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Ten years of the bundler

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«Just like single quantum emitters have revolutionized microscopy by the introduction of superlocalization methods with nanoscale (subdiffraction) resolution, $N$-photon bundles will impact novel quantum imaging and quantum communication schemes, with potential also in the quantum computing domain (boson sampling).»

J. Larson, one of the contemporary Jaynes--Cummings experts, does not make much drama about it but gives an accurate description in his textbook, covering both the Jaynes--Cummings and Mollow aspects, which is a subtle point:

Screenshot 20240630 122203.png

In contrast, González Tudela et al.[1] in their review on light-matter interactions in quantum photonic devices, make uninformed statements, as if the bundler (Ref. 103) is an incremental technological improvement with better cooperativity:

Screenshot 20240630 124331.png

Like most papers, it also cites badly the reference by butchering the name of its first Author as Muñoz C. S. (as it they did not know how to write Spanish names) and, of course, the term "bundle" is not used. I would not quite trust this review for an accurate account of the other papers. It's funny that Larson seems to understand the bundler much better than one of its co-Authors!

The perovskite people seem to like the idea as they see the bundler as a potential beneficiary of their emitters. This is from Raino et al.:[2]

Screenshot 20240630 130532.png

And this is from Cherniukh et al.:[3]

Screenshot 20240630 125528.png

Hamsen et al.[4] comment on direct production under strong driving:

Screenshot 20240630 131432.png

Cygorek et al.[5] quote the bundler as an application of the fluorescence of quantum dots:

Screenshot 20240630 131904.png

 •  • Pscherer et al.[6] highlight the bundler and use the term, although as an application of many emitters, which might even be correct, but properly speaking, the application should go with the single-molecule listing:

Screenshot 20240630 132617.png

Shi et al.[7] cite the bundler for single photons or photons pairs, which is missing the main point:

Screenshot 20240630 133249.png

 •  •  • Bin et al.[8] port the idea to a different (phonon) platform. They retain the term. I am an author but the main work is from the other group(s). This started a whole activity on bundling with phonons (with a separate branch not quoting the original paper anymore, e.g., in 2022, this paper was more cited [23 times] than the bundler itself [22]):

Screenshot 20240630 133650.png
Screenshot 20240630 133754.png

 • Müller et al.[9] rightfully point at the future of the results reported in this text. Although we are authors, most of the work (even theoretical) is from the Vuckovic group and we acted more as consultants on this one, in particular due to our role in planting the seminal idea:

Screenshot 20240630 134317.png

 •  •  • Bin et al.[10] add parity-protection (suppressing even-number bundles) and ultrastrong-coupling dynamics. The bundler paper is cited many times, as various of its concepts, techniques and resulted are used.

 • Loredo et al.:[11]

Screenshot 20240630 135316.png

 • Fischer et al.[12]refers to the temporal structure of the bundle:

Screenshot 20240630 135742.png

 • Boos et al.[13] suggest a time-resolved bundling emission:

Screenshot 20240630 140009.png

Fischer et al.[14] cite the bundler as one of the "multi-photon quantum state generators":

Screenshot 20240630 141048.png

 •  •  • Liu et al.[15], in an already highly-cited paper, although in an obscure journal, study STIRAP technique for high photon-number bundle generation:

Screenshot 20240630 142805.png

Heindel et al.[16] make a general reference:

Screenshot 20240630 145148.png

Kuruma et al.[17] make the technology required for the bundler in the future:

Screenshot 20240630 145828.png

 • Kockum et al.[18] refers to the bundle which could be produced by frequency conversion:

Screenshot 20240630 150226.png

 •  •  • Ma et al.[19] study bundle generations from a Josephson junction:

Screenshot 20240630 150618.png

Krisnanda et al.[20] cites the bundler in connection with NOON states, possibly mistaking this with the superposition ${1\over\sqrt{2}}(\ket{0\mathrm{g}}+\ket{N\mathrm{e}})$:

Screenshot 20240630 151105.png

 •  •  • Yuan  et al.[21] bring the scheme to magnons.

 • Groiseau et al.[22] comment on (two-photon) bundling opportunities from their THz single-photon source:

Screenshot 20240630 161757.png

Qiang et al.[23] report superbunching from perovskites and link that, maybe hurriedly, to entangled multi-photon quantum light:

Screenshot 20240630 162604.png

Rundquist et al.[24] limit the bundler to two-photon emission and attribute themselves the potential of generalization:

Screenshot 20240630 164243.png

Rivera17a et al.[25] bundle the bundler in a list of references that study two-photon spontaneous emission:

Screenshot 20240630 164734.png

Müller et al.[26], in a sister paper to Ref. [9], cites the bundler for potential applications:

Screenshot 20240630 165225.png

Fischer et al.[27] again pack up the bundler among multi-photon quantum state generators:

Screenshot 20240630 170013.png

 • Rivera et al.[28] compare their Fock-laser to the bundler:

Screenshot 20240630 172732.png

Gu et al.[29] cite the bundler as a general $n$-photon source.

Screenshot 20240630 173133.png

 • Nair et al.[30] say that the ultra-strong coupling regime leads to newer possibilities such as the production of output fields in Fock states, suggesting they do not understand the bundling mechanism (that relies neither on ultra-strong coupling nor, which is more subtle, does it produce Fock states):

Screenshot 20240630 173720.png

 • Pashaei Adl et al.[31] again with perovskites refer to bundles or "bursts"

Screenshot 20240630 174847.png
Screenshot 20240630 174957.png

Groiseau et al.[32] make the incorrect statement that the bundler is (like other multiphoton sources) low-yield. It is CW so one could say it is intrinsically probabilistic in the form we have presented it:

Screenshot 20240630 175347.png

Template:Nguyen23a et al.[33] ...

Template:Sanchezmunoz20b et al.[34] are inspired by the bundler and its derived papers, although they do not use the term "bundle" (interestingly, Kockum does when Sánchez is not an author):

Screenshot 20240630 180230.png
Screenshot 20240630 180343.png

Arlt et al.[35] cite the bundler as the pursuit of probabilistic multiparticle emitter:

Screenshot 20240630 182610.png

Sloan et al.[36] cite the bundler in connection to medical applications:

Screenshot 20240630 182926.png

 •  •  • Deng et al.[37] study phonon-bundles from a trapped ion, and introduces a distinction between Mollow and parametric down conversion:

Screenshot 20240630 183543.png

 •  •  • Gou et al.[38]

Chang et al.[39] cites the bundler (without ever using the term "bundle") as a new theoretical proposal using Purcell enhancement on dressed atomic system (not using the term leapfrog either, making the description quite vague and moot) and providing a definition of continuous multiphoton emission.

Screenshot 20240630 184511.png
Screenshot 20240630 185000.png

Hendrikson et al.[40] cite the bundler in the context of integrated quantum nonlinear optics:

Screenshot 20240630 185428.png

Fischer et al.[41] identify a regime of low-detuned photon bundling:

Screenshot 20240630 190143.png

Xing et al.[42] ...

Zou et al.[43] ...

Hamsen et al.[44] cite the bundler as an heralded $n$-photon source:

Screenshot 20240630 201618.png

 • Rainò et al.[45] describe bundling from superradiant (collective) emission:

Screenshot 20240630 204748.png

They write in their concluding remark to their paper:

Screenshot 20240630 203057.png

Note that one Author of this note later won the Nobel Prize in Chemistry.

Katsumi et al.[46] cite the bundler (and frequency-filtering!) for "complex photonic quantum states through judicious manipulation")

Screenshot 20240630 205903.png

Cortese et al.[47] cite the bundler as an example of how light-matter hybridization alters quantum properties:

Screenshot 20240630 210435.png

Mavrogordatos[48] cites the bundler for multiphoton transitions as a mark of nonlinearity:

Screenshot 20240630 210935.png

Tang et al.[49] cite the bundler (last citation of the paper) as an example of possible implementation with variations of their scheme:

Screenshot 20240630 211513.png

Garziano et al.[50] cite the bundler as an eampleof engineering quantum properties of light emitted by a single emitter:

Screenshot 20240630 211818.png

 • Dong et al.[51] discuss multiphoton resonances as bundles:

Screenshot 20240630 212457.png

Their Eq. (29) which is our two-bundle correlation function is also attributed to Glauber (maybe for the particular case $n=1$).

 •  •  • Jiang et al.[52] is maybe the first paper ever to cite the bundler as its first reference and build its narrative from there:

Screenshot 20240630 213039.png

 • Snijders et al.[53] relate bundling to 'photon tunelling' that removes the single-photon component:

Screenshot 20240630 213656.png

Carlos has his two names in this one but is cited as Mufloz.

Vivas-Viaña & Sánchez Muñoz cite the bundler for the dip in $g^{(2)}$ at the bundling peak; Bundling or bundles are nowhere mentioned:

Screenshot 20240630 214131.png

You et al.[54] refer to the bundler for their investigation of multi-particle van Cittert-Zernike theorem, although it is not always clear why it is included or excluded of the respective statements.

Screenshot 20240630 231536.png
Screenshot 20240630 231108.png

 • Gies and Reitzenstein[55]

 • Leppäkangas et al.[56] mention photon bundles from cavity physics as compared to their multiphoton Cooper mechanism:

Screenshot 20240630 232412.png

 •  •  • Cosacchi et al.[57]

Bostelmann et al.[58] ...

 •  •  • Zou et al.[59] cite the bundler (Ref. [11]) as a particular case of bundle generation, making an otherwise nice review of bundler-physics:

Screenshot 20240630 233545.png

 •  •  • Bin et al.[60] review the early days of cavity QED bundling to introduce her extended scheme:

Screenshot 20240630 234323.png

 • Lebreuilly et al.[61] compare their deterministic Fock state creation to the "many" recent other proposals of bundle creation:

Screenshot 20240630 234925.png

 • Cosacchi et al.[62] cite the bundler for multi-photon correlation functions:

Screenshot 20240630 235632.png

 • Schmidt et al.[63] mention bundles as examples of multiphoton sources:

Screenshot 20240701 000358.png

 • Fischer et al.[64] rely on the bundling statistics:

Screenshot 20240701 001028.png

Similarities and differences with the original bundler are pointed out:

Screenshot 20240701 001129.png

 • Stolyarov[65] praises the Jaynes-Cummings model of various feats, including generating bundles:

Screenshot 20240701 001738.png

Dhar et al.[66] cite "nonclassical bundles" as one of the signatures of nonclassical collective features:

Screenshot 20240701 002031.png

Gasparinetti et al.[67] cites the bundler as something useful in quantum photonics, not being quite clear what they mean or how they relate it to the previous work [18]:

Screenshot 20240701 002822.png

Ma et al.[68] cite the bundler for the generalized bundle-statistics:

Screenshot 20240701 003305.png

 • Zhang et al.[69] cite the bundler (Ref. [10]) as a new light source, in between many references to bundles:

Screenshot 20240701 003822.png

 • Li et al.[70] mention the bundler as photonic computing (Ref. 8) in connection with superfluorecence of perovskites. The term "bundles" is later used to describe photon bursts.

Screenshot 20240701 004553.png

 • Zuo et al.[71] propose to use their (spinning) scheme to bundle generation:

Screenshot 20240701 005004.png

López Carreño et al.[72] list the bundler as an exotic source of light:

Screenshot 20240701 005551.png

Macovei and Pálffy[73] ...

Rinaldi et al.[74] cite the bundler as an example producing nontrivial statistics. The term bundle is not used for photons, but it is accepted for the optical fibres that are bundled to make a camera:

Screenshot 20240630 185737.png

Mavrogordatos[75] cites the bundler for two-photon emission:

Screenshot 20240701 011152.png

Yu et al.[76] cite the bundler as a three-photon emitter:

Screenshot 20240701 011444.png

Peng and Dent[77] ...

 • Müller et al.[78] comment again (cf. [41]) on bundling at low detuning:

Screenshot 20240701 012058.png

Lu et al.[79] ...

Dory et al.[80] comment again on high-order Fock states (cf. Ref. [9]):

Screenshot 20240701 012523.png

Lu et al.[81] speak of tailored higher-order statistics:

Screenshot 20240701 012940.png

 •  •  • Gou et al.[82] is the second text that places the bundler as its first reference:

Screenshot 20240701 013418.png

Mîrzac et al.[83] cite the bundler as a novel source of light:

Screenshot 20240701 013852.png

Kamide et al.[84] cite the bundler as a new quantum light source:

Screenshot 20240701 014202.png

Børkje et al.[85] ...

Strekalov and Leuchs[86] compares bundles to flying Fock states:

Screenshot 20240701 014725.png


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