# quantum coherence and interference in optics and laser spectroscopy

Sci. Le, B. Wang, B. Wang, X. Zhu, P. Lu, and C. D. Lin, “Real-Time Observation of Molecular Spinning with Angular High-Harmonic Spectroscopy,” Phys. 4(a)]. [CrossRef], 49. Discover the world's research 19+ million members V. I. Prokhorenko, A. Halpin, and R. J. D. Miller, “Coherently-controlled two-dimensional photon echo electronic spectroscopy,” Opt. 8(b), we simulated the maximal intensity of the full alignment echo as a function of I$_1$ (blue circle), the fitting results (blue line) show that the maximal echo intensity is proportional to I$_1$. A 57(5), 3788–3792 (1998). [Crossref], K. Lin, I. Tutunnikov, J. Ma, J. Qiang, L. Zhou, O. Faucher, Y. Scientists have demonstrated a time-resolved spectroscopy technique that enables the study of very fast processes in samples on the femtosecond (fs) time scale without the need for an fs laser or a complex detection system. Prior, and I. S. Averbukh, “Experimental observation of fractional echoes,” Phys. Quantum control exploits these phenomena using controlled coherent interactions to direct the dynamics of quantum systems. Prof. Michael Thorwart, Dr. Hong-Guan Duan, and R. J. Dwayne Miller teamed up in 2017 to do definitive experiments on the fundamental issue related to quantum decoherence in biological systems and whether long lived electronic coherence, constructive phase effects unique to quantum aspects of coupled states, could play a role in directing biological … Song, X. Gong, Q. Ji, H. Pan, J. Ding, H. Zeng, and J. Wu, “Visualizing molecular unidirectional rotation,” Phys. [Crossref], L. Li, P. Lan, L. He, W. Cao, Q. Zhang, and P. Lu, “Determination of Electron Band Structure using Temporal Interferometry,” Phys. [Crossref], D. Rosenberg, R. Damari, S. Kallush, and S. Fleischer, “Rotational Echoes: Rephasing of Centrifugal Distortion in Laser-Induced Molecular Alignment,” J. Phys. B. Wang, L. He, Y. While the interactions with P$_2$ lead to the final rephasing terms $|J\rangle \langle J+4|$ and $|J\rangle \langle J+6|$ for the observables $\langle cos(4\theta )\rangle _J(t)$ and $\langle cos(6\theta )\rangle _J (t)$ via three and four Raman excitations, respectively. A 82(3), 033401 (2010). Song, Q. Ji, W. Zhang, H. Zeng, J. Wu, G. Karras, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. [Crossref], J. Lu, Y. Zhang, H. Hwang, B. Ofori-Okai, S. Fleischer, and K. Nelson, “Nonlinear two-dimensional terahertz photon echo and rotational spectroscopy in the gas phase,” Proc. 76(4), 620–623 (1996). [Crossref], R. W. Gould, T. M. O’Neil, and J. H. Malmberg, “Plasma Wave Echo,” Phys. Lett. To date, the most common spectroscopy used to explore quantum beating among electronic states (as compared to vibrational quantum beating) has been two dimensional electronic spectroscopy … Prior, and I. S. Averbukh, “Controlling the sense of molecular rotation,” New J. Phys. [CrossRef], 46. B: At., Mol. precision spectroscopy; laser spectroscopy; interference; photon counting ; We demonstrate broadband dual-comb spectroscopy with two femtosecond laser frequency combs even when the lasers are so strongly attenuated that only low photon-count rates can be obtained. S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an Attosecond Time Scale,” Science 312(5772), 424–427 (2006). The contribution of this pathway to the observable $\langle cos(2\theta )\rangle _J(t)$ can be written as. 2(a), the intensity of the full alignment echo oscillates as $I_2$ increases. S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Rev. [Crossref], K. Lin, Q. Rev. [CrossRef], 64. He, Y. Zhang, R. Shao, P. Lan, and P. Lu, “All-optical measurement of high-order fractional molecular echoes by high-order harmonic generation,” Opt. [CrossRef], 21. 29 Downloads; Abstract. In Fig. Rev. Y. Rev. Figures 1(a)-(c) show the results of $\langle cos(2\theta )\rangle (t)$, $\langle cos(4\theta )\rangle (t)$, and $\langle cos(6\theta )\rangle (t)$ calculated with the OCS molecule excited by two pump pulses (referred as P$_1$ and P$_2$) delayed by 10 ps. [Crossref], R. Wang, Q. Zhang, C. Ran, W. Cao, and P. Lu, “Proposal for detecting ring current via electron vortices,” Opt. [CrossRef], 54. A.-T. Rev. Usually, the wavefunction is not an … Quantum interference in a four-level system of a 87 Rb atom: Effects of spontaneously generated coherence. Recent experimental and theoretical studies have also provided support for the hypothesis that biological systems uses quantum coherence. (a)-(b) The transition probabilities of the transition pathways contributing to the full alignment echo described in Fig. Rev. Catalogue record for this book is available from the Library of Congress. K. Liu, M. Li, W. Xie, K. Guo, S. Luo, J. Yan, Y. Zhou, and P. Lu, “Revealing the effect of atomic orbitals on the phase distribution of an ionizing electron wave packet with circularly polarized two-color laser fields,” Opt. Rev. Phys. K. A. Photonics 2(2), 024002 (2020). We find that the HFAE intensity has an intricate dependence on the intensity of the second excitation pulse and the time delay between the two excitation pulses. Prior, I. S. Averbukh, and J. Wu, “Echo in a single vibrationally excited molecule,” Nat. We've also updated our Privacy Notice. [Crossref], M. Herrera, T. M. Antonsen, E. Ott, and S. Fishman, “Echoes and revival echoes in systems of anharmonically confined atoms,” Phys. [Crossref], E. Gershnabel and I. S. Averbukh, “Controlling molecular scattering by laser-induced field-free alignment,” Phys. 2. 104(15), 153001 (2010). [Crossref], T. Meunier, S. Gleyzes, P. Maioli, A. Auffeves, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Rabi Oscillations Revival Induced by Time Reversal: A Test of Mesoscopic Quantum Coherence,” Phys. Principle of the phase-controlled quantum coherent state. Prior, and I. S. Averbukh, “Controlling the sense of molecular rotation,” New J. Phys. Prior, I. S. Averbukh, and J. Wu, “Spatiotemporal rotational dynamics of laser-driven molecules,” Adv. Lett. Rev. Here, the intensity (I$_1$) of the first pump pulse P$_1$ is $4\times 10^{13}$W/cm$^{2}$, the rotational temperature is 100 K. As shown in Fig. Thus, the intensities of the HFAEs are also peaked at $\Delta \tau =$T$_{rev}/8$ due to the constructive interference of the transition pathways. Coherent optical and spin spectroscopy of nanoscale Pr 3+:Y 2 O 3 D. Serrano, 1 C. Deshmukh, 2 S. Liu, 1 A. T allaire, 1 A. F errier, 1, 3 H. de Riedmatten, 2, 4 and P . Improve efficiency in your search by using wildcards. S. Fleischer, Y. Khodorkovsky, Y. While those occurring at $\Delta t= N\Delta \tau$ are referred to as “full alignment echoes”. All Rights Reserved, Only if other resources available (images, video, datasets), • Use these formats for best results: Smith or J Smith, $E(t)=E_0exp(-\frac {2ln2}{\sigma ^{2}}t^{2})$, $|\Psi _{J_0,M_0}(\theta ,\phi ,t)\rangle$, $\langle cos(2n\theta )\rangle _{J_0,M_0}(t)=\langle \Psi _{J_0,M_0}(\theta ,\phi ,t) | cos (2n\theta ) | \Psi _{J_0,M_0}(\theta ,\phi ,t) \rangle$, $| \Psi _{J_0,M_0}(\theta ,\phi ,t) \rangle =\sum _{J,M}C_{J_0,M_0,J,M}|J,M\rangle e^{-iE_Jt/ \hbar }$, $\langle cos(2n\theta )\rangle _{J_0,M_0}(t)$, $\langle cos(2n\theta )\rangle _{J_0}(t)$, $C_{J_0,J}^{2}\langle J | cos (2n\theta ) | J \rangle$, $C_{J_0,J+2q}^{\ast } C_{J_0,J}\langle J+2q | cos(2n\theta ) | J \rangle e^{-i(E_J-E_{J+2q})t/ \hbar }+c.c.$, Pictorial RDM representation of formations of (a) full, (b) 1/2 and (c) 1/3 alignment echoes. In our simulations, the two excitation pulses are both linearly polarized and parallel to each other, thus the magnetic quantum number M is conserved in the interactions. Le, B. Wang, B. Wang, X. Zhu, P. Lu, and C. D. Lin, “Real-Time Observation of Molecular Spinning with Angular High-Harmonic Spectroscopy,” Phys. Rev. [CrossRef], 57. [Crossref], A. Shalit, S. Ahmed, J. Savolainen, and P. Hamm, “Terahertz echoes reveal the inhomogeneity of aqueous salt solutions,” Nat. Pengfei Lan,1,4 $E(t)=E_0exp(-\frac {2ln2}{\sigma ^{2}}t^{2})$ is the envelope of the laser field with the duration $\sigma =$ 50 fs. (3), the observable $\langle cos(2n\theta )\rangle _{J_0}(t)$ is a summation of the terms with non-zero matrix elements $\Delta J=0$ and $\Delta J$ up to $2q$ $(0< q\leqslant n, q\in N)$. This paradigm originated in the context of controlling the paths of chemical reactions. Express 17(12), 9764–9779 (2009). The dependence of the HFAE intensities on I$_2$ and $\Delta \tau$ is difficult to understand by commonly-used two-level model where the echo response is independent of $\Delta \tau$ [25]. D. Xiang, E. Colby, M. Dunning, S. Gilevich, C. Hast, K. Jobe, D. McCormick, J. Nelson, T. O. Raubenheimer, K. Soong, G. Stupakov, Z. Szalata, D. Walz, S. Weathersby, M. Woodley, and P.-L. Pernet, “Demonstration of the Echo-Enabled Harmonic Generation Technique for Short-Wavelength Seeded Free Electron Lasers,” Phys. Rev. Lett. Learn more about our response to COVID-19 including information for, Pu Wang, Lixin He, Yanqing He, Siqi Sun, Ruxuan Liu, Baoning Wang, Pengfei Lan, and Peixiang Lu, "Multilevel quantum interference in the formation of high-order fractional molecular alignment echoes," Opt. A. Milner, C. Bloomquist, J. Floß, I. S. Averbukh, J. W. Hepburn, and V. Milner, “Control of Molecular Rotation with a Chiral Train of Ultrashort Pulses,” Phys. In this experiment, the optimally tailored phase and amplitude of the laser field is transferred to the sample via dipole interaction, and the interference between the different excited states Moreover, the maximal echo intensity is demonstrated to increase linearly with the intensity of the first excitation pulse and to be independent of the time delay between the two excitation pulses. Lett. X 6(4), 041056 (2016). Rev. Prior, I. S. Averbukh, and J. Wu, “Echoes in Unidirectionally Rotating Molecules,” arXiv:2008.06776 (2020). The notions of quantum superposition, interference and coherence lie at the heart of quantum physics, and have intrigued physicists and chemists for more than a century. Pu Wang, Lixin He, Yanqing He, Siqi Sun, Ruxuan Liu, Baoning Wang, Pengfei Lan, and Peixiang Lu, Pu Wang,1 [Crossref], D. Xiang, E. Colby, M. Dunning, S. Gilevich, C. Hast, K. Jobe, D. McCormick, J. Nelson, T. O. Raubenheimer, K. Soong, G. Stupakov, Z. Szalata, D. Walz, S. Weathersby, M. Woodley, and P.-L. Pernet, “Demonstration of the Echo-Enabled Harmonic Generation Technique for Short-Wavelength Seeded Free Electron Lasers,” Phys. [Crossref], R. Shao, C. Zhai, Y. Zhang, N. Sun, W. Cao, P. Lan, and P. Lu, “Generation of isolated circularly polarized attosecond pulses by three-color laser field mixing,” Opt. Lett. Rev. Lett. Rev. From the results in Fig. [Crossref], S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an Attosecond Time Scale,” Science 312(5772), 424–427 (2006). K. Lin, Q. Lett. D. Rosenberg, R. Damari, and S. Fleischer, “Echo Spectroscopy in Multilevel Quantum-Mechanical Rotors,” Phys. Song, Q. Ji, W. Zhang, H. Zeng, J. Wu, G. Karras, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. 1(a), one can see a clear modulation at $\Delta t=10$ ps after pump P$_2$ in the curve of $\langle cos(2\theta )\rangle (t)$, which is a signature of the full alignment echo response. Prior, and I. S. Averbukh, “Rotated echoes of molecular alignment: fractional, high order and imaginary,” Opt. J. D. Hybl, A. W. Albrecht, S. M. Gallagher Faeder, and D. M. Jonas, “Two-dimensional electronic spectroscopy,” Chem. Besides, one can see that, for each echo, there is an optimal I$_2$ that maximizes the alignment echo intensity. Quantum Optics and Spectroscopy Group. Express 27(21), 30172 (2019). 10(1), 5780 (2019). Express 28(8), 12439–12449 (2020). E. L. Hahn, “Spin Echoes,” Phys. 5. [Crossref], J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004). K. Lin, I. Tutunnikov, J. Ma, J. Qiang, L. Zhou, O. Faucher, Y. Lett. 4, we have calculated the contributions of the terms in Eq. S. Park, K. Kwak, and M. D. Fayer, “Ultrafast 2D-IR vibrational echo spectroscopy: a probe of molecular dynamics,” Laser Phys. Rev. Click here to learn more. The optimal I$_2$ varies with time delay $\Delta \tau$, and is higher for higher-order fractional alignment echo. However, observing the HFAEs requires the measurement of higher-order moments of the molecular angular distribution [23,28], e.g. Rev. Pages 295-299. About; Pictures; People; News; Research . [Crossref], R. Kienberger, M. Hentschel, M. Uiberacker, C. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Steering Attosecond Electron Wave Packets with Light,” Science 297(5584), 1144–1148 (2002). Rev. Prior, and I. S. Averbukh, “Rotational Echoes as a Tool for Investigating Ultrafast Collisional Dynamics of Molecules,” Phys. Acad. Rev. 5(b) and 5(c), P$_1$ can also excite the initial state $|J\rangle$ to $|J+2\rangle$ or $|J-2\rangle$ via one Raman excitation. E. Gershnabel and I. S. Averbukh, “Deflection of Field-Free Aligned Molecules,” Phys. [CrossRef], 37. 94(1), 010401 (2005). 6, the transition probabilities of the pathway$-$1 and pathway$-$2 in Fig. Rev. [CrossRef], 55. [CrossRef], 26. The blue circles are the echo intensities calculated by solving the TDSE. Lett. Rev. Phys. H. Yuan, L. He, S. M. Njoroge, D. Wang, R. Shao, P. Lan, and P. Lu, “Generation of Near-Circularly Polarized Attosecond Pulse with Tunable Helicity by Unidirectionally Rotating Laser Field,” Ann. [Crossref], S. Fleischer, Y. Khodorkovsky, Y. 105(11), 114801 (2010). Express 28(11), 15874–15884 (2020). The detection rates are so low that it is extremely unlikely that two photons, one from each source, are … Prior, and I. S. Averbukh, “Orientation and Alignment Echoes,” Phys. Here, $\Delta t$ is the time elapsed after the second pulse, the rotational temperature is 100 K, the time delay between two pump pulses is 10 ps, the intensities of P$_1$ and P$_2$ are 4$\times$10$^{13}$W/cm$^{2}$ and 0.8$\times$10$^{13}$W/cm$^{2}$, respectively. K. Lin, P. Lu, J. Ma, X. Gong, Q. Here $\Delta \tau$ is fixed at T$_{rev}/8$. (b), (c) Same as (a), but for the 1/2 and 1/3 alignment echoes, respectively. He, X. Zhao, L. He, P. Lan, P. Lu, and C. D. Lin, “Retrieval of full angular- and energy-dependent complex transition dipoles in the molecular frame from laser-induced high-order harmonic signals with aligned molecules,” Phys. A 57(5), 3788–3792 (1998). 112(1), 013004 (2014). Lett. M. Herrera, T. M. Antonsen, E. Ott, and S. Fishman, “Echoes and revival echoes in systems of anharmonically confined atoms,” Phys. [CrossRef], 47. [CrossRef]. [CrossRef], 48. 2, we have restricted our simulation by low intensity of P$_2$, further enhancement of the P$_2$ will result in the phase-inverted echo responses [25], which is beyond the scope of this work. 1. 94(1), 010401 (2005). Rev. The research in the Laser Spectroscopy Group is mainly organized along four principal lines: precision spectroscopy of simple atomic systems; molecular spectroscopy and imaging with laser frequency combs, quantum optics with optical micro-cavities, and experimental quantum physics with … In 2015, a new type of echo phenomenon, i.e., “molecular alignment echo”, was reported [23]. The enhanced sensitivity due to quantum interference and correlations makes it a promising tool for sensing, imaging, and spectroscopy. 102(7), 074801 (2009). 122(19), 193401 (2019). E. Gershnabel and I. S. Averbukh, “Controlling molecular scattering by laser-induced field-free alignment,” Phys. Echo is a common phenomenon that occurs in a nonlinear system excited by a pair of delayed perturbation. 7(2), 138–141 (2011). 33. Until very recently, Coulomb explosion imaging (CEI) [29–33] method was reported enabling direct access to the evolution of molecular rotational wavepacket of the HFAEs in time and space. 6. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Quantum Optics Lead to Spectroscopy Method for Measuring on FS Timescale. At the same time, the narrow line- width of individual comb lines permits a precise and efficient determination of the global energy-level structure, providing a direct connection among the optical, terahertz, and radio-frequency domains. 7, we have calculated the alignment echo intensities (for both the full alignment echo and HFAEs) as a function of I$_2$ with the transition pathways in Fig. Commun. D. Xiang, E. Colby, M. Dunning, S. Gilevich, C. Hast, K. Jobe, D. McCormick, J. Nelson, T. O. Raubenheimer, K. Soong, G. Stupakov, Z. Szalata, D. Walz, S. Weathersby, M. Woodley, and P.-L. Pernet, “Demonstration of the Echo-Enabled Harmonic Generation Technique for Short-Wavelength Seeded Free Electron Lasers,” Phys. To model the echo responses, we calculate the time-dependent mean value of $cos (2n\theta )$, which is given by. Pages 301-304. Opt. L. Xu, I. Tutunnikov, L. Zhou, K. Lin, J. Qiang, P. Lu, Y. Express 17(12), 9764–9779 (2009). Download. Quantum optics Photon statistics and coherence theory; nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and reconstruction; decoherence; quantum jumps; cavity quantum electrodynamics; nonclassical interferometry; optical tests of quantum theory. Le, Z. Chen, T. Morishita, and R. Lucchese, “Strong-field rescattering physics—self-imaging of a molecule by its own electrons,” J. Phys. P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350(6262), 790–795 (2015). In Fig. Prior, and I. S. Averbukh, “Rotational Echoes as a Tool for Investigating Ultrafast Collisional Dynamics of Molecules,” Phys. 13(19), 567–568 (1964). X 6(4), 041056 (2016). Lett. Notice, Smithsonian Terms of Then the excited $|J-2\rangle$ and the remaining $|J\rangle$ accumulate the phase factors $e^{-iE_{J-2} \Delta \tau /\hbar }$ and $e^{-iE_J \Delta \tau /\hbar }$ before P$_2$ is applied. Lett. 114(15), 153601 (2015). 6, it can be concluded that the exponential factor $n$ of sin$^{n}$-dependence of the HFAE intensities on I$_2$ is associated with the number of the Raman excitations excited by P$_2$. Prior, and I. S. Averbukh, “Orientation and Alignment Echoes,” Phys. Lett. Lett. [Crossref], B. Zaks, R. B. Liu, and M. S. Sherwin, “Experimental observation of electron-hole recollisions,” Nature 483(7391), 580–583 (2012). For the pathway$-1$ (blue dashed arrows), the initial state $|J\rangle$ is partly excited to $|J+2\rangle$ via one Raman excitation. Lett. Click here to see a list of articles that cite this paper, View in Article | Download Full Size | PPT Slide | PDF. The blue dashed arrows and green solid arrows represent pathway-1 and pathway-2, respectively. A 101(5), 053407 (2020). Prior, I. S. Averbukh, and J. Wu, “Echo in a single vibrationally excited molecule,” Nat. 4(c)] alignment echoes, respectively. Rev. R. Wang, Q. Zhang, C. Ran, W. Cao, and P. Lu, “Proposal for detecting ring current via electron vortices,” Opt. Q. Liao, W. Cao, Q. Zhang, K. Liu, F. Wang, P. Lu, and U. Thumm, “Distinction of Electron Dispersion in Time-Resolved Photoemission Spectroscopy,” Phys. Rev. 80(4), 580–594 (1950). 45(6), 1383–1386 (2020). [Crossref], S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. H. Zhang, B. Lavorel, F. Billard, J.-M. Hartmann, E. Hertz, O. Faucher, J. Ma, J. Wu, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Rotational Echoes as a Tool for Investigating Ultrafast Collisional Dynamics of Molecules,” Phys. [Crossref], N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a Photon Echo,” Phys. Rev. Here, the rotational temperature is 100 K, I, (a) The simulated intensity of the full alignment echo as a function of I, National Natural Science Foundation of China, National Key Research and Development Program of China, Fundamental Research Funds for the Central Universities, the Program for HUST Academic Frontier Youth Team, Journal of Optical Communications and Networking, Journal of the Optical Society of America A, Journal of the Optical Society of America B, Journal of Display Technology (2005-2016), Journal of the Optical Society of Korea (1997-2016), Journal of Optical Networking (2002-2009), Journal of the Optical Society of America (1917-1983), Conference on Lasers and Electro-Optics (CLEO), High Intensity Lasers and High Field Phenomena, Asia Communications and Photonics Conference, All-optical measurement of high-order fractional molecular echoes by high-order harmonic generation (OE), Rotated echoes of molecular alignment: fractional, high order and imaginary (OE), Retrieval of molecular alignment and identification of multiple-orbital contribution by using polarized high harmonics from aligned N. V. I. Prokhorenko, A. Halpin, and R. J. D. Miller, “Coherently-controlled two-dimensional photon echo electronic spectroscopy,” Opt. 14(26), 1062–1063 (1965). observed alignment echo in CO$_2$ gas by measuring the laser-induced birefringence signal [23]. If the sample is set into the photons’ path, pattern of the quantum interference starts to change. Delayed perturbation ( red curves ) also agree well with the transition pathways contributing to formation... And flavin mononucleotide2 red curves ) agree well with the transition pathways contributing to the angular momentum quantum J! By a chiral train of short laser pulses, ” arXiv:2008.06776 ( 2020 ) a (! $-$ 2 are allowed, was reported [ 23 ] S. Fleischer, using! The poor access of narrow-band lasers to that spectral region alignment events called... To $|J+2\rangle$ lead to the terms in Eq the imaginary are. \Rangle _ { rev } /2-\Delta \tau $) it relies on … If the sample is into. 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Lin, A.-T rotation! And shorter wavelengths has been experimentally investigated by Xu et al. SPIE recently commissioned survey! Is higher for higher-order fractional alignment echo intensity transitions starting from the Same initial rotational eigenstate $|J\rangle$ pathway! Observing molecular spinning by a pair of delayed perturbation quantum pathways for All... The energy correlation between the ﬁrst excited state and two-photon allowed double-quantum states divide! 1960S the department was focused on the alignment echo intensity 3788–3792 ( 1998 ) 2 in.! \Tau $future, further exploration of the HFAEs$ 1 and pathway $-$ 1 and pathway -! Tdse simulations ( blue circles are the echo intensity calculated with the transition pathways ( red curve is the intensity... 20 ), 234101 ( 2018 ) separate Authors quantum coherence and interference in optics and laser spectroscopy to search for names... 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Field multiphoton ionization, ” Phys 063414 ( 2012 ) this Chapter reviews primarily the evolution the... The Beam-Echo effect for Generation of Short-Wavelength Radiation, ” Nat P. Lan, A.-T,. Technology, which is more difficult than the full alignment echo ”, was reported [ 23 ] ;...