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Molecular Simulation

First-order phase transition in a gas of resonantly excited Rydberg atoms

Sergey Ya. Bronin, A. B. Klyarfeld, B. V. Zelener

Published Feb 17, 2020• 0 citations
Publisher

Abstract

The possibility of experimental creation of a system of Rydberg atoms with an arbitrary probability distribution of their dipole moments is shown. The equation of state is calculated by the Monte Carlo method in the NVT ensemble for two options of the distribution: isotropic distribution and distribution for the system of identical dipoles. Critical parameters of the phase transition and the binodal are determined in both cases. Critical temperatures for both options virtually coincide. However, critical density for isotropic distribution is 20 times higher. It is shown that the absence of spatial separation in the region of coexistence of dense and dilute phases is a specific feature of the phase transition in dipole systems, and such absence of separation is due to the topological features of clusters of the dense phase. Areas of parameters for the experimental observation of the self-organisation of ultracold Rydberg atoms on the existing experimental stands are determined.

DOI
10.1080/08927022.2020.1726910

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The possibility of experimental creation of a system of Rydberg atoms with an arbitrary probability distribution of their dipole moments is shown. The equation of state is calculated by the Monte Carlo method in the NVT ensemble for two options of the distribution: isotropic distribution and distribution for the system of identical dipoles. Critical parameters of the phase transition and the binodal are determined in both cases. Critical temperatures for both options virtually coincide. However, critical density for isotropic distribution is 20 times higher. It is shown that the absence of spatial separation in the region of coexistence of dense and dilute phases is a specific feature of the phase transition in dipole systems, and such absence of separation is due to the topological features of clusters of the dense phase. Areas of parameters for the experimental observation of the self-organisation of ultracold Rydberg atoms on the existing experimental stands are determined.
We demonstrate a nonequilibrium phase transition in a dilute thermal atomic gas. The phase transition, between states of low and high Rydberg occupancy, is induced by resonant dipole-dipole interactions between Rydberg atoms. The gas can be considered as dilute as the atoms are separated by distances much greater than the wavelength of the optical transitions used to excite them. In the frequency domain, we observe a mean-field shift of the Rydberg state which results in intrinsic optical bistability above a critical Rydberg number density. In the time domain, we observe critical slowing down where the recovery time to system perturbations diverges with critical exponent α=-0.53±0.10. The atomic emission spectrum of the phase with high Rydberg occupancy provides evidence for a superradiant cascade.
The present thesis treats the interacting ultracold Rydberg gas with special emphasison the statistical footprint of the phase transition between unordered and crystalline phase, which can be understood as a consequence of the dipole blockade effect. After mapping the system onto an effective spin-1/2-model, exact diagonalization of the effective Hamiltonian is used to obtain the many-body ground state. Repeated application of this procedure on random realizations reveals the underlying probability distribution of the number of Rydberg atoms, allowing to calculate its statistical moments. In the regimes of weak and strong interaction these observables have power law character. The critical interaction strength is estimated by extrapolating these power laws up to their intersection point. The same procedure is applied to interacting excitons in bilayer heterostructures uncovering a phase transition here as well. Furthermore, new methods are introduced to handle the effects of finite detection efficiency and parameter fluctuations to establish a better connection between experimental and theoretical results. Finally, new models are introduced to include dynamics or additional Rydberg states. The last model is of purely statistical nature and its results may be used as a tool for detecting a potential clustering of Rydberg atoms.
Rydberg atoms have experimentally interestingproperties such as strong long-range Van der Waals interactions and the dipole blockade effect. In optical lattices the blockade effect ensures that only one Rydberg excitation per site is allowed, effectively creating a Rydberg crystal. We theoretically show that it is also possible for a one-dimensional Rydberg crystal to spontaneously form in a random ensemble of atoms, e.g. a magneto-optical trap. This is done using an existing Monte Carlo model [1] to simulate the excitation dynamics inside the intersection of two lasers for a two-step excitation scheme. With a blue-detuned laser for the upper transition, the first Rydberg excitation will occur after a relatively long time. That first Rydberg atom will then seed further Rydberg excitations, as the blockade effect shifts atoms at a certain distance into resonance. If two dimensions of the laser intersection are smaller than the blockade radius, a one-dimensional Rydberg crystal will form.
Phase diagrams for the "shelf Coulomb" and the modified pseudopotential plasma models developed in our previous works are compared. Qualitative agreement is observed between gas-liquid phase transition region of "shelf Coulomb" model and liquid-gas structure region of modified pseudopotential one. The possibility of experimental finding of the phase transition in nonequilibrium ultracold Rydberg plasma is considered. Parameters (density, temperature, levels of Rydberg atoms) for such a transition are estimated. Conclusion is made that "shelf Coulomb" model phase transition is practically impossible to observe in equilibrium strongly coupled plasmas due to high neutral atoms density at low temperatures: T crit ≈ 0.076.
The physical model of the particle system describing the thermodynamics of mixtures of ultracold Rydberg gases with different levels of excitation are proposed. In our model system of particles is a mixture of atoms in S -state and atoms in the P -state. To calculate the thermodynamic of the mixture Rydberg gases the method of Monte-Carlo was used. Computational results of the spatial correlations of dipoles depending on the coupling parameter are presented. At some value of the nonideality parameter the dipole chains are formed.