We study the ground-state phase diagram of Rydberg atoms in a triangular-prism optical tweezer array using the density matrix renormalization group. By tuning the detuning-to-Rabi-frequency ratio and the Rydberg blockade radius, the system realizes several density-wave phases with spontaneous breaking of translational and leg-exchange symmetries. Unlike two-leg Rydberg ladders with $\mathbb{Z}_2$ leg-exchange symmetry, the triangular prism has $\mathbb{D}_3$ symmetry, leading to a richer set of ordered phases and transitions. For blockade radius moderately larger than the lattice spacing, a phase with alternating double and single Rydberg occupancy appears at large detuning. It breaks $\mathbb{Z}_2$ translational and $\mathbb{Z}_3$ rotational symmetry while preserving a rung reflection symmetry. Upon decreasing detuning, it melts through two Berezinskii-Kosterlitz-Thouless transitions with an intermediate critical phase described by a $\mathbb{Z}_6$ clock model. At larger blockade radius, a phase with one Rydberg excitation per triangle and broken $\mathbb{D}_3$ symmetry appears through a first-order transition. When double occupation of neighboring triangles is suppressed, rung-trimerized density waves develop as detuning increases from the disordered phase. Their melting follows the same structure as in Rydberg chains and two-leg ladders: the $\mathbb{Z}_2$ case has Ising critical lines, while the $\mathbb{Z}_3$ and $\mathbb{Z}_4$ cases have chiral critical lines, with Potts and Ashkin-Teller points only on the corresponding commensurate lines. Inside the $\mathbb{Z}_2$ rung-trimerized phase, an entanglement-entropy peak signals a crossover regime with enhanced period-2 density modulation before a first-order transition into a $\mathbb{Z}_2\times\mathbb{D}_3$ phase. Floating phases with incommensurate quasi-long-range order appear between trimerized states of different periods.We study the ground-state phase diagram of Rydberg atoms in a triangular-prism optical tweezer array using the density matrix renormalization group. By tuning the detuning-to-Rabi-frequency ratio and the Rydberg blockade radius, the system realizes several density-wave phases with spontaneous breaking of translational and leg-exchange symmetries. Unlike two-leg Rydberg ladders with $\mathbb{Z}_2$ leg-exchange symmetry, the triangular prism has $\mathbb{D}_3$ symmetry, leading to a richer set of ordered phases and transitions. For blockade radius moderately larger than the lattice spacing, a phase with alternating double and single Rydberg occupancy appears at large detuning. It breaks $\mathbb{Z}_2$ translational and $\mathbb{Z}_3$ rotational symmetry while preserving a rung reflection symmetry. Upon decreasing detuning, it melts through two Berezinskii-Kosterlitz-Thouless transitions with an intermediate critical phase described by a $\mathbb{Z}_6$ clock model. At larger blockade radius, a phase with one Rydberg excitation per triangle and broken $\mathbb{D}_3$ symmetry appears through a first-order transition. When double occupation of neighboring triangles is suppressed, rung-trimerized density waves develop as detuning increases from the disordered phase. Their melting follows the same structure as in Rydberg chains and two-leg ladders: the $\mathbb{Z}_2$ case has Ising critical lines, while the $\mathbb{Z}_3$ and $\mathbb{Z}_4$ cases have chiral critical lines, with Potts and Ashkin-Teller points only on the corresponding commensurate lines. Inside the $\mathbb{Z}_2$ rung-trimerized phase, an entanglement-entropy peak signals a crossover regime with enhanced period-2 density modulation before a first-order transition into a $\mathbb{Z}_2\times\mathbb{D}_3$ phase. Floating phases with incommensurate quasi-long-range order appear between trimerized states of different periods.

cond-mat.quant-gasCross-listedarXiv:2606.01116Jun 2, 20260 citations

Quantum phases of Rydberg atoms in two-dimensional arrays

Rhine Samajdar, Wen Wei Ho, Hannes Pichler +2 more

Bulletin of the American Physical SocietyMar 16, 20210 citations

Quantum phases of Rydberg atoms on a frustrated triangular-lattice array

Chang-Xiao Li, Sheng Yang, Jing-Bo Xu

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.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.

Optics LettersJan 24, 202212 citations

Rydberg States of Atomic Systems

Boris Mikhailovich Karnakov, В. П. Крайнов

Springer eBooksAug 28, 20121 citation

Rydberg Atoms and Their Interactions

Kashif Ammar Yasir, Wu-Ming Liu

Springer series in solid-state sciencesJan 1, 20260 citations

Trimer quantum spin liquid in a honeycomb array of Rydberg atoms

Milan Kornjača, Rhine Samajdar, Tommaso Macrì +3 more

Abstract Quantum spin liquids are elusive but paradigmatic examples of strongly correlated quantum states that are characterized by long-range quantum entanglement. Recently, signatures of a gapped topological ${{\mathbb{Z}}}_{2}$ Z 2 spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.Abstract Quantum spin liquids are elusive but paradigmatic examples of strongly correlated quantum states that are characterized by long-range quantum entanglement. Recently, signatures of a gapped topological $${{\mathbb{Z}}}_{2}$$ Z 2 spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.

arXiv:2211.00653Communications PhysicsDec 13, 202319 citations

\mathbb{Z}_2

leg-exchange symmetry, the triangular prism has

\mathbb{D}_3

symmetry, leading to a richer set of ordered phases and transitions. For blockade radius moderately larger than the lattice spacing, a phase with alternating double and single Rydberg occupancy appears at large detuning. It breaks

\mathbb{Z}_2

translational and

\mathbb{Z}_3

rotational symmetry while preserving a rung reflection symmetry. Upon decreasing detuning, it melts through two Berezinskii-Kosterlitz-Thouless transitions with an intermediate critical phase described by a

\mathbb{Z}_6

clock model. At larger blockade radius, a phase with one Rydberg excitation per triangle and broken

\mathbb{D}_3

symmetry appears through a first-order transition. When double occupation of neighboring triangles is suppressed, rung-trimerized density waves develop as detuning increases from the disordered phase. Their melting follows the same structure as in Rydberg chains and two-leg ladders: the

\mathbb{Z}_2

case has Ising critical lines, while the

\mathbb{Z}_3

and

\mathbb{Z}_4

cases have chiral critical lines, with Potts and Ashkin-Teller points only on the corresponding commensurate lines. Inside the

\mathbb{Z}_2

rung-trimerized phase, an entanglement-entropy peak signals a crossover regime with enhanced period-2 density modulation before a first-order transition into a

\mathbb{Z}_2\times\mathbb{D}_3

phase. Floating phases with incommensurate quasi-long-range order appear between trimerized states of different periods.

{{\mathbb{Z}}}_{2}

Z 2 spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.