Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1909.02649

Optical pumping, decay rates and light shifts of cold-atom dark states

M. Shuker, J. W. Pollock, Valeriy I. Yudin, John E. Kitching, Elizabeth A. Donley

Published Sep 5, 2019• 2 citations
arXivHTMLPDF

Abstract

Coherent dark states in atoms, created by simultaneous interaction of two coherent light fields with a 3-level system, are of prime importance in quantum state manipulation. They are used extensively in quantum sensing and quantum information applications to build atomic clocks, magnetometers, atomic interferometers and more. Here we study the formation and decay of coherent dark-states in an ensemble of laser-cooled free-falling atoms. We measure the optical-pumping rate into the dark-state in the $σ^+-σ^-$ polarization configuration. We find that the pumping rate is linear with the optical field intensity, but about an order-of-magnitude slower than the rate predicted by the commonly used, but simplistic, three-level analytic formula. Using a numerical model we demonstrate that this discrepancy is due to the multi-level Zeeman manifold. Taking into account the slower pumping rate we explain quantitatively the relation between the light-shift and the duration of pumping into dark-state in Ramsey spectroscopy. We also measure the decay of the dark-state coherence and find that in our apparatus it is dominated by the mechanical motion of the atoms out of the probing region, while the atomic decoherence is negligible.

DOI
10.48550/arxiv.1909.02649

Related papers

Light shifts in a pulsed cold-atom coherent-population-trapping clock

E. Blanshan, Simon Rochester, Elizabeth A. Donley +1 more

Field-grade atomic clocks capable of primary standard performance in compact physics packages would be of significant value in applications ranging from network synchronization to inertial navigation. A coherent-population-trapping clock featuring laser-cooled $^{87}\mathrm{Rb}$ atoms and pulsed Ramsey interrogation is a strong candidate for this technology if the frequency biases can be minimized and controlled. Here we characterize the light shift in a cold-atom coherent-population-trapping clock, explaining observed shifts in terms of phase shifts that arise during the formation of dark-state coherences combined with optical-pumping effects caused by unwanted incoherent light in the interrogation spectrum. Measurements are compared with existing and new theoretical treatments, and a laser configuration is identified that would reduce clock frequency uncertainty from light shifts to a fractional frequency level of $\ensuremath{\Delta}\ensuremath{\nu}/\ensuremath{\nu}=4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ per 100 kHz of laser frequency uncertainty.

Physical Review A•Apr 10, 2015•42 citations

Measurements of light shifts in cold atoms using Raman pump-probe spectroscopy

Nathan Souther, R. Wagner, Peter Harnish +2 more

We have measured light shifts, also known as AC Stark shifts, as a function of laser intensity in cold Rubidium atoms by observing sub-natural linewidth gain and loss features in the transmission spectrum of a weak probe beam passing through the atomic sample. The observed energy-level shifts for atoms in a magneto-optical trap (MOT) are found to be consistently higher than that obtained in optical molasses (i.e., when the magnetic field gradient in the MOT is turned off). Using a simple model of a multilevel Rubidium atom interacting with pump and probe beams, we have calculated the theoretical light shift as a function of intensity. A comparison of these calculated values with the light shift data obtained for molasses reveals good agreement between experiment and theory. Further, our model elucidates the role of the Zeeman shifts arising from the magnetic field gradient in the observed probe transmission spectrum for the MOT.

Laser Physics Letters•Feb 8, 2010•15 citations

Ramsey-like measurement of the decoherence rate between Zeeman sublevels

M. Shuker, Ofer Firstenberg, Yoav Sagi +3 more

Two-photon processes that involve different sublevels of the ground state of an atom, are highly sensitive to depopulation and decoherence within the ground state. For example, the spectral width of electromagnetically induced transparency resonances in a $\ensuremath{\Lambda}$-type system, are strongly affected by the ground-state depopulation and decoherence rates. We present a direct measurement of decay rates between hyperfine and Zeeman sublevels in the ground state of $^{87}\mathrm{Rb}$ vapor. Similar to the relaxation-in-the-dark technique, pumping lasers are used to prealign the atomic vapor in a well-defined quantum state. The free propagation of the atomic state is monitored using a Ramsey-like method. Coherence times in the range $1--10\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ were measured for room temperature atomic vapor. In the range of the experimental parameters used in this study, the dominant process inducing Zeeman decoherence is the spin-exchange collisions between rubidium atoms.

arXiv:0807.3110•Physical Review A•Dec 11, 2008•21 citations

Interplay of classical and quantum dynamics in a thermal ensemble of atoms

Arif Warsi Laskar, Niharika Singh, Arunabh Mukherjee +1 more

In a thermal ensemble of atoms driven by coherent fields, how does evolution of quantum superposition compete with classical dynamics of optical pumping and atomic diffusion? Is it optical pumping that first prepares a thermal ensemble, with coherent superposition developing subsequently or is it the other way round: coherently superposed atoms driven to steady state via optical pumping? Using a stroboscopic probing technique, here we experimentally explore these questions. A 100 ns pulse is used to probe an experimentally simulated, closed three-level, Λ-like configuration in rubidium atoms, driven by strong coherent ( control ) and incoherent fields. Temporal evolution of probe transmission shows an initial overshoot with turn-on of control , resulting in a scenario akin to lasing without inversion. The corresponding rise time is dictated by coherent dynamics, with a distinct experimental signature of half-cycle Rabi flop in a thermal ensemble of atoms. Our results indicate that, in fact, optical pumping drives the atoms to a steady state in a significantly longer time-scale that sustains superposed dark states . Eventual control turn-off leads to a sudden fall in transmission with an ubiquitous signature for identifying closed and open systems. Numerical simulations and toy-model predictions confirm our claims. These studies reveal new insights into a rich and complex dynamics associated with atoms in thermal ensemble, which are otherwise absent in state-prepared, cold atomic ensembles.

arXiv:1601.00451•New Journal of Physics•May 12, 2016•8 citations

Ultrahigh-resolution spectroscopy with atomic or molecular dark resonances: Exact steady-state line shapes and asymptotic profiles in the adiabatic pulsed regime

T. Zanon-Willette, Emeric de Clercq, E. Arimondo

Exact and asymptotic line shape expressions are derived from the semiclassical density matrix representation describing a set of closed three-level $\ensuremath{\Lambda}$ atomic or molecular states including decoherences, relaxation rates, and light shifts. An accurate analysis of the exact steady-state dark-resonance profile describing the Autler-Townes doublet, the electromagnetically induced transparency or coherent population trapping resonance, and the Fano-Feshbach line shape leads to the linewidth expression of the two-photon Raman transition and frequency shifts associated to the clock transition. From an adiabatic analysis of the dynamical optical Bloch equations in the weak field limit, a pumping time required to efficiently trap a large number of atoms into a coherent superposition of long-lived states is established. For a highly asymmetrical configuration with different decay channels, a strong two-photon resonance based on a lower states population inversion is established when the driving continuous-wave laser fields are greatly unbalanced. When time separated resonant two-photon pulses are applied in the adiabatic pulsed regime for atomic or molecular clock engineering, where the first pulse is long enough to reach a coherent steady-state preparation and the second pulse is very short to avoid repumping into a new dark state, dark-resonance fringes mixing continuous-wave line shape properties and coherent Ramsey oscillations are created. Those fringes allow interrogation schemes bypassing the power broadening effect. Frequency shifts affecting the central clock fringe computed from asymptotic profiles and related to the Raman decoherence process exhibit nonlinear shapes with the three-level observable used for quantum measurement. We point out that different observables experience different shifts on the lower-state clock transition.

arXiv:1110.2221•Physical Review A•Dec 2, 2011•42 citations

Limits on the atomic description of four-wave mixing

Irvin F. Ángeles-Aguillón, Nieves Arias-Téllez, Pablo Yanes-Thomas +2 more

The limits of the well-established single-atom model for describing photon-pair generation via four-wave mixing in a diamond configuration in atomic ensembles are experimentally tested. Using a cold-atom source, biphotons are generated and detected through polarization analyzers that resolve the emitted light into horizontal and vertical components in the laboratory frame. The pump lasers driving the first and second excitation transitions are horizontally and vertically polarized, respectively. To predict single-photon counts and coincidence rates in all polarization channels, the first- and second-order correlation functions are calculated directly using a comprehensive model that accounts for all Zeeman sublevels of the relevant hyperfine states. Furthermore, the population dynamics with and without the re-pump laser of the magneto-optical trap are compared, revealing substantial differences in the populations of the Zeeman sublevels. This motivates the inclusion of two additional hyperfine levels and their corresponding Zeeman sublevels in the final model. The resulting density matrix is used to calculate expectation values of the far-field electric-field operators and compare them with experimental measurements over a range of pump-laser powers. Excellent agreement with the measured photon counts is obtained over most of this range. For the coincidence measurements, good agreement is found when the polarization of the photon generated by the first (second) decay is parallel to that of the first (second) pump beam. In contrast, the model consistently underestimates the experimental coincidence rates for the opposite polarization configuration. These findings indicate that effects beyond the internal level dynamics of individual atoms, most notably collective phenomena, are required to fully account for photon coincidences generated by four-wave mixing in atomic ensembles.

quant-pharXiv:2609.15843•Sep 15, 2026•0 citations
Coherent dark states in atoms, created by simultaneous interaction of two coherent light fields with a 3-level system, are of prime importance in quantum state manipulation. They are used extensively in quantum sensing and quantum information applications to build atomic clocks, magnetometers, atomic interferometers and more. Here we study the formation and decay of coherent dark-states in an ensemble of laser-cooled free-falling atoms. We measure the optical-pumping rate into the dark-state in the σ+−σ−σ^+-σ^-σ+−σ− polarization configuration. We find that the pumping rate is linear with the optical field intensity, but about an order-of-magnitude slower than the rate predicted by the commonly used, but simplistic, three-level analytic formula. Using a numerical model we demonstrate that this discrepancy is due to the multi-level Zeeman manifold. Taking into account the slower pumping rate we explain quantitatively the relation between the light-shift and the duration of pumping into dark-state in Ramsey spectroscopy. We also measure the decay of the dark-state coherence and find that in our apparatus it is dominated by the mechanical motion of the atoms out of the probing region, while the atomic decoherence is negligible.
Field-grade atomic clocks capable of primary standard performance in compact physics packages would be of significant value in applications ranging from network synchronization to inertial navigation. A coherent-population-trapping clock featuring laser-cooled 87Rb^{87}\mathrm{Rb}87Rb atoms and pulsed Ramsey interrogation is a strong candidate for this technology if the frequency biases can be minimized and controlled. Here we characterize the light shift in a cold-atom coherent-population-trapping clock, explaining observed shifts in terms of phase shifts that arise during the formation of dark-state coherences combined with optical-pumping effects caused by unwanted incoherent light in the interrogation spectrum. Measurements are compared with existing and new theoretical treatments, and a laser configuration is identified that would reduce clock frequency uncertainty from light shifts to a fractional frequency level of $\ensuremath{\Delta}\ensuremath{\nu}/\ensuremath{\nu}=4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ per 100 kHz of laser frequency uncertainty.
We have measured light shifts, also known as AC Stark shifts, as a function of laser intensity in cold Rubidium atoms by observing sub-natural linewidth gain and loss features in the transmission spectrum of a weak probe beam passing through the atomic sample. The observed energy-level shifts for atoms in a magneto-optical trap (MOT) are found to be consistently higher than that obtained in optical molasses (i.e., when the magnetic field gradient in the MOT is turned off). Using a simple model of a multilevel Rubidium atom interacting with pump and probe beams, we have calculated the theoretical light shift as a function of intensity. A comparison of these calculated values with the light shift data obtained for molasses reveals good agreement between experiment and theory. Further, our model elucidates the role of the Zeeman shifts arising from the magnetic field gradient in the observed probe transmission spectrum for the MOT.
Two-photon processes that involve different sublevels of the ground state of an atom, are highly sensitive to depopulation and decoherence within the ground state. For example, the spectral width of electromagnetically induced transparency resonances in a $\ensuremath{\Lambda}$-type system, are strongly affected by the ground-state depopulation and decoherence rates. We present a direct measurement of decay rates between hyperfine and Zeeman sublevels in the ground state of 87Rb^{87}\mathrm{Rb}87Rb vapor. Similar to the relaxation-in-the-dark technique, pumping lasers are used to prealign the atomic vapor in a well-defined quantum state. The free propagation of the atomic state is monitored using a Ramsey-like method. Coherence times in the range 1−−10ms1--10\phantom{\rule{0.3em}{0ex}}\mathrm{ms}1−−10ms were measured for room temperature atomic vapor. In the range of the experimental parameters used in this study, the dominant process inducing Zeeman decoherence is the spin-exchange collisions between rubidium atoms.
In a thermal ensemble of atoms driven by coherent fields, how does evolution of quantum superposition compete with classical dynamics of optical pumping and atomic diffusion? Is it optical pumping that first prepares a thermal ensemble, with coherent superposition developing subsequently or is it the other way round: coherently superposed atoms driven to steady state via optical pumping? Using a stroboscopic probing technique, here we experimentally explore these questions. A 100 ns pulse is used to probe an experimentally simulated, closed three-level, Λ-like configuration in rubidium atoms, driven by strong coherent ( control ) and incoherent fields. Temporal evolution of probe transmission shows an initial overshoot with turn-on of control , resulting in a scenario akin to lasing without inversion. The corresponding rise time is dictated by coherent dynamics, with a distinct experimental signature of half-cycle Rabi flop in a thermal ensemble of atoms. Our results indicate that, in fact, optical pumping drives the atoms to a steady state in a significantly longer time-scale that sustains superposed dark states . Eventual control turn-off leads to a sudden fall in transmission with an ubiquitous signature for identifying closed and open systems. Numerical simulations and toy-model predictions confirm our claims. These studies reveal new insights into a rich and complex dynamics associated with atoms in thermal ensemble, which are otherwise absent in state-prepared, cold atomic ensembles.
Exact and asymptotic line shape expressions are derived from the semiclassical density matrix representation describing a set of closed three-level $\ensuremath{\Lambda}$ atomic or molecular states including decoherences, relaxation rates, and light shifts. An accurate analysis of the exact steady-state dark-resonance profile describing the Autler-Townes doublet, the electromagnetically induced transparency or coherent population trapping resonance, and the Fano-Feshbach line shape leads to the linewidth expression of the two-photon Raman transition and frequency shifts associated to the clock transition. From an adiabatic analysis of the dynamical optical Bloch equations in the weak field limit, a pumping time required to efficiently trap a large number of atoms into a coherent superposition of long-lived states is established. For a highly asymmetrical configuration with different decay channels, a strong two-photon resonance based on a lower states population inversion is established when the driving continuous-wave laser fields are greatly unbalanced. When time separated resonant two-photon pulses are applied in the adiabatic pulsed regime for atomic or molecular clock engineering, where the first pulse is long enough to reach a coherent steady-state preparation and the second pulse is very short to avoid repumping into a new dark state, dark-resonance fringes mixing continuous-wave line shape properties and coherent Ramsey oscillations are created. Those fringes allow interrogation schemes bypassing the power broadening effect. Frequency shifts affecting the central clock fringe computed from asymptotic profiles and related to the Raman decoherence process exhibit nonlinear shapes with the three-level observable used for quantum measurement. We point out that different observables experience different shifts on the lower-state clock transition.
The limits of the well-established single-atom model for describing photon-pair generation via four-wave mixing in a diamond configuration in atomic ensembles are experimentally tested. Using a cold-atom source, biphotons are generated and detected through polarization analyzers that resolve the emitted light into horizontal and vertical components in the laboratory frame. The pump lasers driving the first and second excitation transitions are horizontally and vertically polarized, respectively. To predict single-photon counts and coincidence rates in all polarization channels, the first- and second-order correlation functions are calculated directly using a comprehensive model that accounts for all Zeeman sublevels of the relevant hyperfine states. Furthermore, the population dynamics with and without the re-pump laser of the magneto-optical trap are compared, revealing substantial differences in the populations of the Zeeman sublevels. This motivates the inclusion of two additional hyperfine levels and their corresponding Zeeman sublevels in the final model. The resulting density matrix is used to calculate expectation values of the far-field electric-field operators and compare them with experimental measurements over a range of pump-laser powers. Excellent agreement with the measured photon counts is obtained over most of this range. For the coincidence measurements, good agreement is found when the polarization of the photon generated by the first (second) decay is parallel to that of the first (second) pump beam. In contrast, the model consistently underestimates the experimental coincidence rates for the opposite polarization configuration. These findings indicate that effects beyond the internal level dynamics of individual atoms, most notably collective phenomena, are required to fully account for photon coincidences generated by four-wave mixing in atomic ensembles.