Dear Editor,

first, we would like to thank the Referees for their careful review, and
apologize for the long delay with our reply. As Referee B raised some more
general issues, we revised our manuscript slightly, and would like to comment
on the points raised:

Referee:
"The point made by Schrodinger and Bell is that, if one describes, such an experiment as the authors perform, using standard quantum theory, and includes the apparatus in the state vector description, one ends up with a state vector which is a superposition of the various possible outcomes, including the recording by the apparatus of each outcome. The problem is that one or another outcome actually occurs in the laboratory, and standard quantum theory does not describe how this takes place. Both Schrodinger and Bell objected to the Copenhagen school's "collapse postulate," which simply states that this transition has to take place sometime, somehow, but is silent on both these issues. Both wished for a transition of the state vector from the superposition to the observed state to be described by theory, not by postulate. In his paper, Bell approvingly wrote about a modification of quantum theory, a new theory which provides such a description, giving a characteristic time for this evolution. "

Response:
    We agree with the Referee that standard quantum mechanics does not provide a description of the dynamics of the transition from the superposition of all possible states to the actual measurement outcome, resorting to the concept of "quantum jump" for the transition of a quantum system from one stationary state to another.
    Schroedinger, and Bell later on, emphasized that the idea of jumps appears to be in sharp conflict with the continuity of wave mechanics.
    Both the concept and context it is referred to has evolved as the understanding of quantum theory and open systems has increased.
    In his work, Bell embraces the formalism of Ghirardi, Rimini, and Weber, that describes the spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schroedinger's equation. Other authors, as for example Carmichael, Dalibard, Castin, and Moelmer, included quantum jumps as a link between continuous quantum measurement theory and stochastic quantum evolution.

    We it consider important to provide an experimental frameworks that allows the characterization of the transition between states in different scenarios. It is in this context that we experimentally determine a bound on the timescale of these transitions without assuming any specific extension of quantum mechanics.


Referee:
"The point is that the time involved in such a quantum jump is not what the authors conceive it to be. It is the time it takes the superposition of such macroscopic states to evolve to one of those observed states. What the authors have experimentally done is measure the time between reception of a "signal" photon emitted by an electron dropping to a state (|3> in their notation) and the subsequent emission of an "idler" photon as the electron drops to the ground state ((|0> in their notation). Their theoretical analysis concerns only the microscopic system, does not include the apparatus, so this has nothing to do with the notion of quantum jumps discussed above. Their measurement is not the time it takes the superposition of possible outcomes to become one outcome. "

Response:
    We agree with the Referee that there is no known way to obtain a direct measurement of the transition time of the state vector from all possible state to the measured state, and we do not claim to have performed any such direct measurements.

    In their seminal works, Dehmelt and Wineland demonstrated that it is possible to extract some information regarding the time behavior of "quantum jumps" using the time correlation of a sequence of detection events.
    Similarly, we use a time correlation measurement to establish an upper bound on the transition time, independently of the specific dynamics of the transition itself.

    We disagree with the referee statement that the theoretical analysis does not include the apparatus.  The observed time correlation includes also detection apparatus, i.e., our single photon detectors, in a proven and commonly accepted form in Eq.(1).
We clarified the introductory text before equation (1) to perhaps make this more clear. It now reads: "We establish a relation between the atomic system and the measurement apparatus by considering the correlation function related to the joint probability distribution of detecting a heralding photon in mode $s$ at time $t$ and a correlated photon in mode $i$ at time $t + \Delta t$"

Referee:
"I would add that, while the authors concentrate their interest upon
their data relative to the shortest time the electron stays in state
|3>, the measurement of any time in the range of times given by the
decay curve they present involves a "quantum jump," a transition from the superposition of possibilities to the actuality. "

Response:
    We agree on the referee that there is indeed a second quantum jump associated with the spontaneous decay of level |3>, with statistics perfectly captured by standard quantum mechanics.

    The focus of our interest is the first "quantum jump," associated with the onset of this decay, corresponding to the transition from any possible electronic configuration to a single measurement outcome, that is the occupation of level |3>. The Referee sees this as the minimum time the electron stays in level |3> before decaying.
    Independently of the specific interpretation, in standard quantum mechanics, the spontaneous decay starts as soon as a level is occupied, without any delay. Then, even if we don't espouse this specific interpretation, setting an upper bound on the shortest time the electron stays in state |3> is indeed a way to explore the contrast between a continuous dynamical description, expected by Schroedinger and Bell, and the discontinuity intrinsic in the "collapse postulate".


Referee:
"Now, concerning their analysis, they arrive at the conclusion that standard quantum theory predicts a step-function jump in the time between reception of the signal photon and the earliest idler photon. Again, I have no expertise at all in this area, but I would be surprised if a more careful analysis did not moderate that step function a certain amount. The author's calculation involves a certain amount of idealization, does not deal with the spatial nature of the atomic state within the Rb atom. I would think that the state vector describing the population of state |2>, its depopulation with concurrent photon emission, the population of state |3> and then its depopulation with concurrent photon emission, would end up giving a superposition which would not contain a step function jump between signal photon emission and idler photon emission. However, it might be an alteration that is so small as to be experimentally undetectable. "

Response:
    In our calculations, we adopted approximations compatible with the timescales of the experimental observations. To better clarify this point, we have added supplementary materials to clarify the connection between Eqs.~(1) and~(2) of the manuscript, and added a reference to it in the paragraph following equation (3)


Referee:
"Regardless, if the apparatus is included in the state vector, there certainly would be, as the authors suggest in their concluding remarks, a moderation of this step function behavior due to the behavior of the photodetectors. Indeed, that seems to be what they are measuring. "

Response:
    We thank the Referee for acknowledging that we include the measurement time characteristics in our analysis. We would like to stress that we explicitly clarified that this measurement sets an upper bound limited by the measurement apparatus technical limitation. As opposed to previous approaches, this is a technical and not fundamental limitation, offering the prospective of tighter upper bounds as detection technology improves.


Referee:
"In conclusion, I cannot speak to the value for the photonic community of this experimental upper limit on the briefest correlation time between the signal and idler photons, effectively an upper limit on the amount of time an electron spends in an excited state before dropping to its ground state. It may be that this is a valuable result. However, I object to this being called an experiment that measures the time duration of a quantum jump, since my understanding of the meaning of the time duration of a quantum jump is the time it takes the superposition of possible outcomes (what Schrodinger called in his 1935 paper the "catalog of expectations") given by Schrodinger's equation to become one, actual, outcome. "

Response:
    We agree with the Referee that a direct measurement of the dynamics of the collapse of the state vector due to measurement would be ideal, but until we find a way to achieve it, we consider our indirect approach a valid method to experimentally learn something more about the fundamentals of quantum mechanical systems. The same criticisms the Referee brings forward can be applied to the classic works that of the 80's and 90's, many of which are already referenced in the manuscript.



Additionally, we removed the wrong index 33 for the initializing density matrix |3><3| in the paragraph after equation (3).

We added a difference file, diff.pdf, for easier reference of the revised manuscript.

With this, we hope to have addressed the concerns of the referee. This type of work received recent attention, and we feel Physical Review would really be an appropriate platform for it. Looking forward for your reply,

With Best Regards on behalf of all authors,

Christian Kurtsiefer