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:2601.09180

Many-Body Effects in Dark-State Laser Cooling

Muhammad Miskeen Khan, David Wellnitz, Bhuvanesh Sundar, Ansh Das, Haoqing Zhang, Allison Carter, John J. Bollinger, Athreya Shankar, Ana Maria Rey

quant-phSubmitted Jan 14, 2026• Announced Jan 15, 2026• 0 citations• Revised Oct 8, 2026 (v2)
v1 · Jan 14, 2026v2 · Oct 8, 2026
arXivHTMLPDF

Abstract

We develop a unified many-body theory of two-photon dark-state laser cooling, the workhorse for preparing trapped ions close to their motional quantum ground state. For ions with a $Λ$ level structure, driven by Raman lasers, we identify an ion-number-dependent crossover between weak and strong coupling where both the cooling rate and final temperature are simultaneously optimized. We obtain simple analytic results in both extremes: In the weak coupling limit, we show a Lorentzian spin-absorption spectrum determines the cooling rate and final occupation of the motional state, which are both independent of the number of ions. We also highlight the benefit of including an additional spin dependent force in this case. In the strong coupling regime, our theory reveals the role of collective dynamics arising from phonon exchange between dark and bright states, allowing us to explain the enhancement of the cooling rate with increasing ion number. Our analytic results agree closely with exact numerical simulations and provide experimentally accessible guidelines for optimizing cooling in large ion crystals, a key step toward scalable, high-fidelity trapped-ion quantum technologies.

Comments
22 pages, 10 figures

Related papers

Collective enhancement in sideband cooling of ion crystals

Ivan Vybornyi, Artem Zhdanov, Matthias Bock +4 more

Low-entropy motional states of ion Coulomb crystals are an essential prerequisite for a plethora of applications and are typically prepared by laser cooling. As larger crystals are operated in the quantum regime, it remains unclear, and has recently become debated, whether increasing the ion number can be beneficial for cooling. Here, we investigate theoretically and experimentally many-ion sideband cooling and the role of collective effects in different spin-motion coupling regimes. For weak coupling, the many-body effects are insignificant. In the strong-coupling regime, however, the spin and motional subsystems undergo a coherent state swap, enabling cooling by a suitably timed laser pulse. Using planar Coulomb crystals with up to 91 ions, we demonstrate that the residual mean phonon occupation after one such pulse scales as $1/N^2$ with the number of ions. By iterating the pulses, we measure mean phonon occupations $<2\cdot10^{-4}$. For large crystals in the coherent regime, we further show that the spin-motion dynamics becomes largely independent of the initial phonon statistics. Through spin measurements, the state-swap mechanism can be utilized to probe the phonon distribution in the mode.

quant-pharXiv:2606.21374•Physical Review Letters•Jun 22, 2026•0 citations

Raman cooling and heating of two trapped Ba+ ions

Dirk Reiß, Klaus Abich, Werner Neuhauser +2 more

We study cooling of the collective vibrational motion of two ${}^{138}{\mathrm{Ba}}^{+}$ ions confined in an electrodynamic trap and irradiated by laser light close to the resonances ${S}_{1/2}\ensuremath{-}{P}_{1/2}$ (493 nm) and ${P}_{1/2}\ensuremath{-}{D}_{3/2}$ (650 nm). The motional state of the ions is monitored by a spatially resolving photomultiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions' temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split ${S}_{1/2}\ensuremath{-}{D}_{3/2}$ Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.

arXiv:quant-ph/0104002•Physical Review A•Apr 12, 2002•33 citations

Fast laser cooling using optimal quantum control

Xie-Qian Li, Shuo Zhang, Jie Zhang +3 more

Cooling down a trapped ion into its motional ground state is a central step for trapped-ion-based quantum information processing. State-of-the-art cooling schemes often work under a set of optimal cooling conditions derived analytically using a perturbative approach, in which the sideband coupling is assumed to be the weakest of all the relevant transitions. As a result, the cooling rate is severely limited. Here we propose to use a quantum control technique powered with automatic differentiation to speed up the classical cooling schemes. We demonstrate the efficacy of our approach by applying it to find the optimal cooling conditions for classical sideband cooling and electromagnetically induced transparency cooling schemes, which are in general beyond the weak-sideband-coupling regime. Based on those numerically found optimal cooling conditions, we show that faster cooling can be achieved while at the same time a low average phonon occupation can be retained.

arXiv:2106.05443•Physical Review A•Oct 5, 2021•4 citations

Laser cooling trapped-ion crystal modes beyond the Lamb-Dicke regime

John P. Bartolotta, Brian Estey, Michael Foss‐Feig +2 more

Laser cooling methods for trapped ions are most commonly studied at low energies, i.e., in the Lamb-Dicke regime. However, ions in experiments are often excited to higher energies for which the Lamb-Dicke approximation breaks down. Here we construct a non-perturbative, semiclassical method for predicting the energy-dependent cooling dynamics of trapped-ion crystals with potentially many internal levels and motional modes beyond the Lamb-Dicke regime. This method allows accurate and efficient modeling of a variety of interesting phenomena, such as the breakdown of EIT cooling at high energies and the simultaneous cooling of multiple high-temperature modes. We compare its predictions both to fully-quantum simulations and to experimental data for a broadband EIT cooling method on a Raman $S$-$D$ transition in $^{138}$Ba${^+}$. We find the method can accurately predict cooling rates over a wide range of energies relevant to trapped ion experiments. Our method complements fully quantum models by allowing for fast and accurate predictions of laser-cooling dynamics at much higher energy scales.

arXiv:2411.18818•Nov 27, 2024•0 citations

Multilevel electromagnetically-induced-transparency cooling

Katya Fouka, Athreya Shankar, Ting Rei Tan +1 more

Electromagnetically Induced Transparency (EIT) cooling is a well-established method for preparing trapped ion systems in their motional ground state. However, isolating a three-level system, as required for EIT cooling, is often challenging or impractical. Nonetheless, multilevel systems can inherently host dark states. In this work, we extend the EIT cooling framework to such multilevel systems. We develop a formalism to accurately determine the cooling rate in the weak sideband coupling regime and provide an approximate estimate for cooling rates beyond this regime, without the need for explicit simulation of the motional degree of freedom. We clarify the connection between the cooling rate and the absorption spectrum, offering a pathway for efficient near-ground-state cooling of ions with complex electronic structures.

arXiv:2506.14546•Physical Review A•Nov 18, 2025•0 citations

Superfast Laser Cooling

Shai Machnes, Martin Bodo Plenio, Benni Reznik +2 more

Currently, laser cooling schemes are fundamentally based on the weak coupling regime. This requirement sets the trap frequency as an upper bound to the cooling rate. In this work we present a numerical study that shows the feasibility of cooling in the strong-coupling regime which then allows cooling rates that are faster than the trap frequency with experimentally feasible parameters. The scheme presented here can be applied to trapped atoms or ions as well as to mechanical oscillators. It can also cool medium sized ion chains close to the ground state.

arXiv:1001.2714•Physical Review Letters•May 6, 2010•34 citations
We develop a unified many-body theory of two-photon dark-state laser cooling, the workhorse for preparing trapped ions close to their motional quantum ground state. For ions with a ΛΛΛ level structure, driven by Raman lasers, we identify an ion-number-dependent crossover between weak and strong coupling where both the cooling rate and final temperature are simultaneously optimized. We obtain simple analytic results in both extremes: In the weak coupling limit, we show a Lorentzian spin-absorption spectrum determines the cooling rate and final occupation of the motional state, which are both independent of the number of ions. We also highlight the benefit of including an additional spin dependent force in this case. In the strong coupling regime, our theory reveals the role of collective dynamics arising from phonon exchange between dark and bright states, allowing us to explain the enhancement of the cooling rate with increasing ion number. Our analytic results agree closely with exact numerical simulations and provide experimentally accessible guidelines for optimizing cooling in large ion crystals, a key step toward scalable, high-fidelity trapped-ion quantum technologies.
Low-entropy motional states of ion Coulomb crystals are an essential prerequisite for a plethora of applications and are typically prepared by laser cooling. As larger crystals are operated in the quantum regime, it remains unclear, and has recently become debated, whether increasing the ion number can be beneficial for cooling. Here, we investigate theoretically and experimentally many-ion sideband cooling and the role of collective effects in different spin-motion coupling regimes. For weak coupling, the many-body effects are insignificant. In the strong-coupling regime, however, the spin and motional subsystems undergo a coherent state swap, enabling cooling by a suitably timed laser pulse. Using planar Coulomb crystals with up to 91 ions, we demonstrate that the residual mean phonon occupation after one such pulse scales as 1/N21/N^21/N2 with the number of ions. By iterating the pulses, we measure mean phonon occupations <2⋅10−4<2\cdot10^{-4}<2⋅10−4. For large crystals in the coherent regime, we further show that the spin-motion dynamics becomes largely independent of the initial phonon statistics. Through spin measurements, the state-swap mechanism can be utilized to probe the phonon distribution in the mode.
We study cooling of the collective vibrational motion of two 138Ba+{}^{138}{\mathrm{Ba}}^{+}138Ba+ ions confined in an electrodynamic trap and irradiated by laser light close to the resonances ${S}_{1/2}\ensuremath{-}{P}_{1/2}$ (493 nm) and ${P}_{1/2}\ensuremath{-}{D}_{3/2}$ (650 nm). The motional state of the ions is monitored by a spatially resolving photomultiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions' temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split ${S}_{1/2}\ensuremath{-}{D}_{3/2}$ Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.
Cooling down a trapped ion into its motional ground state is a central step for trapped-ion-based quantum information processing. State-of-the-art cooling schemes often work under a set of optimal cooling conditions derived analytically using a perturbative approach, in which the sideband coupling is assumed to be the weakest of all the relevant transitions. As a result, the cooling rate is severely limited. Here we propose to use a quantum control technique powered with automatic differentiation to speed up the classical cooling schemes. We demonstrate the efficacy of our approach by applying it to find the optimal cooling conditions for classical sideband cooling and electromagnetically induced transparency cooling schemes, which are in general beyond the weak-sideband-coupling regime. Based on those numerically found optimal cooling conditions, we show that faster cooling can be achieved while at the same time a low average phonon occupation can be retained.
Laser cooling methods for trapped ions are most commonly studied at low energies, i.e., in the Lamb-Dicke regime. However, ions in experiments are often excited to higher energies for which the Lamb-Dicke approximation breaks down. Here we construct a non-perturbative, semiclassical method for predicting the energy-dependent cooling dynamics of trapped-ion crystals with potentially many internal levels and motional modes beyond the Lamb-Dicke regime. This method allows accurate and efficient modeling of a variety of interesting phenomena, such as the breakdown of EIT cooling at high energies and the simultaneous cooling of multiple high-temperature modes. We compare its predictions both to fully-quantum simulations and to experimental data for a broadband EIT cooling method on a Raman SSS-DDD transition in 138^{138}138Ba+{^+}+. We find the method can accurately predict cooling rates over a wide range of energies relevant to trapped ion experiments. Our method complements fully quantum models by allowing for fast and accurate predictions of laser-cooling dynamics at much higher energy scales.
Electromagnetically Induced Transparency (EIT) cooling is a well-established method for preparing trapped ion systems in their motional ground state. However, isolating a three-level system, as required for EIT cooling, is often challenging or impractical. Nonetheless, multilevel systems can inherently host dark states. In this work, we extend the EIT cooling framework to such multilevel systems. We develop a formalism to accurately determine the cooling rate in the weak sideband coupling regime and provide an approximate estimate for cooling rates beyond this regime, without the need for explicit simulation of the motional degree of freedom. We clarify the connection between the cooling rate and the absorption spectrum, offering a pathway for efficient near-ground-state cooling of ions with complex electronic structures.
Currently, laser cooling schemes are fundamentally based on the weak coupling regime. This requirement sets the trap frequency as an upper bound to the cooling rate. In this work we present a numerical study that shows the feasibility of cooling in the strong-coupling regime which then allows cooling rates that are faster than the trap frequency with experimentally feasible parameters. The scheme presented here can be applied to trapped atoms or ions as well as to mechanical oscillators. It can also cool medium sized ion chains close to the ground state.