Abstract
As shown in recent experiments (Lienhard et al 2020 Phys. Rev. X 10 021031), spin–orbit coupling in systems of Rydberg atoms can give rise to density-dependent Peierls phases in second-order hoppings of Rydberg spin excitations and nearest-neighbor repulsion. We here study theoretically a one-dimensional zig-zag ladder system of such spin–orbit coupled Rydberg atoms at half filling. The second-order hopping is shown to be associated with an effective gauge field, which in mean-field approximation is static and homogeneous. Beyond the mean-field level the gauge potential attains a transverse quantum component whose amplitude is dynamical and linked to density modulations. We here study the effects of this to the possible ground-state phases of the system. In a phase where strong repulsion leads to a density wave, we find that as a consequence of the induced quantum gauge field a regular pattern of current vortices is formed. However also in the absence of density–density interactions the quantum gauge field attains a non-vanishing amplitude. Above a certain critical strength of the second-order hopping the energy gain due to gauge-field induced transport overcomes the energy cost from the associated build-up of density modulations leading to a spontaneous generation of the quantum gauge field.
Highlights
Due to their strong and non-local interaction, their experimental accessibility and the high degree of tunability and control that can be exerted, Rydberg atoms have become a powerful tool for simulating strongly correlated quantum many-body systems [1]
We studied the effects of a density-dependent, complex hopping of Rydberg excitations arising from second-order processes to the many-body ground state of a one-dimensional zig-zag-chain at half filling
The strength of the second-order hopping can be controlled by microscopic parameters of the Rydberg atoms and the system can be tuned from a regime where these processes are negligible to one where they dominate
Summary
Due to their strong and non-local interaction, their experimental accessibility and the high degree of tunability and control that can be exerted, Rydberg atoms have become a powerful tool for simulating strongly correlated quantum many-body systems [1]. In [18] it was demonstrated that spin-orbit coupling in systems of Rydberg atoms can be used to generate Peierls phases in the hopping matrix elements of Rydberg excitations without external light fields, laser assisted tunneling or lattice shaking. Being a dynamical quantity, the quantum component of the gauge field is gauge invariant as it is a transverse field It substantially modifies the ground-state phase diagram, which we numerically investigate using exact diagonalization methods. It leads to two new liquid phases in addition to a trivial superfluid, which are characterized by alternating vortex currents of Rydberg excitations.
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