Deep Laser Cooling of Thulium Atoms to Sub-µK Temperatures in Magneto-Optical Trap

Round 1

Reviewer 1 Report

In the manuscript the authors presented a detailed discussion of deep laser cooling of thulium atoms to temperatures below recoil temperature via a third-stage cooling. After reading the manuscript, I find the manuscript well written, and the methodology is easy to follow. I would recommend publication when the following concerns are addressed.

 

1.     It is not mentioned throughout the manuscript that whether the experiment is performed with Bosonic or Fermionic isotopes? Please clarify this.

2.     It would be helpful to include the energy level diagram of thulium (if space allows). This allows readers who are not familiar with thulium to better understand which exact transitions for laser cooling, clock interrogation, and magic-wavelength trapping.

3.     A following suggestion is to include an experimental sequence timing diagram.

4.     What is the optical lattice wavelength used in this work? The reviewer failed to find it in the manuscript.

5.     The authors show radial temperature in Fig. 2, however, the axial temperature (or mean axial vibrational number, n_z) in the optical lattice is a critical parameter for such as lattice Stark shift characterization. I wonder what is the typical n_z?

 

Minor comment:

1.     Line 19: “with 2.612” of what? Please clarify this.

Author Response

Thank you for the review. We address the following concerns point by point:

1. It is not mentioned throughout the manuscript that whether the experiment is performed with Bosonic or Fermionic isotopes? Please clarify this.

Indeed, we did not mention this information in the introduction. Thulium has only one stable isotope (which happens to be a boson), and we added this information in the Introduction:

All current experiments with cold atomic thulium use the single stable bosonic isotope thulium-169. The experimental procedure starts with two-stage laser cooling which typically produces several millions of atoms at a temperature of ~20 μK.

2. It would be helpful to include the energy level diagram of thulium (if space allows). This allows readers who are not familiar with thulium to better understand which exact transitions for laser cooling, clock interrogation, and magic-wavelength trapping.
3. A following suggestion is to include an experimental sequence timing diagram.

Thank you for these suggestions. We have added the figure with the level diagram together with the sequence timing for illustration of the experiment.

4. What is the optical lattice wavelength used in this work? The reviewer failed to find it in the manuscript.

Thank you for reminding us of this important point. We added the following text in the Results section:

Here, we operate the optical lattice at a wavelength of 1063.9 nm which is close to the magic wavelength which we will use in clock spectroscopy experiments [18,22].

5. The authors show radial temperature in Fig. 2, however, the axial temperature (or mean axial vibrational number, n_z) in the optical lattice is a critical parameter for such as lattice Stark shift characterization. I wonder what is the typical n_z?

We are sorry for the confusion with Fig. 2. In this figure, we show our measurements of clock transition spectrum in the vertical direction in a free-space. Consequently, we presented the time-of-flight measurement of only the vertical cloud dimensions. With our optical lattice configuration, this would correspond to the axial temperature in the lattice. For a typical longitudinal vibrational frequency of 40 kHz, the typical temperature in the paper ~1 μK corresponds to the mean n_z ≈ 0.2. However, in this work we use the optical lattice only for the multiple-cloud recapture near the end. To clarify the temperature and beam direction for this figure, we changed the caption:

a) Clock line spectroscopy in free-space using vertical clock laser beam: relative number of atoms remained after clock transition excitation depending on clock frequency detuning from resonance.

b) Atomic cloud vertical size (radius at 1/e level) during the time-of-flight experiment. The temperature T_ver = 0.69(6) μK explains 12 kHz of the linewidth which is consistent with clock line spectroscopy.

Minor comment:

1. Line 19: “with 2.612” of what? Please clarify this.

We apologize for the confusion in that sentence. We have changed it:

Laser cooling techniques typically allows to reach temperatures of about 1 μK with typical phase-space density (PSD) of  10^-4 [13-17], while the PSD of 2.612 is required to achieve BEC [6].

Reviewer 2 Report

This is a very useful study on a so far unexplored cooling transition for Thulium, which will support future developments in experiments with this atom, both in BEC studies as well as for optical clocks. the presentation seems sound and is concise, such that I recommend publication as is. 

Author Response

Thank you for the kind words.

Reviewer 3 Report

 

The article in question discusses the laser cooling of thulium atoms to ~ 400µK temperatures in a magneto-optical trap. Overall the article is well put together and the results interesting. However, the following comments would be good to adress before publication:

 

-      The introduction places the developments in good context, however this could be enhanced by commenting on its use in applications such as atom interferometry-based gravity/gravity gradient sensors.  

-        It would be nice if the authors included a brief paragraph at the end of the introduction summarising what will be discussed in the paper.

-        A diagram of the experimental set up would be a good inclusion and improve clarity.

-        Some of the figures are not referenced in the text, this needs to be fixed.

-          In line 101 a reference to a paper explaining time of flight measurements would be a good inclusion.

-         There is some inconsistency in the referencing with some referencing including DOI’s and others not. I would suggest the authors check all of the references for any other issues.

 

If the authors have not already considered submitting their article to a special issue in atoms (i.e Applications of Cold-Atom-Based Quantum Technology) they may wish to do so.

 

 

Author Response

Thank you for your review and comments. Here we have to comment on a possible typo: the temperature we achieve in this work is 400 nK. The following comments are addressed point by point.

-      The introduction places the developments in good context, however this could be enhanced by commenting on its use in applications such as atom interferometry-based gravity/gravity gradient sensors.  

We have listed “gravimetry” with other applications and added several references:

In modern atomic physics, laser cooling of atoms, ions and molecules is an essential technique for producing cold and dense clouds of particles. Such ensembles are the subject of study in many fields, including few- and many-body physics [ 1, 2], gravimetry [3– 5], quantum simulations [2], Bose-Einstein condensate (BEC) [6–10 ], and optical lattice clocks [11,12].

-        It would be nice if the authors included a brief paragraph at the end of the introduction summarising what will be discussed in the paper.

Indeed, the experimental work that is covered by this paper was not very clear from the Introduction. We put the final sentences of the Introduction in the separate paragraph and added the following:

In the section 2 we describe our experimental results: efficient recapture of atoms from the 1st and the 2nd into the 3rd-stage MOT (2.1), optimization of the narrow line cooling process (2.2), confirmation of the low temperature of MOT with the Doppler broadening of the clock transition spectroscopy (2.3), the effect of the intermediate 2nd-stage MOT (2.4), and the possibility to form double-structured clouds in an optical lattice (2.5). Finally, we draw the conclusions in the section 3.

-        A diagram of the experimental set up would be a good inclusion and improve clarity.

We have added a figure with the level diagram together with the sequence timing for illustration of the experiment. Otherwise, we use the standard 6-beam magneto-optical trap with Zeeman cooling which is described in details in our previous works.

-        Some of the figures are not referenced in the text, this needs to be fixed.

We have added another figure in the Introduction (Fig. 1) and checked that every figure is referenced in the text

-          In line 101 a reference to a paper explaining time of flight measurements would be a good inclusion.

Thank you for pointing this out. We added a reference to one of the pioneer works by Williams et al., "Observation of atoms laser cooled below the Doppler limit", 1988.

-         There is some inconsistency in the referencing with some referencing including DOI’s and others not. I would suggest the authors check all of the references for any other issues.

We have checked and fixed all the references. Thank you for your remark.

If the authors have not already considered submitting their article to a special issue in atoms (i.e Applications of Cold-Atom-Based Quantum Technology) they may wish to do so.

We are indeed submitting this article to a special issue, although to another one.