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arXiv:1007.2189 · Physical Review Letters

Two-Stage Melting in Systems of Strongly Interacting Rydberg Atoms

Hendrik Weimer, Hans Peter Büchler

Published Nov 30, 2010• 108 citations
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Abstract

We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil's staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low-energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic correlations. For stronger quantum fluctuations the floating solid eventually melts within a second quantum phase transition and the ground state becomes paramagnetic.

DOI
10.1103/physrevlett.105.230403

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We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil's staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low-energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic correlations. For stronger quantum fluctuations the floating solid eventually melts within a second quantum phase transition and the ground state becomes paramagnetic.
We investigate the quantum melting of one-dimensional crystals that are realized in an atomic lattice in which ground state atoms are laser excited to two Rydberg states. We focus on a regime where both, intra- and interstate density-density interactions as well as coherent exchange interactions contribute. We determine stable crystalline phases in the classical limit and explore their melting under quantum fluctuations introduced by the excitation laser as well as two-body exchange. We find that within a specific parameter range quantum fluctuations introduced by the laser can give rise to a devil's staircase structure which one might associate with transitions in the classical limit. The melting through exchange interactions is shown to also proceed in a steplike fashion, in the case of small crystals, due to the proliferation of Rydberg spin waves.
We consider cold Rydberg atoms in a one-dimensional optical lattice in the Mott regime with a single atom per site at zero temperature. An external laser drive with Rabi frequency $\ensuremath{\Omega}$ and laser detuning $\ensuremath{\Delta}$ creates Rydberg excitations whose dynamics is governed by an effective spin-chain model with (quasi) long-range interactions. This system possesses intrinsically a large degree of frustration resulting in a ground-state phase diagram in the $(\ensuremath{\Delta},\ensuremath{\Omega})$ plane with a rich topology. As a function of $\ensuremath{\Delta}$, the Rydberg blockade effect gives rise to a series of crystalline phases commensurate with the optical lattice that form a so-called devil's staircase. The Rabi frequency $\ensuremath{\Omega}$, on the other hand, creates quantum fluctuations that eventually lead to a quantum melting of the crystalline states. Upon increasing $\ensuremath{\Omega}$, we find that generically a commensurate-incommensurate transition to a floating Rydberg crystal that supports gapless phonon excitations occurs first. For even larger $\ensuremath{\Omega}$, dislocations within the floating Rydberg crystal start to proliferate and a second, Kosterlitz-Thouless-Nelson-Halperin-Young dislocation-mediated melting transition finally destroys the crystalline arrangement of Rydberg excitations. This latter melting transition is generic for one-dimensional Rydberg crystals and persists even in the absence of an optical lattice. The floating phase and the concomitant transitions can, in principle, be detected by Bragg scattering of light.
We discuss the many-body physics of an ensemble of Rydberg dressed atoms with van der Waals dipole–dipole interactions in a one-dimensional lattice. Using a strong coupling expansion and numerical density-matrix renormalization group simulations, we calculate the many-body phase diagram. A devil's staircase structure emerges with Mott-insulating phases at any rational filling fraction. Closed analytic expressions are given for the phase boundaries in second order of the tunneling amplitude and are shown to agree very well with the numerical results. The transition point where the incompressible phases melt due to the kinetic energy term depends strongly on the denominator of the filling fraction and varies over many orders of magnitude between different phases.
Abstract. We discuss the many-body physics of an ensemble of Rydberg dressed atoms with van der Waals dipole-dipole interactions in a one-dimensional lattice. Using a strong coupling expansion and numerical density-matrix renormalisation group simulations, we calculate the many-body phase diagram. A devil’s staircase structure emerges with Mott-insulating phases at any rational filling fraction. Closed analytic expressions are given for the phase boundaries in second order of the tunnelling amplitude and shown to agree very well with the numerical results. The transition point where the incompressible phases melt due to the kinetic energy term depends strongly on the denominator of the filling fraction and varies over many orders of magnitude between different phases.
Experiments on chains of Rydberg atoms appear as a playground to study quantum phase transitions in 1D. As a natural extension, we report a quantitative ground-state phase diagram of Rydberg atoms arranged in a two-leg ladder interacting via van der Waals potential. We address this problem numerically, using the density matrix renormalization group algorithm. Our results suggest that, quite remarkably, Z k crystalline phases, with the exception of the checkerboard phase, appear in pairs characterized by the same pattern of occupied rungs but distinguishable by a spontaneously broken Z ̃ 2 symmetry between the two legs of the ladder. Within each pair, the two phases are separated by a continuous transition in the Ising universality class, which eventually fuses with the Z k transition, whose nature depends on k . According to our results, the transition into the Z 2 ⊗ Z ̃ 2 phase changes its nature multiple times, including an Ashkin-Teller transition that is surprisingly stable over an extended interval, followed by the Z 4 -chiral transition, and finally in a two step-process mediated melting via the floating phase. The transition into the Z 3 phase with resonant states on the rungs belongs to the three-state Potts universality class at the commensurate point, to the Z 3 -chiral Huse-Fisher universality class away from it, and eventually it is through an intermediate floating phase. The Ising transition between Z 3 and Z 3 ⊗ Z ̃ 2 phases, entering the floating phase, opens the possibility to realize lattice supersymmetry in Rydberg quantum simulators.
We study the appearance of correlated many-body phenomena in an ensemble of atoms driven resonantly into a strongly interacting Rydberg state. The ground state of the Hamiltonian describing the driven system exhibits a second order quantum phase transition. We derive the critical theory for the quantum phase transition and show that it describes the properties of the driven Rydberg system in the saturated regime. We find that the suppression of Rydberg excitations known as blockade phenomena exhibits an algebraic scaling law with a universal exponent.