Quantum simulation with circular Rydberg atoms of Strontium

Many experimental platforms are being explored for quantum simulation, including superconducting qubits, trapped ions and cold atoms in optical lattices. One particularly promising platform is Rydberg atoms in optical tweezer arrays. By trapping individual atoms in tightly focused dipole traps, it is possible to arrange up to thousands of atoms in arbitrary geometries. When excited to laser accessible Rydberg states, these atoms exhibit strong interactions, enabling the study of many-body spin-like systems.

In our group, we are working with circular Rydberg states, characterized by maximum angular momentum (l = m = n-1). Unlike low-l Rydberg states, which have lifetimes of about 100 µs, circular states can survive for several milliseconds when placed in a cryogenic environment where blackbody radiation is suppressed. This extended lifetime could allow us to explore dynamics that are inaccessible with conventional Rydberg states.

To study these long-time dynamics, circular atoms must be trapped during the simulation. The nearly free electron in the Rydberg state is affected by the ponderomotive potential of the trapping light, which is repulsive. While blue-detuned traps with specialized geometries can trap these states, they require significant laser power, which is not ideal for scaling purposes. An alternative approach is to use alkaline-earth like species and take advantage of the polarizability of the ionic core to trap the Rydberg atom.

This is why we have built a cryogenic (4K) experimental setup to trap strontium atoms in an optical tweezer array and excite them to circular Rydberg states where they will be trapped for millisecond. Once the atoms are trapped, we will demonstrate that the fast transition of the Sr+ ionic core make it possible to image the Rydberg states directly whithout having to transfer them back to the ground state.

Furthermore, the electric quadrupole interaction between the Rydberg electron and the ionic core induces an energy shift in the bare ion's energy levels, which depends on the Rydberg state. By resolving this shift, it is then possible to implement shelving technique or apply phase shifts to specific Rydberg states using lasers.

This opens the way to perform non-destructive measurements or gate operations.