experimental constraint on dark matter detection with optical atomic clocks

The total mass density of the Universe appears to be dominated by dark matter. However, beyond its gravitational interactions at the galactic scale, little is known about its nature1. Several proposals have been advanced in recent years for the detection of dark matter2–4. In particular, a network of atomic clocks could be used to search for transient indicators of hypothetical dark matter5 in the form of stable topological defects; for example, monopoles, strings or domain walls6. The clocks become desynchronized when a dark-matter object sweeps through the network. This pioneering approach5 requires a comparison between at least two distant optical atomic clocks7–9. Here, by exploiting differences in the susceptibilities of the atoms and the cavity to the fine-structure constant10,11, we show that a single optical atomic clock12 is already sensitive to dark-matter events. This implies that existing optical atomic clocks13,14 can serve as a global topologicaldefect dark-matter observatory, without any further developments in experimental apparatus or the need for long phase-noise-compensated optical-fibre links15. Using optical atomic clocks, we explored a new dimension of astrophysical observations by constraining the strength of atomic coupling to hypothetical dark-matter cosmic objects. Under the conditions of our experiments, the degree of constraint was found to exceed the previously reported limits16 by more than three orders of magnitude. The main components of an optical atomic clock are a sample of cold, trapped atoms that are isolated from the environment and a laser locked to an ultra-stable optical cavity12. Optimal for this purpose are atomic species that posses an ultra-narrow optical transition, called a clock transition. The exceptionally small spectral width of this transition combined with a high frequency value for the optical radiation results in highly accurate spectroscopic measurements that have already reached 10−18 (refs 13,14). In the ideal case of perfectly isolated atoms, the frequency of the clock transition ω0 is dictated by the values of fundamental physical constants. In typical applications, clock transitions serve as the most stable frequency references available. In our experiment, however, the different sensitivities of the clock transition and the optical cavity to variations in the fundamental constants10,11 enable a search for non-gravitational signatures of topological-defect dark matter (TDM). Here we show that a single optical neutral atomic or ion clock is sensitive to such signatures (Fig. 1). The frequency of the laser is tightly locked to the ultra-stable optical cavity. The beam, after passing through the frequency shifter (FS in Fig. 1), probes the trapped atoms. The shifter correction is actively controlled to keep the frequency of the beam locked to the clock transition. Therefore, changes in the frequency correction correspond to changes in the frequency of the clock transition with respect to the cavity. We define the clock readout, r(t), as the frequency correction at the FS. If there is a non-zero coupling between dark matter (DM) and standard model fields (DM–SM coupling), then when the Earth traverses a DM object, this DM will perturb certain standard model parameter values. In particular, we may expect a transient variation in the electromagnetic fine-structure constant, α, that can be expressed as δα α φ Λ = α / / 2 2 , where φ is the DM field and Λα is the energy scale (which inversely parametrizes the strength of the DM–SM coupling)5,17,18. Such a variation will shift the frequency of the electronic clock transition and the frequency of the chosen cavity mode. Different susceptibilities of these two frequencies to variations in α (ω ∝ α2 for non-relativistic atoms and ω ∝ α for the cavity) make a single optical atomic clock sensitive to hypothetical dark matter objects (see Methods for details) and hence will directly manifest in the readout, r(t). The theory of how atomic clock transitions (with respect to an optical cavity) respond to a variation in α was recently developed10,11, and its application in our experiment is discussed in the Methods. The concept that a single optical atomic clock is already sensitive to TDM greatly simplifies establishing a global network of optical atomic clocks aimed at the detection of TDM. With this approach, unlike those described in refs 5,15, the optical frequencies are compared locally, so that phase-noisecompensated optical fibre links of Earth-sized lengths are no longer needed. This implies that the existing network of optical atomic clocks can serve as a global topological-defect dark-matter observatory without any further developments in the experimental apparatus. It will be complementary to other experimental approaches19,11, for example, those originally aimed at gravitational wave detection20 or cosmic microwave background polarization measurements21,22. The capabilities of laser and maser interferometry for dark-matter searches were comprehensively discussed in some recent papers10,11. A single optical atomic clock is sensitive to a transient signal from a hypothetical DM object. Under real experimental conditions, however, the DM signature is expected to be hidden by noise; hence, a potential signal from a DM object cannot be distinguished from other effects. One possible solution is to simultaneously monitor at least two independent channels. If an event occurs that is common to both, but much larger than is possible for a common component estimated from all known physical phenomena, then it may be associated with an as yet unknown interaction. To provide unambiguous evidence for clocks coupling to the DM halo, they should be separated by large distances (on the scale of the Earth). Positive verification of the DM–SM coupling is impossible when the magnitude of other common effects cannot be quantified. Nevertheless, both in distant and co-located arrangements, a measurement