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arXiv:physics/0506061 · Physical Review A

Simultaneous cooling of axial vibrational modes in a linear ion trap

Christof Wunderlich, Giovanna Morigi, Dirk Reiß

Published Aug 31, 2005• 16 citations
arXivHTMLPDF

Abstract

In order to use a collection of trapped ions for experiments where a well-defined preparation of vibrational states is necessary, all vibrational modes have to be cooled to ensure precise and repeatable manipulation of the ions quantum states. A method for simultaneous sideband cooling of all axial vibrational modes is proposed. By application of a magnetic field gradient the absorption spectrum of each ion is modified such that sideband resonances of different vibrational modes coincide. The ion string is then irradiated with monochromatic electromagnetic radiation, in the optical or microwave regime, for sideband excitation. This cooling scheme is investigated in detailed numerical studies. Its application for initializing ion strings for quantum information processing is extensively discussed.

DOI
10.1103/physreva.72.023421

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In order to use a collection of trapped ions for experiments where a well-defined preparation of vibrational states is necessary, all vibrational modes have to be cooled to ensure precise and repeatable manipulation of the ions quantum states. A method for simultaneous sideband cooling of all axial vibrational modes is proposed. By application of a magnetic field gradient the absorption spectrum of each ion is modified such that sideband resonances of different vibrational modes coincide. The ion string is then irradiated with monochromatic electromagnetic radiation, in the optical or microwave regime, for sideband excitation. This cooling scheme is investigated in detailed numerical studies. Its application for initializing ion strings for quantum information processing is extensively discussed.
A novel method of ground-state laser cooling of trapped atoms utilizes the absorption profile of a three- (or multi-) level system that is tailored by a quantum interference. With cooling rates comparable to conventional sideband cooling, lower final temperatures may be achieved. The method was experimentally implemented to cool a single Ca + ion to its vibrational ground state. Since a broad band of vibrational frequencies can be cooled simultaneously, the technique will be particularly useful for the cooling of larger ion strings, thereby being of great practical importance for initializing a quantum register based on trapped ions. We also discuss its application to different level schemes and for ground-state cooling of neutral atoms trapped by a far-detuned standing wave laser field.
Efficient cooling of trapped ions is a prerequisite for various applications of the ions in precision spectroscopy, quantum information, and coherence control. Raman sideband cooling is an effective method to cool the ions to their motional ground state. We investigate both numerically and experimentally the optimization of Raman sideband cooling strategies and propose an efficient one, which can simplify the experimental setup as well as reduce the number of cooling pulses. Several cooling schemes are tested and compared through numerical simulations. The simulation result shows that the fixed-width pulses and varied-width pulses have almost the same efficiency for both the first-order and the second-order Raman sideband cooling. The optimized strategy is verified experimentally. A single 25Mg+{^{25}\mathrm{Mg}}^{+}25Mg+ ion is trapped in a linear Paul trap and Raman sideband cooled, and the achieved average vibrational quantum numbers under different cooling strategies are evaluated. A good agreement between the experimental result and the simulation result is obtained.
We report a detailed investigation on near-ground state cooling of one and two trapped atomic ions. We introduce a simple sideband cooling method for confined atoms and ions, using RF radiation applied to bare ionic states in a static magnetic field gradient, and demonstrate its application to ions confined at secular trap frequencies, ωz≈2π×117 kHz. For a single 171Yb+ ion, the sideband cooling cycle reduces the average phonon number, n from the Doppler limit to n= 0.30(12). This is in agreement with the theoretically estimated lowest achievable phonon number in this experiment. We extend this method of RF sideband cooling to a system of two 171Yb+ ions, resulting in a phonon number of n= 1.1(7) in the centre-of-mass mode. Furthermore, we demonstrate the first realization of sympathetic RF sideband cooling of an ion crystal consisting of two individually addressable identical isotopes of the same species.
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.
Summary form only given. The preparation of quantum systems in pure states is a prerequisite for coherent control. In this context laser cooling of trapped particles to the ground state of the confining potential is a powerful tool for preparing e.g. ions for quantum logic. In particular sideband cooling has been demonstrated to be the most efficient technique, allowing to achieve more than 99% of occupation of the ground state of the trap. This cooling technique relies on two conditions: the Lamb-Dicke regime, and the strong confinement regime. This latter condition, which allows the spectral resolution of individual sidebands of the motion, is however a limitation on the cooling time. We propose a model for cooling single ions inside a trap as an alternative to sideband cooling. The scheme uses electromagnetically induced transparency (EIT) in a /spl Lambda/-level scheme, where one of the transitions is dressed by a strong laser field. For detuning of the dressing laser, the absorption spectrum for the transition shows EIT when the cooling (probe) laser has detuning. Then, by tuning the cooling laser on the dark resonance (or EIT), for a suitable set of parameters and in the Lamb-Dicke regime the atoms are cooled to the ground state by the sideband transitions which are resonantly excited. The scheme achieves efficient ground state cooling and fast cooling rates using a continuous driving, instead of a pulsed one as in Raman sideband cooling schemes. An example is illustrated, where the average vibrational number is plotted as a function of the cooling time, and the final probability of occupation is plotted as a function of the vibrational state. This method may also be applied to reduce phase errors in coherent manipulations of trapped ions for quantum logic.
Miniaturized ion trap arrays with many trap segments present a promising architecture for scalable quantum information processing. The miniaturization of segmented linear Paul traps allows partitioning the microtrap into different storage and processing zones. The individual position control of many ions—each of them carrying qubit information in its long-lived electronic levels—by the external trap control voltages is important for the implementation of next generation large-scale quantum algorithms. We present a novel scalable microchip multi-segmented ion trap with two different adjacent zones, one for the storage and another dedicated to the processing of quantum information using single ions and linear ion crystals. A pair of radio-frequency-driven electrodes and 62 independently controlled dc electrodes allows shuttling of single ions or linear ion crystals with numerically designed axial potentials at axial and radial trap frequencies of a few megahertz. We characterize and optimize the microtrap using sideband spectroscopy on the narrow S 1/2 ↔D 5/2 qubit transition of the 40 Ca + ion, and demonstrate coherent single-qubit Rabi rotations and optical cooling methods. We determine the heating rate using sideband cooling measurements to the vibrational ground state, which is necessary for subsequent two-qubit quantum logic operations. The applicability for scalable quantum information processing is proved.