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arXiv:1503.03259 · New Journal of Physics

Crystalline structures and frustration in a two-component Rydberg gas

Emanuele Levi, Jiří Minář, Juan P. Garrahan, Igor Lesanovsky

Published Dec 14, 2015• 13 citations
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Abstract

We study the static behavior of a gas of atoms held in a one-dimensional lattice where two distinct electronically high-lying Rydberg states are simultaneously excited by laser light. We focus on a situation where interactions of van-der-Waals type take place only among atoms that are in the same Rydberg state. We analytically investigate at first the so-called classical limit of vanishing laser driving strength. We show that the system exhibits a surprisingly complex ground state structure with a sequence of compatible to incompatible transitions. The incompatibility between the species leads to mutual frustration, a feature which pertains also in the quantum regime. We perform an analytical and numerical investigation of these features and present an approximative description of the system in terms of a Rokhsar–Kivelson Hamiltonian which permits the analytical understanding of the frustration effects even beyond the classical limit.

DOI
10.1088/1367-2630/17/12/123017

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We study the static behavior of a gas of atoms held in a one-dimensional lattice where two distinct electronically high-lying Rydberg states are simultaneously excited by laser light. We focus on a situation where interactions of van-der-Waals type take place only among atoms that are in the same Rydberg state. We analytically investigate at first the so-called classical limit of vanishing laser driving strength. We show that the system exhibits a surprisingly complex ground state structure with a sequence of compatible to incompatible transitions. The incompatibility between the species leads to mutual frustration, a feature which pertains also in the quantum regime. We perform an analytical and numerical investigation of these features and present an approximative description of the system in terms of a Rokhsar–Kivelson Hamiltonian which permits the analytical understanding of the frustration effects even beyond the classical limit.
We study the static behavior of a gas of atoms held in a one-dimensional lattice where two distinct electronically high-lying Rydberg states are simultaneously excited by laser light. We focus on a situation where interactions of van-der-Waals type take place only among atoms that are in the same Rydberg state. We analytically investigate at first the so-called classical limit of vanishing laser driving strength. We show that the system exhibits a surprisingly complex ground state structure with a sequence of commensurate to incommensurate transitions. The incommensurability between the species leads to mutual frustration, a feature which pertains also in the quantum regime. We perform an analytical and numerical investigation of these features and present an approximative description of the system in terms of a Rokhsar-Kivelson Hamiltonian which permits the analytical understanding of the frustration effects even beyond the classical limit.
The creation of collective many-body quantum states from a two-dimensional lattice gas of atoms is studied. Our approach relies on the van der Waals interaction that is present between alkali metal atoms which are laser excited to high-lying Rydberg s-states. We focus on a regime in which the laser driving is strong compared to the interaction between Rydberg atoms. Here energetically low-lying many-particle states can be calculated approximately from a quadratic Hamiltonian. The potential usefulness of these states as a resource for the creation of deterministic single-photon sources is illustrated. The properties of these photon states are determined from the interplay between the particular geometry of the lattice and the interatomic spacing.
We study a one-dimensional atomic lattice gas in which Rydberg atoms are excited by a laser and whose external dynamics is frozen. We identify a parameter regime in which the Hamiltonian is well approximated by a spin Hamiltonian with quasilocal many-body interactions which possesses an exact analytic ground state solution. This state is a superposition of all states of the system that are compatible with an interaction induced constraint weighted by a fugacity. We perform a detailed analysis of this state which exhibits a crossover between a paramagnetic phase with short-ranged correlations and a crystal. This study also leads us to a class of spin models with many-body interactions that permit an analytic ground state solution.
We study the conditions for attaining crystalline order in the stationary state of a continuously driven, open many-body system. Specifically, we consider resonant optical excitations of atoms in a one-dimensional lattice to the Rydberg states interacting via the van der Waals potential. Strong blockade of excitations at neighboring lattice sites steers the system toward a crystalline state while competing with the fluctuations associated with relaxation. We analyze the stationary state of the many-body system and the dynamics of its buildup employing numerically exact time-dependent density-matrix renormalization-group simulations for two- and three-level excitation schemes. We also present an approximate rate equation model which provides qualitative conditions for attaining crystalline order.
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 study a two-dimensional lattice gas of atoms that are photoexcited to Rydberg states in which they interact via the van der Waals interaction. We explore the regime of dominant nearest-neighbor interaction where this system is intimately connected with a quantum version of Baxter's hard-squares model. We show that the strongly correlated ground state of the Rydberg gas can be analytically described by a projected entangled pair state that constitutes the ground state of the quantum hard-squares model. This correspondence allows us to identify a phase boundary where the Rydberg gas undergoes a transition from a disordered (liquid) phase to an ordered (solid) phase.