arXiv:1909.02034 · Physical Review A

Doppler-cooled ions in a compact reconfigurable Penning trap

Brian J. McMahon, Curtis Volin, Wade G. Rellergert, Brian C. Sawyer

Published Jan 8, 2020• 14 citations

Abstract

We report the design and experimental demonstration of a compact, reconfigurable Penning ion trap constructed with rare-earth permanent magnets placed outside of a trap vacuum enclosure. We describe the observation of Doppler laser cooling of ions in a permanent magnet Penning trap. We detail a method for quantifying and optimizing the trap magnetic-field uniformity in situ using a thermal beam of neutral $^{40}\mathrm{Ca}$ precursor atoms. Doppler laser cooling of $^{40}\mathrm{Ca}^{+}$ is carried out at 0.65 T, and side-view images of trapped ion fluorescence show crystalline order for both two- and three-dimensional arrays. Measured $^{40}\mathrm{Ca}^{+}$ trap frequencies confirm the magnetic-field characterization with neutral $^{40}\mathrm{Ca}$. The compact trap described here enables a variety of cold ion experiments with low size, weight, power, and cost requirements relative to traditional electromagnet-based Penning traps.

DOI: 10.1103/physreva.101.013408

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Quantum dynamics of small numbers of ions in a penning trap

G. Stutter

Nov 1, 20151 citation

arXiv:1909.02034 · Physical Review A

Doppler-cooled ions in a compact reconfigurable Penning trap

Brian J. McMahon, Curtis Volin, Wade G. Rellergert, Brian C. Sawyer

Published Jan 8, 2020• 14 citations

arXiv HTML PDF

Abstract

^{40}\mathrm{Ca}

precursor atoms. Doppler laser cooling of

^{40}\mathrm{Ca}^{+}

is carried out at 0.65 T, and side-view images of trapped ion fluorescence show crystalline order for both two- and three-dimensional arrays. Measured

^{40}\mathrm{Ca}^{+}

trap frequencies confirm the magnetic-field characterization with neutral

^{40}\mathrm{Ca}

. The compact trap described here enables a variety of cold ion experiments with low size, weight, power, and cost requirements relative to traditional electromagnet-based Penning traps.

DOI: 10.1103/physreva.101.013408

Related papers

Efficient Three-Dimensional Sub-Doppler Cooling of $^{40}$ Ca $^+$ in a Penning TrapEfficient Three-Dimensional Sub-Doppler Cooling of $^{40}$Ca$^+$ in a Penning Trap

Brian J. McMahon, Brian C. Sawyer

We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a $^{40}$ Ca $^+$ ion confined in a compact Penning trap operating with a magnetic field of 0.91 T. Using the same set of laser beams as required for the initial Doppler laser cooling operation, we detune the laser frequencies to produce a narrow two-photon dark resonance. The process achieves a 1/e cooling time constant of 108(8) $μ$ s, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in 800 $μ$ s as measured by resonantly probing an electric quadrupole transition near 729 nm. A parametric drive is applied to the trap electrodes which coherently exchanges the axial mode occupation with that of each radial mode, allowing for three-dimensional sub-Doppler cooling using only the axially-propagating laser beams. This sub-Doppler cooling is achieved for an axial oscillation frequency of $ω_z = 2π~\times~$221 kHz, which places the motion well outside of the Lamb Dicke confinement regime at the Doppler laser cooling limit. Our measured cooling rate and final mode occupation are in good agreement with a semiclassical model which combines a Lindblad master equation solution for ion-photon interactions with classical harmonic oscillator motion of the trapped ion.We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a $^{40}$Ca$^+$ ion confined in a compact Penning trap operating with a magnetic field of 0.91 T. Using the same set of laser beams as required for the initial Doppler laser cooling operation, we detune the laser frequencies to produce a narrow two-photon dark resonance. The process achieves a 1/e cooling time constant of 108(8) $μ$s, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in 800 $μ$s as measured by resonantly probing an electric quadrupole transition near 729 nm. A parametric drive is applied to the trap electrodes which coherently exchanges the axial mode occupation with that of each radial mode, allowing for three-dimensional sub-Doppler cooling using only the axially-propagating laser beams. This sub-Doppler cooling is achieved for an axial oscillation frequency of $ω_z = 2π~\times~$221 kHz, which places the motion well outside of the Lamb Dicke confinement regime at the Doppler laser cooling limit. Our measured cooling rate and final mode occupation are in good agreement with a semiclassical model which combines a Lindblad master equation solution for ion-photon interactions with classical harmonic oscillator motion of the trapped ion.

physics.atom-phCross-listedarXiv:2602.02937Physical Review AFeb 4, 20261 citation

Experimental implementation of laser cooling of trapped ions in strongly inhomogeneous magnetic fields

Christian Mangeng, Yanning Yin, Richard Karl +1 more

We demonstrate the Doppler laser cooling of $^{40}\mathrm{Ca}^{+}$ ions confined in a segmented linear Paul trap in the presence of a strong quadrupolar magnetic field generated by two permanent ring magnets. Magnetic field gradients of 800 to 1600 G/mm give rise to a highly position-dependent Zeeman shift on the energy levels of the trapped ions. Efficient laser cooling is demonstrated using two 397 nm cooling laser beams with appropriate wavelengths and polarizations and one 866 nm repumper laser beam. Coulomb crystals of ions are found to exhibit similar secular temperatures to those trapped in absence of the magnetic field. In addition, the position dependency of the Zeeman effect is used to generate a map of the field strength. This work forms the basis for developing hybrid trapping experiments for cold ions and neutral molecules that consist of an ion and a magnetic trap to study cold interactions between these species, and opens up new possibilities for quantum-science experiments that employ trapped ions in inhomogeneous magnetic fields.We demonstrate the Doppler laser cooling of $^{40}\mathrm{Ca}^{+}$ ions confined in a segmented linear Paul trap in the presence of a strong quadrupolar magnetic field generated by two permanent ring magnets. Magnetic field gradients of 800 to 1600 G/mm give rise to a highly position-dependent Zeeman shift on the energy levels of the trapped ions. Efficient laser cooling is demonstrated using two 397 nm cooling laser beams with appropriate wavelengths and polarizations and one 866 nm repumper laser beam. Coulomb crystals of ions are found to exhibit similar secular temperatures to those trapped in absence of the magnetic field. In addition, the position dependency of the Zeeman effect is used to generate a map of the field strength. This work forms the basis for developing hybrid trapping experiments for cold ions and neutral molecules that consist of an ion and a magnetic trap to study cold interactions between these species, and opens up new possibilities for quantum-science experiments that employ trapped ions in inhomogeneous magnetic fields.

arXiv:2309.03385Physical Review ResearchNov 27, 20233 citations

Optimizing Doppler laser cooling protocols for quantum sensing with 3D ion crystals in a Penning trap

John Zaris, Wes Johnson, Athreya Shankar +4 more

Large, 3D trapped ion crystals offer improved sensitivity in quantum sensing protocols, and are expected to be implemented as platforms in near-future experiments. However, numerical techniques used to study the laser cooling of such crystals are inefficient as the number of ions, $N$ , in the crystal increases. Here we develop a powerful numerical framework to simulate laser cooling of up to $10^5$ ions stored in a Penning trap. We apply this framework to characterize and optimize the cooling of ellipsoidal 3D crystals. We document new pathways to enhanced cooling based on the addition of an axial component to the potential energy-dominated $\boldsymbol{E}\times\boldsymbol{B}$ modes. Furthermore, we observe greatly enhanced cooling of the perpendicular kinetic energy to below 1 mK in prolate ion crystals, enabling a simplified cooling beam setup for such crystals. We propose specific values of trap and laser beam parameters which lead to optimal cooling in a variety of examples. This work illustrates the feasibility of preparing large 3D crystals for high-sensitivity quantum science protocols, motivating their use in future experiments.Large, 3D trapped ion crystals offer improved sensitivity in quantum sensing protocols, and are expected to be implemented as platforms in near-future experiments. However, numerical techniques used to study the laser cooling of such crystals are inefficient as the number of ions, $N$, in the crystal increases. Here we develop a powerful numerical framework to simulate laser cooling of up to $10^5$ ions stored in a Penning trap. We apply this framework to characterize and optimize the cooling of ellipsoidal 3D crystals. We document new pathways to enhanced cooling based on the addition of an axial component to the potential energy-dominated $\boldsymbol{E}\times\boldsymbol{B}$ modes. Furthermore, we observe greatly enhanced cooling of the perpendicular kinetic energy to below 1 mK in prolate ion crystals, enabling a simplified cooling beam setup for such crystals. We propose specific values of trap and laser beam parameters which lead to optimal cooling in a variety of examples. This work illustrates the feasibility of preparing large 3D crystals for high-sensitivity quantum science protocols, motivating their use in future experiments.

quant-pharXiv:2602.22541Feb 27, 20260 citations

Second-Scale 9 Be + Spin Coherence in a Compact Penning Trap

Brian J. McMahon, Brian C. Sawyer

We report microwave spectroscopy of co-trapped ${}^{9}$ $\mathrm{Be}$ ${}^{+}$ and ${}^{40}$ $\mathrm{Ca}$ ${}^{+}$ ions within a compact permanent-magnet-based Penning ion trap. The trap is constructed with a reconfigurable array of $\mathrm{Nd}$ - $\mathrm{Fe}$ - $\mathrm{B}$ rings providing a 0.654-T magnetic field that is near the 0.6774-T magnetic-field-insensitive hyperfine transition in ${}^{9}$ $\mathrm{Be}$ ${}^{+}$ . Performing Ramsey spectroscopy on this hyperfine transition, we demonstrate nuclear spin coherence with a contrast decay time of >1 s. The ${}^{9}$ $\mathrm{Be}$ ${}^{+}$ is sympathetically cooled by a Coulomb crystal of ${}^{40}$ $\mathrm{Ca}$ ${}^{+}$ , which minimizes ${}^{9}$ $\mathrm{Be}$ ${}^{+}$ illumination and thus mitigates reactive loss. Introducing a unique high-magnetic-field optical-detection scheme for ${}^{40}$ $\mathrm{Ca}$ ${}^{+}$ , we perform spin-state readout without a 729-nm shelving laser. We record a fractional trap magnetic field instability below 20 ppb (13 nT) at 43 s of averaging time with no magnetic shielding and only passive thermal isolation. We discuss potential applications of this compact reconfigurable Penning trap.We report microwave spectroscopy of co-trapped ${}^{9}$$\mathrm{Be}$${}^{+}$ and ${}^{40}$$\mathrm{Ca}$${}^{+}$ ions within a compact permanent-magnet-based Penning ion trap. The trap is constructed with a reconfigurable array of $\mathrm{Nd}$-$\mathrm{Fe}$-$\mathrm{B}$ rings providing a 0.654-T magnetic field that is near the 0.6774-T magnetic-field-insensitive hyperfine transition in ${}^{9}$$\mathrm{Be}$${}^{+}$. Performing Ramsey spectroscopy on this hyperfine transition, we demonstrate nuclear spin coherence with a contrast decay time of >1 s. The ${}^{9}$$\mathrm{Be}$${}^{+}$ is sympathetically cooled by a Coulomb crystal of ${}^{40}$$\mathrm{Ca}$${}^{+}$, which minimizes ${}^{9}$$\mathrm{Be}$${}^{+}$ illumination and thus mitigates reactive loss. Introducing a unique high-magnetic-field optical-detection scheme for ${}^{40}$$\mathrm{Ca}$${}^{+}$, we perform spin-state readout without a 729-nm shelving laser. We record a fractional trap magnetic field instability below 20 ppb (13 nT) at 43 s of averaging time with no magnetic shielding and only passive thermal isolation. We discuss potential applications of this compact reconfigurable Penning trap.

arXiv:2110.03053Physical Review AppliedJan 5, 202212 citations

Individual-Ion Addressing and Readout in a Penning Trap

Brian J. McMahon, Kenton R. Brown, Creston D. Herold +1 more

We implement individual addressing and readout of ions in a rigidly rotating planar crystal in a compact, permanent magnet Penning trap. The crystal of ^{40}Ca^{+} is trapped and stabilized without defects via a rotating triangular potential. The trapped ion fluorescence is detected in the rotating frame for parallel readout. The qubit is encoded in the metastable D_{5/2} manifold enabling the use of high-power near-infrared laser systems for qubit operations. Addressed σ_{z} operations are realized with a focused ac Stark shifting laser beam. We demonstrate addressing of ions near the center of the crystal and at large radii. Simulations show that the current addressing operation fidelity is limited to ∼97% by the ion's thermal extent for the in-plane modes near the Doppler limit, but this could be improved to infidelities <10^{-3} with sub-Doppler cooling. The techniques demonstrated in this Letter complete the set of operations for quantum simulation with the platform.We implement individual addressing and readout of ions in a rigidly rotating planar crystal in a compact, permanent magnet Penning trap. The crystal of ^{40}Ca^{+} is trapped and stabilized without defects via a rotating triangular potential. The trapped ion fluorescence is detected in the rotating frame for parallel readout. The qubit is encoded in the metastable D_{5/2} manifold enabling the use of high-power near-infrared laser systems for qubit operations. Addressed σ_{z} operations are realized with a focused ac Stark shifting laser beam. We demonstrate addressing of ions near the center of the crystal and at large radii. Simulations show that the current addressing operation fidelity is limited to ∼97% by the ion's thermal extent for the in-plane modes near the Doppler limit, but this could be improved to infidelities <10^{-3} with sub-Doppler cooling. The techniques demonstrated in this Letter complete the set of operations for quantum simulation with the platform.

arXiv:2404.02105Physical Review LettersOct 23, 202411 citations

Quantum dynamics of small numbers of ions in a penning trap

G. Stutter

Laser-cooled trapped ions are one of the main systems used in experiments in the fields of quantum optics and quantum information. There are two commonly-used types of ion trap, the radiofrequency trap and the Penning trap. In general, the RF trap has been more widely used in quantum information experiments, meaning that the set of experimental tools for conducting these types of experiments in a Penning trap is currently less complete. The aim of the work presented in this thesis is to increase this array of tools. Our experiment uses 40Ca+ ions in a Penning trap alongside lasers. Spectroscopy has been performed on single Doppler cooled ions, and on ions that have been prepared close to their ground state of motion using a multiple-stage sideband cooling technique resulting in an average phonon occupation number of $\nzbar = 0.029\pm 0.011$ from an initial $\nzbar \approx 24$. This corresponds to a quantum ground state population of $97\%$ , which is close to the sideband cooling limit in our system. An axial heating rate measurement of $\dot{\bar{n}}_z=\SI{0.56\pm0.52}{\per\second}$ has also been obtained, which is the lowest recorded to date, due in part to the large dimensions of our trap. Additionally improved control of the Penning trap radial motion has been demonstrated and the average phonon occupation number of the modified cyclotron motion has been reduced from $\ncbar\approx150$ after Doppler cooling to $\ncbar=0.6$ after sideband cooling. Some preliminary single-ion coherent operations have also been performed. In the future we hope that this system of ground state cooled ions in a Penning trap can be used to generate highly-entangled states in two or more ions, with a view to performing simple quantum error-correcting codes and eventually an analogue quantum simulation of spin systems.Laser-cooled trapped ions are one of the main systems used in experiments in the fields of quantum optics and quantum information. There are two commonly-used types of ion trap, the radiofrequency trap and the Penning trap. In general, the RF trap has been more widely used in quantum information experiments, meaning that the set of experimental tools for conducting these types of experiments in a Penning trap is currently less complete. The aim of the work presented in this thesis is to increase this array of tools. Our experiment uses 40Ca+ ions in a Penning trap alongside lasers. Spectroscopy has been performed on single Doppler cooled ions, and on ions that have been prepared close to their ground state of motion using a multiple-stage sideband cooling technique resulting in an average phonon occupation number of $\nzbar = 0.029\pm 0.011$ from an initial $\nzbar \approx 24$. This corresponds to a quantum ground state population of $97\%$, which is close to the sideband cooling limit in our system. An axial heating rate measurement of $\dot{\bar{n}}_z=\SI{0.56\pm0.52}{\per\second}$ has also been obtained, which is the lowest recorded to date, due in part to the large dimensions of our trap. Additionally improved control of the Penning trap radial motion has been demonstrated and the average phonon occupation number of the modified cyclotron motion has been reduced from $\ncbar\approx150$ after Doppler cooling to $\ncbar=0.6$ after sideband cooling. Some preliminary single-ion coherent operations have also been performed. In the future we hope that this system of ground state cooled ions in a Penning trap can be used to generate highly-entangled states in two or more ions, with a view to performing simple quantum error-correcting codes and eventually an analogue quantum simulation of spin systems.

Nov 1, 20151 citation

^{40}\mathrm{Ca}

precursor atoms. Doppler laser cooling of

^{40}\mathrm{Ca}^{+}

is carried out at 0.65 T, and side-view images of trapped ion fluorescence show crystalline order for both two- and three-dimensional arrays. Measured

^{40}\mathrm{Ca}^{+}

trap frequencies confirm the magnetic-field characterization with neutral

^{40}\mathrm{Ca}

. The compact trap described here enables a variety of cold ion experiments with low size, weight, power, and cost requirements relative to traditional electromagnet-based Penning traps.

Efficient Three-Dimensional Sub-Doppler Cooling of

^{40}

^+

in a Penning Trap

We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a

^{40}

^+

ion confined in a compact Penning trap operating with a magnetic field of 0.91 T. Using the same set of laser beams as required for the initial Doppler laser cooling operation, we detune the laser frequencies to produce a narrow two-photon dark resonance. The process achieves a 1/e cooling time constant of 108(8)

μ

s, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in 800

μ

s as measured by resonantly probing an electric quadrupole transition near 729 nm. A parametric drive is applied to the trap electrodes which coherently exchanges the axial mode occupation with that of each radial mode, allowing for three-dimensional sub-Doppler cooling using only the axially-propagating laser beams. This sub-Doppler cooling is achieved for an axial oscillation frequency of $ω_z = 2π~\times~$221 kHz, which places the motion well outside of the Lamb Dicke confinement regime at the Doppler laser cooling limit. Our measured cooling rate and final mode occupation are in good agreement with a semiclassical model which combines a Lindblad master equation solution for ion-photon interactions with classical harmonic oscillator motion of the trapped ion.

We demonstrate the Doppler laser cooling of

^{40}\mathrm{Ca}^{+}

ions confined in a segmented linear Paul trap in the presence of a strong quadrupolar magnetic field generated by two permanent ring magnets. Magnetic field gradients of 800 to 1600 G/mm give rise to a highly position-dependent Zeeman shift on the energy levels of the trapped ions. Efficient laser cooling is demonstrated using two 397 nm cooling laser beams with appropriate wavelengths and polarizations and one 866 nm repumper laser beam. Coulomb crystals of ions are found to exhibit similar secular temperatures to those trapped in absence of the magnetic field. In addition, the position dependency of the Zeeman effect is used to generate a map of the field strength. This work forms the basis for developing hybrid trapping experiments for cold ions and neutral molecules that consist of an ion and a magnetic trap to study cold interactions between these species, and opens up new possibilities for quantum-science experiments that employ trapped ions in inhomogeneous magnetic fields.

N

, in the crystal increases. Here we develop a powerful numerical framework to simulate laser cooling of up to

10^5

ions stored in a Penning trap. We apply this framework to characterize and optimize the cooling of ellipsoidal 3D crystals. We document new pathways to enhanced cooling based on the addition of an axial component to the potential energy-dominated

\boldsymbol{E}\times\boldsymbol{B}

modes. Furthermore, we observe greatly enhanced cooling of the perpendicular kinetic energy to below 1 mK in prolate ion crystals, enabling a simplified cooling beam setup for such crystals. We propose specific values of trap and laser beam parameters which lead to optimal cooling in a variety of examples. This work illustrates the feasibility of preparing large 3D crystals for high-sensitivity quantum science protocols, motivating their use in future experiments.

We report microwave spectroscopy of co-trapped

{}^{9}

\mathrm{Be}

{}^{+}

and

{}^{40}

\mathrm{Ca}

{}^{+}

ions within a compact permanent-magnet-based Penning ion trap. The trap is constructed with a reconfigurable array of

\mathrm{Nd}

\mathrm{Fe}

\mathrm{B}

rings providing a 0.654-T magnetic field that is near the 0.6774-T magnetic-field-insensitive hyperfine transition in

{}^{9}

\mathrm{Be}

{}^{+}

. Performing Ramsey spectroscopy on this hyperfine transition, we demonstrate nuclear spin coherence with a contrast decay time of >1 s. The

{}^{9}

\mathrm{Be}

{}^{+}

is sympathetically cooled by a Coulomb crystal of

{}^{40}

\mathrm{Ca}

{}^{+}

, which minimizes

{}^{9}

\mathrm{Be}

{}^{+}

illumination and thus mitigates reactive loss. Introducing a unique high-magnetic-field optical-detection scheme for

{}^{40}

\mathrm{Ca}

{}^{+}

, we perform spin-state readout without a 729-nm shelving laser. We record a fractional trap magnetic field instability below 20 ppb (13 nT) at 43 s of averaging time with no magnetic shielding and only passive thermal isolation. We discuss potential applications of this compact reconfigurable Penning trap.

97\%

, which is close to the sideband cooling limit in our system. An axial heating rate measurement of $\dot{\bar{n}}_z=\SI{0.56\pm0.52}{\per\second}$ has also been obtained, which is the lowest recorded to date, due in part to the large dimensions of our trap. Additionally improved control of the Penning trap radial motion has been demonstrated and the average phonon occupation number of the modified cyclotron motion has been reduced from $\ncbar\approx150$ after Doppler cooling to $\ncbar=0.6$ after sideband cooling. Some preliminary single-ion coherent operations have also been performed. In the future we hope that this system of ground state cooled ions in a Penning trap can be used to generate highly-entangled states in two or more ions, with a view to performing simple quantum error-correcting codes and eventually an analogue quantum simulation of spin systems.