Non-Abelian adiabatic geometric transformations in a cold strontium gas

Abstract

Topology, geometry, and gauge fields play key roles in quantum physics as exemplified by fundamental phenomena such as the Aharonov–Bohm effect, the integer quantum Hall effect, the spin Hall, and topological insulators. The concept of topological protection has also become a salient ingredient in many schemes for quantum information processing and fault-tolerant quantum computation. The physical properties of such systems crucially depend on the symmetry group of the underlying holonomy. Here, we study a laser-cooled gas of strontium atoms coupled to laser fields through a four-level resonant tripod scheme. By cycling the relative phases of the tripod beams, we realize non-Abelian SU(2) geometrical transformations acting on the dark states of the system and demonstrate their non-Abelian character. We also reveal how the gauge field imprinted on the atoms impact their internal state dynamics. It leads to a thermometry method based on the interferometric displacement of atoms in the tripod beams.

Frequency of the ultranarrow S01−P23 transition in Onishchenko1, Pyatchenkov2, Urech3 et al. 2019Phys. Rev. A10050View full textAdd to dashboardCite

“…Isotopes with nuclear spin exhibit hyperfine structure in the 3 P 2 state, which will make it possible to induce nuclear spin state specific ac Stark shifts and Raman couplings using the 1 S 0 -3 P 2 transition. This property might allow the creation of artificial gauge fields that are significantly less hampered by off-resonant scattering of photons or collisions between metastable state atoms compared to schemes exploiting broader transitions [16][17][18][19][20] or using metastable atoms [3,5,21]. Ultracold mixtures containing 3 P 2 atoms have been obtained from quantum gases of ground-state atoms by excitation on the 1 S 0 -3 P 2 transition, leading to the discovery of Feshbach resonances between Yb 1 S 0 and 3 P 2 atoms [22].…”

Non-equilibrium long-range phase transition in cold atoms : theory and experiment

“…First, for the atomic flux preparation and the trapping. The initial design of the experiment (used to study non-Abelian gauge transformations with the 87 Sr [84]) was substantially modified for the collapse experiment. As such, the apparatus backbone went through a complete overhaul.…”

“…Those values where obtained from photo-association spectra by different groups [79,100]. Degeneracy was first reached on the 84 Sr isotope [101,102]. The next Bosonic isotope is the 86 Sr which shows an extremely large scattering length and is then limited by inelastic three-body losses.…”

Genuine multipath interference

“…The input state is then a ground state of the atom. The role of the tritter, generalisation of the beam-splitter to three paths [23], is to prepare suitable coherent superposition of the energy states and we shall explain how this can be achieved with generalised Raman transitions in Subsec. 2.2.2.…”

“…The measurement can be achieved with a nuclear spin-sensitive shadow imaging technique [23]. The shadow laser shines on the atom from the individual ground states with low intensity, such that optical pumping can be safely ignored.…”