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Dark resonances as a probe for the motional state of a single ion

C. Lisowski, Martina Knoop, C. Champenois, G. Hagel, M. Vedel

Published Jan 1, 2004• 11 citations
OpenAlex

Abstract

Single, rf-trapped ions find various applications ranging from metrology to quantum computation. High-resolution interrogation of an extremely weak transition under best observation conditions requires an ion almost at rest. To avoid line-broadening effects such as the second order Doppler effect or rf heating in the absence of laser cooling, excess micromotion has to be eliminated as far as possible. We have tested a novel method to probe the motional state of a confined three-level ion. Actually, dark resonances observed with two counterpropagating laser beams are very sensitive to the trapped ion's velocity. Their contrast increases with reduced micromotion and allows in this way to control the oscillation amplitude of the stored ion. The influence of different parameters such as laser linewidth and power has been investigated experimentally and numerically.

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The limitations to the achievement of low kinetic energies for laser cooling of single ions confined in electromagnetic traps are discussed. Sideband cooling of an ion in an rf (Paul) trap is reexamined including the effects of finite laser bandwidth and the energy of the rf micromotion. The micromotion is the oscillatory motion of the ion at the same frequency as the rf voltage applied to the trap electrodes. Sideband cooling of ions in a Penning trap is examined for the first time. In both cases, cooling to the zero-point energy of the ion in the trap should be possible and a method for verifying this condition is suggested. The implications for high-resolution, high-accuracy spectroscopy are investigated. Under certain conditions, the uncertainty in the second-order Doppler shift may be significantly less than 1 part in ${10}^{18}$. .AE

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Trapped ions, as one of the pillars of progress in frequency metrology and quantum optics, require a complex experimental environment with well-defined conditions. We present that a feature called dark resonance, provided by the trapped ion itself, can be used as a versatile sensor for enhanced in-situ analysis of interacting fields. The dark resonance is formed in the lambda-type energy level scheme of a laser cooled 40Ca+ ion and corresponds to a fluorescence quenching. The method uses an analysis of the detection times of photons emitted from the upper energy level, which is excited via two optical dipole transitions. The two excitation lasers are phase locked to an optical frequency comb to reduce their linewidths and for precise control of their optical frequencies within the dark resonance. The amplitudes of interacting fields are obtained using the Fourier transform of the ion fluorescence or photon correlation measurements. This paper shows that the method can be applied for sensing of electric, magnetic and electromagnetic fields. Firstly, we present the potential for frequency analysis of the secular motion of a few-ion Coulomb crystal, which corresponds to the axial static electric field of a linear ion trap. Secondly, we demonstrate the optical frequency analysis of the employed lasers driving the two transitions. In the last case we show the analysis of an alternating magnetic field at the position of single ion.

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The “Trapped State” of a Trapped Ion—Line Shifts and Shape

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The fluorescence of a single r.f.-trapped and cooled Ba + ion, induced by the light of two lasers, shows a null at the S 1/2 - D 3/2 resonance of the frequency difference. We have measured the Zeeman effect and power broadening of this "dark line", and also the shift of the associated "bright" line, which is related to the Raman light shift. A 75 kHz wide dark line was observed. Such a resonance might be used to control a 147 THz standard frequency free of systematic shifts in excess of 10 -15 .

Europhysics Letters (EPL)•Feb 14, 1992•68 citations
Single, rf-trapped ions find various applications ranging from metrology to quantum computation. High-resolution interrogation of an extremely weak transition under best observation conditions requires an ion almost at rest. To avoid line-broadening effects such as the second order Doppler effect or rf heating in the absence of laser cooling, excess micromotion has to be eliminated as far as possible. We have tested a novel method to probe the motional state of a confined three-level ion. Actually, dark resonances observed with two counterpropagating laser beams are very sensitive to the trapped ion's velocity. Their contrast increases with reduced micromotion and allows in this way to control the oscillation amplitude of the stored ion. The influence of different parameters such as laser linewidth and power has been investigated experimentally and numerically.
The limitations to the achievement of low kinetic energies for laser cooling of single ions confined in electromagnetic traps are discussed. Sideband cooling of an ion in an rf (Paul) trap is reexamined including the effects of finite laser bandwidth and the energy of the rf micromotion. The micromotion is the oscillatory motion of the ion at the same frequency as the rf voltage applied to the trap electrodes. Sideband cooling of ions in a Penning trap is examined for the first time. In both cases, cooling to the zero-point energy of the ion in the trap should be possible and a method for verifying this condition is suggested. The implications for high-resolution, high-accuracy spectroscopy are investigated. Under certain conditions, the uncertainty in the second-order Doppler shift may be significantly less than 1 part in 1018{10}^{18}1018. .AE
We study the influence of micromotion on the spectrum of trapped ions with a lambda-type level scheme, leading to dark resonances due to coherent population trapping. We work with calcium ions trapped in a ring-shaped Paul trap, in which one can compensate excess micromotion for only one ion of the crystal. We observe that micromotion affects the shapes of the dark resonances and causes the appearance of “echoes” separated by intervals given by the drive frequency. We present a theoretical model that provides good fits to the measurements and can be used to estimate the amplitude of the micromotion modulation of the atomic motion. We estimate an effective temperature of the ions from the spectra and observe clear micromotion heating as well as impaired cooling for sufficiently large excess micromotion.
Trapped ions, as one of the pillars of progress in frequency metrology and quantum optics, require a complex experimental environment with well-defined conditions. We present that a feature called dark resonance, provided by the trapped ion itself, can be used as a versatile sensor for enhanced in-situ analysis of interacting fields. The dark resonance is formed in the lambda-type energy level scheme of a laser cooled 40Ca+ ion and corresponds to a fluorescence quenching. The method uses an analysis of the detection times of photons emitted from the upper energy level, which is excited via two optical dipole transitions. The two excitation lasers are phase locked to an optical frequency comb to reduce their linewidths and for precise control of their optical frequencies within the dark resonance. The amplitudes of interacting fields are obtained using the Fourier transform of the ion fluorescence or photon correlation measurements. This paper shows that the method can be applied for sensing of electric, magnetic and electromagnetic fields. Firstly, we present the potential for frequency analysis of the secular motion of a few-ion Coulomb crystal, which corresponds to the axial static electric field of a linear ion trap. Secondly, we demonstrate the optical frequency analysis of the employed lasers driving the two transitions. In the last case we show the analysis of an alternating magnetic field at the position of single ion.
Laser cooling typically requires one or more repump lasers to clear dark states and enable recycling transitions. Here, we have achieved cooling of Be+ ions using a single laser beam, facilitated by one-dimensional heating through micromotion. By manipulating the displacement from the trap's nodal line, we precisely controlled the ion micromotion direction and speed, reaching up to 3144 m/s, which corresponds to a 7.1 GHz Doppler frequency shift in our experiment. This approach eliminates the necessity of a 1.25 GHz offset repump laser while keeping the Be+ ions cold in the perpendicular direction. Measurements were taken using cooling laser detuning and imaging of ion trajectories. Molecular dynamics simulations, based on machine learned time-dependent electric field E(X, Y, Z, t) inside the trap, accurately reproduced the experimental observation, illuminating the relationship between the direction of micromotion and the trapping electric filed vector. This work not only provides a robust method for managing the micromotion velocity of ions but also sheds light on laser cooling complex systems that require multiple repumping lasers. Additionally, it offers a method for controlling energy in the context of ion-molecule collision investigations.
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.
The fluorescence of a single r.f.-trapped and cooled Ba + ion, induced by the light of two lasers, shows a null at the S 1/2 - D 3/2 resonance of the frequency difference. We have measured the Zeeman effect and power broadening of this "dark line", and also the shift of the associated "bright" line, which is related to the Raman light shift. A 75 kHz wide dark line was observed. Such a resonance might be used to control a 147 THz standard frequency free of systematic shifts in excess of 10 -15 .