Reply to the first reviewer:

i. The state preparation efficiency is calculated and included in the text.

ii. 'magnetic insensitive' has been corrected to 'magnetically sensitive'.

iii. The magnetic field synthesized at the location of the atom is estimated to be an equal superposition of left and right circularly polarized field, with respect to the bias magnetic field axis. While the left circularly polarized magnetic field is used to drive the qubit transition, the magnetic field components of other polarization have a negligible impact due to the large Zeeman detuning introduced by the bias magnetic field.

iv. We agree that the 50 Hz modulation may be induced by the alternating current of the power line. We have included the argument in the text.

v. We have corrected 'Theatomic' to 'The atomic'.


Reply to the second reviewer:

i. A short summary of previous work has been included in the introduction.

ii. While CPMG is commonly implemented with solid-state qubits, it was not completely clear that CPMG has a better performance for the particular noise environment of our single neutral atom system. Therefore, PDD with equal free evolution time is chosen in our preliminary study for its simplicity. We included the experimental results for CP and CPMG protocols in the text.

iii. A plot of signal contrast versus number of pi pulses has been included. The discussion about the impact of pulse imperfections is added in the text.

iv. We agree that the phase shifting protocols can boost the number of pulses before the signal contrast begins to drop. Experimental results for CPMG, which is the phase shifted version of CP, have been included. References for concatenated protocols are included.

v. In the experiment, the atom is prepared in the desired state by optical pumping. However, there is a non-zero probability that the atom will end up in some other Zeeman states in the F=2 level or even in the F=1 ground state. The efficiency of state preparation is inferred to be 88.3(8)% from the Rabi oscillation visibility and state detection efficiency.

The term 'magnetically insensitive' refers to the m_F=0 Zeeman state that does not experience energy shift due to magnetic field. The transition between |2,-2> and |1,-1> is a magnetic dipole allowed transition as such can be coupled using microwave fields.

The results for the magnetic insensitive states are presented because the coherence of the mentioned states for an optically trapped single atom has been widely studied. This has allowed us to check that our noise environment is similar to the other systems with an optically trapped single atom.
The coherence of the stretched states (Zeeman state with the maximal or minimal m_F value), which has the possibility to access a closed optical transition between |3,-3> and |2,-2>, remains relatively unexplored and is our main topic in the text.

An energy diagram has been included to clarify the discussion.

vi. The dark counts of the detector correspond to a mean photon number of 0.28. We attribute the remaining photon counts to the off resonant scattering of the dark state and background light.

The comment about the readout fidelity has been added in the text.