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arXiv:2509.07528 · Journal of Physics B Atomic Molecular and Optical Physics

Different phases in a dissipative Rydberg lattice: roles of occupancy and on-site interaction

Suvechha Indu, Aniruddha Biswas, Raka Dasgupta

Published Jan 26, 2026• 0 citations
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Abstract

Abstract We investigate a two-level dissipative bosonic Rydberg system in an optical lattice with multiple occupancy per site. The system dynamics are analyzed using two complementary approaches: a mean-field solution of the master equation and direct numerical simulations of an equivalent quantum model. We show that on-site interactions drive a transition between a uniform phase and an antiferro-like density-wave order in terms of the Rydberg excitation distribution. In the mean-field framework, the population distribution across sublattices plays a decisive role: homogeneous populations lead to a sharp transition, while initializing alternating sites with unequal occupancies produces a smooth crossover. In contrast, finite-size quantum simulations always yield a smooth crossover, and an abrupt phase transition never takes place. The origins of uniform and non-uniform phases are explored through spatial correlation analysis and the identification of dynamical fixed points. Furthermore, scaling analysis reveals a signature of weak universality in the homogeneous case.

DOI
10.1088/1361-6455/ae3d74

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Abstract We investigate a two-level dissipative bosonic Rydberg system in an optical lattice with multiple occupancy per site. The system dynamics are analyzed using two complementary approaches: a mean-field solution of the master equation and direct numerical simulations of an equivalent quantum model. We show that on-site interactions drive a transition between a uniform phase and an antiferro-like density-wave order in terms of the Rydberg excitation distribution. In the mean-field framework, the population distribution across sublattices plays a decisive role: homogeneous populations lead to a sharp transition, while initializing alternating sites with unequal occupancies produces a smooth crossover. In contrast, finite-size quantum simulations always yield a smooth crossover, and an abrupt phase transition never takes place. The origins of uniform and non-uniform phases are explored through spatial correlation analysis and the identification of dynamical fixed points. Furthermore, scaling analysis reveals a signature of weak universality in the homogeneous case.
We use a density matrix formalism to study the equilibrium phases and nonequilibrium dynamics of a system of dissipative Rydberg atoms in an optical lattice within mean-field theory. We provide equations for the fixed points of the density matrix evolution for atoms with infinite on-site repulsion and analyze these equations to obtain their Mott-insulator--superfluid (MI-SF) phase boundary. A stability analysis around these fixed points provides us with the excitation spectrum of the atoms both in the MI and SF phases. We study the nature of the MI-SF critical point in the presence of finite dissipation of Rydberg excitations, discuss the fate of the superfluid order parameter of the atoms in the presence of such dissipation in the weak-coupling limit using a coherent state representation of the density matrix, and extend our analysis to Rydberg atoms with finite on-site interaction via numerical solution of the density matrix equations. Finally, we vary the boson (atom) hopping parameter JJJ and the dissipation parameter $\mathrm{\ensuremath{\Gamma}}$ according to a linear ramp protocol. We study the evolution of entropy of the system following such a ramp and show that the deviation of the entropy from its steady-state value for the latter protocol exhibits power-law behavior as a function of the ramp time. We discuss experiments that can test our theory.
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.
We study the non-equilibrium dynamics of driven spin lattices in the presence of decoherence caused by either laser phase noise or strong decay. In the first case, we discriminate between correlated and uncorrelated noise and explore their effect on the mean density of Rydberg states and the full counting statistics (FCS). We find that while the mean density is almost identical in both cases, the FCS differ considerably. The main method employed is the Langevin equation (LE) 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 lattices can undergo a dissipative phase transition to a long-range-ordered antiferromagnetic (AF) phase. We identify the advantages of Monte Carlo rate equations over mean field (MF) predictions.
We study dynamical phase transitions in the generalized dissipative Dicke model in an array of trapped Rydberg ions, where their density-density interactions compete with the collective spin-phonon coupling, laser driving and dissipation. This setting offers a versatile approach to study equilibrium as well as non-equilibrium many-body phenomena, as parameters, such as the Ising interaction, laser-ion and spin-phonon coupling can be tuned. Through analyzing the mean-field phase diagram, we find a variety of distinct phases and the emergence of a tricritical point that are sensitively dependent of the interaction between Rydberg ions. We then study the quantum dynamics for a finite system size and characterize parameter dependent dynamics using the spin average, entropy, and Loschmidt echo. Distinctive signatures of the dynamical phases, such as slow relaxation and metastability, arise near the phase transition. This analysis predicts rich quantum dynamics of the finite system that link to the non-equilibrium mean-field phases. Our study widens the exploration of collective and non-equilibrium phases in Dicke models, and reveals that the Rydberg ion interaction drastically affects the phase diagram and dynamics.
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.
Abstract Dynamic structure factor (DSF) is important for understanding excitations in many-body physics; it reveals information about the spectral and spatial correlations of fluctuations in quantum systems. Collective phenomena like quantum phase transitions of ultracold atoms are addressed by harnessing density fluctuations. Here, we calculate the DSF of a nonequilibrium spinless Bose–Hubbard model from the perspective of dissipative phase transition (DPT) in a steady state. Our methodology uses a homogeneous mean-field approximation to make the single-site hierarchy simpler and applies the Lindbladian perturbation method (LPM) to go beyond the single site, limited by the ratio of the inter-site hopping term to the Liouvillian gap as a small parameter. Our results show that the DSF near a DPT point is characteristically different from that away from the transition point, providing a clear density spectral signature of the DPT. In addition to comparing the two numerical frameworks, the mean-field results serve as a benchmark for proof-of-principle robustness of LPM. Despite the numerical difficulty, our methodology provides a computationally accessible route for studying density fluctuations in an open lattice quantum system without requiring large-scale computation.