Trapped circular Rydberg atoms for Quantum Simulation – TRYAQS

TRYAQS proposes a disruptive concept for the quantum simulation of complex systems. Many groups worldwide actively explore quantum simulation. It aims at an in-depth understanding of many-body systems. They are extremely important, both for fundamental issues such as quantum transport or quantum phase transitions, but also for the understanding and development of innovative materials. However, their theoretical description is utterly difficult due to the huge size of the Hilbert space. A 30-spin chain with a general Nearest Neighbor interaction Hamiltonian is already beyond the grasp of analytical and numerical methods. The principle of a quantum simulator is to emulate the system of interest by another, with the same interactions but with totally controlled parameters. Moreover, it should make it possible to measure any observable in the final state. Interesting experiments have been realized with trapped ions, superconducting circuits, Rydberg atoms or cold atoms in lattices. However, it remains extremely difficult to study with these platforms large systems over long time intervals, as required for thermalization or quantum localization effects for instance.

TRYAQS plans to unite the best features of these simulators, by using as spins circular Rydberg levels, trapped in an optical lattice, and placed in a spontaneous emission-inhibiting structure. The circular levels are blessed with remarkable properties: simple structure, long lifetimes (30 ms for 50C), extremely strong coupling to the radiation field and efficient detection by field ionization. A circular atom pair interacts by a van der Waals potential, which can be mapped under the general form of a XXZ spin chain Hamiltonian in a transverse field by dressing the atomic transition with a resonant microwave. The resulting interaction parameters can be tuned at will through the dressing source and through a static electric field applied to the atoms.

To take full benefit of this flexible interaction, TRYAQS plans to extend the circular states lifetime in the tens of seconds range by placing the atoms in a structure below cut-off for the radiated wavelength. TRYAQS will trap the atoms in this structure by the ponderomotive potential experienced by their electron in a laser field. This trapping potential is large (MHz deep for reasonable laser powers), and nearly independent of the atomic level, a major asset for TRYAQS. Due to their high angular momentum, circular atoms are nearly impervious to photoionization. Trapping does not affect their lifetime.

The final objective of TRYAQS is to follow the evolution of a few-spin linear chain over thousand characteristic times of the interaction. This makes it possible to observe the harbinger of a quantum phase transition by varying adiabatically the parameters of the interaction Hamiltonian. This remarkable achievement will demonstrate the interest of the TRYAQS platform for quantum simulation. It will open the way to even more interesting simulations, beyond the range of available numerical methods. The success of TRYAQS would thus be a major enabling step for quantum simulation.

The TRYAQS effort involves closely linked experimental and theoretical developments. They will result from a close collaboration between the Quantum Electrodynamics group at LKB (Collège de France, CdF) and the theory group at LPTMS, Orsay. The theory group will guide the experimental effort, by assessing the influence of experimental imperfections and by determining the optimal choice of parameters. It will also explore the possibilities of this platform, well beyond the time frame of TRYAQS. The experimental group will use its vast experience in circular Rydberg atoms and atom trapping to reach the ambitious objectives of TRYAQS in a four-year time frame.