Dear Editor,

we first like to thank the referees for their careful reception of our manuscript, and for their constructive and detailed remarks. We revised the manuscript accordingly. Our replies to the detailed comments:

Reply to the first referee:

General comment:

We agree that we are currently looking at some relatively simple sequences that do not take into account the pulse imperfections. To clarify this idea, we have extended the discussion as follows: “In our system, we are currently limited to pulse sequences with N ≤ 20 as the contrast of the coherence evolution drops as N increases. This is because pulse imperfections including errors in the flip angles and finite pulse width introduce dephasing to the qubit, as discussed in [39]. More robust pulse sequences with pulse phases that are shifted appropriately can be applied to mitigate the pulse errors. Nevertheless, the preliminary refocusing strategy here has offered us an insight into the dephasing mechanism of a magnetic-sensitive qubit state.”

p.2
i.) The axial trap frequency of our dipole trap is ~12kHz that corresponds to a mean axial vibrational mode number of 25, which infers that our atom is not close to motional ground state

ii.) "subsequent collection of the fluorescence light" change to "collect the fluorescence light from atom within this time window"

iii.) added "by applying a microwave field resonant to this transition using a pair of log-periodic antennae" in section III

iv.) In the first paragraph of section III, we added an explanation of how the fidelity and visibility is related. We also explain why the visibility is lower than the maximum that we could observe.

v.) "decay of the Rabi contrast" change to "decay of the Ramsey contrast"

p.4
i.) and ii.) We have omitted the formulation of the decoherence process. 

iii.) Corrected from "... able to compensate errors of non-ideal pulses and provide suppression of general decoherence" to “... able to provide suppression of general decoherence”. 

iv.) "the physical bound is T2 ≤ 2T1" change to "the physical bound is T2 ≤ T1" for our qubit system

p.6
i.) We change CPMG to CP which is the pulse sequence that we are using

p.7
i.) We think that there is some misunderstanding here as there is already comparison between the simulation and the experimental results show in Fig 9.



Reply to the second referee:

General comment:

	"I find the paper lacking novelty…… There is some additional effort due to the single atom which requires massive averaging but the physics is the same."

With recent demonstration of nonlinear interactions with a single atom in free space, a single neutral atom qubit could be a potential platform to realize memories or repeaters in quantum communication. We think that it would be interesting to look at the dephasing mechanism of a single neutral atom and compare it with atomic ensembles.

	"If the noise is dominated by magnetic noise…… analytically and should be modeled exactly"

As suggested by the second referee, we have included modelling and calculations related to the suspected dominant noise source in the discussion.

Specific comments:

1. Calculated with the analytical expressions from the references and included in the text.

2. We have extended the discussion as follows: “The qubit's sensitivity to the external magnetic field is 21 GHz/T at low fields. Due to the high magnetic sensitivity of the qubit states, fluctuations in magnetic fields can be the dominant factor in the dephasing mechanism. To verify this, we have measured a r.m.s. magnetic field fluctuations of 220 nT dominated by components at 50 Hz using a fluxgate magnetometer. …  This corresponds to a Ramsey coherence time of 43 us, in agreement with our observation.” 

3. We have extended the introduction as follows: “The up state can be coupled to an auxiliary state via a closed optical transition, opening a possible path to protocols originally developed for solid state quantum systems to be implemented in an atomic system. This includes schemes for the generation of time-bin atom-photon entanglement and the sequential generation of an entangled photonic string, which are crucial resources for quantum computations.”

4. The mentioned works have been added as a reference to our manuscript and compared with our results.

5. We are limited by the pulse imperfections. We have extended the discussion as follows: “In our system, we are currently limited to pulse sequences with N  ≤  20 as the contrast of the coherence evolution drops as N increases. This is because pulse imperfections including errors in the flip angles and finite pulse width introduce dephasing to the qubit, as discussed in [39]. More robust pulse sequences with pulse phases that are shifted appropriately can be applied to mitigate the pulse errors. Nevertheless, the preliminary refocusing strategy here has offered us an insight into the dephasing mechanism of a magnetic-sensitive qubit state.”

6. We have added “We would like to point out that in this discussion we are only looking at the coherence of one single state possessing a particular phase. For an arbitrary state on the Bloch sphere, more robust sequences such as KDDx and KDDxy are more effective in preserving the qubit coherence.“ in order to clarify the confusion. 

7. We agree that a DD sequence needs a distinctive noise spectrum to outperform the others. We have added in the discussion: “We also notice that PDD and UDD sequences perform quite similarly because in general a DD sequence requires a rather distinctive noise spectrum to outperform the others.” 

8. Corrected from “CPMG” to “CP”.

9. Reference and assumptions included in the text.

10. With a relatively simple system with a small number of refocusing pulses, we are able to identify an optimal strategy, as pointed out by the first referee. Optimization with a large number of pulses will be addressed in possible future work as it would require the implementation of phase-shifted pulses and would exceed the scope of this work. We have added this outlook in the conclusion.


With this, we believe to have addressed the issues raised by the referees,
and look forward for consideration of publication in Physical Review A.

With Best Regards on behalf of all authors, and looking forward for your reply,

Christian Kurtsiefer