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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Laser stabilization on velocity dependent nonlinear dispersion of Sr atoms in an optical cavity

Bjarke T. R. Christensen, Stefan Alaric Schäffer, Martin R. Henriksen, Philip G. Westergaard, Jun Ye, Jan W. Thomsen

Published Apr 1, 2015• 1 citation
Publisher

Abstract

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.

DOI
10.1109/fcs.2015.7138858

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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.
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.
Ultra stable frequency references such as the ones used in optical atomic clocks and for quantum metrology may be obtained by stabilizing a laser to an optical cavity that is stable over time. State-of-the-art frequency references are constructed in this way, but their stabilities are currently limited by thermally induced length fluctuations in the reference cavity. Several alternative approaches using the potential for frequency discriminating of highly forbidden narrow atomic transitions have been proposed in, e.g., [1] and [2]. In this proceeding we will present some of the ongoing experimental efforts derived from these proposals, to use cavity-enhanced interaction with atomic 88 Sr samples as a frequency reference for laser stabilization. Such systems can be realized using both passive and active approaches where either the atomic phase response is used as an error signal, or the narrow atomic transition itself is used as a source for a spectrally pure laser. Both approaches shows the promise of being able to compete with the current state of the art in stable lasers and have similar limitations on their ultimately achievable linewidths [1, 2].
Hybrid systems of cold atoms and optical cavities are promising systems for increasing the stability of laser oscillators used in quantum metrology and atomic clocks. In this paper we map out the atom-cavity dynamics in such a system and demonstrate limitations as well as robustness of the approach. We investigate the phase response of an ensemble of cold 88Sr^{88}\mathrm{Sr}88Sr atoms inside an optical cavity for use as an error signal in laser frequency stabilization. With this system we realize a regime where the high atomic phase shift limits the dynamical locking range. The limitation is caused by the cavity transfer function relating input field to output field. The cavity dynamics is shown to have only little influence on the prospects for laser stabilization, making the system robust towards cavity fluctuations and ideal for the improvement of future narrow linewidth lasers.
The stability of current state-of-the-art optical atomic clocks [1]-[5] is mostly limited by the frequency noise of the interrogation oscillator through the Dick effect. To achieve the heralded ultimate stability, future optical frequency standards will need to produce light sources with frequency stability at the 10−17fractional level or below at one second of integration time. Recently, a new frontier in cavity stabilized laser sources has pushed the fractional instability to the lower 10−16level at one second of integration time [6]-[8]. However, this instability is limited by thermal noise in the reference cavity elements and may be difficult to reduce further. These state-of-the-art reference cavities are technically challenging to construct and their stability is still at least an order of magnitude too large for lattice clocks to achieve their ultimate performance.
We study the nonlinear interaction of a cold sample of 88Sr^{88}\mathrm{Sr}88Sr atoms coupled to a single mode of a low finesse optical cavity in the so-called bad cavity limit, and we investigate the implications for applications to laser stabilization. The atoms are probed on the weak intercombination line $|5{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}\ensuremath{\rangle}\phantom{\rule{0.16em}{0ex}}\ensuremath{-}\phantom{\rule{0.16em}{0ex}}|5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}\ensuremath{\rangle}$ at 689 nm in a strongly saturated regime. Our measured observables include the atomic induced phase shift and absorption of the light field transmitted through the cavity represented by the complex cavity transmission coefficient. We demonstrate high signal-to-noise-ratio measurements of both quadratures---the cavity transmitted phase and absorption---by employing frequency modulation (FM) spectroscopy (noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy). We also show that when FM spectroscopy is employed in connection with a cavity locked to the probe light, observables are substantially modified compared to the free-space situation in which no cavity is present. Furthermore, the nonlinear dynamics of the phase dispersion slope is experimentally investigated, and the optimal conditions for laser stabilization are established. Our experimental results are compared to state-of-the-art cavity QED theoretical calculations.
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.