 1 -50 G [8], formation of dark resonance having a sub-natural linewidth [9], electromagnetically induced transparency [10] and four-wave mixing process [11]. A theory describing the transmission of Faraday filters based on sodium and potassium vapours is presented in [12]. ...
Selective reflection of a laser radiation from an interface formed by a dielectric window and a potassium atomic vapour confined in a nano-cell with $350~$nm gap thickness is implemented for the first time to study the atomic transitions of K D$_2$ line in external magnetic fields. In moderate $B$-fields, there are 44 individual Zeeman transitions which reduce to two groups (one formed by $\sigma^+$ the other one by $\sigma^-$ circularly-polarised light), each containing eight atomic transitions, as the magnetic field increases. Each of these groups contains one so-called "guiding" transition whose particularities are to have a probability (intensity) as well as a frequency shift slope (in MHz/G) that are constant in the whole range of $0 - 10~$kG magnetic fields. In the case of $\pi$-polarised laser radiation, among eight transitions two are forbidden at $B = 0$, yet their probabilities undergo a giant modification under the influence of a magnetic field. We demonstrate that for $B$-fields $> 165~$G a complete hyperfine Paschen-Back regime is observed. Other peculiarities of K D$_2$ line behaviour in magnetic field are also presented. We show a very good agreement between theoretical calculations and experiments. The recording of the hyperfine Paschen-Back regime of K D$_2$ line with high spectral resolution is demonstrated for the first time.
... atoms were experimentally and theoretically analyzed in [6]. The magnetically induced dichroism for the D 2 line of potassium in a magnetic field of 1-50 G was studied in [7]. The phenomenon of electromagnetically induced transparency in potassium vapors was actualized in [8], and the so-called dark resonance with the linewidth that is significantly smaller than the natural width was formed in this case. ...
The selective reflection of laser radiation from the interface between a dielectric window and the atomic vapors confined in a nanocell of thickness L ≈ 350 nm is used to develop effective Doppler-broadening- free spectroscopy of potassium atoms. A small atomic line width and a relation between the signal intensity and the transition probability allowed us to resolve four lines of atomic transitions responsible for the D1 lines of the 39K and 41K isotopes. Two groups containing four atomic transitions form in an applied magnetic field upon pumping by radiation with circular polarization σ+ or σ–. Different intensities (probabilities) of transitions for the σ+ and σ– excitations are detected in magnetic field B0 ≈ A hfs /μB ≈ 165 G (A hfs is the magnetic dipole constant for the ground state and μB is the Bohr magneton). A substantially different situation is observed at B ≫ B0, since high symmetry appears for the two groups formed by radiation with circular polarization σ+ or σ–. Each group is the mirror image of the other group with respect to the frequency of the 42S1/2–42P1/2 transition, which additionally proves the occurrence of the complete Paschen–Back regime of the hyperfine structure at B ≈ 2.5 kG. A developed theoretical model well reproduces the experimental results. Possible practical applications are described. The results obtained can also be applied to the D1 lines of 87Rb and 23Na.
... Laser spectroscopy free from Doppler shifts experienced by the fast-moving erbium atoms in our HCL is enabled through a well-studied [20][21][22][23][24][25][26], modulation-free variant of Dopplerfree techniques based on overlapping pump and probe beams.In the general Doppler-free spectroscopy setup, the lower intensity probe beam features a narrow response in its interaction with the atomic medium at resonance, i.e. when the probe and the higher intensity pump beam interact with the same class of atoms near zero velocity (projected along the axis of beam propagation) [27,28]. ...
In this work we perform polarization spectroscopy of erbium atoms in a hollow cathode lamp (HCL) for the stabilization of a diode laser to the 401-nm transition. We review the theory behind Doppler-free polarization spectroscopy, theoretically model the expected erbium polarization spectra, and compare the numerically calculated spectra to our experimental data. We further analyze the dependence of the measured spectra on the HCL current and the peak intensities of our pump and probe lasers to determine conditions for optimal laser stabilization.
... This laser is locked using a technique called sub-Doppler magnetically-induced dichroism (MIDL) [85] at the crossover feature of the spectroscopy signal shown in Figure 3.2a), and has been providing a very reliable error signal since it was rst set up (May, 2012). ...
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