We demonstrate minimization of ion micromotion in a linear Paul trap with the use of a high finesse cavity. The excess ion micromotion projected along the optical cavity axis or along the laser propagation direction manifests itself as sideband peaks around the carrier in the ion-cavity emission spectrum. By minimizing the sideband height in the emission spectrum, we are able to reduce the micromotion amplitude along two directions to approximately the spread of the ground state wave function. This method is useful for cavity QED experiments as it describes the possibility of efficient 3-D micromotion compensation despite optical access limitations imposed by the cavity mirrors. We also show that, in principle, sub-nanometer micromotion compensation is achievable with our current system.We demonstrate minimization of ion micromotion in a linear Paul trap with the use of a high finesse cavity. The excess ion micromotion projected along the optical cavity axis or along the laser propagation direction manifests itself as sideband peaks around the carrier in the ion-cavity emission spectrum. By minimizing the sideband height in the emission spectrum, we are able to reduce the micromotion amplitude along two directions to approximately the spread of the ground state wave function. This method is useful for cavity QED experiments as it describes the possibility of efficient 3-D micromotion compensation despite optical access limitations imposed by the cavity mirrors. We also show that, in principle, sub-nanometer micromotion compensation is achievable with our current system.

Optics ExpressApr 24, 201319 citations

Ion-trajectory analysis for micromotion minimization and the measurement of small forces

Timm F. Gloger, Peter Kaufmann, Delia Kaufmann +4 more

For experiments with ions confined in a Paul trap, minimization of micromotion is often essential. In order to diagnose and compensate micromotion we have implemented a method that allows for finding the position of the radio-frequency (rf) null reliably and efficiently, in principle, without any variation of direct current (dc) voltages. We apply a trap modulation technique and focus-scanning imaging to extract three-dimensional ion positions for various rf drive powers and analyze the power dependence of the equilibrium position of the trapped ion. In contrast to commonly used methods, the search algorithm directly makes use of a physical effect as opposed to efficient numerical minimization in a high-dimensional parameter space. Using this method we achieve a compensation of the residual electric field that causes excess micromotion in the radial plane of a linear Paul trap down to $0.09\phantom{\rule{4pt}{0ex}}\text{V}\phantom{\rule{0.16em}{0ex}}{\text{m}}^{\ensuremath{-}1}$. Additionally, the precise position determination of a single harmonically trapped ion employed here can also be utilized for the detection of small forces. This is demonstrated by determining light pressure forces with a precision of 135 yN. As the method is based on imaging only, it can be applied to several ions simultaneously and is independent of laser direction and thus well suited to be used with, for example, surface-electrode traps.For experiments with ions confined in a Paul trap, minimization of micromotion is often essential. In order to diagnose and compensate micromotion we have implemented a method that allows for finding the position of the radio-frequency (rf) null reliably and efficiently, in principle, without any variation of direct current (dc) voltages. We apply a trap modulation technique and focus-scanning imaging to extract three-dimensional ion positions for various rf drive powers and analyze the power dependence of the equilibrium position of the trapped ion. In contrast to commonly used methods, the search algorithm directly makes use of a physical effect as opposed to efficient numerical minimization in a high-dimensional parameter space. Using this method we achieve a compensation of the residual electric field that causes excess micromotion in the radial plane of a linear Paul trap down to $0.09\phantom{\rule{4pt}{0ex}}\text{V}\phantom{\rule{0.16em}{0ex}}{\text{m}}^{\ensuremath{-}1}$. Additionally, the precise position determination of a single harmonically trapped ion employed here can also be utilized for the detection of small forces. This is demonstrated by determining light pressure forces with a precision of 135 yN. As the method is based on imaging only, it can be applied to several ions simultaneously and is independent of laser direction and thus well suited to be used with, for example, surface-electrode traps.

arXiv:1503.07031Physical Review AOct 27, 201539 citations

Minimization of micromotion for nanoparticles in a Paul trap

Jamie Morley, Jean Paul Louys Sansó, Dmitry Bykov +2 more

When a charged particle in a Paul trap is displaced from the node of the AC trapping field, excess micromotion arises as an undesired effect. Excess micromotion heats the particle, limits the precision with which the particle can be localised, and acts as a decoherence channel in quantum mechanical experiments. However, thus far there is no standard procedure for micromotion compensation with mesoscopic particles. Here, we experimentally demonstrate three different methods for minimizing the micromotion of a nanoparticle in a linear Paul trap along three axes. The most precise method allows us to nullify the stray field to within 2.9 V/m, which is comparable to reported values in trapped-ion experiments.When a charged particle in a Paul trap is displaced from the node of the AC trapping field, excess micromotion arises as an undesired effect. Excess micromotion heats the particle, limits the precision with which the particle can be localised, and acts as a decoherence channel in quantum mechanical experiments. However, thus far there is no standard procedure for micromotion compensation with mesoscopic particles. Here, we experimentally demonstrate three different methods for minimizing the micromotion of a nanoparticle in a linear Paul trap along three axes. The most precise method allows us to nullify the stray field to within 2.9 V/m, which is comparable to reported values in trapped-ion experiments.

quant-pharXiv:2608.21011Aug 24, 20260 citations

Enhanced micromotion compensation using a phase-modulated light field

K. J. Arnold, N. Jayjong, M. L. D. Kang +4 more

We investigate sideband spectroscopy of a trapped ion using a probe laser phase modulated at the trap drive frequency. The enhanced sensitivity of our technique provides us 1000-fold improvement in our control of excess micromotion. It allows us to monitor the evolution of stray fields on a timescale of a few minutes and detect differential phases of $5\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{rad}$ between applied ac potentials. We also demonstrate the ability to suppress Doppler shifts from excess motion to well below the limit imposed by the intrinsic motion of the ion in its motional ground state. The technique we introduce can be readily implemented in any ion-trap system that utilizes sideband spectroscopy for micromotion compensation and can be seamlessly integrated into experiments in a fully automated way.We investigate sideband spectroscopy of a trapped ion using a probe laser phase modulated at the trap drive frequency. The enhanced sensitivity of our technique provides us 1000-fold improvement in our control of excess micromotion. It allows us to monitor the evolution of stray fields on a timescale of a few minutes and detect differential phases of $5\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{rad}$ between applied ac potentials. We also demonstrate the ability to suppress Doppler shifts from excess motion to well below the limit imposed by the intrinsic motion of the ion in its motional ground state. The technique we introduce can be readily implemented in any ion-trap system that utilizes sideband spectroscopy for micromotion compensation and can be seamlessly integrated into experiments in a fully automated way.

arXiv:2402.18142Physical Review ASep 23, 20247 citations

Design and Characteristic Measurement of Miniature Three-Segment Linear Paul Trap

T. Furukawa, Jin Nishimura, U. Tanaka +1 more

We have fabricated a miniature three-segment linear Paul trap with r 0=0.6 mm and 2Z 0=4 mm. In order to perform quantum-state manipulation of trapped 40 Ca+ ions, we discuss the required harmonic oscillation frequencies which allow us to perform effective sideband cooling and have measured those that depend on the dimensions of the trap. A laser beam that has a component in the radial direction of the linear trap as well as that propagating along the trap axis has been used to detect the fluorescence spectra of the 42 S 1/2–42 P 1/2 transition. We have observed that the profile of the fluorescence spectrum obtained with the side laser beam is markedly different from that obtained with the axial laser beam due to micromotion. By applying additional DC voltages, the micromotion has been compensated, its amplitude has been estimated, and crystallization has been observed for two 40 Ca+ and four 40 Ca+ ions.We have fabricated a miniature three-segment linear Paul trap with r 0=0.6 mm and 2Z 0=4 mm. In order to perform quantum-state manipulation of trapped 40 Ca+ ions, we discuss the required harmonic oscillation frequencies which allow us to perform effective sideband cooling and have measured those that depend on the dimensions of the trap. A laser beam that has a component in the radial direction of the linear trap as well as that propagating along the trap axis has been used to detect the fluorescence spectra of the 42 S 1/2–42 P 1/2 transition. We have observed that the profile of the fluorescence spectrum obtained with the side laser beam is markedly different from that obtained with the axial laser beam due to micromotion. By applying additional DC voltages, the micromotion has been compensated, its amplitude has been estimated, and crystallization has been observed for two 40 Ca+ and four 40 Ca+ ions.

Japanese Journal of Applied PhysicsOct 1, 200510 citations

Micromotion minimisation by synchronous detection of parametrically excited motion

D. P. Nadlinger, P. Drmota, D. Main +6 more

Precise control of charged particles in radio-frequency (Paul) traps requires minimising excess micromotion induced by stray electric fields. We present a method to detect and compensate such fields through amplitude modulation of the radio-frequency trapping field. Modulation at frequencies close to the motional modes of the trapped particle excites coherent motion whose amplitude linearly depends on the stray field. In trapped-ion experiments, this motion can be detected by recording the arrival times of photons scattered during laser cooling. Only a single laser beam is required to resolve fields in multiple directions. In a demonstration using a $^{88}\mathrm{Sr}^{+}$ ion in a surface electrode trap, we achieve a sensitivity of $0.1\, \mathrm{V}\, \mathrm{m}^{-1}\, /\, \sqrt{\mathrm{Hz}}$ and a minimal uncertainty of $0.015\, \mathrm{V}\, \mathrm{m}^{-1}$ .Precise control of charged particles in radio-frequency (Paul) traps requires minimising excess micromotion induced by stray electric fields. We present a method to detect and compensate such fields through amplitude modulation of the radio-frequency trapping field. Modulation at frequencies close to the motional modes of the trapped particle excites coherent motion whose amplitude linearly depends on the stray field. In trapped-ion experiments, this motion can be detected by recording the arrival times of photons scattered during laser cooling. Only a single laser beam is required to resolve fields in multiple directions. In a demonstration using a $^{88}\mathrm{Sr}^{+}$ ion in a surface electrode trap, we achieve a sensitivity of $0.1\, \mathrm{V}\, \mathrm{m}^{-1}\, /\, \sqrt{\mathrm{Hz}}$ and a minimal uncertainty of $0.015\, \mathrm{V}\, \mathrm{m}^{-1}$.

arXiv:2107.00056Jun 30, 20213 citations

^{88}\mathrm{Sr}^{+}

ion in a surface electrode trap, we achieve a sensitivity of

0.1\, \mathrm{V}\, \mathrm{m}^{-1}\, /\, \sqrt{\mathrm{Hz}}

and a minimal uncertainty of

0.015\, \mathrm{V}\, \mathrm{m}^{-1}