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arXiv:2308.12386 · Physical Review A

Observation of quantum interference of optical transition pathways in Doppler-free two-photon spectroscopy and implications for precision measurements

Bubai Rahaman, Sid C. Wright, Sourav Dutta

Published Apr 22, 2024• 7 citations
arXivHTMLPDF

Abstract

Doppler-free two-photon (DFTP) spectroscopy is a standard technique for precision measurement of transition frequencies of dipole-forbidden transitions. Here, we report the observation of quantum interference (QI) of optical transition pathways in DFTP spectroscopy of the cesium $6S\text{\ensuremath{-}}7D$ transitions chosen as a prototype system. The QI manifests itself as asymmetric line shapes of the hyperfine lines of the $7D$ states, observed through spontaneous emission following excitation by a narrow-linewidth cw laser. The interference persists despite the lines being spectrally well resolved. Ignoring the effect and fitting the spectrum to a Voigt profile causes large systematic shifts in the determination of the line centers, while accounting for QI resolves the apparent line shift and enables the precise determination of hyperfine splitting in the $7D$ states. We calculate the spectral line shape including the effect of QI and show that it agrees with the experimental observations. Our results are broadly applicable to other species and have implications for portable secondary optical clocks and precision measurements of hyperfine splittings, isotope shifts, and transition frequencies.

DOI
10.1103/physreva.109.042820

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Two-color polarization spectroscopy (TCPS) of cesium 6S1/2-6P3/2-8S1/2 (852.3 nm + 794.6 nm) ladder-type system in a room-temperature vapor cell are investigated. The frequency of 852.3 nm laser used as a pump beam is locked on one of the hyperfine transitions between the ground state 6S1/2 and excited state 6P3/2 by the saturated absorption spectroscopy technique, which can populate some atoms on the 6P3/2 excited state and induce anisotropy in the atomic medium. The frequency of 794.6 nm laser serving as a probe beam is scanned across the whole 6P3/2→8S1/2 transition to ascertain this anisotropy, and thus the TCPS is obtained. In experiment, we measure and analyse the influence of frequency detuning of 852.3 nm pump laser on TCPS, and especially reveal that some of hyperfine energy levels of intermediate excited state 6P3/2, which has no direct interaction with the 852.3 nm pump laser, are also populated by a small fraction of atoms with a specific speed in the direction of pump laser beam due to Doppler effect, so they also have contribution to the TCPS when the 794.6 nm probe laser is scanned to the resonance transition line between the 6P3/2 and 8S1/2 states after the Doppler frequency shift has been considered. In addition, we prove that the atomic coherence like electromagnetically induced transparency effect obviously results in a narrower line width of TCPS in the case of counter-propagating experimental configuration than that in the case of pump beam co-propagating with the probe beam in the Cs vapor cell. Finally, we apply the TCPS with dispersive shaped feature to frequency stabilization with no modulation, and the frequency fluctuations of 794.6 nm laser are ～0.5 MHz and ～9.2 MHz for the frequency-locking and free running in ～225 s, respectively. The above research work is expected to play a role in precisely measuring the atomic energy level structure and its related hyperfine structure constant (magnetic dipole and electric quadrupole coupling constants), and also in stabilizing the laser frequency to the excited state transition especially for the optical fiber communication, two-color laser cooling/trapping neutral atoms, optical filter, etc.

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High-sensitivity spectroscopy of caesium's higher excited 8S 1/2 state is obtained by a coherent two-photon transition via an intermediate resonance state. The ladder-type atomic system is driven by two counter-propagating low-power diode lasers, the probe laser being tuned to the transition from the ground state to the intermediate state (6S 1/2 –6P 1/2 ), and the coupling laser to that between the intermediate and the final state (6P 1/2 –8S 1/2 ). By locking the probe laser and scanning the coupling laser, the electromagnetically induced transparency (EIT) peaks appear in the probe transmission when the coupling laser resonates with each of the hyperfine levels. Compared with conventional EIT, where the signal-to-noise ratio is limited by the absorptive Doppler background, here these narrow-linewidth peaks have no Doppler background. The peak centres are well determined from theoretical fits to the experimental data. To accurately measure the 8S 1/2 hyperfine structure splitting, we developed a simple method to eliminate error arising from the nonlinear frequency scanning by employing an optical waveguide phase modulator and a confocal Fabry–Perot cavity. The hyperfine structure constants of the caesium 8S 1/2 state are obtained from hyperfine structure splitting measurements. Systematic effects from the ac-Stark and Zeeman shifts are studied. The measured hyperfine magnetic dipole constant A = (219.08 ± 0.12) MHz is consistent with previous results.

Measurement Science and Technology•Feb 11, 2014•6 citations
Doppler-free two-photon (DFTP) spectroscopy is a standard technique for precision measurement of transition frequencies of dipole-forbidden transitions. Here, we report the observation of quantum interference (QI) of optical transition pathways in DFTP spectroscopy of the cesium 6S\ensuremath-7D6S\text{\ensuremath{-}}7D6S\ensuremath-7D transitions chosen as a prototype system. The QI manifests itself as asymmetric line shapes of the hyperfine lines of the 7D7D7D states, observed through spontaneous emission following excitation by a narrow-linewidth cw laser. The interference persists despite the lines being spectrally well resolved. Ignoring the effect and fitting the spectrum to a Voigt profile causes large systematic shifts in the determination of the line centers, while accounting for QI resolves the apparent line shift and enables the precise determination of hyperfine splitting in the 7D7D7D states. We calculate the spectral line shape including the effect of QI and show that it agrees with the experimental observations. Our results are broadly applicable to other species and have implications for portable secondary optical clocks and precision measurements of hyperfine splittings, isotope shifts, and transition frequencies.
An alternate method of two-photon spectroscopy is presented where cesium atoms interact with a phase-modulated laser beam. Doppler-free two-photon spectroscopy of the cesium atom $6S\ensuremath{\rightarrow}8S$ hyperfine transition was used to experimentally demonstrate quantum interfered two-photon spectra. We calculated the photon-atom interaction by second-order perturbation theory and assumed that the one-photon frequency is detuned far from any intermediate state. Then we calculated the relative transition rates of all spectral lines resolved by the laser carrier and sidebands. A physical picture of multipathway quantum interference in the frequency domain is given that explains the unusual line strength, based on the trick that a phase-modulated laser beam can be decomposed into a series of coherent and collinear laser modes (carrier and sidebands). For all pairs of modes in which the sum frequency of each pair was on resonance with the cesium atom $6S\ensuremath{\rightarrow}8S$ transition, the superposition of all pathways induced by the different mode pairs resulted in a destructive interference, which then leads to a lack of absorption. We have shown in this paper that our calculation agrees very well with our experimental results in terms of the relative interfered line strengths, which were functions of modulation depth. We further discuss some related issues concerning laser stabilization and we demonstrate an approach for simultaneously comparing two cesium cells.
We characterize the effect of quantum interference on the line shapes and measured line positions in atomic spectra. These effects, which occur when the excited-state splittings are of order of the natural line widths, represent an overlooked but significant systematic effect. We show that excited-state interference gives rise to non-Lorentzian line shapes that depend on excitation polarization, and we present expressions for the corrected line shapes. We present spectra of 6,7{}^{6,7}6,7Li DDD lines taken at multiple excitation laser polarizations and show that failure to account for interference changes the inferred line strengths and shifts the line centers by as much as 1 MHz. Using the correct line shape, we determine absolute optical transition frequencies with an uncertainty of $\ensuremath{\le}$25 kHz and provide an improved determination of the difference in mean-square nuclear charge radii between 6{}^{6}6Li and 7{}^{7}7Li. This analysis should be important for a number of high-resolution spectral measurements that include partially resolvable atomic lines.
Spectroscopic measurements of transition frequencies in various atomic systems are a significant part of modern physics. They enable the testing of fundamental interactions, the determination of physical constants, and the study of fundamental symmetries that occur in nature with unprecedented accuracy. Studies based on two-photon spectroscopy of simple atoms represent some of the most accurate experiments to date. The verification of precision experimental results is largely supported by theoretical analysis, which is most rigorous for light, nonrelativistic atoms and ions. In the last decade, much attention in the literature has been paid to the study of the quantum interference effect (QIE) in hydrogen and hydrogenlike atomic systems. This has made it possible to significantly reduce the experimental error in determining the appropriate transition frequency. The theoretical description of the QIE corresponds to the consideration of similar pathways arising for close-lying resonant states into which the transition frequency is measured. In the present work, the influence of the emission process on the absorption profile formation is investigated. The results of the studies carried out in this work show the need to take into account the effect of quantum interference in cascade radiation for the precise determination of the absorption transition frequency to highly excited states in two-photon spectroscopic experiments.
Accessing the 5S1/2→5D5/2\rm 5S_{1/2} \rightarrow 5D_{5/2}5S1/2​→5D5/2​ two-photon transition in Rb using a diode laser system
We report observation of the 5S1/2→5D5/2\rm 5S_{1/2} \rightarrow 5D_{5/2}5S1/2​→5D5/2​ two-photon transition in Rb vapor at 778 nm, using an external cavity diode laser system and a heated vapor cell. The spectra in the two isotopes show well-resolved hyperfine transitions. The peaks are Doppler free, and have a Lorentzian lineshape with a typical linewidth of 2.2 MHz. This linewidth is larger than the natural linewidth of 300 kHz, but is still 5--10 times smaller than the linewidth for single-photon transitions in the D2_22​ line. Since the absolute frequency of this transition is measured with 8 kHz precision, it can form a better secondary reference in the optical regime compared to the D2_22​ line.
Two-color polarization spectroscopy (TCPS) of cesium 6S1/2-6P3/2-8S1/2 (852.3 nm + 794.6 nm) ladder-type system in a room-temperature vapor cell are investigated. The frequency of 852.3 nm laser used as a pump beam is locked on one of the hyperfine transitions between the ground state 6S1/2 and excited state 6P3/2 by the saturated absorption spectroscopy technique, which can populate some atoms on the 6P3/2 excited state and induce anisotropy in the atomic medium. The frequency of 794.6 nm laser serving as a probe beam is scanned across the whole 6P3/2→8S1/2 transition to ascertain this anisotropy, and thus the TCPS is obtained. In experiment, we measure and analyse the influence of frequency detuning of 852.3 nm pump laser on TCPS, and especially reveal that some of hyperfine energy levels of intermediate excited state 6P3/2, which has no direct interaction with the 852.3 nm pump laser, are also populated by a small fraction of atoms with a specific speed in the direction of pump laser beam due to Doppler effect, so they also have contribution to the TCPS when the 794.6 nm probe laser is scanned to the resonance transition line between the 6P3/2 and 8S1/2 states after the Doppler frequency shift has been considered. In addition, we prove that the atomic coherence like electromagnetically induced transparency effect obviously results in a narrower line width of TCPS in the case of counter-propagating experimental configuration than that in the case of pump beam co-propagating with the probe beam in the Cs vapor cell. Finally, we apply the TCPS with dispersive shaped feature to frequency stabilization with no modulation, and the frequency fluctuations of 794.6 nm laser are ～0.5 MHz and ～9.2 MHz for the frequency-locking and free running in ～225 s, respectively. The above research work is expected to play a role in precisely measuring the atomic energy level structure and its related hyperfine structure constant (magnetic dipole and electric quadrupole coupling constants), and also in stabilizing the laser frequency to the excited state transition especially for the optical fiber communication, two-color laser cooling/trapping neutral atoms, optical filter, etc.
High-sensitivity spectroscopy of caesium's higher excited 8S 1/2 state is obtained by a coherent two-photon transition via an intermediate resonance state. The ladder-type atomic system is driven by two counter-propagating low-power diode lasers, the probe laser being tuned to the transition from the ground state to the intermediate state (6S 1/2 –6P 1/2 ), and the coupling laser to that between the intermediate and the final state (6P 1/2 –8S 1/2 ). By locking the probe laser and scanning the coupling laser, the electromagnetically induced transparency (EIT) peaks appear in the probe transmission when the coupling laser resonates with each of the hyperfine levels. Compared with conventional EIT, where the signal-to-noise ratio is limited by the absorptive Doppler background, here these narrow-linewidth peaks have no Doppler background. The peak centres are well determined from theoretical fits to the experimental data. To accurately measure the 8S 1/2 hyperfine structure splitting, we developed a simple method to eliminate error arising from the nonlinear frequency scanning by employing an optical waveguide phase modulator and a confocal Fabry–Perot cavity. The hyperfine structure constants of the caesium 8S 1/2 state are obtained from hyperfine structure splitting measurements. Systematic effects from the ac-Stark and Zeeman shifts are studied. The measured hyperfine magnetic dipole constant A = (219.08 ± 0.12) MHz is consistent with previous results.