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arXiv:1506.08210 · Physical Review A

Laser stabilization using saturated absorption in a cavity-QED system

David Tieri, J. Cooper, Bjarke T. R. Christensen, Jan W. Thomsen, Murray Holland

Published Jul 10, 2015• 12 citations
arXivHTMLPDF

Abstract

We consider the phase stability of a local oscillator (or laser) locked to a cavity-QED system composed of atoms with an ultranarrow optical transition. The atoms are cooled to milli-Kelvin temperatures and then released into the optical cavity. Although the atomic motion introduces Doppler broadening, the standing-wave nature of the cavity causes saturated absorption features to appear, which are much narrower than the Doppler width. These features can be used to achieve an extremely high degree of phase stabilization, competitive with the current state of the art. Furthermore, the inhomogeneity introduced by finite atomic velocities can cause optical bistability to disappear, resulting in no regions of dynamic instability and thus enabling a new regime accessible to experiments where optimum stabilization may be achieved.

DOI
10.1103/physreva.92.013817

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We consider the phase stability of a local oscillator (or laser) locked to a cavity-QED system composed of atoms with an ultranarrow optical transition. The atoms are cooled to milli-Kelvin temperatures and then released into the optical cavity. Although the atomic motion introduces Doppler broadening, the standing-wave nature of the cavity causes saturated absorption features to appear, which are much narrower than the Doppler width. These features can be used to achieve an extremely high degree of phase stabilization, competitive with the current state of the art. Furthermore, the inhomogeneity introduced by finite atomic velocities can cause optical bistability to disappear, resulting in no regions of dynamic instability and thus enabling a new regime accessible to experiments where optimum stabilization may be achieved.
We explore the potential of direct spectroscopy of ultranarrow optical transitions of atoms localized in an optical cavity. In contrast to stabilization against a reference cavity, which is the approach currently used for the most highly stabilized lasers, stabilization against an atomic transition does not suffer from Brownian thermal noise. Spectroscopy of ultranarrow optical transitions in a cavity operates in a very highly saturated regime in which nonlinear effects such as bistability play an important role. From the universal behavior of the Jaynes-Cummings model with dissipation, we derive the fundamental limits for laser stabilization using direct spectroscopy of ultranarrow atomic lines. We find that, with current lattice clock experiments, laser linewidths of about 1 mHz can be achieved in principle, and the ultimate limitations of this technique are at the 1 $\ensuremath{\mu}$Hz level.
As an alternative to state-of-the-art laser frequency stabilization using ultrastable cavities, it has been proposed to exploit the nonlinear effects from coupling of atoms with a narrow transition to an optical cavity. Here, we have constructed such a system and observed nonlinear phase shifts of a narrow optical line by a strong coupling of a sample of strontium-88 atoms to an optical cavity. The sample temperature of a few mK provides a domain where the Doppler energy scale is several orders of magnitude larger than the narrow linewidth of the optical transition. This makes the system sensitive to velocity dependent multiphoton scattering events (Dopplerons) that affect the cavity field transmission and phase. By varying the number of atoms and the intracavity power, we systematically study this nonlinear phase signature which displays roughly the same features as for much lower temperature samples. This demonstration in a relatively simple system opens new possibilities for alternative routes to laser stabilization at the sub-100 mHz level and superradiant laser sources involving narrow-line atoms. The understanding of relevant motional effects obtained here has direct implications for other atomic clocks when used in relation to ultranarrow clock transitions.
A spectrally pure coherent light source is an important component in precision measurement applications, such as an atomic clock. The more spectrally pure the coherent light source, or the narrower the linewidth of its power spectrum, the better for atomic clock experiments. A coherent light light source, such as a laser, is intrinsically an open quantum system, meaning that it gains and loses energy from an external environment.\nThe aim of this thesis is to study various open quantum systems in an attempt to discover a scheme in which an extremely spectrally pure coherent light source might be realized. Therefore, this thesis begins by introducing the two main approaches to treating open quantum systems, the quantum master equation approach, and the quantum Langevin equation approach. In addition to deriving these from first principles, many of the solution methods to these approaches are given and then demonstrated using computer simulations. These include the quantum jump algorithm, the quantum state diffusion algorithm, the cumulant expansion method, and the method of c-number Langevin equations.\nUsing these methods, the theory of the crossover between lasing and steady state superradiance is presented. It is shown that lasing and steady state superradiance might be demonstrated in the same physical system, but in different parameter regimes. The parameter space between these two extreme limits is explored, and the benefits and drawbacks of operating a system at a given set of parameters, i.e. to achieve the most spectrally pure light source, are discussed.\nWe also consider the phase stability of a laser that is locked to a cavity QED system comprised of atoms with an ultra-narrow optical transition. Although the atomic motion introduces Doppler broadening, the standing wave nature of the cavity causes saturated absorption, which can be used to achieve an extremely high degree of phase stabilization. The inhomogeneity introduced by finite atomic velocities can also cause optical bistability to disappear, resulting in no regions of dynamic instability that would otherwise restrict operational parameters in the experiment to be tuned outside of the optimum region where the minimum linewidth occurs.
The development of simple and reliable high stability clock lasers is of great importance for future state-of-the-art optical clocks [1]-[5] and for future transportable optical clocks [6], [7]. Further development of clock lasers with better stability has so far been hindered by thermal noise in the reference cavity used for laser stabilization and conventional approaches for improvements may be technically challenging. It has been proposed [8]-[11] to improve the stability and reduce the complexity of state-of-the-art laser frequency stabilization by exploiting cavity QED systems consisting of atoms with a narrow optical transition coupled to a single mode of an optical cavity. The laser stabilization performance of a cavity QED system is affected by a number of system parameters such as the finite temperature of the atoms, the number of involved atoms and the laser power [12]-[14]. However, the dynamics of those elements have not yet been fully explored. Here we present a simple cavity QED system consisting of laser cooled strontium-88 atoms coupled to an optical cavity. We relate measurable quantities to the complex transmission coefficient which relates the input field to the output field. The optimal input power for stabilizing a laser to this system is experimentally determined and the optimal shot-noise-limited linewidth of the system is evaluated to 500 mHz. Furthermore, theoretical shot-noise-limited linewidths of similar cavity QED systems are evaluated for a number of different two electron systems.
We report on the observation of a novel manifestation of saturation-induced optical bistability in a resonantly pumped optical ring cavity interacting strongly with a cloud of atoms via a narrow atomic transition. The bistability emerges, above a critical pump rate, as an additional peak in the cavity's normal mode spectrum close to atomic resonance. This third transmission peak is usually suppressed due to strong resonant absorption, but in our experiment it is visible because of the linewidth of the atomic transition being much smaller than that of the cavity, which sets the experiment into the bad-cavity regime. Relying on complete saturation of the transition, this bistability has a quantum origin and cannot be mimicked by a classical material presenting a nonlinear refraction index. The appearance of the central peak in addition to the normal modes is predicted by a semi-classical model derived from the Tavis-Cummings Hamiltonian from which we derive a bistability phase diagram that connects our observations with former work on optical bistability in the good cavity regime. The phase diagram reveals several so far unexplored bistable phases.
Abstract We report on the observation of a novel manifestation of saturation-induced optical bistability in a resonantly pumped optical ring cavity interacting strongly with a cloud of atoms via a narrow atomic transition. The bistability emerges, above a critical pump rate, as an additional peak in the cavity’s normal mode spectrum close to atomic resonance. This third transmission peak is usually suppressed due to strong resonant absorption, but in our experiment it is visible because of the linewidth of the atomic transition being much smaller than that of the cavity, which sets the experiment into the bad-cavity regime. Relying on complete saturation of the transition, this bistability has a quantum origin and cannot be mimicked by a classical material presenting a nonlinear refraction index. The appearance of the central peak in addition to the normal modes is predicted by a semi-classical model derived from the Tavis–Cummings Hamiltonian from which we derive a bistability phase diagram that connects our observations with former work on optical bistability in the good cavity regime. The phase diagram reveals several so far unexplored bistable phases.