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Physics Today

A history of hole burning

William Ralph Bennett

Published May 1, 2008• 0 citations
Publisher

Abstract

Richard Brewer, Aram Mooradian, and Boris Stoicheff, in their review “The Early Days of Precision Laser Spectroscopy” (Physics Today, Physics Today 0031-9228 60 1 2007 49 https://doi.org/10.1063/1.2709559. January 2007, page 49 ), implied that Willis Lamb conceived of the notion that his dip at line center could be explained through hole-burning effects. In fact, Lamb had no physical interpretation of the tuning dip when he first showed by purely mathematical analysis that the dip might exist. After reading his original manuscript, I suggested hole burning to him in a letter dated 7 July 1962 (available at the online version of this letter).The subject had come up in a lecture I gave, attended by Gordon Gould, on my previous research on hole-burning effects. 1 1. W. R. Bennett Jr, Phys. Rev. 126, 580 (1962). https://doi.org/10.1103/PhysRev.126.580 I had only discussed the effects of running waves in one direction, and Gordon asked, “What about the other running wave in the standing wave?” After drawing a diagram on the blackboard, I realized, as did Gordon, that the presence of the second running wave would result in a dip as the laser was tuned through line center.These holes in the Doppler line approach each other and overlap at the middle. Because the power stimulated in each hole falls within about a natural width of the atoms’ Doppler-shifted frequency, the number of atoms stimulated to emit at line center can decrease by a factor of two. After showing that interpretation to Lamb, I published it later that year in a review paper on gaseous optical masers. 2 2. W. R. Bennett Jr, in Applied Optics Supplement on Optical Masers, Optical Society of America, Washington, DC (1962), pp. 24, 57, 58. During my time at Bell Laboratories, Ross McFarlane and I started an experiment to look for the dip in a helium–neon laser using a much shorter length than the one I had described in reference 1. I was in the process of moving from Bell Labs to Yale University, and McFarlane had to finish the experiment alone. He was the first to observe the tuning dip experimentally, but for several months we withheld publication of a paper reporting the results 3 3. R. A. McFarlane, W. R. Bennett Jr, W. E. Lamb Jr, Appl. Phys. Lett. 2, 189 (1963). https://doi.org/10.1063/1.1753727 until Abraham Szoke and Ali Javan had had a chance to verify the effect at MIT.While waiting for their experiment, I showed that the “mirror-image” hole in the Doppler profile was responsible for the “mode-pushing” effect described in Lamb’s theory and that the hole-burning interpretation led to the same single-mode equations as his third-order theory (with different notation). I presented those results at the Paris Quantum Electronics Conference in February 1963, but the volume containing my paper describing those equations, wasn’t published until a year later. 4 4. W. R. Bennett Jr, in Quantum Electronics: Proceedings of the Third International Congress, Paris, vol. 1, P. Grivet, N. Bloembergen, eds., Columbia U. Press, New York (1964), pp. 441, 450. That work was discussed in much more detail in an article based on lectures that I gave at Brandeis University in the summer of 1969.One final aspect of the role of hole-burning effects in laser spectroscopy that was omitted in the otherwise fine article by Brewer and coauthors is the narrow absorption peaks initially observed in 1968 by Veniamin Chebotayev and his student V. N. Lisitzin at Novosibirsk, Russia, in a laser containing a saturable absorber. 5 5. V. N. Lisitzin, “Experimental Investigations of Gas Lasers with Saturable Absorbers as Resonators,” research thesis, AcademGorodok, Novosibirsk, Russia (1968). The extremely narrow resonant peaks they found were due to hole-burning effects in the Doppler-broadened absorber. Chebotayev and Lisitzin also extended that work to include tuning dips from strong-wave–weak-wave interactions in external absorption cells, a process that anticipated the later, more elegant work by Theodor Hänsch, Marc Levenson, and Arthur Schawlow. 6 6. T. W. Hänsch, M. D. Levenson, A. L. Schawlow, Phys. Rev. Lett. 26, 945 (1971). In those experiments, the strong wave burns a hole in the line that is probed by a weak wave traveling in the opposite direction. Since the absorber can involve a ground-state atom or molecule, much narrower natural widths can be obtained in the absorber experiments than in those with the amplifying medium.REFERENCESSection:ChooseTop of pageREFERENCES <<1. W. R. Bennett Jr, Phys. Rev. 126, 580 (1962). https://doi.org/10.1103/PhysRev.126.580 , Google ScholarCrossref2. W. R. Bennett Jr, in Applied Optics Supplement on Optical Masers, Optical Society of America, Washington, DC (1962), pp. 24, 57, 58. Google Scholar3. R. A. McFarlane, W. R. Bennett Jr, W. E. Lamb Jr, Appl. Phys. Lett. 2, 189 (1963). https://doi.org/10.1063/1.1753727 , Google ScholarCrossref, CAS4. W. R. Bennett Jr, in Quantum Electronics: Proceedings of the Third International Congress, Paris, vol. 1, P. Grivet, N. Bloembergen, eds., Columbia U. Press, New York (1964), pp. 441, 450. Google Scholar5. V. N. Lisitzin, “Experimental Investigations of Gas Lasers with Saturable Absorbers as Resonators,” research thesis, AcademGorodok, Novosibirsk, Russia (1968). Google Scholar6. T. W. Hänsch, M. D. Levenson, A. L. Schawlow, Phys. Rev. Lett. 26, 945 (1971). Google ScholarCrossref© 2008 American Institute of Physics.

DOI
10.1063/1.2930750

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I read with interest Daniel Kleppner’s lucid column on Hanbury Brown’s “steamroller.” Kleppner mentions an aspect of the Hanbury Brown and Twiss (HBT) effect that at first seemingly defied a quantum interpretation; he terms it “anti-weird,” since in certain cases a completely classical understanding is possible. Other aspects of the Hanbury Brown physics are truly weird in the sense that they violate a Bell inequality. I and collaborators Peter Samuelsson and Eugene Sukhorukov have proposed an interferometry experiment with fermions in an electrical conductor. Carriers are injected into the conductor from two contacts, and the cross correlation of the electrical current is measured at two other contacts along the conductor. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 In that arrangement, it is possible to investigate the Aharonov–Bohm effect in the fermionic HBT interferometer. Our initial discussions of such an effect date back to the early 1990s. 2 2. M. Büttiker, Phys. Rev. Lett. 68, 843 (1992); Physica B 175, 199 (1991). https://doi.org/10.1016/0921-4526(91)90713-O My collaborators and I found a geometry in which the conductance (intensity) shows no Aharonov–Bohm signature, but the current correlation (intensity correlation) is nevertheless a periodic function of the Aharonov–Bohm flux. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 We termed our finding the two-particle Aharonov–Bohm effect. The effect was recently observed by a group headed by Moty Heiblum at the Weizmann Institute of Science. His team cooled a mesoscopic conductor to tens of millikelvin and measured its conductance and noise correlations. 3 3. I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, V. Umansky, Nature 448, 333 (2007). https://doi.org/10.1038/nature05955 Theoretical work by Carlo Beenakker at Leiden University has shown that due to orbital quasiparticle entanglement, 4 4. C. W. J. Beenakker, in Quantum Computers, Algorithms and Chaos, Proceedings of the International School of Physics “E. Fermi,” vol. 162, G. Casati et al. , eds., IOS Press, Washington, DC (2006). the two-particle effect is equivalent at zero temperature to a violation of a Bell inequality. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 The case of nonzero temperature is more complicated and is still a subject of research. 5 5. P. Samuelsson, I. Neder, M. Büttiker, Phys. Rev. Lett. (in press). The possibility of observing truly weird quantum physics is certain to increase interest in Hanbury Brown’s physics.REFERENCESSection:ChooseTop of pageREFERENCES <<1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 , Google ScholarCrossref2. M. Büttiker, Phys. Rev. Lett. 68, 843 (1992); Google ScholarCrossref Physica B 175, 199 (1991). https://doi.org/10.1016/0921-4526(91)90713-O , , Google ScholarCrossref3. I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, V. Umansky, Nature 448, 333 (2007). https://doi.org/10.1038/nature05955 , Google ScholarCrossref4. C. W. J. Beenakker, in Quantum Computers, Algorithms and Chaos, Proceedings of the International School of Physics “E. Fermi,” vol. 162, G. Casati et al. , eds., IOS Press, Washington, DC (2006). Google Scholar5. P. Samuelsson, I. Neder, M. Büttiker, Phys. Rev. Lett. (in press). Google Scholar© 2009 American Institute of Physics.

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Physics Today•May 1, 2001•1 citation
Richard Brewer, Aram Mooradian, and Boris Stoicheff, in their review “The Early Days of Precision Laser Spectroscopy” (Physics Today, Physics Today 0031-9228 60 1 2007 49 https://doi.org/10.1063/1.2709559. January 2007, page 49 ), implied that Willis Lamb conceived of the notion that his dip at line center could be explained through hole-burning effects. In fact, Lamb had no physical interpretation of the tuning dip when he first showed by purely mathematical analysis that the dip might exist. After reading his original manuscript, I suggested hole burning to him in a letter dated 7 July 1962 (available at the online version of this letter).The subject had come up in a lecture I gave, attended by Gordon Gould, on my previous research on hole-burning effects. 1 1. W. R. Bennett Jr, Phys. Rev. 126, 580 (1962). https://doi.org/10.1103/PhysRev.126.580 I had only discussed the effects of running waves in one direction, and Gordon asked, “What about the other running wave in the standing wave?” After drawing a diagram on the blackboard, I realized, as did Gordon, that the presence of the second running wave would result in a dip as the laser was tuned through line center.These holes in the Doppler line approach each other and overlap at the middle. Because the power stimulated in each hole falls within about a natural width of the atoms’ Doppler-shifted frequency, the number of atoms stimulated to emit at line center can decrease by a factor of two. After showing that interpretation to Lamb, I published it later that year in a review paper on gaseous optical masers. 2 2. W. R. Bennett Jr, in Applied Optics Supplement on Optical Masers, Optical Society of America, Washington, DC (1962), pp. 24, 57, 58. During my time at Bell Laboratories, Ross McFarlane and I started an experiment to look for the dip in a helium–neon laser using a much shorter length than the one I had described in reference 1. I was in the process of moving from Bell Labs to Yale University, and McFarlane had to finish the experiment alone. He was the first to observe the tuning dip experimentally, but for several months we withheld publication of a paper reporting the results 3 3. R. A. McFarlane, W. R. Bennett Jr, W. E. Lamb Jr, Appl. Phys. Lett. 2, 189 (1963). https://doi.org/10.1063/1.1753727 until Abraham Szoke and Ali Javan had had a chance to verify the effect at MIT.While waiting for their experiment, I showed that the “mirror-image” hole in the Doppler profile was responsible for the “mode-pushing” effect described in Lamb’s theory and that the hole-burning interpretation led to the same single-mode equations as his third-order theory (with different notation). I presented those results at the Paris Quantum Electronics Conference in February 1963, but the volume containing my paper describing those equations, wasn’t published until a year later. 4 4. W. R. Bennett Jr, in Quantum Electronics: Proceedings of the Third International Congress, Paris, vol. 1, P. Grivet, N. Bloembergen, eds., Columbia U. Press, New York (1964), pp. 441, 450. That work was discussed in much more detail in an article based on lectures that I gave at Brandeis University in the summer of 1969.One final aspect of the role of hole-burning effects in laser spectroscopy that was omitted in the otherwise fine article by Brewer and coauthors is the narrow absorption peaks initially observed in 1968 by Veniamin Chebotayev and his student V. N. Lisitzin at Novosibirsk, Russia, in a laser containing a saturable absorber. 5 5. V. N. Lisitzin, “Experimental Investigations of Gas Lasers with Saturable Absorbers as Resonators,” research thesis, AcademGorodok, Novosibirsk, Russia (1968). The extremely narrow resonant peaks they found were due to hole-burning effects in the Doppler-broadened absorber. Chebotayev and Lisitzin also extended that work to include tuning dips from strong-wave–weak-wave interactions in external absorption cells, a process that anticipated the later, more elegant work by Theodor Hänsch, Marc Levenson, and Arthur Schawlow. 6 6. T. W. Hänsch, M. D. Levenson, A. L. Schawlow, Phys. Rev. Lett. 26, 945 (1971). In those experiments, the strong wave burns a hole in the line that is probed by a weak wave traveling in the opposite direction. Since the absorber can involve a ground-state atom or molecule, much narrower natural widths can be obtained in the absorber experiments than in those with the amplifying medium.REFERENCESSection:ChooseTop of pageREFERENCES <<1. W. R. Bennett Jr, Phys. Rev. 126, 580 (1962). https://doi.org/10.1103/PhysRev.126.580 , Google ScholarCrossref2. W. R. Bennett Jr, in Applied Optics Supplement on Optical Masers, Optical Society of America, Washington, DC (1962), pp. 24, 57, 58. Google Scholar3. R. A. McFarlane, W. R. Bennett Jr, W. E. Lamb Jr, Appl. Phys. Lett. 2, 189 (1963). https://doi.org/10.1063/1.1753727 , Google ScholarCrossref, CAS4. W. R. Bennett Jr, in Quantum Electronics: Proceedings of the Third International Congress, Paris, vol. 1, P. Grivet, N. Bloembergen, eds., Columbia U. Press, New York (1964), pp. 441, 450. Google Scholar5. V. N. Lisitzin, “Experimental Investigations of Gas Lasers with Saturable Absorbers as Resonators,” research thesis, AcademGorodok, Novosibirsk, Russia (1968). Google Scholar6. T. W. Hänsch, M. D. Levenson, A. L. Schawlow, Phys. Rev. Lett. 26, 945 (1971). Google ScholarCrossref© 2008 American Institute of Physics.
When the strong Doppler limit is applicable, a tuned laser containing Doppler-broadened gain and absorption media may produce a steady-state standing-wave field that is both frequency pushed and isolated from the branch of on-resonance steady states. The locus of the isolated states plotted as a function of the linear gain is a pair of closed loops, called isolas. Similar running-wave modes are not found in this limit. A connection is indicated between the isolated steady states and both the mode-pushed states discovered by Bennett [ The Physics of Gas Lasers ( Gordon and Breach, New York, 1977)] and the instability found by Casperson [ Phys. Rev. A21, 911 ( 1980)].
Previous theoretical results on the influence of a laser on the line shape of a coupled transition-laser-induced line narrowing-have been restricted to the case where the laser is detuned from the center of its atomic gain profile or is in the form of a traveling wave. This paper extends those results to include the case where the laser is an intense standing-wave field tunable to the center of its atomic gain profile (conditions for Lamb dip). The effect may be observed either in transmission, by probing the coupled transition with a weak traveling-wave field coaxial with the laser field, or else in spontaneous emission from the coupled transition viewed along the axis of the laser field. It is now well known that for a laser detuned from the center of its atomic gain profile, two narrow Lorentzian resonances of different widths appear superimposed upon the broad background signal at frequencies symmetrically located about the corresponding line center. When the laser is tuned to the center of its gain profile, however, additional fine structure develops. This structure, which is particularly significant when the laser field is intense, may have important applications in highresolution spectroscopy and laser-frequency stabilization. In this paper the laser frequency may be smaller or larger than the frequency of the coupled transition. In the latter case an intense laser introduces additional splitting effects, even when the laser is detuned. Splitting effects due to weakly saturating laser fields are also discussed. The problem is formulated by expanding elements of the ensemble-averaged density matrix in an infinite series of spatial Fourier components. A perturbation technique is employed, valid for a weak probe field and a standing-wave field of arbitrary intensity. One obtains an expression for emission induced by the probe field due to atoms moving with one velocity, written in terms of continued fractions in the general case and with Bessel functions in an important special case. This expression is integrated over the atomic velocity distribution by means of a computer to obtain the total emission due to atoms moving with all velocities. In some cases the integrated expressions may be written in closed algebraic form. A detailed discussions of line shapes and of the physical processes involved is included.
I read with interest Daniel Kleppner’s lucid column on Hanbury Brown’s “steamroller.” Kleppner mentions an aspect of the Hanbury Brown and Twiss (HBT) effect that at first seemingly defied a quantum interpretation; he terms it “anti-weird,” since in certain cases a completely classical understanding is possible. Other aspects of the Hanbury Brown physics are truly weird in the sense that they violate a Bell inequality. I and collaborators Peter Samuelsson and Eugene Sukhorukov have proposed an interferometry experiment with fermions in an electrical conductor. Carriers are injected into the conductor from two contacts, and the cross correlation of the electrical current is measured at two other contacts along the conductor. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 In that arrangement, it is possible to investigate the Aharonov–Bohm effect in the fermionic HBT interferometer. Our initial discussions of such an effect date back to the early 1990s. 2 2. M. Büttiker, Phys. Rev. Lett. 68, 843 (1992); Physica B 175, 199 (1991). https://doi.org/10.1016/0921-4526(91)90713-O My collaborators and I found a geometry in which the conductance (intensity) shows no Aharonov–Bohm signature, but the current correlation (intensity correlation) is nevertheless a periodic function of the Aharonov–Bohm flux. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 We termed our finding the two-particle Aharonov–Bohm effect. The effect was recently observed by a group headed by Moty Heiblum at the Weizmann Institute of Science. His team cooled a mesoscopic conductor to tens of millikelvin and measured its conductance and noise correlations. 3 3. I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, V. Umansky, Nature 448, 333 (2007). https://doi.org/10.1038/nature05955 Theoretical work by Carlo Beenakker at Leiden University has shown that due to orbital quasiparticle entanglement, 4 4. C. W. J. Beenakker, in Quantum Computers, Algorithms and Chaos, Proceedings of the International School of Physics “E. Fermi,” vol. 162, G. Casati et al. , eds., IOS Press, Washington, DC (2006). the two-particle effect is equivalent at zero temperature to a violation of a Bell inequality. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 The case of nonzero temperature is more complicated and is still a subject of research. 5 5. P. Samuelsson, I. Neder, M. Büttiker, Phys. Rev. Lett. (in press). The possibility of observing truly weird quantum physics is certain to increase interest in Hanbury Brown’s physics.REFERENCESSection:ChooseTop of pageREFERENCES <<1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 , Google ScholarCrossref2. M. Büttiker, Phys. Rev. Lett. 68, 843 (1992); Google ScholarCrossref Physica B 175, 199 (1991). https://doi.org/10.1016/0921-4526(91)90713-O , , Google ScholarCrossref3. I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, V. Umansky, Nature 448, 333 (2007). https://doi.org/10.1038/nature05955 , Google ScholarCrossref4. C. W. J. Beenakker, in Quantum Computers, Algorithms and Chaos, Proceedings of the International School of Physics “E. Fermi,” vol. 162, G. Casati et al. , eds., IOS Press, Washington, DC (2006). Google Scholar5. P. Samuelsson, I. Neder, M. Büttiker, Phys. Rev. Lett. (in press). Google Scholar© 2009 American Institute of Physics.
In Chaps. 8 and 9, we considered a laser medium consisting of homo­ geneously broadened, stationary atoms. When the lasing atoms move as in a gas, they see an electric field with shifted frequency due to the Doppler effect, as shown in Fig. 10-1. One might argue that it is merely necessary to average the complex polarization or the susceptibility Xn over the frequency range corresponding to the velocity distribution, that is, calculate a new ^ n , for which Here the frequency co = coo + Kv, where coo is the frequency at atomic line (1) center, v is the component of velocity along the laser (z) axis, and the frequen­ cy distribution is determined by a Maxwell-Boltzmann velocity distribution W(y) = ( w)-1 exp [ - (v/w)2]. (2) Here u is the most probable speed of the atom, and K is the wave number. The simple recipe (1) is, in fact, valid for an inhomogeneously broadened mediumt consisting of stationary atoms such as ruby at low temperatures. However, in the standing-wave laser, the atoms not only see Doppler-shifted frequencies, but also move through the standing-wave electric field, effectively seeing an amplitude-modulated field. Equivalently, each atom sees two frequencies, for the standing-wave field is the sum of oppositely directed running waves, one of which appears to be Doppler upshifted, one down­ shifted. Hence it is necessary to consider both the frequency shift and the time dependence of the atomic z coordinate when calculating the polarization of a gaseous medium.
The review by Daniel M. Greenberger of Russell Stannard’s The New World of Mr. Tompkins (Physics Today, June 2000, page 57) intrigued me sufficiently that I obtained a copy of this revised and extended version of George Gamow’s (now dated) three classic works for the general reader. I agree with much of what Greenberger writes. Stannard has “done a remarkable job of preserving the mood and feeling of the original,” and I hope that at least some of the few small slips will be edited out before this commendable book is reprinted.One error, however, struck me rather forcibly. In the diagram on page 159, the professor is lecturing to his evening audience, which contains the (as usual) dozing Mr. Tompkins. A slide of the Bohr-Sommerfeld orbits for principal quantum numbers n = 2,3 has been projected onto the screen. Unfortunately, the orbits with highest azimuthal quantum number (orbital angular momentum quantum number l) are shown as ellipses with the highest eccentricity, while the s-orbits (l = 0) are shown as circles. This confusion of “penetrating” with “nonpenetrating” orbits is common, occasioned perhaps by the recollection that in the wave-mechanical picture, the s-orbitals are spherically symmetrical, albeit with the important property that their probability densities peak at the origin. This property is of vital importance, for example, for the Lamb shift and the Fermi contact interaction in hyperfine structure, quite apart from the fact that the quantum defects are therefore largest for the s-orbitals in many-electron atoms. For comparison purposes, excellent diagrams of these two distinctly different forms of representation may be found in reference 11. H. E. White, Introduction to Atomic Spectra, McGraw-Hill, New York, (1934), pp. 47–71..How did this unfortunate mistake occur in the new work? On turning to its predecessor, 2 2. G. Gamow, Mr. Tompkins in Paperback, Cambridge U. Press, (1965) pp. 132–133. one finds on page 132 a picture containing the same Bohr–Sommerfeld orbits and, in addition, the quantization rules in the “old quantum theory” and formulas for the energies. (A keen-eyed reader will spot that the electronic charge e is raised to the wrong power in two places.) Moreover, in this diagram by Gamow himself, the orbitals are labeled in exactly the same incorrect fashion: The s- and d-labels should be interchanged.This brought to mind the amusing account in Gamow’s delightful “informal autobiography” My World Line (I write from memory of a book read well over two decades ago), in which he describes his initial difficulties on arrival from Russia at the University in Göttingen, home of the “new quantum theory,” around 1928. The easier problems having already been solved, his contemporaries were then working on aspects of atomic theory requiring considerable dexterity in advanced special function theory, and the sort of heavy algebraic manipulation (“exerei”) that Gamow disliked, topology and group theory being more appealing to him. On a certain day, the frustrated young Gamow was sitting on a park bench, wondering what to do. His eye fell on the description by Ernest Rutherford, in the Philosophical Magazine that he happened to be carrying, of a now rather implausible idea invoked to explain the escape of alpha particles from the atomic nucleus. In a flash of inspiration, Gamow sketched out in his mind the correct explanation, involving “quantum tunneling” and the now famous “Gamow factor.” When one considers the author’s age of barely 24 years, the ensuing paper 3 3. G. Gamow, Z. Phys. 51, 204 (1928) https://doi.org/10.1007/BF01343196. makes an astonishing impression of both maturity and unusual clarity, attributes that of course lent themselves admirably in due course to writing the “Tompkins” books.Making a hypothesis of my own, I surmised that his inattention to detail regarding the electron orbitals was perhaps a consequence of this early predilection for nuclear, rather than atomic, physics. But no—on turning to my last source, 4 4. G. Gamow, Mr. Tompkins Explores the Atom, Cambridge U. Press, (1946), pp. 72–74. I found not only the best drawing of all three (again by Gamow), but the orbits correctly labeled! No doubt the professor himself could comment most aptly on this mutilation of his original over time.REFERENCESSection:ChooseTop of pageREFERENCES <<1. H. E. White, Introduction to Atomic Spectra, McGraw-Hill, New York, (1934), pp. 47–71. Google Scholar2. G. Gamow, Mr. Tompkins in Paperback, Cambridge U. Press, (1965) pp. 132–133. Google Scholar3. G. Gamow, Z. Phys. 51, 204 (1928) https://doi.org/10.1007/BF01343196. Google ScholarCrossref, CAS4. G. Gamow, Mr. Tompkins Explores the Atom, Cambridge U. Press, (1946), pp. 72–74. Google Scholar© 2001 American Institute of Physics.