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Quantum Sensing Using Atomic Clocks for Nuclear and Particle Physics

Akio Kawasaki

TL;DR

This work surveys how quantum sensing with atomic clocks—leveraging two-level atomic systems, optical lattice clocks, and ion clocks—can probe nuclear and particle physics phenomena. It details the experimental platforms, precision limits, and methods to suppress backgrounds, outlining theoretical frameworks for varying constants, ultralight dark matter, and fifth-force searches via isotope shifts. The article also discusses highly charged ions and nuclear clocks as next-generation sensors, and presents current experimental constraints along with future directions that combine entanglement, diverse atomic species, and novel architectures. Overall, state-of-the-art atomic clocks offer a powerful, controllable probe of beyond-Standard-Model physics with potential breakthroughs in fundamental physics and metrology.

Abstract

Technologies for manipulating single atoms have advanced drastically in the past decades. Due to their excellent controllability of internal states, atoms serve as one of the ideal platforms as quantum systems. One major research direction in atomic systems is the precise determination of physical quantities using atoms, which is included in the field of precision measurements. One of such precisely measured physical quantities is energy differences between two energy levels in atoms, which is symbolized by the remarkable fractional uncertainty of $10^{-18}$ or lower achieved in the state-of-the-art atomic clocks. Two-level systems in atoms are sensitive to various external fields and can, therefore, function as quantum sensors. The effect of these fields manifests as energy shifts in the two-level system. Traditionally, such shifts are induced by electric or magnetic fields, as recognized even before the advent of precision spectroscopy with lasers. With high-precision measurements, tiny energy shifts caused by hypothetical fields weakly coupled to ordinary matter or by small effects mediated by massive particles can be potentially detectable, which are conventionally dealt with in the field of nuclear and particle physics. In most cases, the atomic systems as quantum sensors have not been sensitive enough to detect such effects. Instead, experiments searching for these interactions have placed constraints on coupling constants, except in a few cases where effects are predicted by the Standard Model of particle physics. Nonetheless, measurements and searches for these effects in atomic systems have led to the emergence of a new field of physics.

Quantum Sensing Using Atomic Clocks for Nuclear and Particle Physics

TL;DR

This work surveys how quantum sensing with atomic clocks—leveraging two-level atomic systems, optical lattice clocks, and ion clocks—can probe nuclear and particle physics phenomena. It details the experimental platforms, precision limits, and methods to suppress backgrounds, outlining theoretical frameworks for varying constants, ultralight dark matter, and fifth-force searches via isotope shifts. The article also discusses highly charged ions and nuclear clocks as next-generation sensors, and presents current experimental constraints along with future directions that combine entanglement, diverse atomic species, and novel architectures. Overall, state-of-the-art atomic clocks offer a powerful, controllable probe of beyond-Standard-Model physics with potential breakthroughs in fundamental physics and metrology.

Abstract

Technologies for manipulating single atoms have advanced drastically in the past decades. Due to their excellent controllability of internal states, atoms serve as one of the ideal platforms as quantum systems. One major research direction in atomic systems is the precise determination of physical quantities using atoms, which is included in the field of precision measurements. One of such precisely measured physical quantities is energy differences between two energy levels in atoms, which is symbolized by the remarkable fractional uncertainty of or lower achieved in the state-of-the-art atomic clocks. Two-level systems in atoms are sensitive to various external fields and can, therefore, function as quantum sensors. The effect of these fields manifests as energy shifts in the two-level system. Traditionally, such shifts are induced by electric or magnetic fields, as recognized even before the advent of precision spectroscopy with lasers. With high-precision measurements, tiny energy shifts caused by hypothetical fields weakly coupled to ordinary matter or by small effects mediated by massive particles can be potentially detectable, which are conventionally dealt with in the field of nuclear and particle physics. In most cases, the atomic systems as quantum sensors have not been sensitive enough to detect such effects. Instead, experiments searching for these interactions have placed constraints on coupling constants, except in a few cases where effects are predicted by the Standard Model of particle physics. Nonetheless, measurements and searches for these effects in atomic systems have led to the emergence of a new field of physics.

Paper Structure

This paper contains 31 sections, 14 equations, 9 figures, 6 tables.

Figures (9)

  • Figure 1: A two-level system and relevant quantities. $|g \rangle$: the ground state. $|e \rangle$: the excited state. $\hbar \omega_0=h \nu_0$: the energy difference between these two states. $\omega$: frequency for the oscillating electromagnetic field, with $\delta=\omega-\omega_0$. $\Gamma=1/\tau$: natural linewidth of the excited state, with $\tau$ being its lifetime. $\Delta \omega=2 \pi \Delta \nu$: shift in resonant frequency induced by an external field.
  • Figure 2: Historical development of the fractional uncertainty of atomic clocks: the black dotted line shows the average improvement in the accuracy for the Cs clocks, and the red dotted line indicates approximate development of the accuracy for the best optical atomic clocks. The data points correspond to total fractional uncertainties reported in the following references. Cs clocks: Refs. PhilTransRoySocLondon.250.45IRETrans.11.231IEEETransInstrumMeas.15.48IEEETransInstrumMeas.19.156IEEETransInstrumMeas.23.489NBSSpecPub.617.25IEEEIntFreqCtrlSymp.71Proc28thAPTTISAM.225Metrologia.38.427Metrologia.39.321Metrologia.42.411Metrologia.51.174Metrologia.55.789Metrologia.38.343JPhysB.38.S449PhysRevLett.82.4619 Ion clocks: Refs. PhysRevLett.82.3228OptLett.25.1729PhysRevLett.86.4996OptLett.26.1589Science.306.1355PhysRevLett.94.230801PhysRevLett.97.020801Science.319.1808PhysRevLett.104.070802PhysRevLett.109.203002PhysRevLett.116.063001PhysRevLett.123.033201Metrologia.61.045001PhysRevLett.135.033201PhysRevAppl.24.0440822506.17423 Optical lattice clocks: Refs. Nature.435.321PhysRevLett.97.130801JPhysSocJpn.75.104302PhysRevLett.98.083002Science.319.1805PhysRevLett.103.063001Nature.506.71NatPhoton.9.185NatCommun.6.6896Nature.564.87Metrologia.56.065004PhysRevLett.133.023401PhysRevLett.134.023201 Other optical atomic clocks: Refs. ApplOpt.15.734OptLett.8.136PhysRevA.35.4878PhysRevA.39.4591PhysRevLett.69.1923OptCommun.97.29PhysRevLett.76.18PhysRevLett.79.2646IEEETransInstrumMeas.48.613PhysRevLett.84.5496PhysRevLett.86.4996PhysRevLett.92.230802Metrologia.44.146.
  • Figure 3: Typical energy structure of atoms used in optical atomic clocks: (a) alkali-atom-like structure and (b) alkaline-earth-atom-like structure. The blue solid lines show the transitions used for laser cooling. The green dashed line in (b) is the intercombination transition that is allowed by L-S coupling. The red dotted lines are the clock transitions.
  • Figure 4: Historical development of the constraint on the time variation of the fine structure constant set by atomic spectroscopy: atomic species next to the data points indicate the species used to obtain the corresponding data points. Data are cited from H,Cs,Hg$^+$ (1995) PhysRevLett.74.3511, Rb,Cs PhysRevLett.90.150801, Cs,Hg$^+$PhysRevLett.90.150802, H,Cs,Hg$^+$ (2004) PhysRevLett.92.230802, Dy (2007) PhysRevLett.98.040801, Cs,Hg$^+$PhysRevLett.98.070801, Al$^+$,Cs,Hg$^+$Science.319.1808, Sr,Cs NatCommun.4.2109, Dy (2013) PhysRevLett.111.060801, Al$^+$,Yb$^+$,Hg$^+$PhysRevLett.113.210801PhysRevLett.113.210802, Yb$^+$ (2021) PhysRevLett.126.011102, and Yb$^+$ (2023) PhysRevLett.130.253001. Except for Ref.PhysRevLett.74.3511 these original papers report best fit for the linear drift $\dot{\alpha}/\alpha$ with $1\sigma$ uncertainty ($\sigma$: standard deviation). These drift rates are consistent with zero within $1.96\sigma$ width. $|\dot{\alpha}/\alpha|$ in the plot is 95% confidence level (C.L.) upper bound calculated as $1.96\sigma$. For Ref. PhysRevLett.74.3511, the number reported in the original paper is plotted.
  • Figure 5: Energy levels for Pr$^{10+}$: E2 shows an electric quadrupole transition. $\tau$ shows the lifetime of the excited states. $K$ is the sensitivity coefficient for the variation of $\alpha$.
  • ...and 4 more figures