Stefan Alaric Schäffer

Continuous superradiance using a narrow optical transition has the potential to improve the short-term stability of state-of-the-art optical clocks. Even though pulsed superradiant emission on a mHz linewidth clock transition has been shown, true continuous operation, without Fourier limitation, has turned out to be extremely challenging. The trade-off between maintaining a high atomic flux while minimizing decoherence effects presents a significant obstacle. Here, we discuss the design of a machine that could overcome this problem by combining a high-flux continuous beam of ultracold strontium atoms with a bowtie cavity for the generation of superradiant lasing. To evaluate the feasibility of our design, we present simulation results for continuous high-efficiency cooling, loading, and pumping to the upper lasing state inside the bowtie cavity. We then present two different models for simulating the generated superradiant field by taking into account position-dependent shifts, collisional decoherence, light shifts, and atom loss. Finally, we estimate a laser linewidth of less than 100 mHz , limited by atom number fluctuations, resulting in an output power of hundreds of fW .

Atoms coupled to cavities provide an exciting playground for the study of fundamental interactions of atoms mediated through a common channel. Many of the applications of cavity QED and cold-atom experiments more broadly, suffer from limitations caused by the transient nature of an atomic loading cycle. The development of continuous operation schemes is necessary to push these systems to the next level of performance. Here we present a machine designed to produce a continuous flux of collimated atoms that traverse an optical cavity. The atom-light interaction is enhanced by a fast-decaying cavity optimal for studying phenomena where atomic properties dominate. We demonstrate the transition to a collective strong-coupling regime heralded by a normal-mode splitting. We observe a second phase with a binary normal-mode splitting born from an offset in the mean velocity of the atoms. Inverting the atomic ensemble in the collective strong-coupling regime, we measure continuous optical gain. This work sets the stage for studying threshold conditions for continuous collective phenomena, such as continuous superradiant lasing. Published by the American Physical Society 2024

Atoms coupled to cavities provide an exciting playground for the study of fundamental interactions of atoms mediated through a common channel. Many of the applications of cavity-QED and cold-atom experiments more broadly, suffer from limitations caused by the transient nature of an atomic loading cycle. The development of continuous operation schemes is necessary to push these systems to the next level of performance. Here we present a machine designed to produce a continuous flux of collimated atoms that traverse an optical cavity. The atom-light interaction is enhanced by a fast-decaying cavity optimal for studying phenomena where atomic properties dominate. We demonstrate the transition to a collective strong coupling regime heralded by a normal-mode splitting. We observe a second phase with a binary normal-mode splitting born from an offset in the mean velocity of the atoms. Inverting the atomic ensemble in the collective strong coupling regime, we measure continuous optical gain. This work sets the stage for studying threshold conditions for continuous collective phenomena, such as continuous superradiant lasing.

When an inverted ensemble of atoms is tightly packed on the scale of its emission wavelength or when the atoms are collectively strongly coupled to a single cavity mode, their dipoles will align and decay rapidly via a superradiant burst. However, a spread-out dipole phase distribution theory predicts a required minimum threshold of atomic excitation for superradiance to occur. Here we experimentally confirm this predicted threshold for superradiant emission on a narrow optical transition when exciting the atoms transversely and show how to take advantage of the resulting sub- to superradiant transition. A π/2-pulse places the atoms in a subradiant state, protected from collective cavity decay, which we exploit during the free evolution period in a corresponding Ramsey pulse sequence. The final excited state population is read out via superradiant emission from the inverted atomic ensemble after a second π/2-pulse, and with minimal heating this allows for multiple Ramsey sequences within one experimental cycle. Our scheme is an innovative approach to atomic state readout characterized by its speed, simplicity, and highly directional emission of signal photons. It demonstrates the potential of sensors using collective effects in cavity-coupled quantum emitters.

Atomic clocks are vital in a wide array of technologies and experiments, including tests of fundamental physics¹. Clocks operating at optical frequencies have now demonstrated fractional stability and reproducibility at the 10⁻¹⁸ level, two orders of magnitude beyond their microwave predecessors². Frequency ratio measurements between optical clocks are the basis for many of the applications that take advantage of this remarkable precision. However, the highest reported accuracy for frequency ratio measurements has remained largely unchanged for more than a decade^3,4,5. Here we operate a network of optical clocks based on ²⁷Al⁺ (ref. ⁶), ⁸⁷Sr (ref. ⁷) and ¹⁷¹Yb (ref. ⁸), and measure their frequency ratios with fractional uncertainties at or below 8 × 10⁻¹⁸. Exploiting this precision, we derive improved constraints on the potential coupling of ultralight bosonic dark matter to standard model fields^9,10. Our optical clock network utilizes not just optical fibre¹¹, but also a 1.5-kilometre free-space link^12,13. This advance in frequency ratio measurements lays the groundwork for future networks of mobile, airborne and remote optical clocks that will be used to test physical laws¹, perform relativistic geodesy¹⁴ and substantially improve international timekeeping¹⁵.

Artiklen introducerer konceptet om det aktive atomur, hvor laserlys genereres direkte fra ultra-smalle atomare overgange frem for brede forstærkningsmedia. En traditionel laser forstærker et spektrum a frekvenser men filtreres af en optisk kavitet der er følsom overfor mekaniske rystelser og akustisk støj. Det aktive atomur kan væsentligt reducere følsomheden overfor eksterne støjkilder og forbedre frekvensstabiliteten af lasere dramatisk. Der gives en klar forbindelse til eksisterende atomure og deres anvendelser i GPS og fundamentale tests af fysik. Artiklen illustrerer, hvordan avanceret kvanteoptik kan føre til nye standarder for tid og frekvens. For fysikere er det et spændende indblik i frontlinjen af præcisionsmålinger.

The passage of time is tracked by counting oscillations of a frequency reference, such as Earth’s revolutions or swings of a pendulum. By referencing atomic transitions, frequency (and thus time) can be measured more precisely than any other physical quantity, with the current generation of optical atomic clocks reporting fractional performance below the 10⁻¹⁷ level^1,2,3,4,5. However, the theory of relativity prescribes that the passage of time is not absolute, but is affected by an observer’s reference frame. Consequently, clock measurements exhibit sensitivity to relative velocity, acceleration and gravity potential. Here we demonstrate local optical clock measurements that surpass the current ability to account for the gravitational distortion of space-time across the surface of Earth. In two independent ytterbium optical lattice clocks, we demonstrate unprecedented values of three fundamental benchmarks of clock performance. In units of the clock frequency, we report systematic uncertainty of 1.4 × 10⁻¹⁸, measurement instability of 3.2 × 10⁻¹⁹ and reproducibility characterized by ten blinded frequency comparisons, yielding a frequency difference of [−7 ± (5)_stat ± (8)_sys] × 10⁻¹⁹, where ‘stat’ and ‘sys’ indicate statistical and systematic uncertainty, respectively. Although sensitivity to differences in gravity potential could degrade the performance of the clocks as terrestrial standards of time, this same sensitivity can be used as a very sensitive probe of geopotential^5,6,7,8,9. Near the surface of Earth, clock comparisons at the 1 × 10⁻¹⁸ level provide a resolution of one centimetre along the direction of gravity, so the performance of these clocks should enable geodesy beyond the state-of-the-art level. These optical clocks could further be used to explore geophysical phenomena¹⁰, detect gravitational waves¹¹, test general relativity¹² and search for dark matter^{13,14,15,16,17}.