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arXiv:1408.3983 · Physical Review Letters

Observation of Motion-Dependent Nonlinear Dispersion with Narrow-Linewidth Atoms in an Optical Cavity

Philip G. Westergaard, Bjarke T. R. Christensen, David Tieri, Rastin Matin, J. Cooper, Murray Holland, Jun Ye, Jan W. Thomsen

Published Mar 4, 2015• 33 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.114.093002

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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.
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Strontium optical lattice clocks at JILA recently demonstrated record-high accuracy and stability. These advances were enabled by an ultrastable laser with fractional frequency stability of 1x10-16 at 1 second. This laser allows us to study systematic shifts of the 1S0 to 3P0 clock transition with unprecedented precision. Density-dependent frequency shifts represent an unavoidable perturbation for clocks based on many atoms. Our studies of atomic interactions in an optical lattice clock system uncover the nature of these interactions and reveal important many-body atomic correlation effects in this open quantum system. By extending our measurements to all ten nuclear-spin sublevels of the clock states, we observe the first direct evidence of SU(N) symmetric interactions in alkaline earth(-like) atoms. Using the techniques we developed in these studies, we also demonstrate a novel technique for measuring the frequency noise spectrum of an ultrastable laser. We discuss designs for the future direction of our experiment which will place 87Sr atoms within a high finesse cavity that is resonant on the 1S0 to 3P1 transition. We will use this system to study collective effects in cavity quantum electrodynamics. Most notably, strong atom-cavity coupling can enhance the spectroscopic sensitivity of our clock by creating spin-squeezed states via quantum non-demolition measurements. As a precursor to future work studying cavity-mediated collective behavior, we use the unique atomic structure of 88Sr to investigate free-space retarded dipolar coupling in an optically thick sample of atoms.
An ideal superradiant laser on an optical clock transition of noninteracting cold atoms is predicted to exhibit an extreme frequency stability and accuracy far below mHz-linewidth. In any concrete setup sufficiently many atoms have to be confined and pumped within a finite cavity mode volume. Using a magic wavelength lattice minimizes light shifts and allows for almost uniform coupling to the cavity mode. Nevertheless, the atoms are subject to dipole-dipole interaction and collective spontaneous decay which compromises the ultimate frequency stability. In the high density limit the Dicke superradiant linewidth enhancement will broaden the laser line and nearest neighbor couplings will induce shifts and fluctuations of the laser frequency. We estimate the magnitude and scaling of these effects by direct numerical simulations of few atom systems for different geometries and densities. For Strontium in a regularly filled magic wavelength configuration atomic interactions induce small laser frequency shifts only and collective spontaneous emission weakly broadens the laser. These interactions generally enhance the laser sensitivity to cavity length fluctuations but for optimally chosen operating conditions can lead to an improved synchronization of the atomic dipoles.
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].
In my thesis work, I have explored a variety of ways in which narrow linewidth optical transitions can be utilized to extend the capabilities of precision measurement and quantum science. These tools include non-destructive atom counting techniques that may enhance the performance of optical lattice clocks, a novel form of cavity enhanced atomic spectroscopy appropriate for laser frequency stabilization, a new form of laser cooling with reduced reliance on spontaneous emission, several methods for enhancing the sensitivity of proposed atomic gravitational wave detectors, a newly observed form of cavity-mediated spin-spin interactions, and a new class of laser based on optical superradiance from narrow and ultra-narrow linewidth transitions. As part of the superradiant laser project, we have demonstrated the most precise active absolute frequency reference realized to date, which still has great potential for improvement.\nMany of these tools involve coupling atoms to an optical cavity, a field known as cavity quantum electrodynamics, or cavity QED. In my thesis work, a key focus was the extension of cavity QED techniques into the new regime of coupling large ensembles of atoms to a cavity using narrow linewidth optical transitions (in contrast to the previously explored regimes of microwave-frequency transitions or broad-linewidth optical transitions). To this end, I constructed a new experiment to couple an ensemble of atoms to an optical cavity using two optical transitions in atomic strontium, one with a narrow 7.5 kHz linewidth, and another with an ultra-narrow 1 mHz linewidth. This new system has allowed us to access a unique new regime of cavity QED, and a wealth of interesting and useful applications.
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.