Antiferromagnetic long-range order in dissipative Rydberg lattices

Abstract

We study the dynamics of dissipative spin lattices with power-law interactions, realized via fewlevel atoms driven by coherent laser-coupling and decoherence processes. Using Monte-Carlo simulations, we determine the phase diagram in the steady state and analyze the dynamics of its generation. As opposed to mean-field predictions and nearest-neighbour models there is no phase transition to long-range ordered phases for realistic interactions and resonant driving. However, for finite laser detunings, we demonstrate the emergence of crystalline order with a vanishing dissipative gap. Although the found steady states differ considerably from those of an equilibrium Ising magnet, the critical exponent of the revealed dissipative phase transition falls into the 2D Ising universality class. Two complementary schemes for an experimental implementation with cold Rydberg atoms are discussed. [5][6][7]. This requires sufficient time to remain adiabatic, which poses a challenging competition with the finite lifetime of the Rydberg states. Alternatively, this excited-state decay has been proposed as a natural means for dissipative state preparation [8]. The non-equilibrium physics of such driven open systems has recently attracted considerable interest [9][10][11][12], as their properties can differ dramatically from conventional equilibrium situations.Previous work considered lattices of effective spins, represented by an atomic ground and strongly interacting Rydberg state coupled by external laser driving and spontaneous decay [8,13,14]. The emergence of steady states with antiferromagnetic order was predicted on the basis of mean field theory assuming nearest-neighbour (NN) interactions [8]. It was later shown, however, that ordering in these systems is restricted to short length scales for all spatial lattice dimensions due to large singlesite fluctuations associated with a simple two-level driving scheme [14]. Simulations moreover showed that crystallization in 1D is precluded for other driving schemes [14], for which long-range order was predicted using mean field theory [15]. Hence, the possibility of long-range order in dissipative Rydberg lattices has thus far remained an open question.In this letter, we address this issue and show that longrange ordered antiferromagnetic phases can indeed be re- alized in dissipative Rydberg lattices when subject to appropriate coherent driving. However, fluctuations as well as the weak tail of the rapidly decaying interactions are both found to be essential for the physics of the dissipative phase transition. This stands in marked contrast to the equilibrium physics of the corresponding unitary systems, which often is well described by mean field models [16] and NN approximations [17]. The crystalline phase features a vanishing dissipative gap and strongly deviates from that of an equilibrium Ising magnet with finite arXiv:1404.1281v1 [cond-mat.quant-gas]

Experimental observation of controllable kinetic constraints in a cold atomic gas

“…However, it can be difficult [8] to establish unambiguously the relation between microscopic processes and emerging kinetic constraints, or between idealized models with explicit kinetic constraints and actual physical systems. In this Rapid Communication we establish such a direct connection by reporting the experimental observation of correlated manybody excitation dynamics in a strongly interacting Rydberg gas [9][10][11][12] whose origin lies in explicit kinetic constraints that can be theoretically derived from the quantum-mechanical equations of motion of the system. We explore two kinds of kinetic constraints which lead to the suppression or the facilitation of atomic excitations in the vicinity of atoms excited to Rydberg states.…”

“…In this strong dissipation limit the evolution of the many-body system is restricted to the subspace of classical spin configurations by virtue of the quantum Zeno effect [15]. The dynamics can be written as a classical rate equation with rates for excitation and deexcitation [9,11],…”

Linked cluster expansions for open quantum systems on a lattice

“…In the latter context, a careful engineering of the coupling between the system and the environment can stabilize interesting many-body phases in the steady state 21,22 . The phase-diagram of such lattice systems has been predicted to be incredibly rich [23][24][25][26][27][28][29][30] and can display spontaneous ordering associated with the breaking of a discrete [31][32][33] or continuous symmetry 34,35 possessed by the model. Recently, the critical behavior emerging at the onset of phase transitions started to be investigated by means of different analytical and numerical approaches [36][37][38][39] .…”

Control of Rydberg-atom blockade by dc electric-field orientation in a quasi-one-dimensional sample

“…Such systems rely on the Rydberg atom blockade effect [11][12][13], which is a density limitation of Rydberg atomic population due to the strong interaction between the atoms. However, these same interactions may lead to coherenceloss on atomic samples [14]. Such interaction can present either advantages or disadvantages in atomic systems, therefore they need to be well understood.…”