The multi-photon induced Fano effect

The ordinary Fano effect occurs in many-electron atoms and requires an autoionizing state. With such a state, photo-ionization may proceed via pathways that interfere, and the characteristic asymmetric resonance structures appear in the continuum. Here we demonstrate that Fano structure may also be induced without need of auto-ionization, by dressing the continuum with an ordinary bound state in any atom by a coupling laser. Using multi-photon processes gives complete, ultra-fast control over the interference. We show that a line-shape index q near unity (maximum asymmetry) may be produced in hydrogenic silicon donors with a relatively weak beam. Since the Fano lineshape has both constructive and destructive interference, the laser control opens the possibility of state-selective detection with enhancement on one side of resonance and invisibility on the other. We discuss a variety of atomic and molecular spectroscopies, and in the case of silicon donors we provide a calculation for a qubit readout application.

I found the results to be very interesting and I feel that this work is significant, and will be of interest to those working on silicons devices. I therefore feel that the paper should move towards publication in Nature Communications. However, I also felt that at times the work was not as well presented as it could be. I am not sure how close the authors are to the length limit for the main part of the paper, but I felt there were places where an expansion of the text could help the reader. I will discuss these in more detail below.
Apart from these largely presentational issues, there is one main point that needs to be addressed before I can make a final recommendation. The authors claim a ps-switch on of the Fano resonance.
B. Two samples are prepared, one with natural isotopes and one with enriched isotope.s In the manuscript, no further information is proved for the enriched ones. In the supplementary, it is only mentioned that "non-resonant effects more pronounced".
Some discussion in the manuscript may needed.
C. "open the possibility to tune donors in and out of invisibility to a single state-to-charge conversion readout beam." II. The comparison between theory and experiment is bases on the value of F. A direct comparison of q and Gamma may be more straightforward.

RESPONSE TO REFEREES
We thank the referees for their very careful reading and helpful comments. We have addressed all the issues they raise. In particular we have made major changes to the manuscript where requested, including new calculations and a detailed description of applications of the principles and primary discovery. We respond to each of the reviewers points in detail below (our responses in red).
We hope the work is now suitable for publication in Nature Communications.

Reviewer 1
Litvinenko et al. demonstrate the multi-photon Fano e↵ect using a THz laser applied to a phosphorus donor 740 in silicon. Since the interference of single level and continuum that leads to the Fano line shape is induced here using the laser, then changes in the transmission spectrum can be controlled on a picosecond timescale. This could be very important, for example for readout of sili-745 con donors in a quantum information processor.
I found the results to be very interesting and I feel that this work is significant, and will be of interest to those working on silicons devices. I therefore feel that the paper should move towards publication in Nature Communications. However, I also felt that at times the work was not as well presented as it could be. I am not sure how close the authors are to the length limit for the main part of the paper, but I felt there were places where an expansion of the text could help the reader. I 755 will discuss these in more detail below. Agreed -see our response to this Referee's point 1 below.
Apart from these largely presentational issues, there is one main point that needs to be addressed before I can make a final recommendation. The authors claim 760 a ps-switch on of the Fano resonance. For a quantum devices readout, one would want to do this switching repeatedly. Is it possible for the authors to show successive switching on and o↵ of the transmission? Yes. We have already demonstrated ultrafast switch-on shown in Fig   765   2 , and we also already demonstrated successive repeats with laser repetition time of 40ns, which we now mention on line 548. This repetition speed is now emphasised on line 398. Furthermore, we have significantly expanded the general discussion of the applications in response to 770 Referee 3.
I now go through the paper with some further questions and comments: 1. Through the paper I felt that the theory was discussed too briefly, and this makes it hard to fol-775 low. (There is more detail in the supplement, but I feel the main paper presentation could be improved). On page 2, the interaction V is introduced -what is the origin of this interaction and what form does the interaction Hamiltonian take?

780
Similarly, D is introduced but no detail of the kind of interaction this corresponds to is given. Following the general suggestion of the Referee we have moved a significant fraction of the theory from the Supplementary Materials to the main manuscript, 785 and the remainder to the Methods section so that it will appear alongside the manuscript. We have also introduced section headings (according to the Nat Comm style), in order to signal the flow to the reader in a better way. In relation to the 790 specific comments: we now explicitly define V as "the interaction between the discrete state and the continuum, V " and identify it as "the electronelectron configuration interaction in the helium example just given" -see line 86. We have greatly 4. Page 2, col 2. It is quoted that MPICS has q / 1/F 2 *also*. Why use also here? We mean to stress that in LICS only is controllable with field 810 F , not q, but in MPICS both and q are controllable. We have reworded the phrase -see the two sentences ending line 132. Although q and are not independently controllable with F , this has experimental advantages because the window-position is 815 robust against field fluctuations, as we mention on line 417. "reciprocal decay" is I do not think this term is widely known. Also it has the wrong sign in Fig 1. Agreed, the sign in Fig 1 has  it could be improved here. For example, in the discussion of the standard Fano e↵ect, they use the state c in the text but it is k ! in Fig. 1. Regarding the di↵erence between c and k ! , we tried to distinguish between the continuum and the states of dif-855 ferent energy within it (and we defined "|k ! i 2 |ci is the unmixed continuum state at energy E g +~!" just above Eqn 5). We have now significantly expanded the caption of Fig 1 to make this clear. In response to the general point that theory in the 860 supplement was more helpful, we have moved a significant fraction to the main text (see our response to this Referee's point 1 above).

Reviewer 2
This is a fine paper detailing how to create a Fano-865 like interference using multiphoton ionization. This is demonstrated experimentally, and theory is provided to explain the phenomenology in detail. I recommend publication. But there are a few small points of confusion (at least, to me) that I suggest that the authors take care of. uum, all that is necessary is that its natural spectral width is much smaller than the width of the continuum. But the referee is correct that the generality of our statement was unnecessary and could lead to confusion, and therefore we have now simplified 885 it -see line 26.
2. At the end of the first paragraph, the term "shape index" is used and i didn't understand it until later in the paper when it was defined. I suggest that, in parentheses, after shape index, naybe (the Fano 890 q-parameter) or something like that to make the connection with Ref. 1. Agreed. We have followed the referee's suggestion -see line 44 -and also mentioned q in the abstract where the shape index is mentioned.

895
3. The cartoon of FIG. 1. is slightly confusing. In the Fano column of (a) the implication is that the autoionizing state |ai and the continuum state |ki have di↵erent energies which is, of course, not true. I wonder if it can be tweaked a bit to abnegate 900 this incorrect impression, or at least explain in the caption that the vertical axis is not exactly energy. We agree that Fig 1a was confusing, and to answer referee's comment (and others by Referee 1) we have now significantly expanded its caption in 905 order to explain it clearly. Please note: while the detuning must be small for a Fano resonance to be observed, in general the final continuum state in the Fano theory |k ! i and the auto-ionising state |ai have di↵erent energy, the di↵erence being~ , 910 and the figure indicates the situation when > 0 in Eqn 1 (|k ! i above |ai). We now state this explicitly in the caption.

Reviewer 3
In this paper, the authors experimentally demon-915 strated Fano lineshapes by Multi-Photon-Induced Continuum Structure. The experiments were based on a platform they developed before with Giant multiphoton absorption (Nature Photon 12, 179184 (2018)). Taking advantages of an increased Bohr radius of Si:P, the re-920 quired intensity for MPICS is achievable by using a Free-Electron Laser. A Fano lineshape is experimentally observed as shown in Fig. 3b. The values of shape index q from the experiment and theory they developed have a good match.

925
However, I do not see a fundamental impactful advance here. The authors need to critically demonstrate the significance of their work, otherwise it is merely a show-and-tell study, unsuitable for Nature Communications. The fundamental advances here are several and 930 major. Here we produce the experimental demonstration of laser-induced Fano interference with an e↵ect that does not require extreme intensity, for the first time to our knowledge. The idea of the Fano line-shape, which carries both constructive and destructive interference (both a peak and a window), is extremely important because it gives structure to an otherwise flat continuum (line 33), and this allows a great variety of e↵ects in many different disciplines, such as those we illustrated with Refs [2-14] (see first paragraph). To our knowledge, these 940 and all other previous demonstrations of control over q are either: "permanent" influence over the design/choice of atom; slow control with temperature/magnetic field; or with extremely intense, non-perturbative drive lasers (or the control o↵ered is only over the width or centrefrequency, not the shape). As we already stated -see the abstract, the introduction, and in particular line 132 -MPICS o↵ers ultrafast control over q, in essentially any atom, and with relatively weak beams. This idea was first proposed by Armstrong in 1975 [15], which spawned 950 a citation tree that includes hundreds of papers with theoretical developments, but has never actually been realized until this work. Our crucial discovery is that MPICS with q near unity is achieveable with weak beams so long as the coupling beam frequency is low (i.e THz).

955
Although we concentrated our discussion in the first version on the silicon donors of particular interest to us, we now emphasise the more general nature of this discovery at the end of the first paragraph, and in a new final paragraph. The advance here is not only experi-960 mental but also theoretical -we show how to calculate the MPICS q using a new variant of implicit summation, that has allowed us to model our results very well, with no adjustable parameters.
In response to the Referee's request for a specific ap- 2. Two samples are prepared, one with natural isotopes and one with enriched isotope.s In the manuscript, no further information is proved for the enriched ones. In the supplementary, it is only mentioned that "non-resonant e↵ects more pro-and for this field. This was our reason for working backwards from the much more experimentally 1040 reliable q value. Nevertheless we now include a straightforwards comparison of q and 0 (the window position). We have reworded the discussion of uncertaintes in order to make the field comparisons straightforwards also, while emphasizing the 1045 sources of uncertainty. See line 357 to line 368.