Trapped Calcium Ions Cooled to Near Absolute Zero with Laser Precision

Scientists have achieved efficient three-dimensional sub-Doppler cooling of calcium-40 ions confined within a Penning trap, representing a significant advance in precision control of trapped ions for quantum information processing and spectroscopy. Brian J. McMahon and Brian C. Sawyer, both from the Georgia Tech Research Institute, alongside colleagues, demonstrate a method to cool all three motional modes of a single ion using a compact Penning trap operating at 0.91 Tesla. By exploiting a narrow two-photon dark resonance with existing laser cooling infrastructure and applying a parametric drive, the researchers cooled the ion from an initial thermal occupation of 72 to a final occupation of just 1.5 in 800 seconds, achieving a cooling time constant of 108 seconds. This cooling occurs at a frequency placing the ion’s motion outside the conventional Lamb-Dicke regime, opening new possibilities for manipulating and controlling ions with greater precision.

Employing the same laser beams initially used for Doppler cooling, researchers detuned the laser frequencies to induce a narrow two-photon dark resonance, achieving a cooling time constant of 108(8) μs.

This process reduced the mean thermal axial mode occupation from 72(23) to 1.5(3) within 800μs, as determined by resonant probing of an electric quadrupole transition near 729nm. A parametric drive applied to the trap electrodes coherently exchanges axial mode occupation with each radial mode, enabling full three-dimensional sub-Doppler cooling using only axially-propagating laser beams.
This sub-Doppler cooling was achieved at an axial oscillation frequency of 221kHz, positioning the ion’s motion outside the Lamb Dicke confinement regime typically encountered at the Doppler cooling limit. Measured cooling rates and final mode occupations align closely with a semiclassical model integrating a Lindblad master equation for ion-photon interactions with classical harmonic oscillator motion.

The work addresses a critical need in quantum information processing, where finite phonon occupation in trapped ion motional modes can degrade the fidelity of entangling gate operations. Researchers overcame limitations of conventional sideband cooling in strong confinement regimes by utilizing a dark resonance technique, reducing the axial ground state cooling time from 20ms to 3.8ms when combined with pulsed sideband cooling.

To further enhance cooling efficiency across all degrees of freedom, the ground-state-cooled axial mode population is coherently exchanged with a Doppler-cooled radial mode via an oscillating quadrupolar potential. This innovative approach allows for effective sub-Doppler cooling of all motional dimensions using only axial laser beams, representing a significant advancement in Penning trap ion cooling techniques. The Penning trap utilizes a combination of a static magnetic field and an electrostatic quadrupole to confine the ion, with frequencies of (ωz, ω+, ω−) = 2π × (221kHz, 256kHz, 96kHz) achieved in this study.

Ion confinement and sympathetic cooling within a Penning trap are crucial for precision measurements

A 0.91 T Penning trap forms the core of this work, confining single 40Ca+ ions through a combination of static magnetic and electrostatic quadrupole fields. Ion motion parallel to the magnetic field is harmonically oscillated by the electric quadrupole potential, while perpendicular motion results in modified cyclotron and magnetron modes with frequencies determined by the magnetic field strength and trap geometry.

Specifically, frequencies of 2π × (221kHz, 256kHz, 96kHz) were achieved for the axial, modified cyclotron, and magnetron modes respectively. Doppler cooling of the axial and modified cyclotron modes was initially performed using laser beams delivered via photonic crystal fibres. To achieve sub-Doppler cooling, researchers detuned laser frequencies to induce a narrow two-photon dark resonance in the axial mode.

This process yielded a 1/e cooling time constant of 108(8) s, reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) within 800s, as determined by resonant probing of an electric quadrupole transition at 729nm. A parametric drive was then applied to the trap electrodes, coherently exchanging axial mode occupation with each radial mode.

This innovative technique enabled three-dimensional sub-Doppler cooling using only axially-propagating laser beams. The axial oscillation frequency of 221kHz placed the ion motion outside the Lamb Dicke confinement regime, allowing for efficient cooling. Furthermore, this combination of dark resonance and subsequent sideband cooling reduced the axial ground state cooling time from 20ms to 3.8ms, a significant improvement over resolved sideband cooling in comparable systems. Simultaneously, radially-displaced Doppler cooling beams and an oscillating quadrupolar potential were employed to address the differing cooling requirements of the radial modes, further enhancing the overall cooling efficiency.

Three-dimensional sub-Doppler cooling of a single calcium ion in a Penning trap is demonstrated

A 1/e cooling time constant of 108(8) seconds was achieved for sub-Doppler laser cooling of three eigenmodes of a single calcium ion confined within a compact Penning trap operating at a magnetic field of 0.91 T. The research demonstrates a reduction in mean thermal axial mode occupation from 72(23) to 1.5(3) over a duration of 800 seconds, as determined by resonant probing of an electric quadrupole transition near 729nm.

This cooling process utilizes a narrow two-photon dark resonance created by detuning laser frequencies, employing the same laser beams initially used for Doppler laser cooling. The axial oscillation frequency was measured at 221kHz, positioning the ion motion outside of the Lamb Dicke confinement regime at the Doppler laser cooling limit.

A parametric drive applied to the trap electrodes coherently exchanges axial mode occupation with each radial mode, enabling three-dimensional sub-Doppler cooling using only axially-propagating laser beams. Trap frequencies of (ωz, ω+, ω−) = 2π × (221kHz, 256kHz, 96kHz) were established for this work, ensuring stable radial confinement given the 0.91 T magnetic field and a bare cyclotron frequency of ωc = 2π × 351kHz.

Doppler cooling was applied to all degrees of freedom, leveraging Penning trap ion confinement achieved through a combination of a static magnetic field and an electrostatic quadrupole. The axial ion motion, experiencing no Lorentz force, exhibited Doppler cooling dynamics identical to those observed in radio frequency traps.

Cooling of the modified cyclotron mode was similarly straightforward, while the magnetron mode occupation was reduced through heating, necessitating techniques to address the mismatch in radial mode cooling requirements. Simultaneous application of a radially-displaced Doppler cooling laser beam and an oscillating quadrupolar potential facilitated axialization and three-dimensional Doppler cooling. The Doppler cooling limit of approximately 0.5 mK corresponded to an average motional occupation of between 40 and 100 for the established trap frequencies.

Three-dimensional sub-Doppler cooling of calcium ions via coherent mode transfer is demonstrated

Scientists have achieved efficient cooling of calcium ions confined within a Penning trap, a device utilising magnetic and electric fields for particle containment. Employing a technique known as dark resonance cooling, they reduced the thermal motion of the ions along three independent axes, achieving a significant decrease in their energy state.

This cooling process, performed using the same laser beams initially used for Doppler cooling, involved detuning laser frequencies to induce a narrow two-photon dark resonance, ultimately lowering the mean thermal occupation of the axial mode from 72 to 1.5 within 800 seconds. The research extends beyond simple axial cooling by incorporating a method to coherently transfer energy between the axial and radial modes of the ion’s motion.

This coherent mode exchange, facilitated by modulating the trap’s potential, enabled three-dimensional sub-Doppler cooling using only lasers directed along the axial direction. The final temperatures attained in two of the three modes are currently limited by recoil heating inherent in the dark resonance cooling process, but simulations suggest improvements in laser stability could reduce this heating to below five quanta per uncooled mode.

The demonstrated ground state cooling time of 3.8 milliseconds represents a five-fold improvement over previous sideband cooling demonstrations with calcium ions in similar traps. This work demonstrates a robust and efficient cooling scheme applicable to a range of ion confinement conditions, which is crucial for advancing quantum information experiments utilising trapped ions.

Although initial attempts to continuously couple axial and radial degrees of freedom during cooling were unsuccessful, potentially due to micromotion, the researchers suggest this remains a promising avenue for future investigation. The techniques presented contribute to the growing toolkit of laser cooling methods for Penning trap-based quantum computing, paving the way for more complex and precise control of ions for quantum applications.