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

Adiabatic cooling of ions in the penning trap

Guo Zhong Li, R. Poggiani, G. Testera +1 more

Zeitschrift für Physik D Atoms Molecules and ClustersMar 1, 199113 citations

Doppler cooling of Ca+ ions in a Penning trap

Kyo-Woog Koo, J. Sudbery, D. M. Segal +1 more

We have laser cooled a small cloud of ${}^{40}{\mathrm{Ca}}^{+}$ ions stored in a Penning trap. The large Zeeman splittings that result from the presence of the imposed magnetic field necessitate the use of two cooling lasers tuned to the ${}^{2}{S}_{1/2}{\ensuremath{-}}^{2}{P}_{1/2}$ transition near 397 nm (whereas only a single blue laser frequency is required in an rf trap). The 397 nm radiation is provided by a pair of blue diode lasers operated in extended cavities. Ions can escape from the cooling cycle by falling into a ${}^{2}{D}_{3/2}$ state. There is also a small probability that ions can be pumped into a ${}^{2}{D}_{5/2}$ state. The presence of large Zeeman splittings complicates the provision of repumper radiation to empty the D states. We describe two repumping schemes. The first scheme employs five infrared extended cavity diode lasers (ECDL's). The second scheme employs three infrared ECDL's, two of which have their injection current modulated to produce sidebands. An upper bound to the temperature of 1 K is inferred from the linewidth of the 397-nm fluorescence for a small cloud of ${}^{40}{\mathrm{Ca}}^{+}$ ions in our Penning trap. This work is part of a program aimed at using atomic ions in a Penning trap for decoherence studies and quantum information processing.We have laser cooled a small cloud of ${}^{40}{\mathrm{Ca}}^{+}$ ions stored in a Penning trap. The large Zeeman splittings that result from the presence of the imposed magnetic field necessitate the use of two cooling lasers tuned to the ${}^{2}{S}_{1/2}{\ensuremath{-}}^{2}{P}_{1/2}$ transition near 397 nm (whereas only a single blue laser frequency is required in an rf trap). The 397 nm radiation is provided by a pair of blue diode lasers operated in extended cavities. Ions can escape from the cooling cycle by falling into a ${}^{2}{D}_{3/2}$ state. There is also a small probability that ions can be pumped into a ${}^{2}{D}_{5/2}$ state. The presence of large Zeeman splittings complicates the provision of repumper radiation to empty the D states. We describe two repumping schemes. The first scheme employs five infrared extended cavity diode lasers (ECDL's). The second scheme employs three infrared ECDL's, two of which have their injection current modulated to produce sidebands. An upper bound to the temperature of 1 K is inferred from the linewidth of the 397-nm fluorescence for a small cloud of ${}^{40}{\mathrm{Ca}}^{+}$ ions in our Penning trap. This work is part of a program aimed at using atomic ions in a Penning trap for decoherence studies and quantum information processing.

Physical Review AApr 8, 200429 citations

Manipulation of Ca+ Ions in Penning Traps

D. R. Crick

The long term aim of this work is to study the suitability of using laser cooled Ca+ ions in Penning traps as the basic components of a quantum computer. A great deal of progress in the field of quantum computing has been made in recent years with laser cooled ions stored in radio frequency ion traps. Building a useful quantum computer with trapped ions is however extremely challenging. Penning traps offer some possible benefits over radio frequency traps. They also create some additional difficulties. The potential advantages and disadvantages of Penning traps are discussed throughout the thesis. We show that we are able to overcome the problems associated with laser cooling in Penning traps, and have trapped single ions for extended periods of time. Pairs of Ca+ ions have been aligned along the axis of a Penning trap, and have been optically resolved. A novel Penning trap array based on PCB boards has been developed. A prototype was built and tested, along with the electronics required to shuttle ions between different sub-traps. Ions have been shuttled a distance of 10 mm in 2.5 μs. A return trip efficiency of up to 75% was seen. A quantum effect – J-state mixing caused by large magnetic fields – has been observed for the first time in single atomic ions. The magnetic field causes a forbidden [Delta]J = 2 transition to become weakly allowed. This effect is of general interest in atomic physics, and is also very relevant for quantum computation studies. A quantitative prediction of the magnitude of the J-mixing effect has been derived theoretically. This is compared to experimental data, and is found to be in excellent qualitative and good quantitative agreement.The long term aim of this work is to study the suitability of using laser cooled Ca+ ions in Penning traps as the basic components of a quantum computer. A great deal of progress in the field of quantum computing has been made in recent years with laser cooled ions stored in radio frequency ion traps. Building a useful quantum computer with trapped ions is however extremely challenging. Penning traps offer some possible benefits over radio frequency traps. They also create some additional difficulties. The potential advantages and disadvantages of Penning traps are discussed throughout the thesis. We show that we are able to overcome the problems associated with laser cooling in Penning traps, and have trapped single ions for extended periods of time. Pairs of Ca+ ions have been aligned along the axis of a Penning trap, and have been optically resolved. A novel Penning trap array based on PCB boards has been developed. A prototype was built and tested, along with the electronics required to shuttle ions between different sub-traps. Ions have been shuttled a distance of 10 mm in 2.5 μs. A return trip efficiency of up to 75% was seen. A quantum effect – J-state mixing caused by large magnetic fields – has been observed for the first time in single atomic ions. The magnetic field causes a forbidden [Delta]J = 2 transition to become weakly allowed. This effect is of general interest in atomic physics, and is also very relevant for quantum computation studies. A quantitative prediction of the magnitude of the J-mixing effect has been derived theoretically. This is compared to experimental data, and is found to be in excellent qualitative and good quantitative agreement.

May 1, 20091 citation

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 have laser cooled a small cloud of

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

ions stored in a Penning trap. The large Zeeman splittings that result from the presence of the imposed magnetic field necessitate the use of two cooling lasers tuned to the ${}^{2}{S}_{1/2}{\ensuremath{-}}^{2}{P}_{1/2}$ transition near 397 nm (whereas only a single blue laser frequency is required in an rf trap). The 397 nm radiation is provided by a pair of blue diode lasers operated in extended cavities. Ions can escape from the cooling cycle by falling into a

{}^{2}{D}_{3/2}

state. There is also a small probability that ions can be pumped into a

{}^{2}{D}_{5/2}

state. The presence of large Zeeman splittings complicates the provision of repumper radiation to empty the D states. We describe two repumping schemes. The first scheme employs five infrared extended cavity diode lasers (ECDL's). The second scheme employs three infrared ECDL's, two of which have their injection current modulated to produce sidebands. An upper bound to the temperature of 1 K is inferred from the linewidth of the 397-nm fluorescence for a small cloud of

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

ions in our Penning trap. This work is part of a program aimed at using atomic ions in a Penning trap for decoherence studies and quantum information processing.