View source for Nuclear clock

{{Short description|Extremely accurate clock concept}}
{{Infobox machine
| name      = Nuclear Clock
| image     = nuclear_clock_concept.png
| caption   = Concept of a thorium-229 based nuclear optical clock.
|application=time-keeping|industry=scientific, satellite navigation, and data transfer}}

A '''nuclear clock''' or '''nuclear optical clock''' is an [[atomic clock]] being developed that will use the energy of a [[nuclear isomer]]ic transition as its reference frequency,<ref name="Peik2003">{{cite journal
| first1 = Ekkehard | last1 = Peik
| first2 = Christian | last2 = Tamm
| title = Nuclear laser spectroscopy of the 3.5&nbsp;eV transition in <sup>229</sup>Th
| url = https://www.ptb.de/cms/fileadmin/internet/fachabteilungen/abteilung_4/4.4_zeit_und_frequenz/pdf/2003_Peik-Tamm_EuroPhysLett_th001.pdf
| journal = Europhysics Letters
| volume = 61
| issue = 2
| pages = 181–186
| date = 15 January 2003
| doi = 10.1209/epl/i2003-00210-x
| bibcode = 2003EL.....61..181P
| s2cid = 250818523
| access-date = 2019-03-17
| archive-url = https://web.archive.org/web/20240411182912/https://www.ptb.de/cms/fileadmin/internet/fachabteilungen/abteilung_4/4.4_zeit_und_frequenz/pdf/2003_Peik-Tamm_EuroPhysLett_th001.pdf
| archive-date = 2024-04-11
| url-status = live
}}</ref> instead of the [[atomic electron transition]] energy used by conventional atomic clocks. Such a clock is expected to be more accurate than the best current atomic clocks by a factor of about 10, with an achievable accuracy approaching the 10<sup>−19</sup> level.<ref name="Campbell2012">{{cite journal
| first1=Corey |last1=Campbell
| display-authors=etal
| title = Single-ion nuclear clock for metrology at the 19th decimal place
| journal = [[Physical Review Letters]]
| volume = 108
| issue = 12
| article-number = 120802
| date = 23 March 2012
| doi = 10.1103/PhysRevLett.108.120802
| pmid=22540568
| arxiv= 1110.2490
| bibcode=2012PhRvL.108l0802C
| s2cid=40863227
| url=https://sites.lsa.umich.edu/kuzmich-lab/wp-content/uploads/sites/90/2014/05/229ThClock.pdf
}}</ref>

The only nuclear state suitable for the development of a nuclear clock using existing technology is [[thorium-229m]], an isomer of [[thorium]]-229 and the lowest-energy nuclear isomer known. With an energy of {{val|{{#expr:(2020407384335*6.62607015/1.602176634e12) round 12}}|(8)|u=eV}},<ref name=Thirolf2024/><ref name=Tiedau2024>{{cite journal
 |title=Laser Excitation of the Th-229 Nucleus
 |first1=J. |last1=Tiedau  |first2=M. V. |last2=Okhapkin  |first3=K. |last3=Zhang
 |first4=J. |last4=Thielking  |first5=G. |last5=Zitzer  |first6=E. |last6=Peik
 |first7=F. |last7=Schaden  |first8=T. |last8=Pronebner  |first9=I. |last9=Morawetz
 |first10=L. |last10=Toscani De Col |first11=F. |last11=Schneider  |first12=A. |last12=Leitner
 |first13=M. |last13=Pressler  |first14=G.A. |last14=Kazakov  |first15=K. |last15=Beeks
 |first16=T. |last16=Sikorsky  |first17=T. |last17=Schumm
 |display-authors=6
 |journal=[[Physical Review Letters]] |volume=132
 |date=29 April 2024
 |issue=18 |article-number=182501 |doi=10.1103/PhysRevLett.132.182501
 |pmid=38759160 |bibcode=2024PhRvL.132r2501T |url=https://www.tuwien.at/fileadmin/Assets/tu-wien/News/2024/Thorium_Preprint.pdf
 |quote=The nuclear resonance for the Th<sup>4+</sup> ions in Th:CaF<sub>2</sub> is measured at the wavelength {{val|148.3821|(5)|u=nm}}, frequency {{val|2020.409|(7)|u=THz}}, and the fluorescence lifetime in the crystal is {{val|630|(15)|u=s}}, corresponding to an isomer half-life of {{val|1740|(50)|u=s}} for a nucleus isolated in vacuum.
}}</ref><ref name=Zhang2024/> this corresponds to a frequency of {{val|2020407384335|2|u=kHz}},<ref>{{Cite news |last=Conover |first=Emily |author-link=Emily Conover |date=5 September 2024 |title=A nuclear clock prototype hints at ultraprecise timekeeping  |journal=[[Science News]] |url=https://www.sciencenews.org/article/nuclear-clock-ultraprecise-timekeeping}}  Also appears in the 5 October print edition (p. 7) titled "[https://www.sciencenews.org/wp-content/uploads/2024/09/SN_vol206_no5_lo.pdf#page=9 Nuclear clock prototype makes debut]".</ref> or wavelength of {{val|{{#expr:(299792458e6/2020407384335) round 9}}|u=nm}}, in the [[vacuum ultraviolet]] region, making it accessible to laser excitation.<ref name="WenseReview"/><ref name="SlowMotion">{{Cite magazine |last=Miller |first=Johanna L. |date=1 June 2024 |title=Slow-motion spectroscopy paves the way for a nuclear clock |url=https://pubs.aip.org/physicstoday/article/77/6/12/3294387/Slow-motion-spectroscopy-paves-the-way-for-a |magazine=Physics Today |pages=12–14 |volume=77 |issue=6 |doi=10.1063/pt.kvtv.jxde}}</ref>

== Principle of operation ==

[[Atomic clock]]s are today's most accurate timekeeping devices. They operate by exploiting the fact that the gap between the [[energy levels]] of two [[bound states|bound electron states]] in an atom is constant across space and time. A bound electron can be excited with [[electromagnetic radiation]] precisely when the radiation's [[photon energy]] matches the energy of the transition. Via the [[Planck relation]], that transition energy corresponds to a particular frequency. By irradiating an appropriately prepared collection of identical atoms and measuring the number of excitations induced, a light source's frequency can be tuned to maximize this response and therefore closely match the corresponding electron transition energy. The transition energy thus provides a standard of reference which can be used to calibrate such a source reliably.

Conventional atomic clocks use [[microwave]] (high-frequency [[radio wave]]) frequencies, but development of the [[laser]] has made it possible to generate very stable light frequencies, and the [[frequency comb]] makes it possible to count those oscillations (measured in hundreds of THz, meaning hundred of trillions of cycles per second) to extraordinarily high accuracy. A device which uses a laser in this way is known as an [[Atomic clock#Optical clocks|optical atomic clock]].<ref>
{{cite journal
| title=Optical atomic clocks
| first1=Andrew D. |last1=Ludlow  |first2=Martin M. |last2=Boyd
| first3=Jun |last3=Ye |author-link3=Jun Ye
| first4=E. |last4=Peik  |first5=P. O. |last5=Schmidt
| journal=[[Reviews of Modern Physics]] |volume=87 | issue=2 | pages=637–699 | date=26 June 2015
| doi=10.1103/RevModPhys.87.637
| arxiv=1407.3493
| bibcode=2015RvMP...87..637L
| s2cid=119116973
| url=https://www.repo.uni-hannover.de/bitstream/handle/123456789/3111/Ludlow%20et%20al%202015%2C%20Optical%20atomic%20clocks.pdf
}}</ref>

One prominent example of an optical atomic clock is the ytterbium (Yb) lattice clock, where a particular electron transition in the [[ytterbium-171]] isotope is used for laser stabilization.<ref>
{{cite journal |author1=McGrew |first=W. F. |display-authors=etal |date=2018 |title=Atomic clock performance enabling geodesy below the centimetre level |url=https://www.if.ufrj.br/wp-content/uploads/2021/03/Atomic-clock-performance-enabling-geodesy-below-the-centimetre-level.pdf |journal=Nature |type=Letter |volume=564 |issue=7734 |pages=87–90 |arxiv=1807.11282 |bibcode=2018Natur.564...87M |doi=10.1038/s41586-018-0738-2 |pmid=30487601 |s2cid=53803712}}</ref> In this case, one second has elapsed after {{val|518295836590863.63|0.1}} oscillations of the laser light stabilized to the corresponding electron transition.<ref>{{cite journal |author1=Margolis |first=H. S. |author2=Panfilo |first2=G. |author3=Petit |first3=G. |author4=Oates |first4=C. |author5=Ido |first5=T. |author6=Bize |first6=S. |date=25 January 2024 |title=The CIPM list "Recommended values of standard frequencies": 2021 update |journal=Metrologia |volume=61 |issue=3 |arxiv=2401.14537 |bibcode=2024Metro..61c5005M |doi=10.1088/1681-7575/ad3afc |article-number=035005}}</ref> Other examples for optical atomic clocks of the highest accuracy are the Yb-171 single-ion clock,<ref>
{{cite journal |author1=Huntemann |first=N. |author2=Sanner |first2=C. |author3=Lipphardt |first3=B. |author4=Tamm |first4=Chr. |author5=Peik |first5=E. |date=8 February 2016 |title=Single-ion atomic clock with 3×10<sup>−18</sup> systematic uncertainty |url=https://www.ptb.de/cms/fileadmin/internet/fachabteilungen/abteilung_4/4.4_zeit_und_frequenz/pdf/2016_Huntemann_PhysRevLett.116.063001.pdf |journal=Phys. Rev. Lett. |volume=116 |issue=6 |arxiv=1602.03908 |bibcode=2016PhRvL.116f3001H |doi=10.1103/PhysRevLett.116.063001 |pmid=26918984 |s2cid=19870627 |article-number=063001}}</ref> the strontium(Sr)-87 optical lattice clock,<ref>
{{cite journal |author1=Nicholson |first=T. L. |author2=Campbell |first2=S. L. |author3=Hutson |first3=R. B. |author4=Marti |first4=G. E. |author5=Bloom |first5=B. J. |display-authors=etal |date=21 April 2015 |title=Systematic evaluation of an atomic clock at 2×10<sup>−18</sup> total uncertainty |url=https://jila.colorado.edu/sites/default/files/2019-07/Sr%20Clock%202E-18%20accuracy_Nature%20Comm%202015.pdf |journal=Nature Communications |volume=6 |arxiv=1412.8261 |doi=10.1038/ncomms7896 |pmc=4411304 |pmid=25898253 |article-number=6896}}</ref><ref>{{cite journal
 |title=Clock with {{val|8|e=-19}} Systematic Uncertainty
 |first1=Alexander |last1=Aeppli  |first2=Kyungtae |last2=Kim
 |first3=William |last3=Warfield  |first4=Marianna S. |last4=Safronova
 |first5=Jun |last5=Ye |author-link5=Jun Ye
 |journal=Physical Review Letters |arxiv=2403.10664 |date=15 March 2024
 |volume=133 |issue=2 |article-number=023401
 |doi=10.1103/PhysRevLett.133.023401
 |pmid=39073965 |bibcode=2024PhRvL.133b3401A
 |url=https://res.cloudinary.com/apsphysics/image/upload/v1719586349/LQ19131_g9ftr0.pdf
}}</ref> and the aluminum(Al)-27 single-ion clock.<ref>
{{cite journal |author1=Brewer |first=S. M. |display-authors=etal |date=15 July 2019 |title=<sup>27</sup>Al<sup>+</sup> quantum-logic clock with systematic uncertainty below 10<sup>−18</sup> |url=https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=927399 |journal=[[Physical Review Letters]] |volume=123 |issue=3 |arxiv=1902.07694 |doi=10.1103/PhysRevLett.123.033201 |pmid=31386450 |s2cid=119075546 |article-number=033201}} Minor correction in {{cite journal |author1=Brewer |first=S. M. |display-authors=etal |date=1 August 2023 |title=Erratum: <sup>27</sup>Al<sup>+</sup> quantum-logic clock with systematic uncertainty below 10<sup>−18</sup> [Physical Review Letters 123, 033201 (2019)] |url=https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.131.059901 |journal=Physical Review Letters |volume=131 |article-number=059901}}</ref> The achieved accuracies of these clocks vary around 10<sup>−18</sup>, corresponding to about 1 second of inaccuracy in 30 billion years, significantly longer than the age of the universe.

A nuclear optical clock would use the same principle of operation, with the important difference that a ''nuclear'' transition instead of an atomic shell electron transition is used for laser stabilization.<ref name="Peik2003" /> The expected advantage of a nuclear clock is that the atomic nucleus is smaller than the atomic shell by up to five orders of magnitude, with correspondingly smaller [[magnetic dipole]] and [[electric quadrupole]] moments, and is therefore significantly less affected by external magnetic and electric fields. Such external perturbations are the limiting factor for the achieved accuracies of electron-based atomic clocks. Due to this conceptual advantage, a nuclear optical clock is expected to achieve a time accuracy approaching 10<sup>−19</sup>, a ten-fold improvement over electron-based clocks.<ref name="Campbell2012" />

===Ionization===
An excited atomic nucleus can shed its excess energy by two alternative paths:
* radiatively, by direct photon ([[gamma ray]]) emission, or
* by [[internal conversion]], transferring the energy to a shell electron which is ejected from the atom.
For most [[nuclear isomer]]s, the available energy is sufficient to eject any electron, and the inner-shell electrons are the most frequently ejected. In the special case of {{SimpleNuclide|Th|229|m}}, the energy is sufficient only to eject an outer electron (thorium's first [[ionization energy]] is {{val|6.3|u=eV}}), and if the atom is already ionized, there is not enough energy to eject a second (thorium's second ionization energy is {{val|11.5|u=eV}}).

The two decay paths have different [[half-lives]]. Neutral {{SimpleNuclide|Th|229|m}} decays almost exclusively by internal conversion, with a half-life of {{val|7|1|u=us}}.{{r|Seiferle2017}} In thorium [[cation]]s, internal conversion is energetically prohibited, and {{SimpleNuclide|Th|229|m|charge=+}} is forced to take the slower path, decaying radiatively with a half-life of around half an hour.{{r|Tiedau2024}}

Thus, in the typical case that the clock is designed to measure radiated photons, it is necessary to hold the thorium in an ionized state. This can be done in an [[ion trap]], or by embedding it in an [[ionic crystal]] with a [[band gap]] greater than the transition energy.<ref>{{cite journal
 |title=Radiative Decay of the <sup>229m</sup>Th Nuclear Clock Isomer in Different Host Materials
 |author1=S.V. Pineda
 |display-authors=etal
 |journal=Physical Review Research
 |volume=7 |date=2025<!--to appear-->
 |arxiv=2408.12309
 |url=https://journals.aps.org/prresearch/accepted/ed072JfcI3a17f0bb14c1c65338130d0500147020
 |url-access=subscription
}}</ref> In this case, the atoms are not 100% ionized, and a small amount of internal conversion is possible (reducing the half-life to approximately 10 minutes{{r|Tiedau2024}}), but the loss is tolerable.

== Different nuclear clock concepts ==
Two different concepts for nuclear optical clocks have been discussed in the literature: '''trap-based nuclear clocks''' and '''solid-state nuclear clocks'''.

=== Trap-based nuclear clocks ===
For a trap-based nuclear clock either a single <sup>229</sup>Th<sup>3+</sup> ion is trapped in a [[Quadrupole ion trap|Paul trap]], known as the '''single-ion nuclear clock''',{{r|Peik2003|Campbell2012}} or a chain of multiple ions is trapped, considered as the '''multiple-ion nuclear clock'''.<ref name="WenseReview" /> Such clocks are expected to achieve the highest time accuracy, as the ions are to a large extent isolated from their environment. A multiple-ion nuclear clock could have a significant advantage over the single-ion nuclear clock in terms of stability performance.

=== Solid-state nuclear clocks ===
As the nucleus is largely unaffected by the atomic shell, it is also intriguing to embed many nuclei into a crystal lattice environment. This concept is known as the '''crystal-lattice nuclear clock'''.<ref name="Peik2003" /> Due to the high density of embedded nuclei of up to 10<sup>18</sup> per cm<sup>3</sup>, this concept would allow irradiating a huge number of nuclei in parallel, thereby drastically increasing the achievable signal-to-noise ratio,<ref name="Kazakov2012">{{cite journal |author1=Kazakov |first=G. A. |display-authors=etal |date=2012 |title=Performance of a <sup>229</sup>Thorium solid-state nuclear clock |url=https://www.researchgate.net/publication/224039796 |journal=New Journal of Physics |volume=14 |issue=8 |arxiv=1204.3268 |bibcode=2012NJPh...14h3019K |doi=10.1088/1367-2630/14/8/083019 |s2cid=118341064 |doi-access=free |article-number=083019}}</ref> but at the cost of potentially higher external perturbations.<ref name="Rellergert2010">{{cite journal |author1=Rellergert |first=W. G. |display-authors=etal |date=21 May 2010 |title=Constraining the evolution of the fundamental constants with a solid-state optical frequency reference based on the <sup>229</sup>Th nucleus |url=http://www.nat.vu.nl/~wimu/Varying-Constants-Papers/Th-229-Rellergert-2010.pdf |journal=Physical Review Letters |volume=104 |issue=20 |doi=10.1103/PhysRevLett.104.200802 |pmid=20867019 |article-number=200802}}</ref> It has also been proposed to irradiate a metallic <sup>229</sup>Th surface and to probe the isomer's excitation in the [[internal conversion]] channel, which is known as the '''internal-conversion nuclear clock'''.<ref name="Wense2020">{{cite journal |author1=von der Wense |first=L. |author2=Zhang |first2=C. |date=7 July 2020 |title=Concepts for direct frequency-comb spectroscopy of <sup>229m</sup>Th and an internal-conversion-based solid-state nuclear clock |journal=[[Eur. Phys. J. D]] |volume=74 |issue=7 |arxiv=1905.08060 |bibcode=2020EPJD...74..146V |doi=10.1140/epjd/e2020-100582-5 |s2cid=209322360 |article-number=146}}</ref> Both types of solid-state nuclear clocks were shown to offer the potential for comparable performance.

== Transition requirements ==

From the principle of operation of a nuclear optical clock, it is evident that '''direct laser excitation''' of a nuclear state is a central requirement for the development of such a clock. This is impossible for most nuclear transitions, as the typical energy range of nuclear transitions (keV to MeV) is orders of magnitude above the maximum energy which is accessible with significant intensity by today's narrow-bandwidth laser technology (a few eV). There are only two nuclear excited states known which possess a sufficiently low excitation energy (below 100&nbsp;eV). These are
* {{SimpleNuclide|Th|229|m|link}}, a metastable nuclear excited state of the isotope thorium-229 with an excitation energy of only about 8 eV,<ref name="SeiferleEnergy"/><ref name="SikorskyEnergy"/> and
* {{SimpleNuclide|U|235|m1|link}}, a metastable excited state of [[uranium-235]] with an energy of 76.7 eV.<ref>{{cite journal |author1=Ponce |first=F. |display-authors=etal |date=2018 |title=Accurate measurement of the first excited nuclear state in <sup>235</sup>U |journal=[[Phys. Rev. C]] |volume=97 |issue=5 |bibcode=2018PhRvC..97e4310P |doi=10.1103/PhysRevC.97.054310 |doi-access=free |article-number=054310}}</ref>
However, {{SimpleNuclide|U|235|m1}} has such an extraordinarily long radiative half-life (on the order of {{val|e=22|u=s}}, 20,000 times the age of the universe, and far longer than its internal conversion half-life of 26 minutes) that it is not practical to use for a clock.{{r|CERN2022}}<ref name="Peik2021">{{cite journal |author1=Peik |first=E. |author2=Schumm |first2=T. |author3=Safronova |first3=M. S. |author4=Pálffy |first4=A. |author5=Weitenberg |first5=J. |author6=Thirolf<!--Peter Thirolf--> |first6=P. G. |date=15 April 2021 |title=Nuclear clocks for testing fundamental physics |url=https://open.fau.de/handle/openfau/18321 |journal=Quantum Science and Technology |volume=6 |issue=3 |arxiv=2012.09304 |bibcode=2021QS&T....6c4002P |doi=10.1088/2058-9565/abe9c2 |quote=Due to the extremely small transition strength in <sup>235m</sup>U (radiative lifetime ∼ 10<sup>22</sup>&nbsp;s), only <sup>229m</sup>Th qualifies for a direct laser excitation and thus for the development of a nuclear clock. |doi-access=free |article-number=034002}}</ref> This leaves only <sup>229m</sup>Th with a realistic chance of direct nuclear laser excitation.

Further requirements for the development of a nuclear clock are that
* the lifetime of the nuclear excited state is relatively long, thereby leading to a resonance of narrow bandwidth (a high [[quality factor]]) and
* the ground-state nucleus is easily available and sufficiently long-lived to allow one to work with moderate quantities of the material.

Fortunately, with {{SimpleNuclide|Th|229|m|charge=+}} having a radiative half-life (time to decay to {{SimpleNuclide|Th|229|charge=+}}) of around {{val|e=3|u=seconds}},<ref name=Tiedau2024/><ref name=Tkalya>{{cite journal
| title = Radiative lifetime and energy of the low-energy isomeric level in <sup>229</sup>Th
| first1= Eugene V. |last1=Tkalya
| display-authors=etal
| journal = Phys. Rev. C
| volume = 92
| year = 2015
| issue = 5
| article-number = 054324
| doi = 10.1103/PhysRevC.92.054324
| arxiv=1509.09101 | bibcode=2015PhRvC..92e4324T
| s2cid = 118374372
}}</ref><ref>{{cite journal |author1=Minkov |first=N. |author2=Pálffy |first2=A. |year=2017 |title=Reduced transition probabilities for the gamma decay of the 7.8 eV isomer in <sup>229m</sup>Th |journal=Physical Review Letters |volume=118 |issue=21 |arxiv=1704.07919 |bibcode=2017PhRvL.118u2501M |doi=10.1103/PhysRevLett.118.212501 |pmid=28598657 |s2cid=40694257 |article-number=212501}}</ref> and {{SimpleNuclide|Th|229}} having a half-life (time to decay to {{SimpleNuclide|Ra|225}}) of {{val|7917|48|u=years}},<ref>{{cite journal |author1=Varga |first=Z. |author2=Nicholl |first2=A. |author3=Mayer |first3=K. |year=2014 |title=Determination of the <sup>229</sup>Th half-life |journal=[[Phys. Rev. C]] |volume=89 |doi=10.1103/PhysRevC.89.064310 |doi-access=free |article-number=064310}}</ref> both conditions are fulfilled for {{SimpleNuclide|Th|229|m|charge=+}}, making it an ideal candidate for the development of a nuclear clock.

== History ==

=== History of nuclear clocks ===
{{^|This section contains relevant developments OTHER than measurement of the Th-229m transition (e.g. energy and half-life) itself.  It includes non-nuclear work on Th-229 atoms, such as laser trapping of ions.}}
As early as 1996 it was proposed by Eugene V. Tkalya to use the nuclear excitation as a "highly stable source of light for metrology".<ref>{{cite journal
| first1=Eugene V. |last1=Tkalya
| display-authors=etal
| title = Processes of the nuclear isomer <sup>229m</sup>Th(3/2<sup>+</sup>, 3.5±1.0 eV) Resonant excitation by optical photons
| journal = Physica Scripta
| volume = 53 | issue = 3
| pages = 296–299
| date = March 1996
|doi=10.1088/0031-8949/53/3/003
|bibcode=1996PhyS...53..296T
| s2cid=250744766
}}</ref>

With the development (around 2000) of the [[frequency comb]] for measuring optical frequencies exactly, a nuclear optical clock based on {{SimpleNuclide|Th|229|m}} was first proposed in 2003 by Ekkehard Peik and Christian Tamm, who developed an idea of Uwe Sterr.<ref name="Peik2003"/> The paper contains both concepts, the single-ion nuclear clock, as well as the solid-state nuclear clock.

In their pioneering work, Peik and Tamm proposed to use individual laser-cooled {{SimpleNuclide|Th|229|charge=3+}} ions in a Paul trap to perform nuclear laser spectroscopy.<ref name="Peik2003"/> Here the 3+ charge state is advantageous, as it possesses a shell structure suitable for direct laser cooling. It was further proposed to excite an electronic shell state, to achieve 'good' quantum numbers of the total system of the shell plus nucleus that will lead to a reduction of the influence induced by external perturbing fields. A central idea is to probe the successful laser excitation of the nuclear state via the hyperfine-structure shift induced into the electronic shell due to the different nuclear spins of ground- and excited state. This method is known as the ''double-resonance method''.

The expected performance of a single-ion nuclear clock was further investigated in 2012 by Corey Campbell et al. with the result that a systematic frequency uncertainty (accuracy) of the clock of {{val|1.5|e=-19}} could be achieved, which would be by about an order of magnitude better than the accuracy achieved by the best optical atomic clocks today.<ref name="Campbell2012"/> The nuclear clock approach proposed by Campbell et al. slightly differs from the original one proposed by Peik and Tamm. Instead of exciting an electronic shell state in order to obtain the highest insensitivity against external perturbing fields, the nuclear clock proposed by Campbell et al. uses a stretched pair of nuclear hyperfine states in the electronic ground-state configuration, which appears to be advantageous in terms of the achievable quality factor and an improved suppression of the quadratic Zeeman shift.

In 2010, Eugene V. Tkalya showed that it was theoretically possible to use {{SimpleNuclide|Th|229|m}} as a lasing medium to generate an ultraviolet laser.<ref>{{cite journal
 |first=Eugene V. |last=Tkayla
 |title=Proposal for a nuclear gamma-ray laser of optical range
 |journal=[[Physical Review Letters]]
 |volume=106 |issue=16 |article-number=162501
 |date=3 November 2010
 |arxiv=1011.0858
 |doi=10.1103/PhysRevLett.106.162501
 |pmid=21599361
 |quote=A possibility of the amplification of the 7.6&nbsp;eV γ-radiation by the stimulated γ-emission of the ensemble of the <sup>229m</sup>Th isomeric nuclei in a host dielectric crystal is proved theoretically.
}}</ref><ref>{{cite news
 |title=Proposed gamma-ray laser could emit 'nuclear light'
 |first=Lisa |last=Zyga
 |website=Phys.org
 |date=May 2, 2011
 |url=https://phys.org/news/2011-05-gamma-ray-laser-emit-nuclear.html
}}</ref><ref>{{cite news
 |title=Laser from Atomic Nuclei
 |first=David |last=Harris
 |date=April 22, 2011
 |journal=Physical Review Focus |volume=27 |article-number=16
 |quote=A laser that emits visible light using atomic nuclei, rather than electrons, could be made from a thorium alloy. It could be a first step toward a gamma-ray laser.
 |url=https://physics.aps.org/story/v27/st16
}}</ref>

The solid-state nuclear clock approach was further developed in 2010 by W.G. Rellergert et al.<ref name="Rellergert2010"/> with the result of an expected long-term accuracy of about {{val|2|e=-16}}. Although expected to be less accurate than the single-ion nuclear clock approach due to line-broadening effects and temperature shifts in the crystal lattice environment, this approach may have advantages in terms of compactness, robustness and power consumption. The expected stability performance was investigated by G. Kazakov et al. in 2012.<ref name="Kazakov2012"/> In 2020, the development of an internal conversion nuclear clock was proposed.<ref name="Wense2020"/>

Important steps on the road towards a nuclear clock include the successful direct laser cooling of {{SimpleNuclide|Th|229|charge=3+}} ions in a Paul trap achieved in 2011,<ref name="Campbell2011">{{cite journal |author1=Campbell |first=C. J. |author2=Radnaev |first2=A. G. |author3=Kuzmich |first3=A. |date=2 June 2011 |title=Wigner crystals of <sup>229</sup>Th for optical excitation of the nuclear isomer |url=https://link.aps.org/accepted/10.1103/PhysRevLett.106.223001 |journal=[[Physical Review Letters]] |volume=106 |issue=22 |arxiv=1110.2339 |doi=10.1103/PhysRevLett.106.223001 |pmid=21702597 |s2cid=20801170 |article-number=223001}}</ref> and a first detection of the isomer-induced hyperfine-structure shift, enabling the double-resonance method to probe a successful nuclear excitation in 2018.<ref name="Thielking2018">{{cite journal
| first1 = Johannes | last1 = Thielking
| display-authors=etal
| title = Laser spectroscopic characterization of the nuclear-clock isomer <sup>229m</sup>Th
| journal = [[Nature (journal)|Nature]]
| volume = 556
| issue=7701 | year = 2018
| pages = 321–325
| doi = 10.1038/s41586-018-0011-8
| pmid=29670266 | arxiv=1709.05325
| bibcode=2018Natur.556..321T | s2cid=4990345
}}</ref>

=== History of <sup>229m</sup>Th ===
{{main|Isotopes of thorium#Thorium-229m}}

Since 1976, the <sup>229</sup>Th nucleus has been known to possess a low energy excited state,<ref>{{cite journal |author1=Kroger |first=L. A. |author2=Reich |first2=C. W. |date=1976 |title=Features of the low energy level scheme of <sup>229</sup>Th as observed in the α decay of <sup>233</sup>U |journal=[[Nucl. Phys. A]] |volume=259 |issue=1 |pages=29–60 |bibcode=1976NuPhA.259...29K |doi=10.1016/0375-9474(76)90494-2}}</ref> whose excitation energy was originally shown to less than 100 eV,<ref name="SlowMotion" /> and then shown to be less than {{val|10|u=eV}} in 1990.<ref name="Helmer1990">{{cite journal |author1=Reich |first=C. W. |author2=Helmer |first2=R. G. |date=15 January 1990 |title=Energy separation of the doublet of intrinsic states at the ground state of <sup>229</sup>Th |url=https://zenodo.org/record/1233878 |journal=[[Phys. Rev. Lett.]] |publisher=American Physical Society |volume=64 |issue=3 |pages=271–273 |bibcode=1990PhRvL..64..271R |doi=10.1103/PhysRevLett.64.271 |pmid=10041937 |quote=It has been known for some time that the intrinsic state labeled by the asymptotic quantum numbers {{sfrac|3|2}}<sup>+</sup>[631] lies quite close (< 0.1&nbsp;keV) to the {{sfrac|5|2}}<sup>+</sup>[633] ground state of <sup>229</sup>Th. Using the energies of selected γ rays emitted following the α decay of <sup>233</sup>U, we have obtained a value of {{val|1|4|u=eV}} for the energy separation of these two intrinsic states.}}
</ref>

This was, however, too broad an energy range to apply high-resolution [[spectroscopy]] techniques; the transition energy had to be narrowed down first. Initial efforts used the fact that, after the alpha decay of {{SimpleNuclide|U|233}}, the resultant {{SimpleNuclide|Th|229}} nucleus is in an excited state and promptly emits a gamma ray to decay to either the base state or the metastable state. Measuring the small difference in the gamma-ray energies emitted in these processes allows the metastable state energy to be found by subtraction.{{r|Helmer1990|WenseReview|p2=§5.1|WenseThesis|p3=§2.3}} However, nuclear experiments are not capable of finely measuring the difference in frequency between two high gamma-ray energies, so other experiments were needed.<ref name="SlowMotion" /> Because of the natural radioactive decay of <sup>229</sup>Th nuclei, a tightly concentrated laser frequency was required to excite enough nuclei in an experiment to outcompete the background radiation and give a more accurate measurement of the excitation energy.<ref name="SlowMotion" /> Because it was infeasible to scan the entire 100eV range, an estimate of the correct frequency was needed.<ref name="SlowMotion" />

An early mis-step was the (incorrect) measurement of the energy value as 3.5±1.0 eV in 1994.<ref name="Helmer1994">{{cite journal |author1=Helmer |first=R. G. |author2=Reich |first2=C. W. |date=1994 |title=An Excited State of <sup>229</sup>Th at 3.5&nbsp;eV |url=https://zenodo.org/record/1233767 |journal=[[Phys. Rev. C]] |volume=49 |issue=4 |pages=1845–1858 |bibcode=1994PhRvC..49.1845H |doi=10.1103/PhysRevC.49.1845 |pmid=9969412}}</ref> This frequency of light is relatively easy to work with, so many direct detection experiments were attempted which had no hope of success because they were built of materials opaque to photons at the true, higher, energy.{{r|WenseReview|SlowMotion}} In particular:
* [[thorium oxide]] is transparent to 3.5&nbsp;eV photons, but opaque at 8.3&nbsp;eV,
* common optical lens and window materials such as [[fused quartz]] are opaque at energies above 8&nbsp;eV,<ref>{{cite tech report|title=Fused Quartz and Fused Silica for Optical Applications: Data and Properties|publisher=[[Heraeus]]|type=Catalogue|page=6|date=February 2023|url=https://www.heraeus-conamic.com/media/Media/Documents/Products_and_Solutions/OPT/EN/Data_and_Properties_Optics_fused_silica_EN.pdf#page=4}} 8&nbsp;eV corresponds to 155&nbsp;nm wavelength, where even the highest-purity fused silica becomes opaque.</ref>
* molecular oxygen (air) is opaque to photons above {{val|6.2|u=eV}}; experiments must be conducted in a [[nitrogen]] or [[argon]] atmosphere, and
* the ionization energy of thorium is {{val|6.3|u=eV}} so the nuclei will decay by internal conversion unless prevented (see {{alink|Ionization}}).

The energy value remained elusive until 2003, when the nuclear clock proposal triggered a multitude of experimental efforts to pin down the excited state's parameters like energy and half-life. The detection of light emitted in the direct decay of {{SimpleNuclide|Th|229|m}} would significantly help to determine its energy to higher precision, but all efforts to observe the light emitted in the decay of {{SimpleNuclide|Th|229|m}} were failing.<ref name="WenseReview"/> The energy level was corrected to {{val|7.6|0.5|u=eV}} in 2007<ref name="Beck" /> (slightly revised to {{val|7.8|0.5|u=eV}} in 2009<ref name="BeckReview" />). Subsequent experiments continued to fail to observe any signal of light emitted in the direct decay, leading people to suspect the existence of a strong non-radiative decay channel.<ref>{{Cite journal
|first1=Justin |last1=Jeet
|display-authors=etal
|date=23 June 2015
|title=Results of a Direct Search Using Synchrotron Radiation for the Low-Energy <sup>229</sup>Th Nuclear Isomeric Transition
|journal=[[Physical Review Letters]] |volume=114 |issue=25
|article-number=253001
|doi=10.1103/physrevlett.114.253001 |doi-access=free
|pmid=26197124 |arxiv=1502.02189
|bibcode=2015PhRvL.114y3001J |s2cid=1322253
}}</ref><ref>{{Cite journal |author1=Yamaguchi |first=A. |display-authors=etal |date=28 May 2015 |title=Experimental search for the low-energy nuclear transition in <sup>229</sup>Th with undulator radiation |url=http://stacks.iop.org/1367-2630/17/i=5/a=053053 |journal=New Journal of Physics |volume=17 |issue=5 |bibcode=2015NJPh...17e3053Y |doi=10.1088/1367-2630/17/5/053053 |issn=1367-2630 |doi-access=free |article-number=053053}}</ref><ref name=WenseThesis>{{cite thesis
| first = Lars | last = von der Wense
| degree = PhD
| title = On the direct detection of <sup>229m</sup>Th
| publisher = [[Ludwig Maximilian University of Munich]]
| date = 2016
| isbn=978-3-319-70461-6
| url = https://edoc.ub.uni-muenchen.de/20492/7/Wense_Lars_von_der.pdf
}}</ref><ref>{{cite journal
| title=Attempt to optically excite the nuclear isomer in <sup>229</sup>Th
| first1=Simon |last1=Stellmer  |first2=Georgy |last2=Kazakov |first3=Matthias |last3=Schreitl
|first4=Hendrik |last4=Kaser  |first5=Michael |last5=Kolbe  |first6=Thorsten |last6=Schumm
| journal=[[Phys. Rev. A]] |volume=97 | issue=6 |article-number = 062506 |date=18 June 2018
| doi= 10.1103/PhysRevA.97.062506
| arxiv=1803.09294 | bibcode=2018PhRvA..97f2506S | s2cid = 4946329
}}</ref> The detection of light emitted by the decay of <sup>229m</sup>Th was reported in 2012,<ref name="Zhao2012">{{cite journal |author1=Zhao |first=X. |display-authors=etal |year=2012 |title=Observation of the Deexcitation of the <sup>229m</sup>Th Nuclear Isomer |journal=[[Physical Review Letters]] |volume=109 |issue=16 |bibcode=2012PhRvL.109p0801Z |doi=10.1103/PhysRevLett.109.160801 |issn=0031-9007 |pmid=23215066 |doi-access=free |article-number=160801}}</ref> and again in 2018,<ref>{{Cite arXiv |eprint=1804.00299 |class=nucl-th |first=P. V. |last=Borisyuk |title=Excitation of <sup>229</sup>Th nuclei in laser plasma: the energy and half-life of the low-lying isomeric state |date=2018 |display-authors=etal}}</ref> but the observed signals were the subject of controversy within the community.<ref>{{Cite journal |author1=Peik |first=E. |author2=Zimmermann |first2=K. |date=2013 |title=Comment on "Observation of the Deexcitation of the <sup>229m</sup>Th Nuclear Isomer" |journal=[[Physical Review Letters]] |volume=111 |issue=1 |bibcode=2013PhRvL.111a8901P |doi=10.1103/PhysRevLett.111.018901 |pmid=23863029 |article-number=018901}}</ref>

A direct detection of electrons emitted by the isomer's internal conversion decay channel was achieved in 2016.<ref name=Wense2016>
{{cite journal
| journal=[[Nature (journal)|Nature]]
| volume=533 | issue=7601 | pages=47–51
| date=5 May 2016
| title = Direct detection of the <sup>229</sup>Th nuclear clock transition
| first1 = Lars | last1 = von der Wense
| display-authors=etal
| doi=10.1038/nature17669
| pmid=27147026 | arxiv=1710.11398 | bibcode=2016Natur.533...47V | s2cid=205248786
}}</ref> This detection laid the foundation for the determination of the <sup>229m</sup>Th half-life in neutral, surface-bound atoms in 2017<ref name="Seiferle2017">{{cite journal |last1=Seiferle |first1=Benedict |last2=von der Wense |first2=Lars |last3=Thirolf |first3=Peter G. |date=26 January 2017 |title=Lifetime measurement of the <sup>229</sup>Th nuclear isomer |journal=[[Physical Review Letters]] |volume=118 |issue=4 |arxiv=1801.05205 |bibcode=2017PhRvL.118d2501S |doi=10.1103/PhysRevLett.118.042501 |pmid=28186791 |s2cid=37518294 |article-number=042501}}</ref> and a first laser-spectroscopic characterization in 2018.<ref name="Thielking2018"/>

In 2019, the isomer's energy was measured via the detection of internal conversion electrons emitted in its direct ground-state decay to {{val|8.28|0.17|u=eV}}.<ref name="SeiferleEnergy"/> Also a first successful excitation of the {{val|29|u=keV}} nuclear excited state of {{SimpleNuclide|Th|229}} via synchrotron radiation was reported,<ref name="Masuda2019">{{cite journal
| title = X-ray pumping of the <sup>229</sup>Th nuclear clock isomer
| journal=[[Nature (journal)|Nature]]
| volume=573 | issue=7773 | pages=238–242
| date=2019
| last1=Masuda |first1=Takahiko  |last2=Yoshimi |first2=Akihiro |last3=Fujieda |first3=Akira
| last4=Fujimoto |first4=Hiroyuki  |last5=Haba |first5=Hiromitsu  |last6=Hara |first6=Hideaki
| last7=Hiraki |first7=Takahiro  |last8=Kaino |first8=Hiroyuki  |last9=Kasamatsu |first9=Yoshitaka
| last10=Kitao |first10=Shinji  |last11=Konashi |first11=Kenji  |last12=Miyamoto |first12=Yuki
| last13=Okai |first13=Koichi |last14=Okubo |first14=Sho |last15=Sasao |first15=Noboru
| display-authors=6
| doi=10.1038/s41586-019-1542-3 | arxiv=1902.04823 | pmid=31511686
| bibcode=2019Natur.573..238M | s2cid=119083861
}}</ref> enabling a clock transition energy measurement of {{val|8.30|0.92|u=eV}}.<ref name=YamaguchiEnergy/> In 2020, an energy of {{val|8.10|0.17|u=eV}} was obtained from precision gamma-ray spectroscopy.<ref name="SikorskyEnergy"/>

Finally, precise measurements were achieved in 2023 by unambiguous detection of the emitted photons ({{val|8.338|(24)|u=eV}})<ref>{{cite news
| title=Measurements of a key radioactive decay nudge a nuclear clock closer to reality
| first=Emily |last=Conover  |author-link=Emily Conover
| date=June 1, 2023
| journal=[[ScienceNews]]
| url=https://www.sciencenews.org/article/radioactive-decay-nuclear-clock-reality
}}</ref><ref>{{cite journal
| first1=Sandro |last1=Kraemer |display-authors=etal
| title=Observation of the radiative decay of the <sup>229</sup>Th nuclear clock isomer
| journal=[[Nature (journal)|Nature]] |volume=617 |date=May 25, 2023 |issue=7962 |pages=706–710 | doi=10.1038/s41586-023-05894-z
|pmid=37225880 | arxiv=2209.10276
| bibcode=2023Natur.617..706K
| quote=photons of {{val|8.338|(24)|u=eV}} are measured, in agreement with recent measurements and the uncertainty is decreased by a factor of seven. The half-life of <sup>229m</sup>Th embedded in MgF<sub>2</sub> is determined to be {{val|670|(102)|u=s}}
}}</ref> and in April 2024 by two reports of excitation with a tunable laser at {{val|8.355733|(10)|u=eV}}<ref>{{cite journal
 |title=Laser excitation of the <sup>229</sup>Th nuclear isomeric transition in a solid-state host
 |first1=R. |last1=Elwell  |first2=Christian |last2=Schneider  |first3=Justin |last3=Jeet
 |first4=J. E. S. |last4=Terhune  |first5=H. W. T. |last5=Morgan  |first6=A. N. |last6=Alexandrova
 |first7=Hoang Bao |last7=Tran Tan  |first8=Andrei |last8=Derevianko  |first9=Eric R. |last9=Hudson
 |journal=[[Physical Review Letters]] |date=2 July 2024
 |volume=133 |issue=1 |article-number=013201
 |doi=10.1103/PhysRevLett.133.013201
 |pmid=39042795 |arxiv=2404.12311
 |quote=a narrow, laser-linewidth-limited spectral feature at {{val|148.38219|(4)|errend=<sub>stat</sub>(20)<sub>sys</sub>|u=nm}} ({{val|2020407.3|(5)|errend=<sub>stat</sub>(30)<sub>sys</sub>|u=GHz}}) that decays with a lifetime of {{val|568|(13)|errend=<sub>stat</sub>(20)<sub>sys</sub>|u=s}}. This feature is assigned to the excitation of the <sup>229</sup>Th nuclear isomeric state, whose energy is found to be {{val|8.355733|(2)|errend=<sub>stat</sub>(10)<sub>sys</sub>|u=eV}} in <sup>229</sup>Th:LiSrAlF<sub>6</sub>.
}}</ref> and {{val|8.35574|(3)|ul=eV}}.{{r|Thirolf2024|Tiedau2024}}<ref>{{Cite web
| last=Klapetz | first=Patrick
| date=2024-04-29
| title=Thorium-229: Erstmals Atomkern mit Laser angeregt
| trans-title=Thorium-229: First atomic nucleus excited by laser
| url=https://www.golem.de/news/thorium-299-erstmals-atomkern-mit-laser-angeregt-2404-184657.html
| access-date=2024-04-30
| website=Golem.de: IT-News für Profis
| language=de
| archive-url=https://web.archive.org/web/20240430163220/https://www.golem.de/news/thorium-299-erstmals-atomkern-mit-laser-angeregt-2404-184657.html
| archive-date=2024-04-30
}}</ref><ref>{{cite press release
 |title=We did it !
 |date=29 April 2024
 |publisher=Thoriumclock.eu project
 |url=https://thoriumclock.eu/publication/we-did-it/
 |quote=We are overly excited to announce: Our teams from TU Wien and PTB Braunschweig successfully managed the laser excitation of the Th-229 Nucleus. 
}}</ref> The light frequency is now known with sufficient accuracy to enable future construction of a prototype clock,<ref name=Thirolf2019>{{cite journal
 |title='Phase Transition' in the 'Thorium-Isomer Story'
 |first=Peter G. |last=Thirolf  |display-authors=etal
 |journal=Acta Physica Polonica B
 |volume=51 |issue=3 |pages=561–570
 |date=March 2020
 |url=https://www.actaphys.uj.edu.pl/R/51/3/561/pdf
 |doi=10.5506/APhysPolB.51.561 |doi-access=free
 |arxiv=2108.13388
|bibcode=2020AcPPB..51..561T }} Originally presented as ''[https://mazurian.fuw.edu.pl/wp-content/uploads/2019/09/2019Program.pdf Characterization of the elusive <sup>229m</sup>Th isomer – milestones towards a nuclear clock]''.</ref><ref>{{cite journal
 |title=Best ever clocks: breakthrough paves way for ultra-precise 'nuclear' timekeepers
 |first=Elizabeth |last=Gibney |author-link=Elizabeth Gibney
 |date=8 May 2024
 |journal=[[Nature (journal)|Nature]]
 |volume=629 |issue=8012 |pages=514–515 |doi=10.1038/d41586-024-01353-5 |doi-access=free
 |pmid=38719967 |bibcode=2024Natur.629..514G |quote=To turn the system into an actual clock, physicists will need to markedly reduce the resolution of the laser, so that it stimulates the nucleus at almost exactly the right frequency to be read off reliably, says Peik. Building such a laser 'remains a big challenge, but there are little doubts that it will be achievable in the near future', adds Kocharovskaya.
}}</ref><ref name=Conover2024-04>{{cite news
 |title=Physicists take a major step toward making a nuclear clock
 |first=Emily|last=Conover |author-link=Emily Conover
 |date=4 April 2024
 |journal=[[ScienceNews]]
 |url=https://www.sciencenews.org/article/nuclear-clock-thorium-physics
 |quote=There's still much more work to be done to build a nuclear clock. And even once scientists have built them, [[Jun Ye|Ye]] says, 'it will take years, if not decades, of work to catch up with atomic clocks.' But 'just being able to see the transition opens the door.'
}}</ref> and determine the transition's exact frequency and its stability.

Precision frequency measurements began immediately, with [[Jun Ye]]'s laboratory at [[JILA]] making a direct comparison to a {{SimpleNuclide|Sr|87}} optical atomic clock. Published in September 2024, the frequency was measured as {{val|2020407384335|2|u=kHz}},<ref name=Zhang2024>{{cite journal
 |title=Frequency ratio of the <sup>229m</sup>Th nuclear isomeric transition and the <sup>87</sup>Sr atomic clock
 |first1=Chuankun |last1=Zhang  |first2=Tian |last2=Ooi  |first3=Jacob S. |last3=Higgins
 |first4=Jack F. |last4=Doyle  |first5=Lars |last5=von der Wense  |first6=Kjeld |last6=Beeks
 |first7=Adrian |last7=Leitner  |first8=Georgy |last8=Kazakov  |first9=Peng |last9=Li
 |first10=Peter G. |last10=Thirolf  |first11=Thorsten |last11=Schumm  |first12=Jun |last12=Ye |author-link12=Jun Ye
 |journal=[[Nature (journal)|Nature]] |volume=633 |issue=8028 |pages=63–70
 |date=4 September 2024
 |doi=10.1038/s41586-024-07839-6
 |pmid=39232152 |arxiv=2406.18719
 |quote=The transition frequency between the {{math|1=''I'' = 5/2}} ground state and the {{math|1=''I'' = 3/2}} excited state is determined as: {{math|1=
''𝜈''<sub>Th</sub> =}} {{math|1={{sfrac|1|6}} (''𝜈''<sub>a</sub> + 2''𝜈''<sub>b</sub> + 2''𝜈''<sub>c</sub> + ''𝜈''<sub>d</sub>) =}} {{math|{{val|2020407384335|(2)|u=kHz}}}}.
}}</ref><ref>{{cite news
 |title=A nuclear clock prototype hints at ultraprecise timekeeping
 |first=Emily |last=Conover |author-link=Emily Conover 
 |date=4 September 2024
 |journal=[[ScienceNews]]
 |url=https://www.sciencenews.org/article/nuclear-clock-ultraprecise-timekeeping
}}</ref><ref>{{cite press release
 |title=Major leap for nuclear clock paves way for ultraprecise timekeeping
 |date=4 September 2024
 |publisher=[[NIST]]
 |url=https://www.nist.gov/news-events/news/2024/09/major-leap-nuclear-clock-paves-way-ultraprecise-timekeeping
}}</ref><ref>{{cite press release
 |title=The first ultra precised nuclear clock is built!
 |date=4 September 2024
 |publisher=Thoriumclock.eu project
 |url=https://thoriumclock.eu/uncategorized/the-first-ultra-precised-nuclear-clock-is-built/
 |quote=While this laboratory demonstration is not a fully developed nuclear clock, it contains all the core technology for one.
}}</ref> a relative uncertainty of {{val|e=-12}}. This implies a wavelength of {{val|{{#expr:(299792458e6/2020407384335) round 10}}|(15)|u=nm}} and an energy of {{val|{{#expr:(2020407384335*6.62607015/1.602176634e12) round 12}}|(8)|u=eV}}. The work also resolved different nuclear quadrupole sublevels and measured the ratio of the ground and excited state nuclear quadrupole moment. Improvements will surely follow.{{r|Conover2024-04|Howlett2024}}

== Applications ==

When operational, a nuclear optical clock is expected to be applicable in various fields. In addition to the capabilities of today's atomic clocks, such as satellite-based navigation or data transfer, its high precision will allow new applications inaccessible to other atomic clocks, such as relativistic geodesy, the search for topological dark matter,<ref>{{cite journal |author1=Derevianko |first=A. |author2=Pospelov |first2=M. |date=December 2014 |title=Hunting for topological dark matter with atomic clocks |journal=Nature Physics |volume=10 |issue=12 |pages=933–936 |arxiv=1311.1244 |bibcode=2014NatPh..10..933D |doi=10.1038/nphys3137 |s2cid=53630878}}</ref> or the determination of time variations of fundamental constants.<ref>{{cite journal |author1=Thirolf |first=P. G. |author2=Seiferle |first2=B. |author3=von der Wense |first3=L. |year=2019 |title=Improving Our Knowledge on<!--sic--> the <sup>229m</sup>Thorium Isomer: Toward a Test Bench for Time Variations of Fundamental Constants |journal=Annalen der Physik |volume=531 |issue=5 |bibcode=2019AnP...53100381T |doi=10.1002/andp.201800381 |doi-access= |article-number=1800381}}</ref>

A nuclear clock has the potential to be particularly sensitive to possible time variations of the [[fine-structure constant]].<ref>{{cite journal |author1=Flambaum |first=V. V. |date=September 2006 |title=Enhanced Effect of Temporal Variation of the Fine Structure Constant and the Strong Interaction in <sup>229m</sup>Th |journal=[[Physical Review Letters]] |volume=97 |issue=9 |arxiv=physics/0601034 |doi=10.1103/PhysRevLett.97.092502 |pmid=17026357 |s2cid=4109230 |article-number=092502}}</ref> The central idea is that the low energy is due to a fortuitous cancellation between strong nuclear and electromagnetic effects within the nucleus which are individually much stronger. Any variation the fine-structure constant would affect the electromagnetic half of this balance, resulting in a proportionally very large change in the total transition energy.<ref name=CERN2022>{{Cite news
| journal=[[CERN Courier]]
| first1=Peter |last1=Thirolf  |first2=Benedict |last2=Seiferle  |first3=Lars |last3=von der Wense
| date=2022-09-05
| title=From atomic to nuclear clocks
| url=https://cerncourier.com/a/from-atomic-to-nuclear-clocks/
| access-date=2024-04-30
}}</ref><ref name=Howlett2024>{{cite news
| first=Joseph |last=Howlett
| title=The First Nuclear Clock Will Test if Fundamental Constants Change
| date=4 September 2024
| journal=Quanta Magazine
| url=https://www.quantamagazine.org/the-first-nuclear-clock-will-test-if-fundamental-constants-change-20240904/
}}</ref> A change of even one part in 10<sup>18</sup> could be detected by comparison with a conventional atomic clock (whose frequency would also be altered, but not nearly as much), so this measurement would be extraordinarily sensitive to any potential variation of the constant. Recent measurements and analysis are consistent with enhancement factors [[on the order of]] 10<sup>4</sup>.<ref name="Thielking2018"/><ref>{{cite journal
| title=Sensitivity of <sup>229</sup>Th nuclear clock transition to variation of the fine-structure constant
| first1=Pavel |last1=Fadeev  |first2=Julian C. |last2=Berengut  |first3=Victor V. |last3=Flambaum
| journal=Physical Review A |volume=102 |issue=5 |article-number=052833
| date=November 2020
| doi=10.1103/PhysRevA.102.052833 |bibcode=2020PhRvA.102e2833F |arxiv=2007.00408
| quote=The enhancement factor for ''α'' variation is ''K'' = −{{val|0.82|0.25|e=4}}. 
}}</ref><ref>{{cite arXiv
 |title=On the sensitivity of nuclear clocks to new physics
 |first1=Andrea |last1=Caputo  |first2=Doron |last2=Gazit  |first3=Hans-Werner |last3=Hammer
 |first4=Joachim |last4=Kopp  |first5=Gil |last5=Paz  |first6=Gilad |last6=Perez
 |first7=Konstantin |last7=Springmann
 |eprint=2407.17526 |class=hep-ph
 |date=22 July 2024
 |quote=We find that the nuclear clock's sensitivity to variations in the effective fine structure constant is enhanced by a factor of order 10<sup>4</sup>.
}}</ref><ref>{{cite arXiv
| title=Fine-structure constant sensitivity of the Th-229 nuclear clock transition
| first1=Kjeld |last1=Beeks  |first2=Georgy A. |last2=Kazakov
| first3=Fabian |last3=Schaden   |first4=Ira |last4=Morawetz
| first5=Luca Toscani |last5=de Col  |first6=Thomas |last6=Riebner
| first7=Michael |last7=Bartokos  |first8=Tomas |last8=Sikorsky
| first9=Thorsten |last9=Schumm  |first10=Chuankun |last10=Zhang
| first11=Tian |last11=Ooi  |first12=Jacob S. |last12=Higgins
| first13=Jack F. |last13=Doyle  |first14=Jun |last14=Ye |author-link14=Jun Ye
| first15=Marianna S. |last15=Safronova
| eprint=2407.17300 |class=nucl-th
| date=24 July 2024
| quote=this allows to quantify the sensitivity of ''α'' to ''K''={{val|5900|(2300)}}
}}</ref>

== References ==

{{Reflist|refs=
<ref name="Beck">{{cite journal
|title=Energy splitting in the ground state doublet in the nucleus <sup>229</sup>Th
| journal=[[Phys. Rev. Lett.]] | volume=98
| date=2007
| author1 = B.R. Beck
| issue=14 | article-number=142501 |display-authors=etal
| doi=10.1103/PhysRevLett.98.142501
| pmid=17501268 | bibcode=2007PhRvL..98n2501B
|url=https://zenodo.org/record/1233955
 }}</ref>
<ref name="BeckReview">{{cite conference
| title = Improved value for the energy splitting of the ground-state doublet in the nucleus <sup>229m</sup>Th
| date=15–19 June 2009
| author1 = B.R. Beck
|display-authors=etal
| conference = 12th Int. Conf. on Nuclear Reaction Mechanisms
| location = Varenna, Italy
| id = LLNL-PROC-415170
| url = https://cds.cern.ch/record/1237922/files/p255.pdf
| access-date = 2024-09-02
| archive-url = https://web.archive.org/web/20170127104504/https://e-reports-ext.llnl.gov/pdf/375773.pdf
| archive-date = 2017-01-27
| url-status = live
}}</ref>
<ref name="SeiferleEnergy">{{cite journal
| title = Energy of the <sup>229</sup>Th nuclear clock transition
| journal=[[Nature (journal)|Nature]]
| volume=573  | issue=7773 | pages=243–246
| date=2019
| author1 = B. Seiferle
|display-authors=etal
| doi=10.1038/s41586-019-1533-4
| arxiv=1905.06308 | pmid=31511684 | bibcode=2019Natur.573..243S
| s2cid=155090121
}}</ref>
<ref name="YamaguchiEnergy">{{cite journal
| title = Energy of the <sup>229</sup>Th nuclear clock isomer determined by absolute gamma-ray energy difference
| journal=Phys. Rev. Lett. | volume=123
| date=2019
| author1 = A. Yamaguchi
| issue=22 | article-number=222501 |display-authors=etal
| doi=10.1103/PhysRevLett.123.222501
| arxiv=1912.05395  | pmid=31868403 | bibcode=2019PhRvL.123v2501Y
| s2cid=209202193
}}</ref><ref name="SikorskyEnergy">{{cite journal
| title = Measurement of the <sup>229</sup>Th isomer energy with a magnetic micro-calorimeter
| journal=Phys. Rev. Lett. | volume=125
| date=2020
| author1 = T. Sikorsky
| issue=14 | article-number=142503 |display-authors=etal
| doi=10.1103/PhysRevLett.125.142503
| pmid=33064540 | arxiv=2005.13340
| bibcode=2020PhRvL.125n2503S | s2cid=218900580
}}</ref>
<ref name="WenseReview">{{cite journal
| title=The <sup>229</sup>Th isomer: prospects for a nuclear optical clock
| first1=Lars |last1=von der Wense  |first2=Benedict |last2=Seiferle
| journal=[[Eur. Phys. J. A]] |volume=56 |issue=11 |article-number=277
| date=2 November 2020
| doi=10.1140/epja/s10050-020-00263-0 |doi-access=free
<!--|pages=1-58-->
| arxiv=2009.13633
| bibcode=2020EPJA...56..277V
| s2cid=221995928
| url=https://link.springer.com/article/10.1140/epja/s10050-020-00263-0
}}</ref>
<ref name=Thirolf2024>{{cite journal
 |title=Shedding Light on the Thorium-229 Nuclear Clock Isomer
 |first=Peter |last=Thirolf
 |date=April 29, 2024
 |journal=[[Physics (magazine)|Physics]] |volume=17 |article-number=71
 |doi=10.1103/Physics.17.71 |doi-access=free
 |bibcode=2024PhyOJ..17...71T |url=https://physics.aps.org/articles/v17/71
}}</ref>
}}

== Further reading ==
* "[[doi:10.1140/epja/s10050-020-00263-0|The <sup>229</sup>Th isomer: prospects for a nuclear optical clock]]" (November 2020) [[European Physical Journal|European Physics Journal A]].<ref name="WenseReview"/>

==External links==
* [https://www.thoriumclock.eu EU thorium nuclear clock (nuClock) project]

[[Category:Nuclear physics]]
[[Category:Atomic clocks]]
[[Category:Thorium]]