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Phase diagram of non-equilibrium phase transition in a strongly-interacting Rydberg atom vapour

Dong-Sheng Ding, Hannes Busche, Bao-Sen Shi, Guang‐Can Guo, Charles S. Adams

Published Jun 28, 2016• 1 citation
OpenAlex

Abstract

Abstract Far-from equilibrium dynamics that lead to self-organization are highly relevant to complex dynamical systems not only in physics, but also in life-, earth-, and social sciences. It is challenging however to find systems with sufficiently controllable parameters that allow quantitatively modelling of emergent properties. Here, we study a non-equilibrium phase transition and observe signatures of self-organized criticality in a dilute thermal vapour of atoms optically excited to strongly interacting Rydberg states. Electromagnetically induced transparency (EIT) provides excellent control over the population dynamics and enables high-resolution probing of the driven-dissipative dynamics, which also exhibits phase bistability. Increased sensitivity compared to previous work allows us to reconstruct the complete phase diagram including in the vicinity of the critical point. We observe that interaction-induced energy shifts and enhanced decay only occur in one of the phases above a critical Rydberg population. This limits the application of generic mean-field models, however a modified, threshold-dependent approach is in qualitative agreement with experimental data. Near threshold, we observe self-organized dynamics in the form of population jumps that return the density to a critical value.

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Far-from-equilibrium dynamics that lead to self-organization are highly relevant to complex dynamical systems not only in physics but also in life, earth, and social sciences.However, it is challenging to find systems with sufficiently controllable parameters that allow quantitatively modeling of emergent properties.Here, we study a nonequilibrium phase transition and observe signatures of self-organized criticality in a dilute thermal vapor of atoms optically excited to strongly interacting Rydberg states.Electromagnetically induced transparency provides excellent control over the population dynamics and enables highresolution probing of the driven-dissipative dynamics, which also exhibits phase bistability.Increased sensitivity compared to previous work allows us to reconstruct the complete phase diagram, including in the vicinity of the critical point.We observe that interaction-induced energy shifts and enhanced decay only occur in one of the phases above a critical Rydberg population.This case limits the application of generic mean-field models; however, a modified, threshold-dependent approach is in qualitative agreement with experimental data.Near threshold, we observe self-organized dynamics in the form of population jumps that return the density to a critical value.

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Cooperative non-equilibrium dynamics in a thermal Rydberg ensemble

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This thesis reports the investigation of cooperative non-equilibrium dynamics in a thermal Rydberg ensemble. Cooperative behaviour arises due to resonant dipole-dipole interactions between highly excited Rydberg atoms. In order to transfer atomic population from the ground state to the Rydberg state in a caesium vapour, a three-photon excitation scheme is developed. This scheme has a number of benefits over traditional two-photon Rydberg excitation as each transition utilises in- expensive high-power diode lasers. The process of developing the excitation scheme produces a number of important results, including an excited-state polarisation spectroscopy technique and the observation of coherent three-photon electromagnetically induced transparency. The optical response and atomic dynamics of the interacting ensemble can be separated into two distinct phases. When the Rydberg number density is low and the interactions are negligible, the system can be described by the behaviour of a single atom. However, when the Rydberg number density is high, resonant dipole-dipole interactions result in a significant modification of the ensemble properties. This cooperative many-body phase cannot be described by the behaviour of a single atom. In the frequency domain, the interactions produce an excitation-dependent cooperative energy shift that is observed using probe transmission spectroscopy. In the time domain, the interactions result in a cooperative enhancement of the atomic decay rate that is analysed using fluorescence spectroscopy. At the transition between the single-body and many-body phase, a first-order non-equilibrium phase transition occurs. This is observed spatially along the length of the excitation region as a sharp switch in the emitted fluorescence. The first-order phase transition is also observed in the temporal response of the ensemble through critical slowing down. The divergence of the switching time to steady state follows a universal scaling law for phase transitions and the determined critical exponent is in excellent agreement with previous work on non-equilibrium phase transitions.

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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.

quant-pharXiv:2608.05955•Aug 7, 2026•0 citations
Abstract Far-from equilibrium dynamics that lead to self-organization are highly relevant to complex dynamical systems not only in physics, but also in life-, earth-, and social sciences. It is challenging however to find systems with sufficiently controllable parameters that allow quantitatively modelling of emergent properties. Here, we study a non-equilibrium phase transition and observe signatures of self-organized criticality in a dilute thermal vapour of atoms optically excited to strongly interacting Rydberg states. Electromagnetically induced transparency (EIT) provides excellent control over the population dynamics and enables high-resolution probing of the driven-dissipative dynamics, which also exhibits phase bistability. Increased sensitivity compared to previous work allows us to reconstruct the complete phase diagram including in the vicinity of the critical point. We observe that interaction-induced energy shifts and enhanced decay only occur in one of the phases above a critical Rydberg population. This limits the application of generic mean-field models, however a modified, threshold-dependent approach is in qualitative agreement with experimental data. Near threshold, we observe self-organized dynamics in the form of population jumps that return the density to a critical value.
Far-from-equilibrium dynamics that lead to self-organization are highly relevant to complex dynamical systems not only in physics but also in life, earth, and social sciences.However, it is challenging to find systems with sufficiently controllable parameters that allow quantitatively modeling of emergent properties.Here, we study a nonequilibrium phase transition and observe signatures of self-organized criticality in a dilute thermal vapor of atoms optically excited to strongly interacting Rydberg states.Electromagnetically induced transparency provides excellent control over the population dynamics and enables highresolution probing of the driven-dissipative dynamics, which also exhibits phase bistability.Increased sensitivity compared to previous work allows us to reconstruct the complete phase diagram, including in the vicinity of the critical point.We observe that interaction-induced energy shifts and enhanced decay only occur in one of the phases above a critical Rydberg population.This case limits the application of generic mean-field models; however, a modified, threshold-dependent approach is in qualitative agreement with experimental data.Near threshold, we observe self-organized dynamics in the form of population jumps that return the density to a critical value.
This thesis reports the investigation of cooperative non-equilibrium dynamics in a thermal Rydberg ensemble. Cooperative behaviour arises due to resonant dipole-dipole interactions between highly excited Rydberg atoms. In order to transfer atomic population from the ground state to the Rydberg state in a caesium vapour, a three-photon excitation scheme is developed. This scheme has a number of benefits over traditional two-photon Rydberg excitation as each transition utilises in- expensive high-power diode lasers. The process of developing the excitation scheme produces a number of important results, including an excited-state polarisation spectroscopy technique and the observation of coherent three-photon electromagnetically induced transparency. The optical response and atomic dynamics of the interacting ensemble can be separated into two distinct phases. When the Rydberg number density is low and the interactions are negligible, the system can be described by the behaviour of a single atom. However, when the Rydberg number density is high, resonant dipole-dipole interactions result in a significant modification of the ensemble properties. This cooperative many-body phase cannot be described by the behaviour of a single atom. In the frequency domain, the interactions produce an excitation-dependent cooperative energy shift that is observed using probe transmission spectroscopy. In the time domain, the interactions result in a cooperative enhancement of the atomic decay rate that is analysed using fluorescence spectroscopy. At the transition between the single-body and many-body phase, a first-order non-equilibrium phase transition occurs. This is observed spatially along the length of the excitation region as a sharp switch in the emitted fluorescence. The first-order phase transition is also observed in the temporal response of the ensemble through critical slowing down. The divergence of the switching time to steady state follows a universal scaling law for phase transitions and the determined critical exponent is in excellent agreement with previous work on non-equilibrium phase transitions.
Summary form only given. Understanding and probing phase transitions in non-equilibrium systems is an ongoing challenge in physics. A particular instance are phase transitions that occur between a non-fluctuating absorbing phase [1], e.g., an extinct population, and one in which the relevant order parameter, such as the population density, assumes a finite value. Here we report the observation of signatures of such a non-equilibrium phase transition in an open driven quantum system. In our experiment rubidium atoms in a quasi one-dimensional cold disordered gas are laser-excited to Rydberg states under so-called facilitation conditions [2]. This conditional excitation process competes with spontaneous decay (see Fig. 1a) and leads to a crossover between a stationary state with no excitations and one with a finite number of Rydberg excitations (see Fig. 1b, where the phase diagram is plotted as a function of the driving strength and detuning from resonance) [3]. We relate the underlying physics to that of an absorbing state phase transition in the presence of a field which slightly offsets the system from criticality. We observe a characteristic power-law scaling of the Rydberg excitation density as well as increased fluctuations close to the transition point. Furthermore, we argue that the observed transition relies on the presence of atomic motion which introduces annealed disorder into the system and enables the formation of long-ranged correlations. Our study paves the road for future investigations into the largely unexplored physics of non-equilibrium phase transitions in open many-body quantum systems.
Highly-excited Rydberg atoms have strong long-range interactions resulting in exotic optical prop erties such as large single photon non-linearities and intrinsic bistability. In this paper we study optical-driven non-equilibrium phase transitions in a thermal Rydberg gas with a sensitivity two order of magnitude higher than in previous work. In this regime we can elucidate the effect of inter actions on the bistable optical response, and exploit different branches in the potential in order to study multi-component Rydberg gases with a rich of phase diagram including overlapping bistable regions. In addition, we study the effect of polarization on the width of the hysteresis loop. Finally, we observe that the medium exhibits a dynamical instability resulting from the competing dynamics of excitation and decay.
We investigate the out-of-equilibrium behavior of a dissipative gas of Rydberg atoms that features a dynamical transition between two stationary states characterized by different excitation densities. We determine the structure and properties of the phase diagram and identify the universality class of the transition, both for the statics and the dynamics. We show that the proper dynamical order parameter is in fact not the excitation density and find evidence that the dynamical transition is in the "model A" universality class; i.e., it features a nontrivial Z2 symmetry and a dynamics with nonconserved order parameter. This sheds light on some relevant and observable aspects of dynamical transitions in Rydberg gases. In particular it permits a quantitative understanding of a recent experiment [C. Carr, Phys. Rev. Lett. 111, 113901 (2013)] which observed bistable behavior as well as power-law scaling of the relaxation time. The latter emerges not due to critical slowing down in the vicinity of a second order transition, but from the nonequilibrium dynamics near a so-called spinodal line.
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.