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Evaporative cooling of a Rydberg atom chain to near its ground state

M. Brune, D. J. Papoular

Published Nov 14, 2019• 0 citations
OpenAlex

Abstract

We theoretically analyze a novel evaporative cooling scheme applicable to Rydberg chains. We consider an initially thermal chain of circular Rydberg atoms confined to a one-dimensional (1D) setting in the absence of periodic potentials. We show that the evaporation of about one half of the atoms of the chain brings it near its quantum ground state, which is a 1D Rydberg crystal. We describe the scheme thermodynamically, applying the truncated Boltzmann distribution to the collective excitations of the chain, and show that it leads to a novel quasi--equilibrium many-body state. The evaporation is driven by slowly compressing the chain. For a given atom number, this process is adiabatic down to a minimal chain size. At this point, a single atom is expelled, causing the energy and entropy per particle to decrease. Then, adiabatic compression resumes. For longer chains, comprising about $1000$ atoms, we emphasize the quasi-universality of the evaporation curve.

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arXiv:1601.01554•Jan 7, 2016•1 citation
We theoretically analyze a novel evaporative cooling scheme applicable to Rydberg chains. We consider an initially thermal chain of circular Rydberg atoms confined to a one-dimensional (1D) setting in the absence of periodic potentials. We show that the evaporation of about one half of the atoms of the chain brings it near its quantum ground state, which is a 1D Rydberg crystal. We describe the scheme thermodynamically, applying the truncated Boltzmann distribution to the collective excitations of the chain, and show that it leads to a novel quasi--equilibrium many-body state. The evaporation is driven by slowly compressing the chain. For a given atom number, this process is adiabatic down to a minimal chain size. At this point, a single atom is expelled, causing the energy and entropy per particle to decrease. Then, adiabatic compression resumes. For longer chains, comprising about 100010001000 atoms, we emphasize the quasi-universality of the evaporation curve.
We investigate dynamics of a linear chain of Rydberg atoms driven by a constrained four-body interaction, where two neighboring atoms are excited simultaneously from the electronic ground state ∣0⟩|0\rangle∣0⟩ to Rydberg state ∣1⟩|1\rangle∣1⟩ only when their closest neighbors are in ∣0⟩|0\rangle∣0⟩ state. By employing an ansatz for the many-body ground state, the low-energy Hamiltonian is given by a tridiagonal form. The many-body ground state energy, which scales linearly with the chain length LLL, is obtained analytically in the thermodynamic limit and agrees with the one of the exact diagonalization. Our model supports quantum many-body scar eigenstates that are nearly equally spaced energetically. The scar states overlap strongly with the basis state ∣0⟩=∣0⋯0⟩|\mathbf{0}\rangle=|0\cdots 0\rangle∣0⟩=∣0⋯0⟩. We show that the overlap distribution is tilted by the state-dependent four-body interaction. This leads to non-ergodic dynamics, evidenced by the revival of the initial state. The four-body constrained model can be realized with Rydberg atoms in a Peierls array with alternating bond lengths, where atoms on the shorter and longer bonds experience Rydberg blockade and antiblockade, respectively. Our study provides a pathway to explore constrained non-ergodic dynamics with four-body interactions by combining the Rydberg blockade and antiblockade.
We develop a semiclassical thermodynamic framework for the evaporative cooling of trapped atomic gases that treats Maxwell--Boltzmann, Bose--Einstein, and Fermi--Dirac statistics on equal footing across box, harmonic, mixed, and linear-quadrupole potentials. Using the global thermodynamic variables of inhomogeneous confinement, we show that all geometries are unified by a single parameter sss, which fixes the polylogarithm order, the density of states exponent, and the number of degrees of freedom 2s2s2s. Modeling evaporation as a recursive sequence of energy truncation and rethermalization, we derive closed-form recurrence relations for the particle number and internal energy that track the full thermodynamic state, with the classical energy budget set by a virial factor Ctrap=1+3/(2s)C_{\mathrm{trap}} = 1 + 3/(2s)Ctrap​=1+3/(2s). Quantum degeneracy emerges not as a singularity in the global susceptibilities, but as a smooth, geometry-dependent crossover in which bosons and fermions display opposite thermodynamic signatures. The results provide a versatile theoretical tool for modeling evaporative cooling across experimentally relevant geometries and offer quantitative guidance for optimizing the cooling process in ultracold atomic systems.
Summary form only given. Condensed-matter systems are interesting and important to understand, for fundamental science as well as towards more applied objectives in the development of new materials for instance. Unfortunately, these many-body quantum systems are difficult to study: both the theoretical approach and the numerical simulation are proving impossible to carry out to relevant system sizes. Quantum simulation proposes to mimic those out-of-reach systems with more controllable and accessible quantum systems. Rydberg atoms gained renewed interest in the last decades thanks to their very high polarizability, allowing for strong and tunable short-range interactions. They constitute an interesting candidate for a quantum simulation platform. However, low angular momentum Rydberg states have limited, despite relatively long, lifetimes which limit the scope of such a quantum simulator. Moreover, low-l Rydberg states cannot be efficiently laser-trapped. In order to overcome these limitations, we propose to use circular Rydberg states, i.e., of maximum angular momentum. Circular Rydberg states exhibit much longer lifetimes, and can be trapped using laser light. By placing the circular Rydberg atoms inside a spontaneous emission-inhibiting capacitor, we hope to achieve the deterministic preparation of a 1D-chain of 40 atoms, with a collective lifetime of over 2 seconds. With expected exchange energies in the 10-100 kHz range, this would provide a platform capable of simulating quantum many-body physics up to 105exchange times. The first step towards the experimental realization of such a quantum simulator is the demonstration of the laser-trapping of circular Rydberg atoms. To this end, we use a Laguerre-Gauss hollow beam at 1064 nm, imposing a ponderomotive potential on the nearly-free electron of the Rydberg atoms. I will present our latest experimental results of light-trapping of circular Rydberg atoms.
We report experiments on evaporative cooling of spin-polarized atomic hydrogen gas confined in a cryogenic magnetic trap, and present a model of the trapped gas based on a generalized truncated Boltzmann approximation for the phase-space distribution function. The model takes into account the dimension of the evaporation [three-dimensional (3D) or 1D] and the time dependence of both the depth and the shape of the confining potential. Our observations are consistent with 1D evaporative cooling. To attain maximal phase-space density, we used the model assuming 1D evaporative cooling to optimize the evaporation procedure. With this work, the low dimension of evaporation was identified as the bottleneck thus far preventing us from achieving Bose-Einstein condensation in trapped atomic hydrogen.
We question the microcanonical hypothesis, often made to account for the thermalization of complex closed quantum systems, on the specific example of a chain of two-level atoms optically driven by a resonant laser beam and strongly interacting via Rydberg-Rydberg dipole-dipole interactions. Along its (necessarily unitary) evolution, this system is indeed expected to thermalize, i.e. observables, such as the number of excitations, stop oscillating and reach equilibrium-like expectation values. The latter are often calculated through assuming the system can be effectively described by a thermal-like microcanonical state. Here, we compare the distribution of excitations in the chain calculated either according to the microcanonical assumption or through direct exact numerical simulation. This allows us to show the limitations of the thermal equilibrium hypothesis and precise its applicability conditions.