Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Photonics for Quantum (PfQ)

Sensing fields with ion in a dark state

Adam Lešundák, Tuan Minh Pham, Martin Čížek, Jakub Grim, Petr Jedlička, Lukáš Podhora, L. Slodička, Ondřej Čı́p

Published Jul 9, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2599764

Related papers

Optical frequency analysis on dark state of a single trapped ion

Adam Lešundák, Tuan M. Pham, Martin Čížek +3 more

ion. The response of the detected photon rate to the relative laser frequency deviations is recorded within the slope of a dark resonance formed in the lambda-type energy level scheme corresponding to two optical dipole transitions. This approach enhances the sensitivity to the small frequency deviations and does so with reciprocal dependence on the fluorescence rate. The employed lasers are phase locked to an optical frequency comb, which allows for precise calibration of optical frequency analysis by deterministic modulation of the analyzed laser beam with respect to the reference beam. The attainable high signal-to-noise ratios of up to a MHz range of modulation deviations and up to a hundred kHz modulation frequencies promise the applicability of the presented results in a broad range of optical spectroscopic applications.

arXiv:2005.02651•Optics Express•Mar 24, 2020•5 citations

Motional studies of one and two laser-cooled trapped ions for electric-field sensing applications

Francisco Domínguez, M. J. Gutiérrez, Íñigo Arrazola +7 more

We have studied the dynamics of one and two laser-cooled trapped 40Ca+ ions by applying electric fields of different nature along the axial direction of the trap, namely, driving the motion with a harmonic dipolar field, or with white noise. These two types of driving induce distinct motional states of the axial modes: a coherent oscillation with the dipolar field, or an enhanced Brownian motion due to an additional contribution to the heating rate from the electric noise. In both scenarios, the sensitivity of an isolated ion and a laser-cooled two-ion crystal has been evaluated and compared. The analysis and understanding of this dynamics is important towards the implementation of a novel Penning trap mass-spectroscopy technique based on optical detection, aiming at improving precision and sensitivity.

arXiv:1708.06786•Journal of Modern Optics•Dec 6, 2017•7 citations

Versatile operations with calcium and multi-species ion crystals

Johannes Andreas Eble

Coherence effects in a Lambda system of a 40Ca+ ion are investigated. Zeeman sublevels are utilized to evoke electromagnetically induced transparencies. The characteristic dark resonance and line shape alterations are analyzed for varying light field intensities. New features arise by avoiding all coherences in a Lambda-system. This is achieved by exposing the ion to only one single laser light field, going the spectroscopy. Pulsed light sequences ensure stable cooling and spectroscopy. A quantum mechanical description of the process is given, revealing the dark-resonance-free shape of the spectrum. This enables the determination of the Rabi frequency of the applied laser light field as well as the photon collection efficiency of the imaging system. In many cases in QIPC, it is important to precisely determine the position of the ions, for this information obtained from the ions" fluorescence is utilized. The capability of the segmented Paul trap to create custom electric potentials is utilized to form time dependent potentials with multiple trapping wells. The application of feedback control allows purposeful movement of a predefined number of ions and position regulation by altering the trapping voltages. Ion transport over 1 mm with more than 99.8 % success probability is accomplished without any knowledge of the potentials. By means of the feedback control this allows automated dividing of a linear ion crystal into two distinct potentials as well as the opposite process of merging. In order to perform these experiments, several novel techniques for the operation of an ion trap have been developed. A technique for automatic compensation is introduced to minimize the RF driven micromotion of the ion crystal. Additionally, a precise method for simultaneous measuring the oscillation frequencies for individual ions in an ion crystal is presented. Hereby, the oscillation modes of multi-species ion crystals can be analyzed for the determination of dopant isotopes.

•Jan 1, 2011•0 citations

Dark-resonance Doppler cooling and high fluorescence in trapped Ca-43 ions at intermediate magnetic field

D. T. C. Allcock, T. P. Harty, M. A. Sepiol +5 more

We demonstrate simple and robust methods for Doppler cooling and obtaining high fluorescence from trapped 43 Ca + ions at a magnetic field of 146 Gauss. This field gives access to a magnetic-field-independent 'atomic clock' qubit transition within the ground level hyperfine structure of the ion, but also causes the complex internal structure of the 64 states relevant to Doppler cooling to be spread over many times the atomic transition line-width. Using a time-dependent optical Bloch equation simulation of the system we develop a simple scheme to Doppler-cool the ion on a two-photon dark resonance, which is robust to typical experimental variations in laser intensities, detunings and polarizations. We experimentally demonstrate cooling to a temperature of 0.3 mK, slightly below the Doppler limit for the corresponding two-level system, and then use Raman sideband laser cooling to cool further to the ground states of the ion's radial motional modes. These methods will enable two-qubit entangling gates with this ion, which is one of the most promising qubits so far developed.

arXiv:1510.08958•New Journal of Physics•Feb 12, 2016•12 citations

Spectroscopy of Single Trapped Ions and Application to Frequency Standards

HERBERT WALTHER

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.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1998•0 citations

Ion dynamics and oscillation frequencies in a linear combined trap

T. Nakamura, S. Ohtani, M. Wada +3 more

Ion traps have been pivotal in opening new frontiers for the precision spectroscopy of stable ions. We report on the demonstration of an additional ion trap: the linear combined trap. This device is particularly well suited for trapping ions with unstable nuclei, due to its large range of stability parameters that facilitates external injection online to an accelerator. The motion of an ion in such a linear combined trap is investigated theoretically and experimentally. In the trap ions oscillate harmonically in the radial direction and move nearly harmonically between fixed boundaries along the longitudinal axis. The presence of a homogeneous magnetic field and the applied dc and rf electric fields, lead to a set of coupled Mathieu equations. Their approximate solutions exhibit motional frequencies, which are combinations of shifted macromotion frequencies and the cyclotron frequency. The dependence of these motional frequencies on the applied trapping fields was studied in detail. For the measurements we used small clouds of laser cooled B9e+ ions and crystallized B9e+ ions. The observed oscillation frequencies are compared to both the results of zeroth order analytical solutions and to numerical simulations in which the frequency spectrum was obtained from the ion orbits by using the fast fourier transform formalism. The various motional resonances were experimentally recorded by applying a weak dipole excitation field to one of the trap electrodes, and by simultaneously observing at resonance the changes in the fluorescence intensity. Depending on the detuning of the cooling laser the ions gain energy during the motional excitation process in such a way that they are shifted further in or out of optical resonance by the Doppler effect. This leads to either positive or negative ion motion signals at the various ion oscillation frequencies.

Journal of Applied Physics•Mar 1, 2001•11 citations
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.
ion. The response of the detected photon rate to the relative laser frequency deviations is recorded within the slope of a dark resonance formed in the lambda-type energy level scheme corresponding to two optical dipole transitions. This approach enhances the sensitivity to the small frequency deviations and does so with reciprocal dependence on the fluorescence rate. The employed lasers are phase locked to an optical frequency comb, which allows for precise calibration of optical frequency analysis by deterministic modulation of the analyzed laser beam with respect to the reference beam. The attainable high signal-to-noise ratios of up to a MHz range of modulation deviations and up to a hundred kHz modulation frequencies promise the applicability of the presented results in a broad range of optical spectroscopic applications.
We have studied the dynamics of one and two laser-cooled trapped 40Ca+ ions by applying electric fields of different nature along the axial direction of the trap, namely, driving the motion with a harmonic dipolar field, or with white noise. These two types of driving induce distinct motional states of the axial modes: a coherent oscillation with the dipolar field, or an enhanced Brownian motion due to an additional contribution to the heating rate from the electric noise. In both scenarios, the sensitivity of an isolated ion and a laser-cooled two-ion crystal has been evaluated and compared. The analysis and understanding of this dynamics is important towards the implementation of a novel Penning trap mass-spectroscopy technique based on optical detection, aiming at improving precision and sensitivity.
Coherence effects in a Lambda system of a 40Ca+ ion are investigated. Zeeman sublevels are utilized to evoke electromagnetically induced transparencies. The characteristic dark resonance and line shape alterations are analyzed for varying light field intensities. New features arise by avoiding all coherences in a Lambda-system. This is achieved by exposing the ion to only one single laser light field, going the spectroscopy. Pulsed light sequences ensure stable cooling and spectroscopy. A quantum mechanical description of the process is given, revealing the dark-resonance-free shape of the spectrum. This enables the determination of the Rabi frequency of the applied laser light field as well as the photon collection efficiency of the imaging system. In many cases in QIPC, it is important to precisely determine the position of the ions, for this information obtained from the ions" fluorescence is utilized. The capability of the segmented Paul trap to create custom electric potentials is utilized to form time dependent potentials with multiple trapping wells. The application of feedback control allows purposeful movement of a predefined number of ions and position regulation by altering the trapping voltages. Ion transport over 1 mm with more than 99.8 % success probability is accomplished without any knowledge of the potentials. By means of the feedback control this allows automated dividing of a linear ion crystal into two distinct potentials as well as the opposite process of merging. In order to perform these experiments, several novel techniques for the operation of an ion trap have been developed. A technique for automatic compensation is introduced to minimize the RF driven micromotion of the ion crystal. Additionally, a precise method for simultaneous measuring the oscillation frequencies for individual ions in an ion crystal is presented. Hereby, the oscillation modes of multi-species ion crystals can be analyzed for the determination of dopant isotopes.
We demonstrate simple and robust methods for Doppler cooling and obtaining high fluorescence from trapped 43 Ca + ions at a magnetic field of 146 Gauss. This field gives access to a magnetic-field-independent 'atomic clock' qubit transition within the ground level hyperfine structure of the ion, but also causes the complex internal structure of the 64 states relevant to Doppler cooling to be spread over many times the atomic transition line-width. Using a time-dependent optical Bloch equation simulation of the system we develop a simple scheme to Doppler-cool the ion on a two-photon dark resonance, which is robust to typical experimental variations in laser intensities, detunings and polarizations. We experimentally demonstrate cooling to a temperature of 0.3 mK, slightly below the Doppler limit for the corresponding two-level system, and then use Raman sideband laser cooling to cool further to the ground states of the ion's radial motional modes. These methods will enable two-qubit entangling gates with this ion, which is one of the most promising qubits so far developed.
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.
Ion traps have been pivotal in opening new frontiers for the precision spectroscopy of stable ions. We report on the demonstration of an additional ion trap: the linear combined trap. This device is particularly well suited for trapping ions with unstable nuclei, due to its large range of stability parameters that facilitates external injection online to an accelerator. The motion of an ion in such a linear combined trap is investigated theoretically and experimentally. In the trap ions oscillate harmonically in the radial direction and move nearly harmonically between fixed boundaries along the longitudinal axis. The presence of a homogeneous magnetic field and the applied dc and rf electric fields, lead to a set of coupled Mathieu equations. Their approximate solutions exhibit motional frequencies, which are combinations of shifted macromotion frequencies and the cyclotron frequency. The dependence of these motional frequencies on the applied trapping fields was studied in detail. For the measurements we used small clouds of laser cooled B9e+ ions and crystallized B9e+ ions. The observed oscillation frequencies are compared to both the results of zeroth order analytical solutions and to numerical simulations in which the frequency spectrum was obtained from the ion orbits by using the fast fourier transform formalism. The various motional resonances were experimentally recorded by applying a weak dipole excitation field to one of the trap electrodes, and by simultaneously observing at resonance the changes in the fluorescence intensity. Depending on the detuning of the cooling laser the ions gain energy during the motional excitation process in such a way that they are shifted further in or out of optical resonance by the Doppler effect. This leads to either positive or negative ion motion signals at the various ion oscillation frequencies.