Question regarding two-color MOT coupling F=1,2 and F'=1,2

[Gabin Yun]

Hi all,

Thank you for this amazing package.

I am designing a blue-detuned MOT and before moving to my situation, I am first trying to reproduce the results of Jarvis et al. Blue-detuned MOT () Fig.1. Which is a MOT that has two lasers which has a detuning of delta11 and delta22 from the F=1 to F'=1 and F=2 to F'=2 transition of 87Rb respectively. If you have any experience in dealing with this problem, it would be great if I can get some insights. I using hyperfine_coupled() to generate the ground and excited state manifolds and creating a coupling hamiltonian with dqij_two_hyperfine_manyfolds(). Then, I define two conventional 3d mots but with different detunings such that it matches the 1-to-1 and 2-to-2 detunings in the lab frame. Running the simulation with the OBE takes super-long, so I only tried the rateeq. However, the rateeq results does not match with the paper.

If you have any idea or good references, it would be great to have some tips. Thanks in advance.

Best, 
Gabin

[Lajos Palanki]

Hi Gabin,

The rate-equations would be unable to reproduce the results of that paper since they rely on coherences, which the rate model does not take into account. The OBEs do generally take quite long,  but in this case I suspect they may take longer than necessary for what you want to simulate. It sounds to me that you set up your system with two states (one for the ground manifold and one for the excited one). Generally the limit for the integrator timestep will be near timescale of the fastest oscillating term within the system, which in this case will be ~4-5GHz. One way of reducing this is to split the ground state into two manifolds so the large detuning is not simulated. This eliminates some of the cross terms between these states, but those would not really come into play until fields much higher than what is discussed here. By doing this, the integrator can run faster in theory. The EIT example has a basic example of how to set this up and there are some discussion on this topic here as well.

Best,

Lajos

[Gabin Yun]

Hi Lajos,

(sorry for sending the message twice, I am new to google groups and did not know the difference between reply all and reply author) :)

Thanks for the quick and instructive explanation regarding the issue I was facing. Splitting the ground state manifold into two indeed helped to boost the computation, and now I am able to calculate the force profile using the OBE solver.

Now, the system is defined with all the hyperfine manifolds involved in the D2 transitions of Rb87. Two laser beams are coupling F=1 to F'=0,1,2 and F=2 to F'=1,2,3 with a detuning det11 and det22 blue-detuned from the F=1-to-F'=1 and F=2-to-F'=2 transitions as the conventional 3d MOTs with the quadrupole magnetic field whose gradient is 87 G/cm. Here, the detunings were corrected for each transition such that it effectively simulates the real physical situation, like F=1-to-F'=2's detuning should be det11-energy offset of F'=2 and F'=1. Also, as you mentioned I ignored the beam 11 coupling transitions starting from F=2, since they have a large detuning.

However, the simulation still could not reproduce the results of the paper. Maybe the sign convention of the field or polarizaiton might be an issue, but I checked by changing the sign that it did not help. It would be great, if you or anyone can give some insight to resolve the issue and help understanding the problems better. For reference, I've attached my script.

Thank you for the support and insights.

Best,

Gabin

[Eckel, Stephen P. (Fed)]

Hi Gabin,

 

Looking over your code, I think I see a potential issue.  Ordinarily, what I do in your situation is have just three manifolds: one for the F=1 in the ground state, one for the F=2 in the ground state, and one for all the excited F’ states.

 

I usually generate them by first using hyperfine_coupled as you did,

 

H_g[species], muq_g[species], basis_g[species] = pylcp.hamiltonians.hyperfine_coupled(

    Jg, I, gJ_g_Rb, gI_Rb,

    Ahfs=Ahfs_g_Rb/gammaHz[species],

    Bhfs=Bhfs_g_Rb/gammaHz[species],

    Chfs=0, muB=1, return_basis=True

)

 

H_e[species], muq_e[species], basis_e[species] = pylcp.hamiltonians.hyperfine_coupled(

    Je, I, gJ_e_Rb, gI_Rb,

    Ahfs=Ahfs_e_Rb/gammaHz[species],

    Bhfs=Bhfs_e_Rb/gammaHz[species],

    Chfs=0, muB=1, return_basis=True

)

 

But then break apart only the ground state:

H_g1[species] = H_g1[species][:3,:3]

H_g2[species] = H_g2[species][3:,3:]

(up to three because there are three m_F states in F=1). I similarly break up the mu_q.

 

Then your Hamiltonian can be made from just three blocks, rather than the 6 or so that you have.

 

This effectively turns off the quadratic Zeeman shift in the ground state but leaves the quadratic Zeeman shift in the excited state. It also, in principle, keeps the possibility of off-resonant excitation to other F states. Remember that manifolds assume that the transitions are isolated from each other, and in this case, they probably aren’t.

 

But I am not sure what matters physically in your problem, so I am not sure that these suggestions will fix your problem. They will slow the computation back down though.

 

-Steve

 

-- 

Dr. Stephen Eckel
Group Leader
Fundamental Thermodynamics Group
Sensor Sciences Division

 

From: py...@googlegroups.com <py...@googlegroups.com> on behalf of Gabin Yun <gabin....@gmail.com>
Date: Tuesday, March 17, 2026 at 11:36 AM
To: pylcp <py...@googlegroups.com>
Subject: [EXTERNAL] Re: Question regarding two-color MOT coupling F=1,2 and F'=1,2

You don't often get email from gabin....@gmail.com. Learn why this is important

Hi Lajos,

(sorry for sending the message twice, I am new to google groups and did not know the difference between reply all and reply author) :)

 

Thanks for the quick and instructive explanation regarding the issue I was facing. Splitting the ground state manifold into two indeed helped to boost the computation, and now I am able to calculate the force profile using the OBE solver.

 

Now, the system is defined with all the hyperfine manifolds involved in the D2 transitions of Rb87. Two laser beams are coupling F=1 to F'=0,1,2 and F=2 to F'=1,2,3 with a detuning det11 and det22 blue-detuned from the F=1-to-F'=1 and F=2-to-F'=2 transitions as the conventional 3d MOTs with the quadrupole magnetic field whose gradient is 87 G/cm. Here, the detunings were corrected for each transition such that it effectively simulates the real physical situation, like F=1-to-F'=2's detuning should be det11-energy offset of F'=2 and F'=1. Also, as you mentioned I ignored the beam 11 coupling transitions starting from F=2, since they have a large detuning.

 

However, the simulation still could not reproduce the results of the paper. Maybe the sign convention of the field or polarizaiton might be an issue, but I checked by changing the sign that it did not help. It would be great, if you or anyone can give some insight to resolve the issue and help understanding the problems better. For reference, I've attached my script.

Thank you for the support and insights.

 

Best,

Gabin

 

 

On Monday, March 16, 2026 at 3:26:35 PM UTC+1 lal...@gmail.com wrote:

Hi Gabin,

 

The rate-equations would be unable to reproduce the results of that paper since they rely on coherences, which the rate model does not take into account. The OBEs do generally take quite long,  but in this case I suspect they may take longer than necessary for what you want to simulate. It sounds to me that you set up your system with two states (one for the ground manifold and one for the excited one). Generally the limit for the integrator timestep will be near timescale of the fastest oscillating term within the system, which in this case will be ~4-5GHz. One way of reducing this is to split the ground state into two manifolds so the large detuning is not simulated. This eliminates some of the cross terms between these states, but those would not really come into play until fields much higher than what is discussed here. By doing this, the integrator can run faster in theory. The EIT example has a basic example of how to set this up and there are some discussion on this topic here as well.

 

Best,

Lajos

 

On Thursday, 12 March 2026 at 15:24:26 UTC gabin....@gmail.com wrote:

Hi all,

 

Thank you for this amazing package.

 

I am designing a blue-detuned MOT and before moving to my situation, I am first trying to reproduce the results of Jarvis et al. Blue-detuned MOT () Fig.1. Which is a MOT that has two lasers which has a detuning of delta11 and delta22 from the F=1 to F'=1 and F=2 to F'=2 transition of 87Rb respectively. If you have any experience in dealing with this problem, it wouldError! Filename not specified. be great if I can get some insights. I using hyperfine_coupled() to generate the ground and excited state manifolds and creating a coupling hamiltonian with dqij_two_hyperfine_manyfolds(). Then, I define two conventional 3d mots but with different detunings such that it matches the 1-to-1 and 2-to-2 detunings in the lab frame. Running the simulation with the OBE takes super-long, so I only tried the rateeq. However, the rateeq results does not match with the paper.

If you have any idea or good references, it would be great to have some tips. Thanks in advance.

 

Best, 
Gabin

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