A quantum many-body spin system in an optical lattice clock (1212.6291v1)

Abstract: Strongly interacting quantum many-body systems are fundamentally compelling and ubiquitous in science. However, their complexity generally prevents exact solutions of their dynamics. Precisely engineered ultracold atomic gases are emerging as a powerful tool to unravel these challenging physical problems. Here we present a new laboratory for the study of many-body effects: strongly interacting two-level systems formed by the clock states in ${}^{87}$Sr, which are used to realize a neutral atom optical clock that performs at the highest level of optical-atomic coherence and with precision near the limit set by quantum fluctuations. Our measurements of the collective spin evolution reveal signatures of many-body dynamics, including beyond-mean-field effects. We derive a many-body Hamiltonian that describes the experimental observation of severely distorted lineshapes, atomic spin coherence decay, density-dependent frequency shifts, and correlated quantum spin noise. These investigations open the door to exploring quantum many-body effects and entanglement in quantum systems with optical energy splittings, using highly coherent and precisely controlled optical lattice clocks.

A Quantum Many-Body Spin System in an Optical Lattice Clock

The paper "A quantum many-body spin system in an optical lattice clock" presents the experimental realization and theoretical exploration of a strongly interacting many-body system using clock states in ${}^{87}$Sr. Optical lattice clocks, which employ fermionic alkaline earth atoms, such as ${}^{87}$Sr, have demonstrated remarkable optical-atomic coherence, making them ideal for studying collective quantum behaviors that are otherwise elusive in classical systems. This research advances our understanding of quantum many-body dynamics, specifically the entanglement and correlations within systems of ultracold atoms.

Experimental Observations and Theoretical Model

The authors present a detailed paper of many-body effects and spin dynamics via precise manipulation and measurement of atomic states in optical lattice clocks. Using Ramsey and Rabi spectroscopic techniques, they uncover significant density-dependent frequency shifts and distorted excitation lineshapes that deviate from ideal single-particle predictions. The results challenge traditional mean-field models and necessitate consideration of beyond-mean-field interactions.

A many-body Hamiltonian is derived, encapsulating the collective spin behavior and revealing complex phenomena such as quadrature-dependent quantum noise and the decay of atomic spin coherence. The paper highlights the role of elastic and inelastic $p$-wave interactions, particularly in the strongly interacting regime where $s$-wave interactions are suppressed.

Experimental Results

The paper reports strong numerical findings, such as the density shift in Ramsey spectroscopy which is measured to be proportional to the interaction energy exceeding sub-Hz levels. At high atomic densities (with approximately 20 atoms per lattice site), the collective spin evolution, characterized by the Hamiltonian, indicates many-body dynamics that cannot be explained by conventional mean-field treatments.

The experimental setup allows coherent interrogation of clock states with atom-light coherence times exceeding several seconds, enabling the exploration of fragile quantum correlations at high resolutions. The paper shows consistent agreements between experimental results and theoretical predictions using a many-body master equation that accounts for quantum fluctuations and two-body losses.

Implications and Future Directions

This pioneering investigation illustrates the experimental capacity to probe and manipulate strongly correlated quantum systems at temperatures of several $\mu$K in optical lattice clocks. It opens pathways not only for advanced quantum simulations of condensed matter systems but also enhances practical applications such as precision measurements and quantum information processing.

The findings suggest further exploration of SU(N) symmetries in nuclear spin degrees of freedom and potential investigations of unconventional magnetic models. Additionally, the research implications extend to other systems like ultracold polar molecules, indicating a broad applicability of the experimental methodologies and theoretical insights developed.

The authors also speculate on the generation of entangled states through interaction-induced spin squeezing, which could have profound implications for enhancing the stability and precision of optical clocks. As ultrastable lasers continue to improve, the potential to explore the quantum regime becomes increasingly promising.

In summary, this paper contributes a significant step toward harnessing quantum many-body systems for both fundamental studies and practical applications. The experimental and theoretical advancements described challenge existing models and set the stage for future exploration of entangled states and quantum phases governed by optical interactions.