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Molecular Physics

Percolation-driven, self-organising evolution from a nitric oxide Rydberg gas to a molecular ultracold plasma

Amin Allahverdian, Smilla Colombini, Nathan Durand-Brousseau, Edward R. Grant

Published May 18, 2026• 0 citations
Publisher

Abstract

Driven dissipative atomic and molecular systems can undergo self-organising dynamics that offer a microscopic framework for understanding key large-scale self-organised processes in nature. In the work described here, double-resonant excitation prepares a state-selected Rydberg gas of nitric oxide seeded in a supersonic molecular beam. This system evolves to create a long-lived molecular ultracold plasma. Time-resolved selective field ionisation reveals strongly fluctuating avalanche sizes that evolve, for all initial Rydberg gas densities and selected principal quantum numbers, to fit a universal, scale-invariant power law. Three-dimensional simulations using a three-state lattice model reproduce this behaviour, capturing the initial avalanche followed by the onset of percolation, as indicated by a sharp increase in the order parameter. The susceptibility peaks at the onset, then decays, giving rise to a second susceptibility peak and a decrease in the order parameter as the spanning clusters disappear. Experimental observations offer evidence for an invariant endpoint. The model reflects this by approaching an absorbing, non-percolating state. Together, the experimental results and the model support a percolation-driven, self-organising mechanism in which kinetic rules initially promote long-range connectivity and subsequently dismantle it, yielding a transient regime of self-organised criticality.

DOI
10.1080/00268976.2026.2657009

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Driven dissipative atomic and molecular systems can undergo self-organising dynamics that offer a microscopic framework for understanding key large-scale self-organised processes in nature. In the work described here, double-resonant excitation prepares a state-selected Rydberg gas of nitric oxide seeded in a supersonic molecular beam. This system evolves to create a long-lived molecular ultracold plasma. Time-resolved selective field ionisation reveals strongly fluctuating avalanche sizes that evolve, for all initial Rydberg gas densities and selected principal quantum numbers, to fit a universal, scale-invariant power law. Three-dimensional simulations using a three-state lattice model reproduce this behaviour, capturing the initial avalanche followed by the onset of percolation, as indicated by a sharp increase in the order parameter. The susceptibility peaks at the onset, then decays, giving rise to a second susceptibility peak and a decrease in the order parameter as the spanning clusters disappear. Experimental observations offer evidence for an invariant endpoint. The model reflects this by approaching an absorbing, non-percolating state. Together, the experimental results and the model support a percolation-driven, self-organising mechanism in which kinetic rules initially promote long-range connectivity and subsequently dismantle it, yielding a transient regime of self-organised criticality.
Spontaneous avalanche to plasma begins in the core of an ellipsoidal Rydberg gas of nitric oxide. Ambipolar expansion of NO +^++ draws energy from avalanche-heated electrons. Then, cycles of long-range resonant electron transfer from Rydberg molecules to ions equalize their relative velocities. This sequence of steps gives rise to a remarkable mechanics of self-assembly, in which the kinetic energy of initially formed hot electrons and ions drives an observed separation of plasma volumes. These dynamics adiabatically sequester energy in a reservoir of mass transport, starting a process that anneals separating volumes to form an apparent glass of strongly coupled ions and electrons. Short-time electron spectroscopy provides experimental evidence for complete ionization. The long lifetime of this system, particularly its stability with respect to recombination and neutral dissociation, suggests that this transformation affords a robust state of arrested relaxation, far from thermal equilibrium. We see this most directly in the excitation spectrum of transitions to states in the initially selected Rydberg series, detected as the long-lived signal that survives a flight time of 500 μ500\ \mathrm {\mu }500 μ s to reach an imaging detector. The initial density of electrons produced by prompt Penning ionization, which varies with the selected initial principal quantum number and density of the Rydberg gas, determines a balance between the rising density of ions and the falling density of Rydberg molecules. This Penning-regulated ion-Rydberg molecule balance appears necessary as a critical factor in achieving the long ultracold plasma lifetime to produce spectral features detected after very long delays.
Abstract Not long after metastable xenon was photoionized in a magneto-optical trap, groups in Europe and North America found that similar states of ionized gas evolved spontaneously from state-selected, high principal quantum number Rydberg gases. Studies of atomic xenon and molecular nitric oxide entrained in a supersonically cooled molecular beam subsequently showed much the same final state evolved from a sequence of prompt Penning ionization and electron-impact avalanche to plasma, well-described by coupled rate-equation simulations. But, measured over longer times, the molecular ultracold plasma was found to exhibit an anomalous combination of very long lifetime and very low apparent electron temperature. This review first summarizes early developments in the general study of ultracold plasmas formed by atomic and molecular Rydberg gases, and then turns to describe the particular properties of the nitric oxide molecular ultracold plasma that appear to call for an explanation beyond the realm of conventional plasma physics.
Ultracold molecular plasmas represent a new frontier of plasma physics. They offer an easy and accessible laboratory for the study of strongly coupled Coulomb systems. Strong Coulomb coupling can give rise to exotic materials such as Wigner crystals and liquid like plasmas. In this thesis, I present a set of experiments and theoretical models that explore the properties of ultracold plasma in great detail. A supersonic beam of nitric oxide in helium creates a cold ensemble of ground state molecules. Upon two-color excitation, a Rydberg gas of nitric oxide evolves on a time scale of nanoseconds to form an ultracold plasma. The excited volume is imaged using a multichannel plate detector mounted on a movable grid. By moving the detector back and forth, we can observe the expansion dynamics of the plasma and its decay. Selective field ionization captures the relaxation of the Rydberg states to a plasma. We use a very reliable coupled-rate-equation model to understand the decay dynamics and evolution of Rydberg gas to a plasma by accounting for all the major processes that happen during the avalanche process. We find that a plasma evolved from an ultracold Rydberg gas expands very slowly, exhibits long relaxation time, and shows evidence suggesting the development of spatial order.
Out-of-equilibrium, strong correlation in a many-body system can trigger emergent properties that act to constrain the natural dissipation of energy and matter. Signs of such self-organization appear in the avalanche, bifurcation, and quench of a state-selected Rydberg gas of nitric oxide to form an ultracold, strongly correlated ultracold plasma. Work reported here focuses on the initial stages of avalanche and quench and uses the mm-wave spectroscopy of an embedded quantum probe to characterize the intermolecular interaction dynamics associated with the evolution to plasma. Double-resonance excitation prepares a Rydberg gas of nitric oxide composed of a single selected state of principal quantum number, n0. Penning ionization, followed by an avalanche of electron–Rydberg collisions, forms a plasma of NO+ ions and weakly bound electrons, in which a residual population of n0 Rydberg molecules evolves to a state of high orbital angular momentum, ℓ. Predissociation depletes the plasma of low-ℓ molecules. Relaxation ceases and n0ℓ(2) molecules with ℓ ≥ 4 persist for very long times. At short times, varying excitation spectra of mm-wave Rydberg–Rydberg transitions mark the rate of electron-collisional ℓ-mixing. Deep depletion resonances that persist for long times signal energy redistribution in the basis of central-field Rydberg states. The widths and asymmetries of Fano line shapes witness the degree to which coupling in the arrested bath (i) broadens the allowed transition and (ii) mixes the local network of levels in the ensemble.
We report the spontaneous formation of a plasma from a gas of cold Rydberg molecules. Double-resonant laser excitation promotes nitric oxide, cooled to 1 K in a seeded supersonic molecular beam, to single Rydberg states extending as deep as $80\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}1}$ below the lowest ionization threshold. The density of excited molecules in the illuminated volume approaches $1\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$. This population evolves to produce free electrons and a durable cold plasma of electrons and intact NO+{\mathrm{NO}}^{+}NO+ ions.
Abstract Double-resonant transitions excite nitric oxide in a seeded supersonic molecular beam, yielding a state-selected Rydberg gas that evolves to form an ultracold plasma. This plasma propagates in z with the molecular beam over a variable distance as great as 600 mm to strike an imaging detector, which records the charge distribution in the dimensions, x and y . The laser-crossed molecular beam excitation geometry convolutes an axial Gaussian distribution of NO about z with the Gaussian intensity distribution of the laser beam about x to create an ellipsoidal volume of Rydberg gas. Plasma images provide evidence for the relaxation of this Rydberg gas volume in an electron impact avalanche that breaks the ellipsoidal symmetry in x to form repelling plasma volumes. We find that the energy deposited in the recoil velocity of mass transport, V x depends systematically on the initially selected Rydberg gas principal quantum number, n 0 , and the initial density of the Rydberg gas, ρ 0 . These quantities combine to determine ρ e , the initial density of electrons formed by the prompt Penning ionization of closely spaced pairs of Rydberg molecules. Above a threshold density of Penning electrons, we find that V x depends linearly on ρ e . We argue that this bifurcation occurs as a consequence of the initial geometry of the Rydberg gas. Ambipolar electron expansion accelerates initially formed core ions. Resonant charge transfer redistributes this ion energy to the column of Rydberg molecules on the long axis of the ellipsoid. The equalized velocities in each direction give rise to a ± x streaming motion that concentrates density in opposing plasma volumes, causing the symmetric gas volume to split like a rotating liquid drop. Significantly, these dynamics reduce electron temperature with little decrease in the ion density or increase in the ion temperature. This appears to facilitate the formation of a strongly coupled plasma.