Features of Magnetically-induced atomic transitions of Rb D$_1$ line studied by Doppler-free method based on the second derivative of the absorption spectra
Armen Sargsyan, Arevik Amiryan, Emmanuel Klinger, David Sarkisyan
We show that the Second Derivative (SD) technique of the absorption spectra of Rb atomic vapours confined in a nanocell with a thickness $\ell= λ/2=398$ nm allows to achieve close to Doppler-free spectroscopy. Narrow linewidth and linearity of the SD signal response with respect to transition probabilities allow us to study separately, in an external transverse magnetic field (0.6 to 4 kG), a big number of the atomic transitions of $^{85}$Rb and $^{87}$Rb atoms. Atomic transitions $|F_g,0\rangle \rightarrow |F_e=F_g,0'\rangle$, for which the dipole moment is null at zero magnetic field (so-called magnetically-induced transitions), show a gigantic increase in probability with increasing magnetic field. When a magnetic field is applied on the vapour, we show the possibility of forming a dark resonance on these transitions by adding a coupling laser. We hence demonstrate a five-fold increase in the transmission of the probe radiation when the coupling laser is on. Theoretical calculations are in a very good agreement with experimental results.
We study the absorptive and dispersive properties of Doppler-broadened atomic media as a function of detuning. Beginning from the exact lineshape calculated for a two-level atom, a series of approximations to the electric susceptibility are made. These simplified functions facilitate direct comparison between absorption and dispersion, and show that dispersion dominates the atom-light interaction far from resonance. The calculated absorption and dispersion are compared to experimental data, showing the validity of the approximations.
We report on Doppler-free laser spectroscopy in a Cs vapor cell using a dual-frequency laser system tuned on the Cs D$_1$ line. Using counter-propagating beams with crossed linear polarizations, an original sign-reversal of the usual saturated absorption dip and large increase in Doppler-free atomic absorption is observed. This phenomenon is explained by coherent population trapping (CPT) effects. The impact of laser intensity and light polarization on absorption profiles is reported in both single-frequency and dual-frequency regimes. In the latter, frequency stabilization of two diode lasers…
We propose and demonstrate a laser frequency stabilization scheme which generates a dispersion-like tunable Doppler-free dichroic lock (TDFDL) signal. This signal offers a wide tuning range for lock point (i.e. zero-crossing) without compromising on the slope of the locking signal. The method involves measurement of magnetically induced dichroism in an atomic vapour for a weak probe laser beam in presence of a counter propagating strong pump laser beam. A simple model is presented to explain the basic principles of this method to generate the TDFDL signal. The spectral shift in the locking sig…
Applying a many mode Floquet formalism for magnetically trapped atoms interacting with a polychromatic rf-field, we predict a large two photon transition probability in the atomic system of cold $^{87}Rb$ atoms. The physical origin of this enormous increase in the two photon transition probability is due to the formation of avoided crossings between eigen-energy levels originating from different Floquet sub-manifolds and redistribution of population in the resonant intermediate levels to give rise to the resonance enhancement effect. Other exquisite features of the studied atom-field composite…
We investigate cooling mechanisms in magneto-optically and magnetically trapped erbium. We find efficient sub-Doppler cooling in our trap, which can persist even in large magnetic fields due to the near degeneracy of two Lande g factors. Furthermore, a continuously loaded magnetic trap is demonstrated where we observe temperatures below 25 microkelvin. These favorable cooling and trapping properties suggest a number of scientific possibilities for rare-earth atomic physics, including narrow linewidth laser cooling and spectroscopy, unique collision studies, and degenerate bosonic and fermionic…
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-induced dichroism is found to suffer from a small dispersion and large background offset. We therefore introduce a modified scheme, using two spatially separated pump-probe beam pairs. Finally we compare our results to methods using phase modulation and …
We report experimental observation of velocity-selective resonances in the Doppler-broadened probe absorption spectra of 85Rb and 87Rb D2 transitions in the presence of a strong copropagating pump laser locked to a frequency within the Doppler profile of the transition. The set of three dips having the separation of allowed hyperfine transitions can be moved along the Doppler profile by tuning the pump laser frequency indicating a resonance between the pump laser frequency and the velocity shifted probe laser frequency.
Doppler broadening in thermal ensembles degrades the absorption cross-section and the coherence time of collective excitations. In two photon transitions, it is common to assume that this problem becomes worse with larger wavelength mismatch. Here we identify an opposite mechanism, where such wavelength mismatch leads to cancellation of Doppler broadening via the counteracting effects of velocity-dependent light-shifts and Doppler shifts. We show that this effect is general, common to both absorption and transparency resonances, and favorably scales with wavelength mismatch. We experimentally …
We report on the observation of sub-Doppler resonances on the back-scattered light from a random porous glass medium with rubidium vapor filling its interstices. The sub-Doppler spectral lines are the consequence of saturated absorption where the incident laser beam saturates the atomic medium and the back-scattered light probes it. Some specificities of the observed spectra reflect the transient atomic evolution under confinement inside the pores. Simplicity, robustness and potential miniaturization are appealing features of this system as a spectroscopic reference.
Magnetically Induced Transparency-Absorption and Normal-Anomalous Dispersion Characteristics of ${}^{87}\text{Rb}$ Medium or Any J-Type Configuration Atomic Vapors Subject to a Vector Magnetic Field and a Weak Resonant Pump
Using the z-scan technique, we have measured the self-induced absorptive and refractive nonlinear behavior of hot atomic rubidium vapor within the Doppler profile of the D2 line. We observe large nonlinear amplitude and phase effects with only tens of microwatts of incident power. Our results are in good agreement with numerical calculations based on an analytic model of a Doppler- broadened two-level system.
We present a detailed study of the absolute Doppler-broadened absorption of a probe beam scanned across the potassium D lines in a thermal vapour. Spectra using a weak probe were measured on the 4S $\rightarrow$ 4P transition and compared to the theoretical model of the electric susceptibility detailed by Zentile et al. (2015) in the code named ElecSus. Comparisons were also made on the 4S $\rightarrow$ 5P transition with an adapted version of ElecSus. This is the first experimental test of ElecSus on an atom with a ground state hyperfine splitting smaller than that of the Doppler width. An ex…
In this paper, we describe an experiment performed at the Laboratoire de Physique des Lasers and dedicated to an optical measurement of the Boltzmann constant. With the proposed innovative technique, determining comes down to an ordinary frequency measurement. The method consists in measuring as accurately as possible the Doppler absorption profile of a rovibrational line of ammonia in thermal equilibrium. This profile is related to the Maxwell-Boltzmann molecular velocity distribution along the laser beam. A fit of the absorption line shape leads to a determination of the Doppler width propor…
We propose and demonstrate pump-probe spectroscopy of rubidium absorption which reveals the sub-Doppler hyperfine structure of the $^{5}$S$_{1/2} \leftrightarrow$ $^{5}$P$_{3/2}$ (D2) transitions. The counter propagating pump and probe lasers are independently tunable in frequency, with the probe operating at the single-photon-level. The two-dimensional spectrum measured as the laser frequencies are scanned shows fluorescence, Doppler-broadened absorption dips and sub-Doppler features. The detuning between the pump and probe lasers allows compensation of the Doppler shift for all atomic veloci…
Literature mentions only incidentally a sub-Doppler contribution in the excitation spectrum of the backward fluorescence of a dense vapor. This contribution is here investigated on Cs vapor, both on the first resonance line (894 nm) and on the weaker second resonance line (459 nm). We show that in a strongly absorbing medium, the quenching of excited atoms moving towards a window irradiated under near normal incidence reduces the fluorescence on the red side of the excitation spectrum. Atoms moving slowly towards the window produce a sub- Doppler velocity-selective contribution, whose visibili…
We compute the interaction of a sodium vapor with a static magnetic field ranging from 0 up to 1 Tesla, which allows to obtain the behavior of all Zeeman transitions as a function of the magnetic field for any polarization of incident laser radiation: $π, σ^\pm$. We use these results combined with a Fabry-Pérot microcavity model to describe the transmitted and reflected signal of a sodium vapor confined in a nanometric-thin cell. This allows us to present for the first time high resolution absorption spectra, and provide a complete description of the Zeeman transitions, along with some importa…
Weak transitions in the (2,0) overtone band of the HD molecule at $λ= 1.38 \, μ$m were measured in saturated absorption using the technique of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Narrow Doppler-free lines were interrogated with a spectroscopy laser locked to a frequency comb laser referenced to an atomic clock to yield transition frequencies [R(1) = $217\,105\,181\,895\,(20)$ kHz; R(2) = $219\,042\,856\,621\,(28)$ kHz; R(3) = $220\,704\,304\,951\,(28)$ kHz] at three orders of magnitude improved accuracy. These benchmark values provide a test of QED in the sm…
We demonstrate Doppler-free saturated absorption spectroscopy of cold molecular radicals formed by laser ablation inside a cryogenic buffer gas cell. By lowering the temperature, congested regions of the spectrum can be simplified, and by using different temperatures for different regions of the spectrum a wide range of rotational states can be studied optimally. We use the technique to study the optical spectrum of YbF radicals with a resolution of 30 MHz, measuring the magnetic hyperfine parameters of the electronic ground state. The method is suitable for high resolution spectroscopy of a g…
We propose a four-level model where sub-Doppler resolution as well as enhanced absorption of a weak probe field are realized by using two coherently driving fields. We show that spectral resolution can be improved by modifying the coherent fields intensity and frequencies.
An influence of nonlinear interference processes at quantum transitions under strong resonance electromagnetic fields on absorption, amplification and refractive indices as well as on four-wave mixing processes is investigated. Doppler broadening of the coupled transitions, incoherent excitation, relaxation processes, as well as power saturation processes associated with the coupled levels are taken into account. Both closed (ground state is involved) and open (only excited states are involved) energy level configurations are considered. Common expressions are obtained which allow one to analy…
We study modulation spectroscopy of the potassium D2 transitions at 766.7 nm. The vapour pressure, controlled by heating a commercial reference cell, is optimized using conventional saturated absorption spectroscopy. Subsequent heterodyne detection yields sub-Doppler frequency discriminants suitable for stabilizing lasers in experiments with cold atoms. Comparisons are made between spectra obtained by direct modulation of the probe beam, and those using modulation transfer from the pump via nonlinear mixing. Finally, suggestions are made for further optimization of the signals.
We consider the phase stability of a local oscillator (or laser) locked to a cavity QED system comprised of atoms with an ultra-narrow optical transition. The atoms are cooled to millikelvin temperatures and then released into the optical cavity. Although the atomic motion introduces Doppler broadening, the standing wave nature of the cavity causes saturated absorption features to appear, which are much narrower than the Doppler width. These features can be used to achieve an extremely high degree of phase stabilization, competitive with the current state-of-the-art. Furthermore, the inhomogen…
A density matrix based analytical model is developed to study the coherent probe field propagation through a four-level V type system in presence of a coherent control field. The model allows coupling of the probe field from the upper ground level to both of the excited levels keeping the control field locked to a particular transition. The addition of an extra ground level to a conventional three-level V type system creates extra decay paths to the ground levels for the upper level population. A set of sixteen density matrix based equations are formed and then solved analytically under rotati…
We obtain subnatural linewidth (i.e. $<Γ$) for probe absorption in room-temperature Rb vapor using electromagnetically induced transparency (EIT) in a $Λ$ system. For stationary atoms, the EIT dip for a resonant control laser is as wide as the control Rabi frequency $Ω_c$. But in thermal vapor, the moving atoms fill the transparency band so that the final EIT dip remains subnatural even when $Ω_c > Γ$. We observe linewidths as small as $Γ/7$ in the $D_2$ line of Rb.
We present a theoretical investigation of the phenomenon of electromagnetically induced absorption (EIA) in a 4-level system consisting of vee and ladder subsystems. The four levels are coupled using one weak probe field, and two strong control fields. We consider an experimental realization using energy levels of Rb. This necessitates dealing with different conditions of wavelength mismatch---near-perfect match where all three wavelengths are approximately equal; partial mismatch where the wavelength of one control field is less than the other fields; and complete mismatch where all three wav…
In this paper, we present significant progress performed on an experiment dedicated to the determination of the Boltzmann constant, k, by accurately measuring the Doppler absorption profile of a line in a gas of ammonia at thermal equilibrium. This optical method based on the first principles of statistical mechanics is an alternative to the acoustical method which has led to the unique determination of k published by the CODATA with a relative accuracy of 1.7 ppm. We report on the first measurement of the Boltzmann constant by laser spectroscopy with a statistical uncertainty below 10 ppm, mo…
Warm atomic vapor quantum memories are simple and robust, yet suffer from a number of parasitic processes which produce excess noise. For operating in a single-photon regime precise filtering of the output light is essential. Here we report a combination of magnetically tuned absorption and Faraday filters, both light-direction-insensitive, which stop the driving lasers and attenuate spurious fluorescence and four-wave mixing while transmitting narrowband Stokes and anti-Stokes photons generated in write-in and readout processes. We characterize both filters with respect to adjustable working …
We have detected and analysed narrow high-contrast coherent population trapping (CPT) resonances, which are induced in absorption of the weak probe light beam by the counterpropagating two-frequency pumping radiation. Our experimental investigations have been carried out on example of nonclosed three level Lambda systems formed by spectral components of the Doppler broadened D2 line of cesium atoms. We have established that CPT resonances in transmission of the probe beam (in the cesium vapor), at definite conditions, may have not only more contrast but also much lesser width in comparison wit…
Laser cooling is theoretically investigated in a cascade three-level scheme, where the excited state of a laser-driven transition is coupled by a second laser to a top, more stable level, as for alkali-earth atoms. The second laser action modifies the atomic scattering cross section and produces temperatures lower than those reached by Doppler cooling on the lower transition. When multiphoton processes due to the second laser are relevant, an electromagnetic induced transparency modifies the absorption of the first laser, and the final temperature is controlled by the second laser parameters. …
We demonstrate a new technique for saturated-absorption spectroscopy using co-propagating beams that does not have the problem of crossover resonances. The pump beam is locked to a transition and its absorption signal is monitored while the probe beam is scanned. As the probe comes into resonance with another transition, the pump absorption is reduced and the signal shows a Doppler-free dip. We use this technique to measure hyperfine intervals in the $D_2$ line of $^{85}$Rb with a precision of 70 kHz, and to resolve hyperfine levels in the $D_2$ line of $^{39}$K that are less than 10 MHz apart…
In this paper, we present the latest results on the measurement of the Boltzmann constant kB, by laser spectroscopy of ammonia at 10 ?m. The Doppler absorption profile of a ro-vibrational line of an NH3 gas sample at thermal and pressure equilibrium is measured as accurately as possible. The absorption cell is placed inside a large 1m3 thermostat filled with an ice-water mixture, which sets the temperature very close to 273.15 K. Analysing this profile, which is related to the Maxwell-Boltzmann molecular speed distribution, leads to a determination of the Boltzmann constant via a measurement o…
We report an experimental investigation on the Doppler-free saturated absorption spectroscopy of buffer-gas-cooled Barium monofluoride (BaF) molecules in a 4~K cryogenic cell. The obtained spectra with a resolution of 19~MHz, much smaller than previously observed in absorption spectroscopy, clearly resolve the hyperfine transitions. Moreover, we use these high-resolution spectra to fit the hyperfine splittings of excited $A(v=0)$ state and find the hyperfine splitting of the laser-cooling-relevant $A^2Π_{1/2}(v=0, J=1/2, +)$ state is about 18 MHz, much higher than the previous theoretically pr…
The Voigt profile - a convolution of a Gaussian and a Lorentzian - accurately describes the absorption lines of atomic and molecular gases at low probe powers. Fitting such to experimental spectra yields both the Lorentzian natural linewidth and the Gaussian Doppler broadening. However, as the probe power increases saturation effects introduce spurious power dependence into the fitted Doppler width. Using a simple atomic model, we calculate power-dependent corrections to the Voigt profile, which are parametrized by the Gaussian Doppler width, the Lorentzian natural linewidth, and the optical d…
Traditionally, measuring the center-of-mass (c.m.) velocity of an atomic ensemble relies on measuring the Doppler shift of the absorption spectrum of single atoms in the ensemble. Mapping out the velocity distribution of the ensemble is indispensable when determining the c.m. velocity using this technique. As a result, highly sensitive measurements require preparation of an ensemble with a narrow Doppler width. Here, we use a dispersive measurement of light passing through a moving room temperature atomic vapor cell to determine the velocity of the cell in a single shot with a short-term sensi…
In this paper, we describe two complementary non-linear spectroscopy methods which both allow to achieve Doppler-free spectra of atomic gases. First, saturated absorption spectroscopy is used to investigate the structure of the $5{\rm S}_{1/2}\to 5{\rm P}_{3/2}$ transition in rubidium. Using a slightly modified experimental setup, Doppler-free two-photon absorption spectroscopy is then performed on the $5{\rm S}_{1/2}\to 5{\rm D}_{5/2}$ transition in rubidium, leading to accurate measurements of the hyperfine structure of the $5{\rm D}_{5/2}$ energy level. In addition, electric dipole selectio…
The method of Doppler - free comb - spectroscopy for dipole transitions was proposed. The calculations for susceptibility spectrum for moving two-level atoms driving by strong counter propagating combs have been done. The used theoretical method based on the Fourier expansion of the components of density matrix on two rows on kv (v-velocity of group of atoms, k-projection of wave vector) and Ω (frequency between comb components). For testing of validity of this method the direct numerical integration was done. The narrow peaks with homogeneous width arise on the background of Doppler counter. …
