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

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Repetitive interrogation of 2-level quantum systems

John D. Prestage, Sang Kun Chung

Published Jun 1, 2010• 2 citations
Publisher

Abstract

Trapped ion clocks derive information from a reference atomic transition by repetitive interrogations of the same quantum system, either a single ion or ionized gas of many millions of ions. Atomic beam frequency standards, by contrast, measure reference atomic transitions in a continuously replenished “flow through” configuration where initial ensemble atomic coherence is zero. We will describe some issues and problems that can arise when atomic state selection and preparation of the quantum atomic system is not completed, that is, optical pumping has not fully relaxed the coherence and also not fully transferred atoms to the initial state. We present a simple two-level density matrix analysis showing how frequency shifts during the state-selection process can cause frequency shifts of the measured clock transition. Such considerations are very important when a low intensity lamp light source is used for state selection, where there is relatively weak relaxation and re-pumping of ions to an initial state and much weaker `environmental' relaxation of the atomic coherence set-up in the atomic sample.

DOI
10.1109/freq.2010.5556339

Related papers

Light shifts in a pulsed cold-atom coherent-population-trapping clock

E. Blanshan, Simon Rochester, Elizabeth A. Donley +1 more

Field-grade atomic clocks capable of primary standard performance in compact physics packages would be of significant value in applications ranging from network synchronization to inertial navigation. A coherent-population-trapping clock featuring laser-cooled $^{87}\mathrm{Rb}$ atoms and pulsed Ramsey interrogation is a strong candidate for this technology if the frequency biases can be minimized and controlled. Here we characterize the light shift in a cold-atom coherent-population-trapping clock, explaining observed shifts in terms of phase shifts that arise during the formation of dark-state coherences combined with optical-pumping effects caused by unwanted incoherent light in the interrogation spectrum. Measurements are compared with existing and new theoretical treatments, and a laser configuration is identified that would reduce clock frequency uncertainty from light shifts to a fractional frequency level of $\ensuremath{\Delta}\ensuremath{\nu}/\ensuremath{\nu}=4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ per 100 kHz of laser frequency uncertainty.

Physical Review A•Apr 10, 2015•42 citations

Optical Atomic Clock and Laser Applications to Length and Time Metrology

Ye Jiang, Yuefeng Huang, K. Gao

In the mid-20th century, atoms were realized to be good candidates for time or frequency standards since transition energies or frequencies between two energy levels of some unperturbed atoms are more stable than those defined by the rotation of the earth or artefact-based clocks such as quartz crystal clocks. This motivated extensive research on realization and improvement of such kind of quantum-based time or frequency standards. The ultra-stable laser, referred to as a local oscillator in a clock, still drifts over time due to environmentally induced length fluctuations of the reference cavity. With the development of ion traps, ultra-narrow linewidth lasers and optical frequency combs, optical clocks based on single trapped ions as a new type of clocks have been realized in many laboratories. Ions can only stay in the trap within a certain region, which is called stability region. There is a variety of potential sources of systematic shifts associated with the clock transition in ion optical clocks.

CRC Press eBooks•Apr 29, 2021•0 citations

Quantum state control of trapped ions for computation and multi-ensemble atomic clocks

Thomas E. deLaubenfels

The purpose of this work is to investigate methods by which the quantum states of trapped ions may be better controlled and measured for the applications of quantum computing, quantum simulation, and the generation of atomic frequency standards. We report on two primary projects: first, we control the relative coupling strengths of carrier and first-order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding the technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions, with the cycles for the two cases 180◦ out of phase with each other. This technique allows for the suppression of off-resonant carrier excitations when addressing the motional sidebands, and has applications in quantum computation and quantum simulation. Second, we investigate methods proposed in Ref. [36] which may improve the performance of trapped ion (or atom) frequency standards when the interrogating local oscillator is of limited quality. These methods could be applied to future generations of small-scale frequency standards, which are in demand for applications such as local GPS networks and distributed sensors. We propose a scheme for implementing these methods in a 40Ca+ based frequency standard, and outline the technical requirements for doing so. Finally, we present preliminary results characterizing single-ion coherence times and ion “state destruction” events in our system, and discuss how they will affect the realization of the proposed scheme.

•Nov 10, 2017•0 citations

Extending the fundamental limit of atomic clock stability

Ravid Shaniv, Ayush Agrawal, David B. Hume

Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite all atomic frequency references having more than two energy-levels, the commonly used model for evaluating their ultimate limits assumes a two-level atom. This leads to frequency interrogation protocols and theoretical stability bounds that are suboptimal for a true multi-level atom. The most fundamental stability bound assumes two noise sources - quantum projection noise and spontaneous decay from the excited state. In this work, we analyze a model that includes these noise types and is generalized beyond the two-level assumption, where spontaneous decay can branch to more than a single ground state. This model allows for detection and exclusion of atomic frequency interrogations in which the atom decayed, leading to a frequency stability improvement of up to $\approx 4.5 \text{ dB}$ compared with the two-level model. Furthermore, we identify an even greater stability enhancement of $\approx 5.4 \text{ dB}$ for frequency comparisons between atoms in an odd parity Bell state. These enhancements are particularly relevant for the numerous trapped-ion optical clock species that operate close to lifetime-limited stability. We calculate new stability limits for those cases and provide a detailed experimental protocol for frequency interrogation with an $^{27}\text{Al}^{+}$ optical ion clock.

physics.atom-phCross-listedarXiv:2604.01099•Apr 2, 2026•0 citations

Single ion spectroscopy for optical clocks

Chr. Tamm, E. Peik, T. Schneider +5 more

The 435 mum171Yb+transition is a good candidate for an atomic clock based on an optical transition. We have stored single171Yb ions for several months in RF traps. The ions are cooled, repumped and the clock transition is interrogated by (frequency-doubled) diode lasers. The interrogation laser linewidth was 30 Hz determining the resolvable linewidth of the Yb+transition interrogated. The absolute frequency of this transition was measured using an optical comb generator, self referenced by broadening the spectrum to above one octave, with respect to a Cs fountain clock. Of all systematic frequency shifts to which this transition is subject an estimate indicates that the electric quadruple shift appears is the largest. To obtain a magnitude of the quadruple shift (and the quadruple moment) the clock frequencies of two independently stored and cooled171Yb ions were compared while varying the static electric field in one trap. The measured frequency shift amounting to ~1 Hz/V. This result would seem to permit clocks with much higher accuracy than the clocks based on microwave transition, particularly if the technique of aligning the ions with respect to the electric field were applicable. Anticipating even more precise clocks, we are presently investigating a blue nuclear transition in229Th. Such a nuclear transition should be even better shielded from environmental influences than transitions in the electron shell. This nuclear transition has not yet been directly optically observed. We are presently investigating the luminescence after incoherent broad band optical excitation. The triply ionized223Th is then a suitable system for trapped single ion spectroscopy. The cooling transition lies conveniently in the near infrared and the nuclear clock transition can be read out by nuclear/electron shell double resonance

CAOL . International Conference on Advanced Optoelectronics and Lasers•Jul 8, 2004•1 citation

Ultrahigh-resolution spectroscopy with atomic or molecular dark resonances: Exact steady-state line shapes and asymptotic profiles in the adiabatic pulsed regime

T. Zanon-Willette, Emeric de Clercq, E. Arimondo

Exact and asymptotic line shape expressions are derived from the semiclassical density matrix representation describing a set of closed three-level $\ensuremath{\Lambda}$ atomic or molecular states including decoherences, relaxation rates, and light shifts. An accurate analysis of the exact steady-state dark-resonance profile describing the Autler-Townes doublet, the electromagnetically induced transparency or coherent population trapping resonance, and the Fano-Feshbach line shape leads to the linewidth expression of the two-photon Raman transition and frequency shifts associated to the clock transition. From an adiabatic analysis of the dynamical optical Bloch equations in the weak field limit, a pumping time required to efficiently trap a large number of atoms into a coherent superposition of long-lived states is established. For a highly asymmetrical configuration with different decay channels, a strong two-photon resonance based on a lower states population inversion is established when the driving continuous-wave laser fields are greatly unbalanced. When time separated resonant two-photon pulses are applied in the adiabatic pulsed regime for atomic or molecular clock engineering, where the first pulse is long enough to reach a coherent steady-state preparation and the second pulse is very short to avoid repumping into a new dark state, dark-resonance fringes mixing continuous-wave line shape properties and coherent Ramsey oscillations are created. Those fringes allow interrogation schemes bypassing the power broadening effect. Frequency shifts affecting the central clock fringe computed from asymptotic profiles and related to the Raman decoherence process exhibit nonlinear shapes with the three-level observable used for quantum measurement. We point out that different observables experience different shifts on the lower-state clock transition.

arXiv:1110.2221•Physical Review A•Dec 2, 2011•42 citations
Trapped ion clocks derive information from a reference atomic transition by repetitive interrogations of the same quantum system, either a single ion or ionized gas of many millions of ions. Atomic beam frequency standards, by contrast, measure reference atomic transitions in a continuously replenished “flow through” configuration where initial ensemble atomic coherence is zero. We will describe some issues and problems that can arise when atomic state selection and preparation of the quantum atomic system is not completed, that is, optical pumping has not fully relaxed the coherence and also not fully transferred atoms to the initial state. We present a simple two-level density matrix analysis showing how frequency shifts during the state-selection process can cause frequency shifts of the measured clock transition. Such considerations are very important when a low intensity lamp light source is used for state selection, where there is relatively weak relaxation and re-pumping of ions to an initial state and much weaker `environmental' relaxation of the atomic coherence set-up in the atomic sample.
Field-grade atomic clocks capable of primary standard performance in compact physics packages would be of significant value in applications ranging from network synchronization to inertial navigation. A coherent-population-trapping clock featuring laser-cooled 87Rb^{87}\mathrm{Rb}87Rb atoms and pulsed Ramsey interrogation is a strong candidate for this technology if the frequency biases can be minimized and controlled. Here we characterize the light shift in a cold-atom coherent-population-trapping clock, explaining observed shifts in terms of phase shifts that arise during the formation of dark-state coherences combined with optical-pumping effects caused by unwanted incoherent light in the interrogation spectrum. Measurements are compared with existing and new theoretical treatments, and a laser configuration is identified that would reduce clock frequency uncertainty from light shifts to a fractional frequency level of $\ensuremath{\Delta}\ensuremath{\nu}/\ensuremath{\nu}=4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ per 100 kHz of laser frequency uncertainty.
In the mid-20th century, atoms were realized to be good candidates for time or frequency standards since transition energies or frequencies between two energy levels of some unperturbed atoms are more stable than those defined by the rotation of the earth or artefact-based clocks such as quartz crystal clocks. This motivated extensive research on realization and improvement of such kind of quantum-based time or frequency standards. The ultra-stable laser, referred to as a local oscillator in a clock, still drifts over time due to environmentally induced length fluctuations of the reference cavity. With the development of ion traps, ultra-narrow linewidth lasers and optical frequency combs, optical clocks based on single trapped ions as a new type of clocks have been realized in many laboratories. Ions can only stay in the trap within a certain region, which is called stability region. There is a variety of potential sources of systematic shifts associated with the clock transition in ion optical clocks.
The purpose of this work is to investigate methods by which the quantum states of trapped ions may be better controlled and measured for the applications of quantum computing, quantum simulation, and the generation of atomic frequency standards. We report on two primary projects: first, we control the relative coupling strengths of carrier and first-order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding the technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions, with the cycles for the two cases 180◦ out of phase with each other. This technique allows for the suppression of off-resonant carrier excitations when addressing the motional sidebands, and has applications in quantum computation and quantum simulation. Second, we investigate methods proposed in Ref. [36] which may improve the performance of trapped ion (or atom) frequency standards when the interrogating local oscillator is of limited quality. These methods could be applied to future generations of small-scale frequency standards, which are in demand for applications such as local GPS networks and distributed sensors. We propose a scheme for implementing these methods in a 40Ca+ based frequency standard, and outline the technical requirements for doing so. Finally, we present preliminary results characterizing single-ion coherence times and ion “state destruction” events in our system, and discuss how they will affect the realization of the proposed scheme.
Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite all atomic frequency references having more than two energy-levels, the commonly used model for evaluating their ultimate limits assumes a two-level atom. This leads to frequency interrogation protocols and theoretical stability bounds that are suboptimal for a true multi-level atom. The most fundamental stability bound assumes two noise sources - quantum projection noise and spontaneous decay from the excited state. In this work, we analyze a model that includes these noise types and is generalized beyond the two-level assumption, where spontaneous decay can branch to more than a single ground state. This model allows for detection and exclusion of atomic frequency interrogations in which the atom decayed, leading to a frequency stability improvement of up to ≈4.5 dB\approx 4.5 \text{ dB}≈4.5 dB compared with the two-level model. Furthermore, we identify an even greater stability enhancement of ≈5.4 dB\approx 5.4 \text{ dB}≈5.4 dB for frequency comparisons between atoms in an odd parity Bell state. These enhancements are particularly relevant for the numerous trapped-ion optical clock species that operate close to lifetime-limited stability. We calculate new stability limits for those cases and provide a detailed experimental protocol for frequency interrogation with an 27Al+^{27}\text{Al}^{+}27Al+ optical ion clock.
The 435 mum171Yb+transition is a good candidate for an atomic clock based on an optical transition. We have stored single171Yb ions for several months in RF traps. The ions are cooled, repumped and the clock transition is interrogated by (frequency-doubled) diode lasers. The interrogation laser linewidth was 30 Hz determining the resolvable linewidth of the Yb+transition interrogated. The absolute frequency of this transition was measured using an optical comb generator, self referenced by broadening the spectrum to above one octave, with respect to a Cs fountain clock. Of all systematic frequency shifts to which this transition is subject an estimate indicates that the electric quadruple shift appears is the largest. To obtain a magnitude of the quadruple shift (and the quadruple moment) the clock frequencies of two independently stored and cooled171Yb ions were compared while varying the static electric field in one trap. The measured frequency shift amounting to ~1 Hz/V. This result would seem to permit clocks with much higher accuracy than the clocks based on microwave transition, particularly if the technique of aligning the ions with respect to the electric field were applicable. Anticipating even more precise clocks, we are presently investigating a blue nuclear transition in229Th. Such a nuclear transition should be even better shielded from environmental influences than transitions in the electron shell. This nuclear transition has not yet been directly optically observed. We are presently investigating the luminescence after incoherent broad band optical excitation. The triply ionized223Th is then a suitable system for trapped single ion spectroscopy. The cooling transition lies conveniently in the near infrared and the nuclear clock transition can be read out by nuclear/electron shell double resonance
Exact and asymptotic line shape expressions are derived from the semiclassical density matrix representation describing a set of closed three-level $\ensuremath{\Lambda}$ atomic or molecular states including decoherences, relaxation rates, and light shifts. An accurate analysis of the exact steady-state dark-resonance profile describing the Autler-Townes doublet, the electromagnetically induced transparency or coherent population trapping resonance, and the Fano-Feshbach line shape leads to the linewidth expression of the two-photon Raman transition and frequency shifts associated to the clock transition. From an adiabatic analysis of the dynamical optical Bloch equations in the weak field limit, a pumping time required to efficiently trap a large number of atoms into a coherent superposition of long-lived states is established. For a highly asymmetrical configuration with different decay channels, a strong two-photon resonance based on a lower states population inversion is established when the driving continuous-wave laser fields are greatly unbalanced. When time separated resonant two-photon pulses are applied in the adiabatic pulsed regime for atomic or molecular clock engineering, where the first pulse is long enough to reach a coherent steady-state preparation and the second pulse is very short to avoid repumping into a new dark state, dark-resonance fringes mixing continuous-wave line shape properties and coherent Ramsey oscillations are created. Those fringes allow interrogation schemes bypassing the power broadening effect. Frequency shifts affecting the central clock fringe computed from asymptotic profiles and related to the Raman decoherence process exhibit nonlinear shapes with the three-level observable used for quantum measurement. We point out that different observables experience different shifts on the lower-state clock transition.