Searching for Stability in a Bistable Atomic Clock: Coupling strontium atoms into optical resonantors in the weak and strong cavity cooperativity regimes

There are four main aspects to improve an optical atomic clock. 1) increase the number of atoms in the cloud, 2) reduce the temperature of the atom cloud, 3) increase the effective interaction length with an optical cavity, and 4) selecting an atomic transition with a longer lifetime. Dialling up all four quantities at once introduces new challenges that hinder typical clock operation methods. However, if correctly tamed, these effects can be used to enable spin-squeezing [1], super-radiance [2], and one of the topics in this thesis, the operation near the optical bi-stability regime [3] for enhancing the next generation of atomic clocks.
In this thesis, several topics of optical atomic clocks are covered that share the common narrative of path finding non-standard techniques for a continuous optical atomic clock enhanced by an optical cavity in the “bad” cavity regime. We specifically focus on the measurement technique called NICE-OHMS, the design and construction of a continuous laser cooled beam machine, and searching for stability in a pulsed atomic clock that exhibits quantum bi-stability.
Chapter 1 starts with the theory of optical atomic clocks and chapter 2 covers the methods of laser cooling and includes simulations of an angled 1D MOT which guided design choices for later chapters.
Chapter 3 and 4 takes a deep dive into the measurement scheme NoiseImmune Cavity-Enhanced Optical Heterodyne Molecular Spectroscopy (NICEOHMS) in the context of a continuous optical frequency standard. NICEOHMS is to date the most sensitive measurement scheme for atomic concentrations with a part in 10−14 [4] sensitivity. However, it is not yet widely used as a frequency standard/atomic clock. We consider the scaling and limits of NICE-OHMS in the context of frequency metrology and discuss expected light shifts when using NICE-OHMS on a strontium beam. This lays the foundation for continuous NICE-OHMS spectroscopy on the strontium beam machine and supports the theory for the experimental data in chapter 8.
In preparation for the experimental measurement on the strontium beam machine, chapter 5 explores simulations of the optical phase spectrum for a strontium beam travelling through a cavity in the low cavity cooperativity regime. These simulations helped to anticipate the signal size for continous NICE-OHMS on the strontium beam machine.
Chapter 6 details the design and construction of a strontium beamline machine (Sr2) from scratch to look into continuous operation of an optical atomic clock to avoid Dicke noise and explore continuous high cavitycooperativity phenomena. The design is simple and implements a Zeeman slower and a 45◦-angled 1D MOT to deflect and focus an atomic beam into the path of an optical cavity. The goal is to probe continuous NICE-OHMS and continuous super-radiance, the latter of which is a topic of global competition to be the first to demonstrate. In chapter 7, the machine was characterized, and we identified we were two orders of magnitude shy in phase-space density to reach super-radiance threshold. This could be compensated for by continuous cooling on the narrow cooling transition of strontium which was built but time ran out to test it. Time also ran out to find a first signal of continuous NICE-OHMS due to technical challenges that slowed progress. The main issues are 1) the frequency instability of the injection locked 461 nm cooling lasers means operation is unreliable from day-to-day, and hour-to-hour, and 2) the optical losses of the spectroscopy light due to a lossy EOM and a lossy optical cavity means the signal-to-noise was a few orders of magnitude below the shot-noise limit. The combination of these two problems made searching for a first signal unfruitful. A Master student dedicated his thesis to stabilizing the injection locked lasers using a technique called squash-locking, which momentarily worked for short timescales but needs more debugging before it is robust enough for long-term stabilization.
Chapter 8 introduces an analytical model for the bi-stability regime explored experimentally in chapter 9 in the context of frequency metrology. The model is based on the method introduced by Rivero et al. [5] and it discards most quantum coherent effects to be able to analytically calculate the cavity transmission for the high-cooperativity, high intra-cavity photons, and bad-cavity regime. The emergence of a narrow saturation peak between the normal modes of the dressed cavity motivates probing its use as an extremely narrow frequency discriminator.
Chapter 9 shows experimental data on the already established pulsed strontium experiment. The bi-stability regime is probed using a measurement technique that borrows several noise evading properties of NICE-OHMS, but also allows the retrieval of the optical cavity output transmission and phase simultaneously. These measurements are compared to the model in chapter 8, and the frequency stability is estimated and discussed.
Finally, chapter 10 looks into simulations of a novel geometry of a dissipative atom ring trap that uses a hollow conical mirror combined with two pairs of anti-aligned anti-Helmholtz coils to realize an ”ARC” (Atoms Recycling Continuously) MOT where the potential minimum is to confine the circulating atomic beam along a ring. Similar to light circulating in a cavity, the atomic beam circulating in the ARC MOT could allow for a flux enhancement by a factor of 100. This could be a path to realizing a continuous high-cooperativity source of flux in a compact form.