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arXiv:1407.6121 · Physical Review Letters

Resolved-Sideband Laser Cooling in a Penning Trap

Joseph F. Goodwin, G. Stutter, Richard Claude Thompson, D. M. Segal

Published Apr 6, 2016• 68 citations
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Abstract

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.

DOI
10.1103/physrevlett.116.143002

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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.

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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.

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Sideband cooling to the quantum ground state in a penning trap

Joseph F. Goodwin

For 35 years, laser-cooled trapped ions have been at the frontier of progress in quantum computing, quantum simulation and precision measurement, and remain one of the most valuable tools in these fields to this day. Most of these experiments are predicated upon or benefit from the ability to place ions in the motional quantum ground state, a technique that was first demonstrated in radiofrequency ion traps 25 years ago. For a range of crucial experiments that are impossible to conduct in radiofrequency traps or are not well suited to this architecture, Penning traps provide an important alternative. However, the performance of Penning traps had been limited by the fact that ground-state cooling was yet to be achieved in such a system. This thesis reports the first demonstration of resolved-sideband cooling in a Penning trap, for 40Ca+ions cooled with light at 729-nm, achieving a ground state occupation of 99% in one dimension. Demonstrations of the coherent manipulations possible at this level of confinement are presented. The ion heating rate is measured and although higher than might be expected given the unusually large ion-electrode distance remains amongst the lowest reported in any trap to date. Achieving this result required the development of a number of new experimental systems and major upgrades to the stability and reliability of the experiment, the details of which are also given. The thesis also presents theoretical work into the use of two-dimensional Coulomb crystals in a Penning trap as a resource for quantum information. Using the symmetries of the crystal, we find that it is possible to engineer complex entangled states, specifically two small quantum error correcting codes, using a very small number of global entangling pulses. Efficient entanglement protocols such as these are vital for the implementation of useful quantum error correction.

•Nov 1, 2014•1 citation
We report the laser cooling of a single 40Ca+{^{40}\mathrm{Ca}}^{+}40Ca+ 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 S1/2\ensuremath↔D5/2{S}_{1/2}\ensuremath{\leftrightarrow}{D}_{5/2}S1/2​\ensuremath↔D5/2​ transition, broadened by a quench laser coupling the D5/2{D}_{5/2}D5/2​ and P3/2{P}_{3/2}P3/2​ 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 n‾\ifmmode˙\else\textperiodcentered\fi\ensuremath≈0.3(2)  s\ensuremath−1\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\overline{n}}\ensuremath{\approx}0.3(2)\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}n\ifmmode˙\else\textperiodcentered\fi\ensuremath≈0.3(2)  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 40Ca+^{40}\text{Ca}^+40Ca+ 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 S1/2↔D5/2S_{1/2}\leftrightarrow D_{5/2}S1/2​↔D5/2​ transition, broadened by a quench laser coupling the D5/2D_{5/2}D5/2​ and P3/2P_{3/2}P3/2​ levels. We find the final phonon number to be nˉ=0.014±0.009\bar{n}=0.014\pm0.009nˉ=0.014±0.009. We measure the heating rate of the trap to be very low with nˉ˙=2.5±0.3s−1\dot{\bar{n}}=2.5\pm 0.3\textrm{s}^{-1}nˉ˙=2.5±0.3s−1 and a scaled spectral noise density of ωSE(ω)∼1.6−8V2m−2Hz−1s−1\omega S_{E}(\omega)\sim1.6^{-8}\textrm{V}^2\textrm{m}^{-2}\textrm{Hz}^{-1}\textrm{s}^{-1}ωSE​(ω)∼1.6−8V2m−2Hz−1s−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±0.1ms0.7\pm 0.1\textrm{ms}0.7±0.1ms, noting that the practical performance is currently limited by the intensity noise of the probe laser.
We perform resolved optical sideband spectroscopy on a single 40Ca+ ion in a Penning trap. We probe the electric quadrupole allowed S1/2↔D5/2 transition at 729 nm and observe equally spaced sidebands for the three motional modes. The axial mode, parallel to the trap axis, is a one-dimensional harmonic oscillator, whereas the radial cyclotron and magnetron modes are circular motions perpendicular to the magnetic field. The total energy associated with the magnetron motion is negative, but here we probe only the (positive) kinetic energy. From the equivalent Doppler widths of the sideband spectra corresponding to the three motions we find effective temperatures of 1.1±0.2 mK, 7±3 mK, and 42±8 μK for the axial, modified cyclotron, and magnetron modes, respectively. These should be compared to the cooling limits, estimated using optimal laser parameters, of 0.38 mK, 0.8 mK, and ∼10 μK. In future work we aim to perform resolved-sideband cooling of the ion on the 729-nm transition.Received 3 December 2013DOI:https://doi.org/10.1103/PhysRevA.89.032502©2014 American Physical Society
We have recently demonstrated the laser cooling of a single 40Ca+ ion to the motional ground state in a Penning trap using the resolved-sideband cooling technique on the electric quadrupole transition S12↔ D52. Here we report on the extension of this technique to small ion Coulomb crystals made of two or three 40Ca+ ions. Efficient cooling of the axial motion is achieved outside the Lamb-Dicke regime on a two-ion string along the magnetic field axis as well as on two- and three-ion planar crystals. Complex sideband cooling sequences are required in order to cool both axial degrees of freedom simultaneously. We measure a mean excitation after cooling of n¯COM=0.30(4) for the centre of mass (COM) mode and n¯B=0.07(3) for the breathing mode of the two-ion string with corresponding heating rates of 11(2) s-1 and 1(1)s-1 at a trap frequency of 162 kHz. The occupation of the ground state of the axial modes (ntilt=nCOM=0) is above 75% for the two-ion planar crystal and the associated heating rates 0.8(5) s-1 at a trap frequency of 355 kHz.
Efficient Three-Dimensional Sub-Doppler Cooling of 40^{40}40Ca+^++ in a Penning Trap
We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a 40^{40}40Ca+^++ 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) μμμs, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in 800 μμμs 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.
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.
For 35 years, laser-cooled trapped ions have been at the frontier of progress in quantum computing, quantum simulation and precision measurement, and remain one of the most valuable tools in these fields to this day. Most of these experiments are predicated upon or benefit from the ability to place ions in the motional quantum ground state, a technique that was first demonstrated in radiofrequency ion traps 25 years ago. For a range of crucial experiments that are impossible to conduct in radiofrequency traps or are not well suited to this architecture, Penning traps provide an important alternative. However, the performance of Penning traps had been limited by the fact that ground-state cooling was yet to be achieved in such a system. This thesis reports the first demonstration of resolved-sideband cooling in a Penning trap, for 40Ca+ions cooled with light at 729-nm, achieving a ground state occupation of 99% in one dimension. Demonstrations of the coherent manipulations possible at this level of confinement are presented. The ion heating rate is measured and although higher than might be expected given the unusually large ion-electrode distance remains amongst the lowest reported in any trap to date. Achieving this result required the development of a number of new experimental systems and major upgrades to the stability and reliability of the experiment, the details of which are also given. The thesis also presents theoretical work into the use of two-dimensional Coulomb crystals in a Penning trap as a resource for quantum information. Using the symmetries of the crystal, we find that it is possible to engineer complex entangled states, specifically two small quantum error correcting codes, using a very small number of global entangling pulses. Efficient entanglement protocols such as these are vital for the implementation of useful quantum error correction.