Probing many-body interactions in an optical lattice clock

• Published in: Annals of physics Vol. 340; no. 1; pp. 311 - 351
• Main Authors: Rey, A.M., Gorshkov, A.V., Kraus, C.V., Martin, M.J., Bishof, M., Swallows, M.D., Zhang, X., Benko, C., Ye, J., Lemke, N.D., Ludlow, A.D.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01-01-2014; Elsevier BV
• Subjects: Approximation; APPROXIMATIONS; ATOMIC CLOCKS; ATOMS; Clocks; Collisions; Decay; Density; EXCITATION; FERMIONS; INTERACTIONS; Interrogation; MANY-BODY PROBLEM; Mathematical analysis; Mathematical models; MATHEMATICAL SOLUTIONS; MEAN-FIELD THEORY; NUCLEAR DECAY; NUCLEAR PHYSICS AND RADIATION PHYSICS; Optical lattice; Optical lattices; P WAVES; S WAVES; SPECTROSCOPY; SPIN; STRONTIUM 87; TEMPERATURE DEPENDENCE; YTTERBIUM 171; Optical lattice; Collisions; Atomic clocks
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2013.11.002

We present a unifying theoretical framework that describes recently observed many-body effects during the interrogation of an optical lattice clock operated with thousands of fermionic alkaline earth atoms. The framework is based on a many-body master equation that accounts for the interplay between elastic and inelastic p-wave and s-wave interactions, finite temperature effects and excitation inhomogeneity during the quantum dynamics of the interrogated atoms. Solutions of the master equation in different parameter regimes are presented and compared. It is shown that a general solution can be obtained by using the so called Truncated Wigner Approximation which is applied in our case in the context of an open quantum system. We use the developed framework to model the density shift and decay of the fringes observed during Ramsey spectroscopy in the JILA 87Sr and NIST 171Yb optical lattice clocks. The developed framework opens a suitable path for dealing with a variety of strongly-correlated and driven open-quantum spin systems.
•Derived a theoretical framework that describes many-body effects in a lattice clock.•Validated the analysis with recent experimental measurements.•Demonstrated the importance of beyond mean field corrections in the dynamics.