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Title: Lindblad equation for the inelastic loss of ultracold atoms

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 95; Journal Issue: 1; Related Information: CHORUS Timestamp: 2017-01-27 16:45:16; Journal ID: ISSN 2469-9926
American Physical Society
Country of Publication:
United States

Citation Formats

Braaten, Eric, Hammer, H. -W., and Lepage, G. Peter. Lindblad equation for the inelastic loss of ultracold atoms. United States: N. p., 2017. Web. doi:10.1103/PhysRevA.95.012708.
Braaten, Eric, Hammer, H. -W., & Lepage, G. Peter. Lindblad equation for the inelastic loss of ultracold atoms. United States. doi:10.1103/PhysRevA.95.012708.
Braaten, Eric, Hammer, H. -W., and Lepage, G. Peter. Thu . "Lindblad equation for the inelastic loss of ultracold atoms". United States. doi:10.1103/PhysRevA.95.012708.
title = {Lindblad equation for the inelastic loss of ultracold atoms},
author = {Braaten, Eric and Hammer, H. -W. and Lepage, G. Peter},
abstractNote = {},
doi = {10.1103/PhysRevA.95.012708},
journal = {Physical Review A},
number = 1,
volume = 95,
place = {United States},
year = {Thu Jan 26 00:00:00 EST 2017},
month = {Thu Jan 26 00:00:00 EST 2017}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevA.95.012708

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Cited by: 2works
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  • The loss of ultracold trapped atoms in the vicinity of a Feshbach resonance is treated as a two-stage reaction, using the Breit-Wigner theory. The first stage is the formation of a resonant diatomic molecule, and the second one is its deactivation by inelastic collisions with other atoms. This model is applied to the analysis of recent experiments on {sup 87}Rb, leading to an estimated value of 7x10{sup -11} cm{sup 3}/s for the deactivation rate coefficient.
  • We report new calculations of two-body associative ionization collisions between sodium atoms confined in a magneto-optic trap at ultracold temperatures. These collisions represent a new kind of {open_quotes}open{close_quotes} or dissipative collision for which the energy of the atom + applied light field need not be conserved due to spontaneous emission coupling to the vacuum modes of the radiation field and require density matrix methods rather than wavefunction methods to describe the collision. In these collisions the Na atoms must absorb a photon when they are in close enough proximity that a significant fraction of the excited population survives relaxation backmore » to the ground state. The Na atoms accelerate towards each other on the excited molecular state and absorbs a second photon to a doubly excited state which then proceeds to associatively ionize at close range. Our calculations incorporate a molecular picture of the atomic collision, laser optical-field dressing of the molecular states participating in the dynamics, and population and coherence decay due to spontaneous emission. The effect of excited state hyperfine structure, which plays a critical role in the dynamics, is simulated by simplified models with a reduced number of states based on the full set of molecular-hyperfine adiabatic potential curves. Comparison is made with recent measurements of photo-associative ionization. rates as a function of optical field intensity from about 20 to 130 mW cm{sup -2}.« less
  • The so-called Lindblad equation, a typical master equation describing the dissipative quantum dynamics, is shown to be solvable for finite-level systems in a compact form without resort to writing it down as a set of equations among matrix elements. The solution is then naturally given in an operator form, known as the Kraus representation. Following a few simple examples, the general applicability of the method is clarified.
  • A Lindblad master equation for a harmonic oscillator, which describes the dynamics of an open system, is formally solved. The solution yields the spectral resolution of the Liouvillian, that is, all eigenvalues and eigenprojections are obtained. This spectral resolution is discussed in depth in the context of the biorthogonal system and the rigged Hilbert space, and the contribution of each eigenprojection to expectation values of physical quantities is revealed. We also construct the ladder operators of the Liouvillian, which clarify the structure of the spectral resolution.
  • The ''correlated-projection technique'' has been successfully applied to derive a large class of highly non-Markovian dynamics, the so called non-Markovian generalized Lindblad-type equations or Lindblad rate equations. In this article, general unravelings are presented for these equations, described in terms of jump-diffusion stochastic differential equations for wave functions. We show also that the proposed unraveling can be interpreted in terms of measurements continuous in time but with some conceptual restrictions. The main point in the measurement interpretation is that the structure itself of the underlying mathematical theory poses restrictions on what can be considered as observable and what is not;more » such restrictions can be seen as the effect of some kind of superselection rule. Finally, we develop a concrete example and discuss possible effects on the heterodyne spectrum of a two-level system due to a structured thermal-like bath with memory.« less