Rights statement: Copyright 2018 American Institute of Physics. The following article appeared in Journal of Mathematical Physics, 59, (3) 2018 and may be found at http://dx.doi.org/10.1063/1.5016495 This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Dynamical decoupling of unbounded Hamiltonians
AU - Arenz, Christian
AU - Burgarth, Daniel
AU - Facchi, Paolo
AU - Hillier, Robin Oliver
N1 - Copyright 2018 American Institute of Physics. The following article appeared in Journal of Mathematical Physics, 59, (3) 2018 and may be found at http://dx.doi.org/10.1063/1.5016495 This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
PY - 2018/3/20
Y1 - 2018/3/20
N2 - We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.
AB - We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.
U2 - 10.1063/1.5016495
DO - 10.1063/1.5016495
M3 - Journal article
VL - 59
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 3
M1 - 032203
ER -