What are the energy/time/temperature... units used in QuTiP?

[Xing]

Dear All,

I've been trying to use QuTiP to reproduce the results in literature. However I cannot figure out the units used in QuTiP. For example, in the Jaynes-Cumming model tutorial (http://nbviewer.jupyter.org/github/jrjohansson/qutip-lectures/blob/master/Lecture-1-Jaynes-Cumming-model.ipynb), could someone kindly tell me the unit of "time" in the Rabi oscillation figure? Is the energy unit in the Hamiltonian Hatree or some other things like cm-1 (seems not possible)

Thanks very much!

[nonher...@gmail.com]

There are no fixed units. It depends on the units of the coefficients that you enter. 

-P

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[Xing]

Dear Paul,

Thanks! If I enter a Hamiltonian in SI (joule) for the Lindblad Master Equation Solver (http://qutip.org/docs/3.1.0/guide/dynamics/dynamics-master.html), then the time unit of the output would be in seconds? Is there a built-in unit for the Planck constant?

[nonher...@gmail.com]

Correct. However, we do not have an hbar or h defined as it is best to work in non-dimensional units. Since E=hbar*w or h*f, taking h=1, then the coefficients are frequencies. These frequencies set the timescale. 

[Xing]

Dear Paul,

Thanks! But I'm still a confused. I though h (or hbar) has the dimension of "energy multiplied by time"...if we set it to 1, does that imply some kind of "Natural units (https://en.wikipedia.org/wiki/Natural_units)"?

[nonher...@gmail.com]

Think of it mote like dividing the Hamiltonian by hbar. Then the units are frequency. 

On Jul 21, 2016, at 13:06, luduju...@gmail.com wrote:

Dear Paul,

Thanks! But I'm still a confused. I though h (or hbar) has the dimension of "energy multiplied by time"...if we set it to 1, does that imply some kind of "Natural units (https://en.wikipedia.org/wiki/Natural_units)"?

[Clarissa]

Dear Paul,

Does this mean that I have to enter the Hamiltonian in frequency units?

[Paul Nation]

All energies can be written as hbar*w or h*f, where w and f are angular frequency and frequency, respectively.  If you have some Hamiltonian H = something, then dividing both sides by hbar or h leaves units of angular frequency or frequency on both sides. 

[xiy...@gmail.com]

Dear Paul

Thanks very much! I just another question: The \gamma (dephasing rate) used in the Lindblad solver has the dimension of 1/Time. If I use "angular frequency" in the Hamiltonian input (e.g., set hbar to 1), should I use the "rad per unit time" for \gamma or simply "cycle per unit                                                                                                                                                                                                                                    time" for \gamma? The 2 pi difference is large in some applications.

[Paul Nation]

Preferably everything should be in units of hbar*w.  If you have mixed units, then like you said, you need to be careful of the 2pi factors.

-P

[Pu ZHANG]

Hi, fellows! 

I also have a question regarding the unit of time. As I understand, the unit of time should be obtained through the relation between time and energy, that is, t = 1 / f = (2 * pi) / omega = (2 * pi) / (E / hbar). In this way I got the time unit as about 4.16 fs, yet I see elsewhere the natural time unit as 0.658 fs. So there's 2 * pi difference. I wonder which one does QuTiP use internally? 

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

E-mail: puzha...@hust.edu.cn

Homepage: www.researchgate.net/profile/Pu_Zhang4

Phone: +86 18871860394

On Sun, Oct 9, 2016 at 5:29 AM, Paul Nation <nonher...@gmail.com> wrote:

Preferably everything should be in units of hbar*w.  If you have mixed units, then like you said, you need to be careful of the 2pi factors.

-P

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[nonher...@gmail.com]

The timescale depends on the units of the Hamiltonian. If your coefficients are written as 2pi*f then your timescale is 1/f. However, if your frequency units in the Hamiltonian are natural, then the units of time have an extra 2pi. This is because the Schrodinger equation has an hbar on the left side, so when you go to normalize your equation you must keep that in mind. 

-P

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[Pu ZHANG]

Thanks! I see the point. 

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

E-mail: puzha...@hust.edu.cn

Homepage: www.researchgate.net/profile/Pu_Zhang4

Phone: +86 18871860394

[xiy...@gmail.com]

I see. Thanks very much!

[freja....@gmail.com]

Dear Paul
I realize this is a slightly older thread, but I am not completely sure what the answer to the units of the Hamiltonian means.
Looking at the Jaynes-Cumming model  (nbviewer.jupyter.org/github/jrjohansson/qutip-lectures/blob/master/Lecture-1-Jaynes-Cumming-model.ipynb), as far as I understand setting hbar=1 results in the cavity and atom frequencies to be written as angular frequencies, and thereby the Hamiltonian is in units of angular frequency as well.
This would then mean that the time-scale for the "Vacuum Rabi Oscillations"-plot is in seconds (1/f)?

If I then want to model the dephasing of a system using a noise-power spectrum, in the Redfield equations, could I then use frequency units for both the spectral density and the Hamiltonian (dividing with h), and do I then get a timescale of (1/f)?, or should I write everything in angular frequencies?

Den søndag den 9. oktober 2016 kl. 07.02.40 UTC+2 skrev Paul Nation:

The timescale depends on the units of the Hamiltonian. If your coefficients are written as 2pi*f then your timescale is 1/f. However, if your frequency units in the Hamiltonian are natural, then the units of time have an extra 2pi. This is because the Schrodinger equation has an hbar on the left side, so when you go to normalize your equation you must keep that in mind. 

-P

On Oct 8, 2016, at 21:51, Pu ZHANG <puzha...@gmail.com> wrote:

Hi, fellows! 

I also have a question regarding the unit of time. As I understand, the unit of time should be obtained through the relation between time and energy, that is, t = 1 / f = (2 * pi) / omega = (2 * pi) / (E / hbar). In this way I got the time unit as about 4.16 fs, yet I see elsewhere the natural time unit as 0.658 fs. So there's 2 * pi difference. I wonder which one does QuTiP use internally? 

Thanks! 

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

E-mail: puzha...@hust.edu.cn

Homepage: www.researchgate.net/profile/Pu_Zhang4

Phone: +86 18871860394

On Sun, Oct 9, 2016 at 5:29 AM, Paul Nation <nonher...@gmail.com> wrote:

Preferably everything should be in units of hbar*w.  If you have mixed units, then like you said, you need to be careful of the 2pi factors.

-P

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[MOUHCINE ELOMARI]

Good evening professor, I hope you are doing well, I am a Master student at the University of Sciences of Ben M'sik HASSAN II-CASABLANCA specialized in quantum computing,

We want to know which unit of evo_time  used  in  program on the QuTiP platform in Calculation fields for QFTgate on two qubits using the CRAB algorithm ??