Phase transitions in the early universe can give rise to microscopic topological defects: vacuum domain walls, strings, walls bounded by strings, and monopoles connected by strings. This article reviews the formation, physical properties and the cosmological evolution of various defects. A particular attention is paid to strings and their cosmological consequences, including the string scenario of galaxy formation and possible observational effects of strings.

Cosmic Strings and Domain Walls

We compare two optical clocks based on the ${^{2}S}_{1/2}(F=0)\ensuremath{\rightarrow}{^{2}D}_{3/2}(F=2)$ electric quadrupole (E2) and the ${^{2}S}_{1/2}(F=0)\ensuremath{\rightarrow}{^{2}F}_{7/2}(F=3)$ electric octupole (E3) transition of ${^{171}\mathrm{Yb}}^{+}$ and measure the frequency ratio ${\ensuremath{\nu}}_{\mathrm{E}3}/{\ensuremath{\nu}}_{\mathrm{E}2}=0.932829404530965376(32)$, improving upon previous measurements by an order of magnitude. Using two caesium fountain clocks, we find ${\ensuremath{\nu}}_{E3}=642121496772645.10(8)\text{ }\text{ }\mathrm{Hz}$, the most accurate determination of an optical transition frequency to date. Repeated measurements of both quantities over several years are analyzed for potential violations of local position invariance. We improve by factors of about 20 and 2 the limits for fractional temporal variations of the fine structure constant $\ensuremath{\alpha}$ to $1.0(1.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}/\mathrm{yr}$ and of the proton-to-electron mass ratio $\ensuremath{\mu}$ to $\ensuremath{-}8(36)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}/\mathrm{yr}$. Using the annual variation of the Sun's gravitational potential at Earth $\mathrm{\ensuremath{\Phi}}$, we improve limits for a potential coupling of both constants to gravity, $({c}^{2}/\ensuremath{\alpha})(d\ensuremath{\alpha}/d\mathrm{\ensuremath{\Phi}})=14(11)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ and $({c}^{2}/\ensuremath{\mu})(d\ensuremath{\mu}/d\mathrm{\ensuremath{\Phi}})=7(45)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$.

Improved Limits for Violations of Local Position Invariance from Atomic Clock Comparisons

Atom interferometers have been developed in the last three decades as new powerful tools to investigate gravity. They were used for measuring the gravity acceleration, the gravity gradient, and the gravity-field curvature, for the determination of the gravitational constant, for the investigation of gravity at microscopic distances, to test the equivalence principle of general relativity and the theories of modified gravity, to probe the interplay between gravitational and quantum physics and to test quantum gravity models, to search for dark matter and dark energy, and they were proposed as new detectors for the observation of gravitational waves. Here I describe past and ongoing experiments with an outlook on what I think are the main prospects in this field and the potential to search for new physics.

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Testing gravity with cold atom interferometry: Results and prospects.

The low-energy, long-lived isomer in 229Th, first studied in the 1970s as an exotic feature in nuclear physics, continues to inspire a multidisciplinary community of physicists. It has stimulated innovative ideas and studies that expand the understanding of atomic and nuclear structure of heavy elements and of the interaction of nuclei with bound electrons and coherent light. Using the nuclear resonance frequency, determined by the strong and electromagnetic interactions inside the nucleus, it is possible to build a highly precise nuclear clock that will be fundamentally different from all other atomic clocks based on resonant frequencies of the electron shell. The nuclear clock will open opportunities for highly sensitive tests of fundamental principles of physics, particularly in searches for violations of Einstein’s equivalence principle and for new particles and interactions beyond the standard model. It has been proposed to use the nuclear clock to search for variations of the electromagnetic and strong coupling constants and for dark matter searches. The 229Th nuclear optical clock still represents a major challenge in view of the tremendous gap of nearly 17 orders of magnitude between the present uncertainty in the nuclear transition frequency (about 0.2 eV, corresponding to ∼48 THz) and the natural linewidth (in the mHz range). Significant experimental progress has been achieved in recent years, which will be briefly reviewed. Moreover, a research strategy will be outlined to consolidate our present knowledge about essential 229mTh properties, to determine the nuclear transition frequency with laser spectroscopic precision, realize different types of nuclear clocks and apply them in precision frequency comparisons with optical atomic clocks to test fundamental physics. Two avenues will be discussed: laser-cooled trapped 229Th ions that allow experiments with complete control on the nucleus–electron interaction and minimal systematic frequency shifts, and Th-doped solids enabling experiments at high particle number and in different electronic environments.

Nuclear clocks for testing fundamental physics

Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers. Optical atomic clocks are useful tools for frequency metrology. Here the authors explore the stability of the atomic clocks and the role of the spin squeezed states for the noise reduction in these clocks.

/pdf/prospects-and-challenges-for-squeezing-enhanced-optical-1rquj01dg9.pdf

Prospects and challenges for squeezing-enhanced optical atomic clocks

We search for transient variations of the fine structure constant using data from a European network of fiber-linked optical atomic clocks. By searching for coherent variations in the recorded clock frequency comparisons across the network, we significantly improve the constraints on transient variations of the fine structure constant. For example, we constrain the variation to |δα/α| ~10^4 km) objects.

https://iopscience.iop.org/article/10.1088/1367-2630/abaace/pdf

Search for transient variations of the fine structure constant and dark matter using fiber-linked optical atomic clocks

We search for transient variations of the fine structure constant using data from a European network of fiber-linked optical atomic clocks. By searching for coherent variations in the recorded clock frequency comparisons across the network, we significantly improve the constraints on transient variations of the fine structure constant. For example, we constrain the variation in alpha to ~10^4 km) objects.

Guy Vallet

Papers

Search for transient variations of the fine structure constant and dark matter using fiber-linked optical atomic clocks

Search for transient variations of the fine structure constant and dark matter using fiber-linked optical atomic clocks