Physical Review A

Doppler cooling of Ca+ ions in a Penning trap

Kyo-Woog Koo, J. Sudbery, D. M. Segal, Richard Claude Thompson

Published Apr 8, 2004• 29 citations

Abstract

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.

DOI: 10.1103/physreva.69.043402

Related papers

Towards Sideband Cooling of a Single 40Ca+ Ion in a Penning Trap

S. Donnellan

Nov 1, 20111 citation

Sideband cooling an ion to the quantum ground state in a Penning trap with very low heating rate

Joseph F. Goodwin, G. Stutter, Richard Claude Thompson +1 more

Jul 23, 20140 citations

Resolved-Sideband Laser Cooling in a Penning Trap

Joseph F. Goodwin, G. Stutter, Richard Claude Thompson +1 more

arXiv:1407.6121Physical Review LettersApr 6, 201668 citations

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

Brian J. McMahon, Brian C. Sawyer

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

Investigating a qubit candidate: Spectroscopy on the S1/2 to D5/2 transition of a trapped calcium ion in a linear Paul trap

Hanns‐Christoph Nägerl, Christian F. Roos, Dietrich G. Leibfried +5 more

Physical Review AJan 7, 200082 citations

Manipulation of Ca+ Ions in Penning Traps

D. R. Crick

May 1, 20091 citation

Physical Review A

Doppler cooling of Ca+ ions in a Penning trap

Kyo-Woog Koo, J. Sudbery, D. M. Segal, Richard Claude Thompson

Published Apr 8, 2004• 29 citations

Publisher

Abstract

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.

DOI: 10.1103/physreva.69.043402

Related papers

Towards Sideband Cooling of a Single 40Ca+ Ion in a Penning Trap

S. Donnellan

This thesis presents work aimed towards achieving sideband cooling of 40Ca+ ions in a Penning trap. The observation of an increase in the number of quantum jumps as a function of the trapping magnetic field is first presented. This observation is explained by the ion falling into a long-lived D5/2 state, out of which the ion is not being re-pumped. The ion can fall into this state due to mixing of the fine structure components with the same mJ quantum number induced by the applied magnetic field. A calculation of the mixing and shelving rate as a function of magnetic field strength is presented. This theory matches well with the experimental results observed. This work has been presented in a publication in which a perturbative analysis was used. An alternative analysis is presented here in which the full Hamiltonian is diagonalised. The essential conclusions however remain unchanged. This ‘J-state mixing’ effect means re-pumping from each of the six D5/2 state sub-levels of our ion is required for efficient laser cooling. This is achieved by the addition of a system comprising an 854 nm laser and a fibre EOM to provide the radiation required to re-pump these levels. The same EOM is then used to re-pump out of the four sub-levels of the D3/2 state using a single 866 nm laser. This is a great simplification of the experimental setup required to cool a 40Ca+ ion in a Penning trap which would otherwise require ten separate lasers to independently address each of the D sub-states. Achieving efficient repumping leads to the ability to perform pulsed spectroscopy on the quadrupole S1/2 → D5/2 transition in 40Ca+ . Preliminary results of this spectroscopy in a radio-frequency trap are presented.This thesis presents work aimed towards achieving sideband cooling of 40Ca+ ions in a Penning trap. The observation of an increase in the number of quantum jumps as a function of the trapping magnetic field is first presented. This observation is explained by the ion falling into a long-lived D5/2 state, out of which the ion is not being re-pumped. The ion can fall into this state due to mixing of the fine structure components with the same mJ quantum number induced by the applied magnetic field. A calculation of the mixing and shelving rate as a function of magnetic field strength is presented. This theory matches well with the experimental results observed. This work has been presented in a publication in which a perturbative analysis was used. An alternative analysis is presented here in which the full Hamiltonian is diagonalised. The essential conclusions however remain unchanged. This ‘J-state mixing’ effect means re-pumping from each of the six D5/2 state sub-levels of our ion is required for efficient laser cooling. This is achieved by the addition of a system comprising an 854 nm laser and a fibre EOM to provide the radiation required to re-pump these levels. The same EOM is then used to re-pump out of the four sub-levels of the D3/2 state using a single 866 nm laser. This is a great simplification of the experimental setup required to cool a 40Ca+ ion in a Penning trap which would otherwise require ten separate lasers to independently address each of the D sub-states. Achieving efficient repumping leads to the ability to perform pulsed spectroscopy on the quadrupole S1/2 → D5/2 transition in 40Ca+ . Preliminary results of this spectroscopy in a radio-frequency trap are presented.

Nov 1, 20111 citation

Sideband cooling an ion to the quantum ground state in a Penning trap with very low heating rate

Joseph F. Goodwin, G. Stutter, Richard Claude Thompson +1 more

We report the laser cooling of a single $^{40}\text{Ca}^+$ ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole $S_{1/2}\leftrightarrow D_{5/2}$ transition, broadened by a quench laser coupling the $D_{5/2}$ and $P_{3/2}$ levels. We find the final phonon number to be $\bar{n}=0.014\pm0.009$ . We measure the heating rate of the trap to be very low with $\dot{\bar{n}}=2.5\pm 0.3\textrm{s}^{-1}$ and a scaled spectral noise density of $\omega S_{E}(\omega)\sim1.6^{-8}\textrm{V}^2\textrm{m}^{-2}\textrm{Hz}^{-1}\textrm{s}^{-1}$ , which is consistent with the large ion-electrode distance. We perform Rabi oscillations on the sideband-cooled ion and observe a coherence time of $0.7\pm 0.1\textrm{ms}$ , noting that the practical performance is currently limited by the intensity noise of the probe laser.We report the laser cooling of a single $^{40}\text{Ca}^+$ ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole $S_{1/2}\leftrightarrow D_{5/2}$ transition, broadened by a quench laser coupling the $D_{5/2}$ and $P_{3/2}$ levels. We find the final phonon number to be $\bar{n}=0.014\pm0.009$. We measure the heating rate of the trap to be very low with $\dot{\bar{n}}=2.5\pm 0.3\textrm{s}^{-1}$ and a scaled spectral noise density of $\omega S_{E}(\omega)\sim1.6^{-8}\textrm{V}^2\textrm{m}^{-2}\textrm{Hz}^{-1}\textrm{s}^{-1}$, which is consistent with the large ion-electrode distance. We perform Rabi oscillations on the sideband-cooled ion and observe a coherence time of $0.7\pm 0.1\textrm{ms}$, noting that the practical performance is currently limited by the intensity noise of the probe laser.

Jul 23, 20140 citations

Resolved-Sideband Laser Cooling in a Penning Trap

Joseph F. Goodwin, G. Stutter, Richard Claude Thompson +1 more

We report the laser cooling of a single ${^{40}\mathrm{Ca}}^{+}$ ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole ${S}_{1/2}\ensuremath{\leftrightarrow}{D}_{5/2}$ transition, broadened by a quench laser coupling the ${D}_{5/2}$ and ${P}_{3/2}$ levels. We find the final ground-state occupation to be 98(1)%. We measure the heating rate of the trap to be very low with $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\overline{n}}\ensuremath{\approx}0.3(2)\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for trap frequencies from 150--400 kHz, consistent with the large ion-electrode distance.We report the laser cooling of a single ${^{40}\mathrm{Ca}}^{+}$ ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole ${S}_{1/2}\ensuremath{\leftrightarrow}{D}_{5/2}$ transition, broadened by a quench laser coupling the ${D}_{5/2}$ and ${P}_{3/2}$ levels. We find the final ground-state occupation to be 98(1)%. We measure the heating rate of the trap to be very low with $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\overline{n}}\ensuremath{\approx}0.3(2)\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for trap frequencies from 150--400 kHz, consistent with the large ion-electrode distance.

arXiv:1407.6121Physical Review LettersApr 6, 201668 citations

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

Investigating a qubit candidate: Spectroscopy on the S1/2 to D5/2 transition of a trapped calcium ion in a linear Paul trap

Hanns‐Christoph Nägerl, Christian F. Roos, Dietrich G. Leibfried +5 more

A single ${}^{40}{\mathrm{Ca}}^{+}$ ion is confined in a linear Paul trap and Doppler-cooled on the ${S}_{1/2}$ to ${P}_{1/2}$ dipole transition. Then the narrow quadrupole ${S}_{1/2}$ to ${D}_{5/2}$ transition at 729 nm is probed. The observed spectrum is interpreted in terms of the Zeeman substructure superimposed with oscillation sidebands due to the harmonic motion in the trap. The height of the motional sidebands provides a sensitive method to determine the ion's temperature and thus allows us to test sub-Doppler laser cooling schemes needed for quantum state preparation and quantum computation. We also observe the dynamics induced by Rabi oscillations on a carrier transition and interpret it in terms of the thermal state which is reached after Doppler cooling.A single ${}^{40}{\mathrm{Ca}}^{+}$ ion is confined in a linear Paul trap and Doppler-cooled on the ${S}_{1/2}$ to ${P}_{1/2}$ dipole transition. Then the narrow quadrupole ${S}_{1/2}$ to ${D}_{5/2}$ transition at 729 nm is probed. The observed spectrum is interpreted in terms of the Zeeman substructure superimposed with oscillation sidebands due to the harmonic motion in the trap. The height of the motional sidebands provides a sensitive method to determine the ion's temperature and thus allows us to test sub-Doppler laser cooling schemes needed for quantum state preparation and quantum computation. We also observe the dynamics induced by Rabi oscillations on a carrier transition and interpret it in terms of the thermal state which is reached after Doppler cooling.

Physical Review AJan 7, 200082 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

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}

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

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

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

{}^{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 report the laser cooling of a single

^{40}\text{Ca}^+

ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole

S_{1/2}\leftrightarrow D_{5/2}

transition, broadened by a quench laser coupling the

D_{5/2}

and

P_{3/2}

levels. We find the final phonon number to be

\bar{n}=0.014\pm0.009

. We measure the heating rate of the trap to be very low with

\dot{\bar{n}}=2.5\pm 0.3\textrm{s}^{-1}

and a scaled spectral noise density of

\omega S_{E}(\omega)\sim1.6^{-8}\textrm{V}^2\textrm{m}^{-2}\textrm{Hz}^{-1}\textrm{s}^{-1}

, which is consistent with the large ion-electrode distance. We perform Rabi oscillations on the sideband-cooled ion and observe a coherence time of

0.7\pm 0.1\textrm{ms}

, noting that the practical performance is currently limited by the intensity noise of the probe laser.

We report the laser cooling of a single

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

ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole ${S}_{1/2}\ensuremath{\leftrightarrow}{D}_{5/2}$ transition, broadened by a quench laser coupling the

{D}_{5/2}

and

{P}_{3/2}

levels. We find the final ground-state occupation to be 98(1)%. We measure the heating rate of the trap to be very low with $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\overline{n}}\ensuremath{\approx}0.3(2)\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for trap frequencies from 150--400 kHz, consistent with the large ion-electrode distance.

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.

A single

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

ion is confined in a linear Paul trap and Doppler-cooled on the

{S}_{1/2}

{P}_{1/2}

dipole transition. Then the narrow quadrupole

{S}_{1/2}

{D}_{5/2}

transition at 729 nm is probed. The observed spectrum is interpreted in terms of the Zeeman substructure superimposed with oscillation sidebands due to the harmonic motion in the trap. The height of the motional sidebands provides a sensitive method to determine the ion's temperature and thus allows us to test sub-Doppler laser cooling schemes needed for quantum state preparation and quantum computation. We also observe the dynamics induced by Rabi oscillations on a carrier transition and interpret it in terms of the thermal state which is reached after Doppler cooling.