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Physical Review A

Quantum-limited cooling and detection of radio-frequency oscillations by laser-cooled ions

Daniel J. Heinzen, David J. Wineland

Published Sep 1, 1990• 282 citations
Publisher

Abstract

A single trapped ion, laser cooled into its quantum ground state of motion, may be used as a very-low-temperature detector of radio-frequency signals applied to the trap end caps. If the signal source is a resonant oscillator of sufficiently high Q, the source may also be placed in its quantum ground state by coupling to the ion. Parametric couplings may be used to cool and detect source modes other than the mode directly coupled to the ion. A theoretical analysis of these cooling and detection processes is presented, and as an example, their application to single trapped electron and proton spectroscopy is examined. Squeezing and low noise detection of one quadrature component of the source oscillation are also discussed. The techniques discussed here may lead to radio-frequency measurements of improved accuracy and sensitivity. Cooling and detection of vibrations of macroscopic oscillators also appear possible.

DOI
10.1103/physreva.42.2977

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A single trapped ion, laser cooled into its quantum ground state of motion, may be used as a very-low-temperature detector of radio-frequency signals applied to the trap end caps. If the signal source is a resonant oscillator of sufficiently high Q, the source may also be placed in its quantum ground state by coupling to the ion. Parametric couplings may be used to cool and detect source modes other than the mode directly coupled to the ion. A theoretical analysis of these cooling and detection processes is presented, and as an example, their application to single trapped electron and proton spectroscopy is examined. Squeezing and low noise detection of one quadrature component of the source oscillation are also discussed. The techniques discussed here may lead to radio-frequency measurements of improved accuracy and sensitivity. Cooling and detection of vibrations of macroscopic oscillators also appear possible.
An experimental study of sideband laser cooling of trapped ions in miniature radio-frequency traps is presented. In+{\mathrm{In}}^{+}In+ ions are laser cooled by exciting the narrow intercombination line ${5s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5s5p{}^{3}{P}_{1}$, which shows resolved sidebands due to the vibrational motion of the ions in the trap. The influence of the micromotion at the frequency of the oscillating trapping field is investigated. Heating processes through coupling with the trapping field occur for certain regions of negative laser detuning. A method of bichromatic sideband cooling is introduced that combines efficient cooling from high temperatures with the possibility of reaching low mean vibrational quantum numbers 〈n〉<1〈n〉<1〈n〉<1 by using narrow optical transitions. This technique allows recording of high-resolution excitation spectra of the cooling transition in the Lamb-Dicke regime and thus determination of 〈n〉〈n〉〈n〉. Single ions as well as two-ion Coulomb crystals have been cooled to temperatures below $100 \ensuremath{\mu}\mathrm{K}$, and population of the ground state of motion to more than 50% over long time scales is demonstrated. These values are close to the lower limit for the detection of vibrational excitation with the present method.
Single ions trapped and laser cooled provide ideal objects for high resolution spectroscopy and frequency standards. For the latter purpose we are investigating the 5s2 1S0 → 5s5p 3P0 transition of In+. With a natural linewidth of only 1.1 Hz this resonance offers very high resolution and is highly immune to frequency shifts due to external electromagnetic fields, because it connects two levels with vanishing electronic magnetic momenta [1]. The wavelength of this clock transition is 236.5 nm and is technically very convenient, since it coincides with the fourth harmonic of the 946 nm Nd:YAG laser line. So this intrinsically frequency stable solid-state laser can be used to excite the transition [2]. For laser cooling and fluorescence detection of the indium ion the 5s2 1So -> 5s5p 3P1 transition at 230.6 nm can be employed. The use of the relatively narrow intercombination line for laser cooling allows us to study optical sideband cooling in the strong binding regime, where the oscillation frequencies of the ion in the trap (around 1 MHz) are larger than the optical linewidth of 360 kHz. In this parameter range laser cooling is possible to the quantum ground state of the vibrational motion in the trap corresponding to a temperature of roughly 100 μK. The same low temperature was obtained with sideband cooling of a small Coulomb crystal consisting of two ions, creating an interesting new quantum few-particle system.
Atomic ions, confined in radio-frequency Paul ion traps, are a promising candidate to host a future quantum information processor. In this article, we demonstrate a method to couple two motional modes of a single trapped ion, where the coupling mechanism is based on applying electric fields rather than coupling the ion's motion to a light field. This reduces the design constraints on the experimental apparatus considerably. As an application of this mechanism, we cool a motional mode close to its ground state without accessing it optically. As a next step, we apply this technique to measure the mode's heating rate, a crucial parameter determining the trap quality.
Trapped laser-cooled atomic ions are a new tool for understanding cold molecular ions. The atomic ions not only sympathetically cool the molecular ions to millikelvin temperatures, but the bright atomic ion fluorescence can also serve as a detector of both molecular reactions and molecular spectra. We are working towards the detection of single molecular ion spectra by sympathetic heating spectroscopy. Sympathetic heating spectroscopy uses the coupled motion of two trapped ions to measure the spectra of one ion by observing changes in the fluorescence of the other ion. Sympathetic heating spectroscopy is a generalization of quantum logic spectroscopy, but does not require ions in the motional ground state or coherent control of the ion internal states. We have recently demonstrated this technique using two isotopes of Ca+ [Phys. Rev. A, 81, 043428 (2010)]. Limits of the method and potential applications for molecular spectroscopy are discussed.
We demonstrate ground-state cooling of a trapped ion using radio-frequency (rf) radiation. This is a powerful tool for the implementation of quantum operations, where rf or microwave radiation instead of lasers is used for motional quantum state engineering. We measure a mean phonon number of n[over ¯]=0.13(4) after sideband cooling, corresponding to a ground-state occupation probability of 88(7)%. After preparing in the vibrational ground state, we demonstrate motional state engineering by driving Rabi oscillations between the |n=0⟩ and |n=1⟩ Fock states. We also use the ability to ground-state cool to accurately measure the motional heating rate and report a reduction by almost 2 orders of magnitude compared with our previously measured result, which we attribute to carefully eliminating sources of electrical noise in the system.
Cooling the motion of trapped ions to near the quantum ground state is crucial for many applications in quantum information processing and quantum metrology. However, certain motional modes of trapped-ion crystals can be difficult to cool due to weak or zero interaction between the modes and the cooling radiation, typically laser beams. We overcome this challenge by coupling a mode with weak cooling radiation interaction to one with strong cooling radiation interaction using parametric modulation of the trapping potential, thereby enabling indirect cooling of the former. In this way, we demonstrate near-ground-state cooling of motional modes with weak or zero cooling radiation interaction in multi-ion crystals of the same and mixed ion species, specifically 9^99Be+^++-9^99Be+^++, 9^99Be+^++-25^{25}25Mg+^++, and 9^99Be+^++-25^{25}25Mg+^++-9^99Be+^++ crystals. This approach can be generally applied to any Coulomb crystal where certain motional modes cannot be directly cooled efficiently, including crystals containing molecular ions, highly-charged ions, charged fundamental particles, or charged macroscopic objects.