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Physics Today

Femtosecond currents via the dynamic Stark effect

Paul W. Brumer, Ignacio Franco

Published Oct 1, 2013• 0 citations
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Abstract

The Search and Discovery report titled “An electrical insulator turns metallic within a femtosecond” (Physics Today, February 2013, page 13) is a compelling account of the recent breakthrough experiments on dynamic Stark effects performed by Ferenc Krausz and collaborators. It describes how a strong nonresonant 4-fs laser pulse can be used to generate electric currents along a nanojunction on a femtosecond time scale. Phenomenologically, the current arises from the nonlinear interaction of the active material in the silica glass nanojunction with an incident laser pulse of low temporal symmetry. By varying the degree of time asymmetry of the laser, one can change the sign and magnitude of the photoinduced current. Microscopically, the underlying rectification mechanism of that rather spectacular effect is Stark shifts so large that they can dramatically modify the electronic structure of the silica glass and even bridge its large energy gap.Significantly, and in a broader context, the groundbreaking experiment by Krausz and coworkers falls into a class of symmetry-breaking laser-control scenarios known to induce net currents in spatially symmetric systems through laser fields of low temporal symmetry.11. E. Dupont et al., Phys. Rev. Lett. 74, 3596 (1995); https://doi.org/10.1103/PhysRevLett.74.3596A. Haché et al., Phys. Rev. Lett. 78, 306 (1997); https://doi.org/10.1103/PhysRevLett.78.306S. Flach, O. Yevtushenko, Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000); https://doi.org/10.1103/PhysRevLett.84.2358G. Kurizki, M. Shapiro, P. Brumer, Phys. Rev. B 39, 3435 (1989); https://doi.org/10.1103/PhysRevB.39.3435S. Kohler, P. Hänggi, Nat. Nanotechnol. 2, 675 (2007). https://doi.org/10.1038/nnano.2007.357 The idea of using Stark effects as the main microscopic mechanism for the production of currents arose in an earlier theoretical proposal to use Stark effects to bridge the energy gap of a semiconducting material.22. I. Franco, M. Shapiro, P. Brumer, Phys. Rev. Lett. 99, 126802 (2007). https://doi.org/10.1103/PhysRevLett.99.126802 The experiments demonstrate how such ideas can be applied to induce currents in a material with an energy gap as large as 9 eV.REFERENCESSection:ChooseTop of pageREFERENCES <<1. E. Dupont et al., Phys. Rev. Lett. 74, 3596 (1995); https://doi.org/10.1103/PhysRevLett.74.3596, Google ScholarCrossref, ISIA. Haché et al., Phys. Rev. Lett. 78, 306 (1997); https://doi.org/10.1103/PhysRevLett.78.306, , Google ScholarCrossref, ISIS. Flach, O. Yevtushenko, Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000); https://doi.org/10.1103/PhysRevLett.84.2358, , Google ScholarCrossref, ISIG. Kurizki, M. Shapiro, P. Brumer, Phys. Rev. B 39, 3435 (1989); https://doi.org/10.1103/PhysRevB.39.3435, , Google ScholarCrossref, ISIS. Kohler, P. Hänggi, Nat. Nanotechnol. 2, 675 (2007). https://doi.org/10.1038/nnano.2007.357, , Google ScholarCrossref2. I. Franco, M. Shapiro, P. Brumer, Phys. Rev. Lett. 99, 126802 (2007). https://doi.org/10.1103/PhysRevLett.99.126802, Google ScholarCrossref© 2013 American Institute of Physics.

DOI
10.1063/pt.3.2130

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Permit me to add some information to the article entitled, “Bohr’s molecular model, a century later.” The authors discuss the idea of “dimensional scaling,” approximating the spectra of atoms and molecules by employing perturbation theory to expand around the infinite-dimension/classical limit. That technique of approximating the Schrödinger equation, originally called the 1/N expansion, was developed and applied to numerous problems in the 1980s, including simple atoms, quarkonium, and the hydrogen molecule.11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0,22. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305,33. T. Imbo, U. Sukhatme, Phys. Rev. D 31, 2655 (1985); https://doi.org/10.1103/PhysRevD.31.2655M. Kumar, A. Srivastava, J. K. Bhattacharjee, K. Banerjee, Phys. Lett. A 117, 226 (1986). https://doi.org/10.1016/0375-9601(86)90081-2 It grew out of attempts in the 1970s to formulate quantum chromodynamics in the limit of a large number of colors. The use of the 1/N expansion in atomic physics was discussed by Edward Witten (Physics Today, July 1980, page 38), who pointed out that his discussion was based on work that applied the method to hydrogen and helium atoms.11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0The work in reference 11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0 made use of algebraic methods for the analysis, but the coordinate space method was also developed and was initially used to treat the strong-field Zeeman effect.22. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305 A nice description of the status of the field at the time was given by Laurence Yaffe (Physics Today, August 1983, page 50). Many additional applications of that method in the physics literature may be found in reference 44. A. Chatterjee, Phys. Rep. 186, 249 (1990). https://doi.org/10.1016/0370-1573(90)90048-7.REFERENCESSection:ChooseTop of pageREFERENCES <<1. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 , Google ScholarCrossref, ISIL. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0, , Google ScholarCrossref, ISI2. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305, Google ScholarCrossref, ISI3. T. Imbo, U. Sukhatme, Phys. Rev. D 31, 2655 (1985); https://doi.org/10.1103/PhysRevD.31.2655, Google ScholarCrossref, ISIM. Kumar, A. Srivastava, J. K. Bhattacharjee, K. Banerjee, Phys. Lett. A 117, 226 (1986). https://doi.org/10.1016/0375-9601(86)90081-2, , Google ScholarCrossref, ISI4. A. Chatterjee, Phys. Rep. 186, 249 (1990). https://doi.org/10.1016/0370-1573(90)90048-7, Google ScholarCrossref, ISI© 2014 American Institute of Physics.

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The Search and Discovery report titled “An electrical insulator turns metallic within a femtosecond” (Physics Today, February 2013, page 13) is a compelling account of the recent breakthrough experiments on dynamic Stark effects performed by Ferenc Krausz and collaborators. It describes how a strong nonresonant 4-fs laser pulse can be used to generate electric currents along a nanojunction on a femtosecond time scale. Phenomenologically, the current arises from the nonlinear interaction of the active material in the silica glass nanojunction with an incident laser pulse of low temporal symmetry. By varying the degree of time asymmetry of the laser, one can change the sign and magnitude of the photoinduced current. Microscopically, the underlying rectification mechanism of that rather spectacular effect is Stark shifts so large that they can dramatically modify the electronic structure of the silica glass and even bridge its large energy gap.Significantly, and in a broader context, the groundbreaking experiment by Krausz and coworkers falls into a class of symmetry-breaking laser-control scenarios known to induce net currents in spatially symmetric systems through laser fields of low temporal symmetry.11. E. Dupont et al., Phys. Rev. Lett. 74, 3596 (1995); https://doi.org/10.1103/PhysRevLett.74.3596A. Haché et al., Phys. Rev. Lett. 78, 306 (1997); https://doi.org/10.1103/PhysRevLett.78.306S. Flach, O. Yevtushenko, Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000); https://doi.org/10.1103/PhysRevLett.84.2358G. Kurizki, M. Shapiro, P. Brumer, Phys. Rev. B 39, 3435 (1989); https://doi.org/10.1103/PhysRevB.39.3435S. Kohler, P. Hänggi, Nat. Nanotechnol. 2, 675 (2007). https://doi.org/10.1038/nnano.2007.357 The idea of using Stark effects as the main microscopic mechanism for the production of currents arose in an earlier theoretical proposal to use Stark effects to bridge the energy gap of a semiconducting material.22. I. Franco, M. Shapiro, P. Brumer, Phys. Rev. Lett. 99, 126802 (2007). https://doi.org/10.1103/PhysRevLett.99.126802 The experiments demonstrate how such ideas can be applied to induce currents in a material with an energy gap as large as 9 eV.REFERENCESSection:ChooseTop of pageREFERENCES <<1. E. Dupont et al., Phys. Rev. Lett. 74, 3596 (1995); https://doi.org/10.1103/PhysRevLett.74.3596, Google ScholarCrossref, ISIA. Haché et al., Phys. Rev. Lett. 78, 306 (1997); https://doi.org/10.1103/PhysRevLett.78.306, , Google ScholarCrossref, ISIS. Flach, O. Yevtushenko, Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000); https://doi.org/10.1103/PhysRevLett.84.2358, , Google ScholarCrossref, ISIG. Kurizki, M. Shapiro, P. Brumer, Phys. Rev. B 39, 3435 (1989); https://doi.org/10.1103/PhysRevB.39.3435, , Google ScholarCrossref, ISIS. Kohler, P. Hänggi, Nat. Nanotechnol. 2, 675 (2007). https://doi.org/10.1038/nnano.2007.357, , Google ScholarCrossref2. I. Franco, M. Shapiro, P. Brumer, Phys. Rev. Lett. 99, 126802 (2007). https://doi.org/10.1103/PhysRevLett.99.126802, Google ScholarCrossref© 2013 American Institute of Physics.
Recent works in the area of ultrafast nonlinearities due to virtual carriers in semiconductor heterostructures have generated significant interest among researchers. It has been shown1 that excitons in QW’s behave very much like conventional two-level atoms, to the extent that exciton-exciton interaction can be neglected. Therefore, fast coherent phenomena usually associated with two-level system may occur in excitonic QW transitions. Indeed, dynamic (AC) Stark effect in QW’s have been demonstrated2,3.
Permit me to add some information to the article entitled, “Bohr’s molecular model, a century later.” The authors discuss the idea of “dimensional scaling,” approximating the spectra of atoms and molecules by employing perturbation theory to expand around the infinite-dimension/classical limit. That technique of approximating the Schrödinger equation, originally called the 1/N expansion, was developed and applied to numerous problems in the 1980s, including simple atoms, quarkonium, and the hydrogen molecule.11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0,22. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305,33. T. Imbo, U. Sukhatme, Phys. Rev. D 31, 2655 (1985); https://doi.org/10.1103/PhysRevD.31.2655M. Kumar, A. Srivastava, J. K. Bhattacharjee, K. Banerjee, Phys. Lett. A 117, 226 (1986). https://doi.org/10.1016/0375-9601(86)90081-2 It grew out of attempts in the 1970s to formulate quantum chromodynamics in the limit of a large number of colors. The use of the 1/N expansion in atomic physics was discussed by Edward Witten (Physics Today, July 1980, page 38), who pointed out that his discussion was based on work that applied the method to hydrogen and helium atoms.11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0The work in reference 11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0 made use of algebraic methods for the analysis, but the coordinate space method was also developed and was initially used to treat the strong-field Zeeman effect.22. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305 A nice description of the status of the field at the time was given by Laurence Yaffe (Physics Today, August 1983, page 50). Many additional applications of that method in the physics literature may be found in reference 44. A. Chatterjee, Phys. Rep. 186, 249 (1990). https://doi.org/10.1016/0370-1573(90)90048-7.REFERENCESSection:ChooseTop of pageREFERENCES <<1. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 , Google ScholarCrossref, ISIL. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0, , Google ScholarCrossref, ISI2. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305, Google ScholarCrossref, ISI3. T. Imbo, U. Sukhatme, Phys. Rev. D 31, 2655 (1985); https://doi.org/10.1103/PhysRevD.31.2655, Google ScholarCrossref, ISIM. Kumar, A. Srivastava, J. K. Bhattacharjee, K. Banerjee, Phys. Lett. A 117, 226 (1986). https://doi.org/10.1016/0375-9601(86)90081-2, , Google ScholarCrossref, ISI4. A. Chatterjee, Phys. Rep. 186, 249 (1990). https://doi.org/10.1016/0370-1573(90)90048-7, Google ScholarCrossref, ISI© 2014 American Institute of Physics.
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.
Irradiation of a medium with non-resonant light leads to a shift of the energy levels in the system. This optical, or dynamical Stark effect has been studied for many years in atomic gases. It is only recently, however, that it could be detected for excitonic transitions in solids. This development has stirred considerable interest, because the optical Stark effect has inherent features which makes it well suited for applications such as in ultrafast all-optical data processing. Since the pump light beam falls in a transparency region of the medium, it experiences little loss, in contrast to optical non-linearities based on a saturation mechanism. Also, because virtual transitions are involved, the light-induced shift of exciton levels follows closely the pump pulse duration, making it possible to design ultrafast all-optical logic gates with subpicosecond switch-on and -off times.
The Search and Discovery piece by Ashley Smart in the April 2017 issue of Physics Today (page 18) reported the excellent work on magnetic stopping and trapping of methyl radicals by the group of Takamasa Momose (University of British Columbia). I am writing to provide a different perspective on the field than what was conveyed by the author. The very first sentence of Smart’s article brings up a whole discussion: “By and large, physicists have succeeded in their quest to tame the atom.”The past few decades have seen remarkable advances in the ability to control and cool atoms in the gas phase. Those advances have been enabled by laser-cooling, which produces ultracold atomic gases. The atoms are then further cooled by evaporation to create quantum degenerate gases. However, those methods are far from ideal, even for atoms.Laser cooling is not a general method. Due to the requirements of a cycling transition and available lasers, it works on only a small set of elements in the periodic table. Evaporative cooling requires the right balance between elastic and inelastic collisions, again severely limiting generality. Furthermore, evaporative cooling leads to a large loss of atoms. For the alkalis, the optimum cases for laser cooling and evaporative cooling, the flux of ultracold atoms has been limited by optical density to around 109 atoms per second.It is natural to ask whether one can invent new methods that work on most elements and that break the current limit on flux. Such a development would open many new possibilities for fundamental science and for real-life applications. The challenges and limitations have motivated several groups to explore alternative approaches. One method is buffer-gas cooling, pioneered by John Doyle at Harvard University.11. J. M. Doyle et al., Phys. Rev. A 52, R2515 (1995). https://doi.org/10.1103/PhysRevA.52.R2515 A different approach was developed independently and in parallel by Frédéric Merkt and his group at ETH Zürich and by my group at the University of Texas at Austin: magnetic stopping and trapping of paramagnetic atoms in a supersonic beam.22. S. D. Hogan et al., Phys. Rev. Lett. 101, 143001 (2008). https://doi.org/10.1103/PhysRevLett.101.143001,33. E. Narevicius et al., Phys. Rev. Lett. 100, 093003 (2008). https://doi.org/10.1103/PhysRevLett.100.093003 That work was summarized in an invited review article I wrote for Science.44. M. G. Raizen, Science 324, 1403 (2009). https://doi.org/10.1126/science.1171506 Since then, many new developments have continued to advance the field.Now that the first sentence of the Search and Discovery piece is out of the way, I can discuss the rest—in particular, the motivation of studying quantum chemistry and the question of whether one actually needs to trap molecules. The goal of studying chemical reactions at ultralow temperatures is to observe unique quantum pathways that can dominate the reaction dynamics. Until recently it has been an elusive goal. Stopping and trapping molecules, either by electrostatic or magnetic forces, has produced a phase-space density that is too low for the study of chemical reactions. Molecules at much higher phase-space density can be produced by starting with Bose–Einstein condensates and “making” molecules with lasers. However, those experiments have so far been limited to alkali chemistry.Work by the Narevicius group at the Weizmann Institute of Science in Israel provided a major breakthrough in quantum chemistry without the need for stopping and trapping. Their approach relies on the merging of two supersonic beams by magnetically deflecting one of them.55. A. B. Henson et al., Science 338, 234 (2012). https://doi.org/10.1126/science.1229141 The copropagating beams have controllable collision energies down to temperatures of several millikelvin. The resulting chemical reactions, observed as a function of energy, reveal striking quantum resonances in the reaction dynamics. That work is continuing, and it demonstrates the power of merged beams, which do not require trapping and cooling. To study slower chemical reactions, trapping at high phase-space density is necessary. New ideas and work along those lines are in progress and will hopefully prove successful.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. J. M. Doyle et al., Phys. Rev. A 52, R2515 (1995). https://doi.org/10.1103/PhysRevA.52.R2515, Google ScholarCrossref, ISI2. S. D. Hogan et al., Phys. Rev. Lett. 101, 143001 (2008). https://doi.org/10.1103/PhysRevLett.101.143001, Google ScholarCrossref3. E. Narevicius et al., Phys. Rev. Lett. 100, 093003 (2008). https://doi.org/10.1103/PhysRevLett.100.093003, Google ScholarCrossref, ISI4. M. G. Raizen, Science 324, 1403 (2009). https://doi.org/10.1126/science.1171506, Google ScholarCrossref5. A. B. Henson et al., Science 338, 234 (2012). https://doi.org/10.1126/science.1229141, Google ScholarCrossref, ISI© 2017 American Institute of Physics.
Progress in the production of tunable femtosecond pulses enables us to study resonant coherent optical transients in semiconductors such as AC stark effect, photon echo and quantum beats.1 It has been shown that many body Coulomb and exchange interaction lead to features which are specific to semiconductors.2,3 The semiconductor Bloch equations (SBE) within the mean field approximation have been successfully applied to explain the essential features of experiments performed with III–V and II–VI semiconductors.