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Register a new userThe effect of atomic response time in the theory of Doppler cooling of trapped ions
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We describe a simple approach to the problem of incorporating the response time of an atom or ion being Doppler-cooled into the theory of the cooling process. The system being cooled does not in general respond instantly to the changing laser frequencies it experiences in its rest frame, and this dynamic effect can affect significantly the temperatures attainable. It is particularly important for trapped ions when there is a slow decay out of the cooling cycle requiring the use of a repumping beam. We treat the cases of trapped ions with two and three internal states, then apply the theory to $^{40}{rm Ca}^+$. For this ion experimental data exist showing the ion to be cold under conditions for which heating is predicted if the dynamic effect is neglected. The present theory accounts for the observed behaviour.
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Using a laser polarization gradient, we realize 3D Sisyphus cooling of $^{171}$Yb$^+$ ions confined in and near the Lamb-Dicke regime in a linear Paul trap. The cooling rate and final mean motional energy of a single ion are characterized as a function of laser intensity and compared to semiclassical and quantum simulations. Sisyphus cooling is also applied to a linear string of four ions to obtain a mean energy of 1-3 quanta for all vibrational modes, an approximately order-of-magnitude reduction below Doppler cooled energies. This is used to enable subsequent, efficient sideband laser cooling.
We demonstrate the ability to load, cool and detect singly-charged calcium ions in a surface electrode trap using only visible and infrared lasers for the trapped-ion control. As opposed to the standard methods of cooling using dipole-allowed transitions, we combine power broadening of a quadrupole transition at 729 nm with quenching of the upper level using a dipole allowed transition at 854 nm. By observing the resulting 393 nm fluorescence we are able to perform background-free detection of the ion. We show that this system can be used to smoothly transition between the Doppler cooling and sideband cooling regimes, and verify theoretical predictions throughout this range. We achieve scattering rates which reliably allow recooling after collision events and allow ions to be loaded from a thermal atomic beam. This work is compatible with recent advances in optical waveguides, and thus opens a path in current technologies for large-scale quantum information processing. In situations where dielectric materials are placed close to trapped ions, it carries the additional advantage of using wavelengths which do not lead to significant charging, which should facilitate high rate optical interfaces between remotely held ions.
We implement three-dimensional polarization gradient cooling of trapped ions. Counter-propagating laser beams near $393,$nm impinge in lin$,perp,$lin configuration, at a frequency below the S$_{1/2}$ to P$_{3/2}$ resonance in $^{40}$Ca$^+$. We demonstrate mean phonon numbers of $5.4(4)$ at a trap frequency of $2pi times 285,$kHz and $3.3(4)$ at $2pitimes480,$kHz, in the axial and radial directions, respectively. Our measurements demonstrate that cooling with laser beams detuned to lower frequencies from the resonance is robust against an elevated phonon occupation number, and thus works well for an initial ion motion far out of the Lamb-Dicke regime, for up to four ions, and for a micromotion modulation index $betaleq 0.1$. Still, we find that the spectral impurity of the laser field influences both, cooling rates and cooling limits. Thus, a Fabry-P{e}rot cavity filter is employed for efficiently suppressing amplified spontaneous emission of the diode laser.
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