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arXiv:1305.6687 · Physical Review A

Quantum phases of strongly interacting Rydberg atoms in triangular lattices

Jing Qian, Lu Zhou, Weiping Zhang

Published Jun 24, 2013• 19 citations
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Abstract

We present a theoretical study on the system of laser-driven strongly interacting Rydberg atoms trapped in a two-dimensional triangular lattice, in which the dipole-dipole interactions between Rydberg states result in exotic quantum phases. By using the mean-field theory, we investigate the steady state solutions and analyze their dynamical stabilities. We find that in the strong-interaction limit, the dynamics of the system is chaotic and exhibits random oscillations under appropriate laser detunings. The Lyapunov exponent criterion is introduced to confirm the existence of this chaotic behavior. In addition, we present a full quantum calculation based on a six-atom model, and find that the system exhibits some biantiferromagnetic properties in every triangular cell when the one-photon detuning is exactly resonant or blue shifted.

DOI
10.1103/physreva.87.063421

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We present a theoretical study on the system of laser-driven strongly interacting Rydberg atoms trapped in a two-dimensional triangular lattice, in which the dipole-dipole interactions between Rydberg states result in exotic quantum phases. By using the mean-field theory, we investigate the steady state solutions and analyze their dynamical stabilities. We find that in the strong-interaction limit, the dynamics of the system is chaotic and exhibits random oscillations under appropriate laser detunings. The Lyapunov exponent criterion is introduced to confirm the existence of this chaotic behavior. In addition, we present a full quantum calculation based on a six-atom model, and find that the system exhibits some biantiferromagnetic properties in every triangular cell when the one-photon detuning is exactly resonant or blue shifted.
The work presented in this dissertation concerns dynamics of Rydberg atom lattices in the presence of noise and dissipation. Rydberg atoms possess a number of exaggerated properties, such as a strong van der Waals interaction. The interplay of that interaction, coherent driving and decoherence leads to intriguing non-equilibrium phenomena. Here, we study the non-equilibrium physics of driven atom lattices in the presence of decoherence caused by either laser phase noise or strong decay. In the first case, we compare between global and local noise and explore their effect on the number of excitations and the full counting statistics. We find that both types of noise give rise to a characteristic distribution of the Rydberg excitation number. The main method employed is the Langevin equation but for the sake of efficiency in certain regimes, we use a Markovian master equation and Monte Carlo rate equations, respectively. In the second case, we consider dissipative systems with more general power-law interactions. We determine the phase diagram in the steady state and analyse its generation dynamics using Monte Carlo rate equations. In contrast to nearest-neighbour models, there is no transition to long-range-ordered phases for realistic interactions and resonant driving. Yet, for finite laser detunings, we show that Rydberg atom lattices can undergo a dissipative phase transition to a long-range-ordered antiferromagnetic phase. We identify the advantages of Monte Carlo rate equations over mean field predictions. Having studied the dynamics of Rydberg atom lattices, we study an application of the strong interactions in such systems for quantum information processing. We investigate the coherent exchange of a single photon between a superconducting microwave cavity and a lattice of strongly interacting Rydberg atoms in the presence of local electric field fluctuations plaguing the cavity surface. We show that despite the increased sensitivity of Rydberg states to electric fields, as compared to ground state atoms, the Rydberg dipole-dipole interaction can be used to protect the system against the dephasing induced by the local noise. Using 1/f1/f1/f and laser phase noise models, we show that compared to the case with non-interacting atoms, our system exhibits longer coherence lifetimes and larger retrieval efficiency of the photon after storing into the atoms.
The neutral atoms coupled to a highly excited Rydberg state on a two-dimensional triangular lattice are investigated by employing the density matrix renormalization group technique in the matrix product state form. The full ground-state phase diagram as a function of blockade radius and the detuning of the exciting laser is determined by the behavior of entanglement entropy. We find several quantum phases including stripe-ordered and symmetry-breaking density-wave-ordered phases featured with regular excitation patterns of different excitation densities ρ = 1/3, 1/4, and 1/7. In addition, a ρ = 2/3 ordered phase and an interesting "order-by-disorder" phase, which has been prepared experimentally, are also observed in this work. Our work provides an exploration of the possible quantum phases that can occur in a triangularly arrayed Rydberg system, and thus could be a faithful theoretical guide for further experimental research.
We study the dynamics of dissipative spin lattices with power-law interactions, realized via few-level atoms driven by coherent laser-coupling and decoherence processes. Using Monte Carlo simulations, we determine the phase diagram in the steady state and analyze its generation dynamics. As opposed to mean-field predictions and nearest-neighbor models, there is no transition to long-range-ordered phases for realistic interactions and resonant driving. However, for finite laser detunings, we demonstrate the emergence of crystalline order. Although the static and dynamical critical exponents of the revealed dissipative phase transition fall into the two-dimensional Ising universality class, the found steady states differ considerably from those of an equilibrium Ising magnet. Two complementary schemes for an experimental implementation with cold Rydberg atoms are discussed.
We theoretically investigate the dynamical phase diagram of a one-dimensional chain of laser-excited two-species Rydberg atoms. The existence of a variety of unique dynamical phases in the experimentally achievable parameter region is predicted under the mean-field approximation, and the change in those phases when the effect of the next-nearest-neighbor interaction is included is further discussed. In particular, we find that the com-petition of the strong Rydberg-Rydberg interactions and the optical excitation imbalance can lead to the presence of complex multiple chaotic phases, which are highly sensitive to the initial Rydberg-state population and the strength of the next-nearest-neighbor interactions.
We studied signatures of quantum chaos in dynamics of Rydberg-dressed bosonic atoms held in a one-dimensional triple-well potential. Long-range nearest-neighbor and next-nearest-neighbor interactions, induced by laser dressing atoms to strongly interacting Rydberg states, drastically affect mean-field and quantum many-body dynamics. By analyzing the mean-field dynamics, classical chaos regions with positive and large Lyapunov exponents were identified as a function of the potential well tilting and dressed interactions. In the quantum regime, it was found that level statistics of the eigen-energies gain a Wigner–Dyson distribution when the Lyapunov exponents are large, giving rise to signatures of strong quantum chaos. We found that both the time-averaged entanglement entropy and survival probability of the initial state have distinctively large values in the quantum chaos regime. We further showed that population variances could be used as an indicator of the emergence of quantum chaos. This might provide a way to directly probe quantum chaotic dynamics through analyzing population dynamics in individual potential wells.
The glass phase and its quantum analog are prominent challenges of current non-equilibrium statistical mechanics and condensed matter physics. As a model system to study the transition from classical to quantum glassy dynamics, we propose a setup of laser driven three-level atoms trapped in an optical lattice. Tuning the strength of the laser driving to the intermediate level allows one to study the transition from a classical kinetically constrained model to the coherent regime. For strong driving, Rydberg excitations evolve analogously to defects in the one-spin facilitated model, a minimal model known to exhibit glassy dynamics. In our setup, the constraints result from the interplay between Rydberg interactions and the laser detuning from the Rydberg state. The emerging heterogeneous relaxation timescales are tuneable over several orders of magnitudes. In the opposite limit of weak driving of the intermediate level, we find an effective cluster model which describes the dynamics in a reduced subspace of the allowed number and positions of Rydberg excitations. This subspace is uniquely determined by the initial state and is characterized by a fixed number of clusters of Rydberg excitations. In addition, we investigate the influence of random fields on the classical relaxation. We find that the glassy dynamics can relax faster in the presence of weak random fields.