Condensation versus long-range interaction: Competing quantum phases in bosonic optical lattice systems at near-resonant Rydberg dressing

Abstract

Recent experiments have shown that (quasi-)crystalline phases of Rydberg-dressed quantum many-body systems in optical lattices (OL) are within reach. Rydberg systems naturally possess strong long-range interactions due to the large polarizability of Rydberg atoms. Thus a wide range of quantum phases have been predicted, such as a devil's staircase of lattice incommensurate density wave phases as well as more exotic lattice supersolid order for bosonic systems, as considered in our work. Guided by results in the "frozen" gas limit, we study the ground state phase diagram at finite hopping amplitudes and in the vicinity of resonant Rydberg driving, while fully including the long-range tail of the van der Waals interaction. Simulations within real-space bosonic dynamical mean-field theory (RB-DMFT) yield an extension of the devil's staircase into the supersolid regime where the competition of condensation and interaction leads to a sequence of crystalline phases.

Supersolid phases of Rydberg-excited bosons on a triangular lattice

“…We note that in the frozen-limit a simple expression was found for the critical value of the detuning at which the system undergoes a phase transition to vacuum [41]. This expression can be easily extended beyond the frozenlimit as the transition between the vacuum and a very dilute gas, in which van der Waals type interactions are negligible, can be treated as a single-particle problem (see also App.…”

“…For each lattice site i we introduce bosonic annihilation operatorsâ i of an atom in its ground state andb i of an atom in its highly excited Rydberg state. The corresponding Hamiltonian reads [40,41]…”

“…We also set the value of η = 0 which translates to immobile Rydberg atoms. The effect of non-vanishing η was considered in [41] and only small changes in the values of observables were observed. This is not surprising as the excited atoms interact strongly via the van der Waals interaction, which leads either to a very small fraction of excited atoms or to crystalline order where kinetic processes are suppressed.…”

“…These impurity problems might have different parameters and solutions, resulting in different values of local observables, such as the condensate order parameter for ground φ i,g = â i and excited state φ i,e = b i bosons, expectation value of the occupation of ground n g,i and excited state n e,i bosons, connected local Green functions, self-energies, etc. As impurity solver within the B-DMFT calculations we apply the exact diagonalization method [41,54,55].…”

“…III A we have established a relation between the behavior of long-range interacting bosons on the triangular and square lattices. In order to make this comparison, we have chosen the same parameters as used in [41]. However, these values of the parameters are not optimally suited for experimental realization of the model (1) with Rydberg atoms loaded into an optical lattice.…”