Quantitative modeling towards continuous superradiant laser on Sr

Abstract

Optical clocks, with an accuracy of 10−19 level, corresponding to being off by only 1 second over the universe’s age, are the most precise clocks ever built. Optical clocks promise a huge impact on the development of quantum technologies like atom interferometry and quantum metrology with applications in telecommunication, specifically in network synchronization and accuracy navigation through 5G networks instead of GPS. Other than this, if optical clocks are operated on satellites then they could be used for gravitational wave detectors, performing experiments of general relativity. Further applications are in geology, astronomy, and fundamental physics.Current optical clocks are passive frequency standards. In these systems, the frequency of a highly coherent probe laser (local oscillator) is intermittently compared with the frequency of a narrow and robust clock transition in trapped atoms or ions. This laser is pre-stabilized by an ultrastable macroscopic cavity (flywheel), keeping the frequency in between interrogation cycles. Thermal and mechanical fluctuations in the local oscillator are among the main factors limiting the short-term stability of modern optical clocks. They entirely determine the overall clock stability on the time less than a single interrogation cycle and do not utilize the full potential of a clock transition. Finally, down-conversion of the broad-band laser frequency noise contributes to the measurement error of the frequency offset, what is known as a Dick effect.To overcome this problem, one may create an active optical clock based on a superradiant laser, where the atoms with population inversion on the clock transition are coupled to a resonator mode in the bad cavity regime. The cavity mode of such a laser is much broader than its gain profile, and the laser frequency is inherently insensitive to cavity length fluctuations, in contrast to ordinary good-cavity lasers.Achieving a 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. This problem is being tackled by the FET-Flag project iqClock and European Innovative Training Network MoSaiQC, short for “Modular Systems for Advanced Integrated Quantum Clocks”, and includes a wide range of academic and industrial institutions. At TU Wien, we, as a theoretical partner, have studied the ultimate characteristics of the active optical clocks, and performed simulations to assist our experimental partners with the design of such a Laser.We then present two different models for stimulating 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, and resulting in an output power of hundreds of fW.This thesis is divided into two main sections. The first section introduces the necessary tools for studying the superradiant laser. We begin by developing an understanding of quantum optics and open quantum systems. Then, we compare different models for simulating the superradiant laser and estimate the ultimate stability achievable using an active optical clock.The second section of the thesis focuses on the realization of a superradiant laser. Specifically, we performed a feasibility study for the design and simulation of the continuous high-efficiency cooling, loading, and pumping to the upper lasing state inside the cavity for the superradiant mHz machine at the University of Amsterdam. The goal is to combine a high-flux continuous beam of ultra-cold strontium atoms with a bowtie cavity for the generation of superradiant lasing. This machine operates on forbidden transitions 3P0 to 1S0 in ultracold alkaline-earth atoms confined by a magic optical lattice.After establishing a method for continuously injecting atoms into the upper state and ejecting ground state atoms from the bowtie cavity, We introduce two different models for stimulating 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 the fluctuation of the atomic flux, r, leading to an output power of several hundred fW.