Collapse operator for pure dephasing

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Pu ZHANG

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Oct 9, 2016, 11:55:44 PM10/9/16
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Hi, QuTiP users! 

I have a question about the form of the collapse operator for pure dephasing. 

From examples in the user guide, I find it as sqrt(gamma)*sigmaz(). Yet in an article (titled complete coherent control of a quantum dot strongly coupled to a nanocavity), where QuTiP was applied, the collapse operator is written as sqrt(gamma)*|1><1|. Since sigmaz() = |1><1| - |0><0|, there is difference between the two. 

My question is which one is correct. Thanks! 

Best regards, Pu Zhang

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Faculty at School of Physics, Huazhong University of Science and Technology
Room 819 (N.), Yifu Science and Technology Building
1037 Luoyu Road, Wuhan, China

Pu ZHANG

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Oct 10, 2016, 3:24:57 AM10/10/16
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I figured that for a two-level system the two expressions are essentially equivalent except a factor of 2. But for a system with more than 2 levels the form of |1><1| seems more reasonable to me. 

Best regards, Pu Zhang

--
Faculty at School of Physics, Huazhong University of Science and Technology
Room 819 (N.), Yifu Science and Technology Building
1037 Luoyu Road, Wuhan, China

Kevin Fischer

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Oct 10, 2016, 5:50:28 PM10/10/16
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Hi Pu,

Yes you are correct that for a two-level system they are essentially equivalent, but for multiple level systems the form |n><n| allows for the dephasing of each level to be tuned individually. Additionally in the case of excitonic levels in a quantum dot, the dominant dephasing mechanism is an electron-phonon interaction that results in a dephasing rate proportional to the exciton number.

Kevin

Pu ZHANG

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Oct 10, 2016, 7:52:38 PM10/10/16
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Thanks for clarifying my question! 

As for the QD case, do you mean the sigmaz() form makes more sense? 

Best regards, Pu Zhang

--
Faculty at School of Physics, Huazhong University of Science and Technology
Room 819 (N.), Yifu Science and Technology Building
1037 Luoyu Road, Wuhan, China

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Kevin Fischer

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Oct 13, 2016, 5:16:46 PM10/13/16
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Hi Pu,

I actually think the sigmaz() form has less connection with the underlying dephasing mechanism - I would recommend using the |X><X| operator in case you add multiple excitons later.

Kevin
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Pu ZHANG

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Oct 13, 2016, 8:25:49 PM10/13/16
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Thanks, Kevin! 

Best regards, Pu Zhang

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Faculty at School of Physics, Huazhong University of Science and Technology
Room 819 (N.), Yifu Science and Technology Building
1037 Luoyu Road, Wuhan, China

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