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:0707.1314 · Physical Review A

Fluorescence during Doppler cooling of a single trapped atom

Janus H. Wesenberg, R. J. Epstein, Dietrich G. Leibfried, R. B. Blakestad, J. Britton, Jonathan Home, Wayne M. Itano, John D. Jost, Emanuel H. Knill, C. Langer, Roee Ozeri, Signe Louise Seidelin, D. J. Wineland

Published Nov 26, 2007• 100 citations
arXivHTMLPDF

Abstract

We investigate the temporal dynamics of Doppler cooling of an initially hot single trapped atom in the weak-binding regime using a semiclassical approach. We develop an analytical model for the simplest case of a single vibrational mode for a harmonic trap, and show how this model allows us to estimate the initial energy of the trapped particle by observing the time-dependent fluorescence during the cooling process. The experimental implementation of this temperature measurement provides a way to measure atom heating rates by observing the temperature rise in the absence of cooling. This method is technically relatively simple compared to conventional sideband detection methods, and the two methods are in reasonable agreement. We also discuss the effects of rf micromotion, relevant for a trapped atomic ion, and the effect of coupling between the vibrational modes on the cooling dynamics.

DOI
10.1103/physreva.76.053416

Related papers

Doppler cooling thermometry of a multilevel ion in the presence of micromotion

Tomáš Šikorský, Ziv Meir, Nitzan Akerman +2 more

We study the time-dependent fluorescence of an initially hot, multilevel, single atomic ion trapped in a radio-frequency Paul trap during Doppler cooling. We have developed an analytical model that describes the fluorescence dynamics during Doppler cooling which is used to extract the initial energy of the ion. While previous models of Doppler cooling thermometry were limited to atoms with a two-level energy structure and neglected the effect of the trap oscillating electric fields, our model applies to atoms with multilevel energy structure and takes into account the influence of micromotion on the cooling dynamics. This thermometry applies to any initial energy distribution. We experimentally test our model with an ion prepared in coherent, thermal, and Tsallis energy distributions.

arXiv:1705.00453•Physical Review A•Jul 28, 2017•27 citations

Sympathetic cooling and detection of a hot trapped ion by a cold one

M Guggemos, D. Heinrich, O. A. Herrera-Sancho +2 more

We investigate the dynamics of an ion sympathetically cooled by another laser-cooled ion or small ion crystal. To this end, we develop simple models of the cooling dynamics in the limit of weak Coulomb interactions. Experimentally, we create a two-ion crystal of Ca + and Al + by photo-ionization of neutral atoms produced by laser ablation. We characterize the velocity distribution of the laser-ablated atoms crossing the trap by time-resolved fluorescence spectroscopy. We observe neutral atom velocities much higher than the ones of thermally heated samples and find as a consequence long sympathethic cooling times before crystallization occurs. Our key result is a new technique for detecting the loading of an initially hot ion with energy in the eV range by monitoring the motional state of a Doppler-cooled ion already present in the trap. This technique not only detects the ion but also provides information about the dynamics of the sympathetic cooling process.

arXiv:1507.07761•New Journal of Physics•Sep 30, 2015•40 citations

Determining temperature and Rabi frequency regarding trapped ions in Doppler cooling: An analytic investigation

L.-L. Yan, Shi‐Lei Su, Feng, Mang

Doppler cooling with lasers is essential to ions' trapping and also a preliminary step towards achievement of ultracold ions. Due to lack of effective tools, experimentally monitoring the ions' temperature and the laser-ion coupling is difficult in Doppler cooling. Here we analytically explore the Doppler cooling process of trapped ions, exemplified by $^{40}$Ca$^{+}$, by solving the friction coefficient in the Doppler cooling with respect to a thermal bath, particularly, to a bath with large heating rate. We show four regions for cooling and heating induced by the three-level electromagnetically induced transparency and propose a practical method for measuring the Rabi frequency by the Doppler cooling window. In addition, the final temperature of the laser-cooled ions can be obtained analytically in the case of a weak thermal bath, whereas for the strong thermal bath this requires numerical treatment due to involvement of the Doppler shift and large Lamb-Dicke parameter. Our analytic results would help for understanding many experimental observations, such as configuration phase transition, phonon laser and thermodynamics regarding hot trapped ions.

arXiv:1902.00302•Feb 1, 2019•0 citations

Simplified motional heating rate measurements of trapped ions

R. J. Epstein, Signe Louise Seidelin, Dietrich G. Leibfried +13 more

We have measured motional heating rates of trapped atomic ions, a factor that can influence multi-ion quantum logic gate fidelities. Two simplified techniques were developed for this purpose: one relies on Raman sideband detection implemented with a single laser source, while the second is even simpler and is based on time-resolved fluorescence detection during Doppler recooling. We applied these methods to determine heating rates in a microfrabricated surface-electrode trap made of gold on fused quartz, which traps ions $40\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{m}$ above its surface. Heating rates obtained from the two techniques were found to be in reasonable agreement. In addition, the trap gives rise to a heating rate of $300\ifmmode\pm\else\textpm\fi{}30\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for a motional frequency of $5.25\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, substantially below the trend observed in other traps.

arXiv:0707.1528•Physical Review A•Sep 19, 2007•124 citations

Broadband laser cooling of trapped atoms with ultrafast pulses

B. B. Blinov, R. N. Kohn, M. J. Madsen +3 more

We demonstrate broadband laser cooling of atomic ions in an rf trap using ultrafast pulses from a mode-locked laser. The temperature of a single ion is measured by observing the size of a time-averaged image of the ion in the known harmonic trap potential. Although the lowest observed temperature was only about 1K, this method efficiently cools very hot atoms and can sufficiently localize trapped atoms to produce near diffraction-limited atomic images.

arXiv:quant-ph/0507074•Journal of the Optical Society of America B•Jun 1, 2006•30 citations

The effect of atomic response time in the theory of Doppler cooling of trapped ions

H. Janacek, Andrew M. Steane, D. M. Lucas +1 more

We describe a simple approach to the problem of incorporating the response time of an atom or ion being Doppler-cooled into the theory of the cooling process. The system being cooled does not in general respond instantly to the changing laser frequencies it experiences in its rest frame, and this ‘dynamic effect’ can affect significantly the temperatures attainable. It is particularly important for trapped ions when there is a slow decay out of the cooling cycle requiring the use of a repumping beam. We treat the cases of trapped ions with two and three internal states, then apply the theory to 40Ca+. For this ion experimental data exist showing the ion to be cold under conditions for which heating is predicted if the dynamic effect is neglected. The present theory accounts for the observed behaviour.

arXiv:1706.04423•Journal of Modern Optics•Feb 9, 2018•4 citations
We investigate the temporal dynamics of Doppler cooling of an initially hot single trapped atom in the weak-binding regime using a semiclassical approach. We develop an analytical model for the simplest case of a single vibrational mode for a harmonic trap, and show how this model allows us to estimate the initial energy of the trapped particle by observing the time-dependent fluorescence during the cooling process. The experimental implementation of this temperature measurement provides a way to measure atom heating rates by observing the temperature rise in the absence of cooling. This method is technically relatively simple compared to conventional sideband detection methods, and the two methods are in reasonable agreement. We also discuss the effects of rf micromotion, relevant for a trapped atomic ion, and the effect of coupling between the vibrational modes on the cooling dynamics.
We study the time-dependent fluorescence of an initially hot, multilevel, single atomic ion trapped in a radio-frequency Paul trap during Doppler cooling. We have developed an analytical model that describes the fluorescence dynamics during Doppler cooling which is used to extract the initial energy of the ion. While previous models of Doppler cooling thermometry were limited to atoms with a two-level energy structure and neglected the effect of the trap oscillating electric fields, our model applies to atoms with multilevel energy structure and takes into account the influence of micromotion on the cooling dynamics. This thermometry applies to any initial energy distribution. We experimentally test our model with an ion prepared in coherent, thermal, and Tsallis energy distributions.
We investigate the dynamics of an ion sympathetically cooled by another laser-cooled ion or small ion crystal. To this end, we develop simple models of the cooling dynamics in the limit of weak Coulomb interactions. Experimentally, we create a two-ion crystal of Ca + and Al + by photo-ionization of neutral atoms produced by laser ablation. We characterize the velocity distribution of the laser-ablated atoms crossing the trap by time-resolved fluorescence spectroscopy. We observe neutral atom velocities much higher than the ones of thermally heated samples and find as a consequence long sympathethic cooling times before crystallization occurs. Our key result is a new technique for detecting the loading of an initially hot ion with energy in the eV range by monitoring the motional state of a Doppler-cooled ion already present in the trap. This technique not only detects the ion but also provides information about the dynamics of the sympathetic cooling process.
Doppler cooling with lasers is essential to ions' trapping and also a preliminary step towards achievement of ultracold ions. Due to lack of effective tools, experimentally monitoring the ions' temperature and the laser-ion coupling is difficult in Doppler cooling. Here we analytically explore the Doppler cooling process of trapped ions, exemplified by 40^{40}40Ca+^{+}+, by solving the friction coefficient in the Doppler cooling with respect to a thermal bath, particularly, to a bath with large heating rate. We show four regions for cooling and heating induced by the three-level electromagnetically induced transparency and propose a practical method for measuring the Rabi frequency by the Doppler cooling window. In addition, the final temperature of the laser-cooled ions can be obtained analytically in the case of a weak thermal bath, whereas for the strong thermal bath this requires numerical treatment due to involvement of the Doppler shift and large Lamb-Dicke parameter. Our analytic results would help for understanding many experimental observations, such as configuration phase transition, phonon laser and thermodynamics regarding hot trapped ions.
We have measured motional heating rates of trapped atomic ions, a factor that can influence multi-ion quantum logic gate fidelities. Two simplified techniques were developed for this purpose: one relies on Raman sideband detection implemented with a single laser source, while the second is even simpler and is based on time-resolved fluorescence detection during Doppler recooling. We applied these methods to determine heating rates in a microfrabricated surface-electrode trap made of gold on fused quartz, which traps ions $40\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{m}$ above its surface. Heating rates obtained from the two techniques were found to be in reasonable agreement. In addition, the trap gives rise to a heating rate of $300\ifmmode\pm\else\textpm\fi{}30\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for a motional frequency of 5.25MHz5.25\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}5.25MHz, substantially below the trend observed in other traps.
We describe a simple approach to the problem of incorporating the response time of an atom or ion being Doppler-cooled into the theory of the cooling process. The system being cooled does not in general respond instantly to the changing laser frequencies it experiences in its rest frame, and this ‘dynamic effect’ can affect significantly the temperatures attainable. It is particularly important for trapped ions when there is a slow decay out of the cooling cycle requiring the use of a repumping beam. We treat the cases of trapped ions with two and three internal states, then apply the theory to 40Ca+. For this ion experimental data exist showing the ion to be cold under conditions for which heating is predicted if the dynamic effect is neglected. The present theory accounts for the observed behaviour.