dorsal/arxiv
View SchemaDoppler cooling of a Coulomb crystal
| Authors | Giovanna Morigi, Juergen Eschner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0105150 |
| URL | https://arxiv.org/abs/quant-ph/0105150 |
| DOI | 10.1103/PhysRevA.64.063407 |
| Journal | Phys. Rev. A 64, 063407 (2001). |
Abstract
We study theoretically Doppler laser-cooling of a cluster of 2-level atoms confined in a linear ion trap. Using several consecutive steps of averaging we derive, from the full quantum mechanical master equation, an equation for the total mechanical energy of the one dimensional crystal, defined on a coarse-grained energy scale whose grid size is smaller than the linewidth of the electronic transition. This equation describes the cooling dynamics for an arbitrary number of ions and in the quantum regime. We discuss the validity of the ergodic assumption (i.e. that the phase space distribution is only a function of energy). From our equation we derive the semiclassical limit (i.e. when the mechanical motion can be treated classically) and the Lamb-Dicke limit (i.e. when the size of the mechanical wave function is much smaller than the laser wavelength). We find a Fokker-Planck equation for the total mechanical energy of the system, whose solution is in agreement with previous analytical calculations which were based on different assumptions and valid only in their specific regimes. Finally, in the classical limit we derive an analytic expression for the average coupling, by light scattering, between motional states at different energies.
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"abstract": "We study theoretically Doppler laser-cooling of a cluster of 2-level atoms\nconfined in a linear ion trap. Using several consecutive steps of averaging we\nderive, from the full quantum mechanical master equation, an equation for the\ntotal mechanical energy of the one dimensional crystal, defined on a\ncoarse-grained energy scale whose grid size is smaller than the linewidth of\nthe electronic transition. This equation describes the cooling dynamics for an\narbitrary number of ions and in the quantum regime. We discuss the validity of\nthe ergodic assumption (i.e. that the phase space distribution is only a\nfunction of energy). From our equation we derive the semiclassical limit (i.e.\nwhen the mechanical motion can be treated classically) and the Lamb-Dicke limit\n(i.e. when the size of the mechanical wave function is much smaller than the\nlaser wavelength). We find a Fokker-Planck equation for the total mechanical\nenergy of the system, whose solution is in agreement with previous analytical\ncalculations which were based on different assumptions and valid only in their\nspecific regimes. Finally, in the classical limit we derive an analytic\nexpression for the average coupling, by light scattering, between motional\nstates at different energies.",
"arxiv_id": "quant-ph/0105150",
"authors": [
"Giovanna Morigi",
"Juergen Eschner"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"physics.atom-ph"
],
"doi": "10.1103/PhysRevA.64.063407",
"journal_ref": "Phys. Rev. A 64, 063407 (2001).",
"title": "Doppler cooling of a Coulomb crystal",
"url": "https://arxiv.org/abs/quant-ph/0105150"
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