Search for new physics with atoms and molecules

This article reviews recent developments in tests of fundamental physics using atoms and molecules, including the subjects of parity violation, searches for permanent electric dipole moments, tests of the $CPT$ theorem and Lorentz symmetry, searches for spatiotemporal variation of fundamental constants, tests of quantum electrodynamics, tests of general relativity and the equivalence principle, searches for dark matter, dark energy, and extra forces, and tests of the spin-statistics theorem. Key results are presented in the context of potential new physics and in the broader context of similar investigations in other fields. Ongoing and future experiments of the next decade are discussed.

Figure 1

Constraints on temporal variations of $\alpha$ and $\mu$ from comparisons of atomic transition frequencies. Filled stripes mark the 1 standard deviation $\sigma$ uncertainty regions of individual measurements and the central blank region is bounded by the standard uncertainty ellipse resulting from the combination of all data. From [511].

Figure 2

Schematic experimental arrangement for measuring the $E2$ and $E3$ clock frequencies of a single ${}^{171}{\mathrm{Yb}}^{+}$ ion. The $E3/E2$ frequency ratio was determined by stabilizing one laser to the $E3$ transition and the other laser to the $E2$ transition and measuring the ratio between the laser frequencies with an optical frequency comb. For experimental reasons, the researchers used infrared lasers that have to be frequency doubled to excite the $E2$ and $E3$ optical transitions. Adapted from [870].

Figure 3

Evolution of fractional frequency uncertainties of atomic frequency standards based on microwave (Cs clocks) and optical transitions. Data points are from [807], [753], and [513].

Figure 4

Earth orbiting the Sun (mass $m_{\odot }$) in gravitational potential; the orbit eccentricity is exaggerated. Image credit: Jun Ye’s group and Greg Kuebler.

Figure 5

Major diagrams contributing to the parity violation in atoms. $\mathcal{N}$ and $e^{-}$ label nucleons and atomic electrons. $A_{e,N}$ and $V_{e,N}$ denote axial-vector and vector currents. (a) $Z$-boson exchange between electron axial-vector and nucleon-vector currents ($A_n{V}_e$); (b) $Z$-boson exchange between nucleon axial-vector and electron-vector currents ($V_n{A}_e$); (c) electromagnetic interaction of atomic electrons with the nuclear anapole moment (shown as a blob); (d) combined effect of the (a) $A_n{V}_e$ and hyperfine interaction. The vertical line separates nuclear (a) spin-independent and (b)–(d) spin-dependent diagrams.

Figure 6

Running of the weak mixing angle with momentum transfer $Q$. The solid red curve is the SM prediction. The Cs APV result is supplemented with data from particle physics experiments: $E158$, Møller (electron-electron) scattering; $Q$-weak, PNC electron-proton scattering, $\nu$-DIS, deep inelastic scattering; LEP, and SLAC results. The area colored in yellow comes from one of the “new physics” scenarios ([265]): a dark boson of mass 50 MeV. The colored area is limited by constraints on model parameters that would explain the discrepancy ([114]) between the muon’s experimental anomalous magnetic moment and the SM prediction. Adapted from [265].

Figure 7

The toroidal component of current density $\mathit{j}$ produces anapole moment $\mathit{a}$, with magnetic field $\mathcal{B}$ that is entirely confined inside the “doughnut.” The azimuthal component of current density generates the magnetic dipole moment aligned with $\mathit{a}$ with its associated conventional dipolar magnetic field not shown.

Figure 8

Constraints on combinations of parity-violating meson couplings ($\times {10}^7$) derived from the Cs anapole moment (yellow band) and nuclear experiments. Bands have a width of 1 standard deviation. The best value predicted by the DDH analysis is also shown. This figure combines the Cs NAM band from [472] with more recent nuclear physics constraints. From [473].

Figure 9

Basic concept of EDM measurements. When a particle has an EDM $\mathbf{d}$ along its spin axis $\mathbf{s}$, an electric field $\mathcal{E}$ causes $\mathbf{s}$ to precess about $\mathcal{E}$.

Figure 10

Schematic of the ACME eEDM experiment. The figure shows only the magnetically shielded region where spin precession takes place. From [97].

Figure 11

Schematic of the ${}^{199}\mathrm{Hg}$ EDM experiment. Purple arrows show probe laser beams, polarization analyzed by the combination of Wollaston prisms and photodiodes. (a) Section through the $y\text{−}z$ plane of the vessel containing all four vapor cells, showing probe beams through the outer cells (where $\mathcal{E}=0$). (b) Section through the $x\text{−}y$ plane showing probe beams through the inner cells. From [439].

Figure 12

Example Feynman diagrams leading to particle EDMs. Crosses represent CPV phases and tildes indicate SUSY partners of SM fields. (a) One-loop diagram leading to an eEDM in a SUSY model. The vertical photon represents the coupling of the EDM to an electric field. The CPV phase arises from the mechanism that leads to breaking of SUSY at low energies. (b) Two-loop diagram leading to an up quark cEDM in a multi-Higgs doublet model. $H_{i,j}$ represent different Higgs fields, and the CPV phase arises from mixing between them. The dominant diagram includes $t$ quarks since their large mass indicates a strong coupling to the Higgs field. (c) Dominant two-loop diagrams leading to an eEDM in SUSY models where partners of fermions are heavy. Here ${\omega }^{\pm }$ are SUSY partners of $W^{\pm }$ bosons.

Figure 13

Laboratory constraints [shaded light blue (gray), see text for discussion of individual experiments] on monopole-dipole (scalar-pseudoscalar) couplings, $|{\mathrm{g}}_p{\mathrm{g}}_s|/\hslash c$ [the ${\mathcal{V}}_{9+10}$ potentials as described in Eq. (63)], for neutrons, protons, and electrons as a function of the range $\lambda$ of the interaction (${\mathrm{g}}_p$ and ${\mathrm{g}}_s$ are the pseudoscalar and scalar coupling constants, respectively). Astrophysical constraints are from the analysis of [830] [excluded parameter space outlined with the solid double green (gray) line, dashed green (gray) shading].

Figure 14

Experimental setup. $\mathrm{LP}=\text{linear polarizer}$, $\lambda /4=\text{quarter-wave plate}$, $\mathrm{I}=\text{iris}$, $\mathrm{PMT}=\text{photomultiplier tube}$, and $\mathrm{PEM}=\text{photoelastic}$ modulator. Arrows on the right-hand side indicate computer control and data acquisition. The angles ${\varphi }_{\pm }$ indicate the projection of $\widehat{\mathbf{r}}$ (parallel to $\mathit{g}$) along $\widehat{\mathbf{z}}$ (parallel to $\mathcal{B}$) for the two magnetic field orientations. From [1017].

Figure 15

The left panel shows the 20-pole spin-polarized torsion pendulum and the right panel shows the unpolarized and polarized sources (upper and lower figures, respectively) used to search for monopole-dipole and dipole-dipole interactions in the experiment of [972]. The $\mu$-metal shielding surrounding the spin-polarized pendulum and the sources is cut away to show the alternating alnico (green) and ${\mathrm{SmCo}}_5$ (blue) segments and one of the four pairs of calibration cylinders (red). The mirror cube (in the middle of the pendulum’s support structure) is used to monitor the pendulum twist angle. The entire apparatus is contained within a system of magnetic shields. The arrows on the spin attractor indicate net spin density and direction of the alternating segments. From [972]

Figure 16

Laboratory constraints [shaded light blue (gray), see text for discussion of individual experiments] on pseudoscalar dipole-dipole couplings $|{\mathrm{g}}_{\mathrm{p}}{\mathrm{g}}_{\mathrm{p}}|/(4\pi \hslash c)$ [the ${\mathcal{V}}_3$ potential as described in Eq. (62)], between nucleons and electrons as a function of the range $\lambda$ of the interaction. The short- and long-dashed red (dark gray) lines in the upper plot show constraints derived from spin-independent measurements that apply only to the Yukawa form of the pseudoscalar interaction [Eq. (67)]. The dotted red (dark gray) line in the lower plot shows constraints based on positronium spectroscopy which in order to be compared with electron-electron constraints must assume $CPT$ invariance.

Figure 17

Experimental setup. $\mathrm{PD}=\text{photodiode}$, $\mathrm{SP}=\text{stress}$ plate to control polarization of the probe beam, $\mathrm{T}=\text{translation}\text{stage to shift the probe beam}$, $\mathrm{P}=\text{polarizer}$, $\mathrm{PMF}=\text{polarization}\text{maintaining fiber}$, $\mathrm{OA}=\text{optical amplifier}$, $\mathrm{LCW}=\text{liquid crystal}\text{wave plate}$, $\mathrm{PEM}=\text{photoelastic}$ modulator, $\lambda /4=\text{quarter-wave}\text{plate}$, and $\mathrm{LDA}=\text{laser diode array}$. From [1014].

Figure 18

Laboratory constraints [shaded light blue (gray), see text for discussion of individual experiments] on axial-vector dipole-dipole couplings $|{\mathrm{g}}_{\mathrm{A}}{\mathrm{g}}_{\mathrm{A}}|/(4\pi \hslash c)$ [the ${\mathcal{V}}_2$ potential as described in Eq. (64)], for various particles as a function of the range $\lambda$ of the interaction.

Figure 19

Schematic diagram of the ADMX experiment. Photons produced in the microwave cavity by the interaction of an axion field $a(\mathbf{r},t)$ with the magnetic field $\mathcal{B}$ [Eq. (86)] are detected by the electric field probes. Tuning rods enable the resonant frequency of the cavity to be scanned to search for axions of different masses. (Fields from the rf signal source can be sent through the setup for calibration purposes.) The signals are recorded after multiple amplification stages and heterodyning. The 2001 experiment employed cryogenic heterojunction field-effect transistors built by the National Radio Astronomy Observatory (NRAO), while new versions of ADMX employ SQUID amplifiers ([81]). From [80].

Figure 20

Experimental concept of CASPEr. The oscillating axion field $a(\mathbf{r},t)$ acts as a pseudomagnetic field ${\mathcal{B}}_1^{*}$, either by inducing an oscillating EDM via the axion-gluon interaction that couples to an electric field (CASPEr electric), or via the interaction of spins with the gradient of $a(\mathbf{r},t)$ arising from the motion of the sample through the axion field (CASPEr wind). The oscillating ${\mathcal{B}}_1^{*}$ causes polarized nuclear spins to tip away from the leading field ${\mathcal{B}}_0$ and precess at the Larmor frequency. The approach is based on the principles of NMR experiments. From [177].

Figure 21

Spatially separated and initially synchronized identical clocks are expected to exhibit a distinct desynchronization and resynchronization pattern due to an encounter with a DM object. Two clocks are separated by a distance $\ell$, and because the wall propagates through the network with a speed $v_g\approx 300\mathrm{km}/\mathrm{s}$, the characteristic “hump” persists over time $\ell /v_g$. Adapted from [280].

Figure 22

Schematic of an axion and ALP domain-wall crossing event as searched for by the GNOME. The crossings recorded in four distinct locations (marked with stars) allow determination of the normal velocity $v_{\perp }$ to the wall and prediction of the timing of the fifth event. From [813].

Figure 23

Rotation of the quantization axis of the experiment with respect to the Sun as the Earth rotates. A magnetic field ($B$) is applied vertically in the laboratory frame to define the eigenstates of the system. As the Earth rotates with an angular frequency given by ${\omega }_{\oplus }=2\pi /(23.93\mathrm{h})$, the orientation of the magnetic field and, consequently, that of the electron wave packet (as shown in the inset in terms of probability envelopes) changes with respect to the Sun’s rest frame. The angle $\chi$ is the colatitude of the experiment. From [823].

Figure 24

Change of $\mathrm{K}\text{−}{}^3\mathrm{He}$ self-compensating SERF comagnetometer signal for 180° platform rotation as a function of the initial platform angle. From [168].