najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2020-11-3-307-313najo-426Research ArticlePHYSICSФИЗИКАHigh harmonic generation by an atom confined in nanoscale cavityRakhmanovS. Z.

Vuzgorodok, 100174, Tashkent

saparboy92@gmail.comKarpovaO. V.

17 Niyazov Str., 100095, Tashkent

KhashimovaF. S.

Galaba street, Navoi

EshchanovB. Kh.

Vuzgorodok, 100174, Tashkent

104 Amir Temur Str., Chirchik

Physics Department, National Universty of UzbekistanUzbekistanTurin Polytechnic University in TashkentUzbekistanNavoi State Mining InstituteUzbekistanPhysics Department, National Universty of Uzbekistan; Chirchik State Pedagogical InstituteUzbekistan202030072025113307–313Copyright © Rakhmanov S.Z., Karpova O.V., Khashimova F.S., Eshchanov B.K., 20252025Rakhmanov S.Z., Karpova O.V., Khashimova F.S., Eshchanov B.K.Rakhmanov S.Z., Karpova O.V., Khashimova F.S., Eshchanov B.K.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/426

We consider optical high harmonic generation in a hydrogen-like atom confined in a spherical cavity caused by interaction with a monochromatic field. The whole system is considered as to be centrally symmetric, i.e., atomic nucleus as fixed at the center of sphere. In such a spherically symmetric atom, the high harmonic generation spectrum is calculated at different values of the oscillation amplitude, frequency of the external field and size of the confining domain.

high harmonic generationspectrum of high harmonic generationatom in cavityatom in monochromatic fieldconfined atomReferencesTong X., Chu Sh. Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: A new generalized pseudospectral time-dependent method. Chem. Phys. B, 1997, 217(2-3), P. 119–130.Tong X., Chu Sh. Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: A new generalized pseudospectral time-dependent method. Chem. Phys. B, 1997, 217(2-3), P. 119–130.Brabec T. and Krausz F. Intense few-cycle laser fields: Frontiers of nonlinear optics. Rev. Mod. Phys., 2000, 72(2), P. 545–591.Brabec T. and Krausz F. Intense few-cycle laser fields: Frontiers of nonlinear optics. Rev. Mod. Phys., 2000, 72(2), P. 545–591.Yousef I., et.al. Relativistic high-power laser matter interactions. Phys. Rep., 2006, 427(2-3), P. 41–155.Yousef I., et.al. Relativistic high-power laser matter interactions. Phys. Rep., 2006, 427(2-3), P. 41–155.Winterfeldt C., Spielmann C., and Gerber G. Colloquium: Optimal control of high-harmonic generation. Rev. Mod. Phys. 2008, 80(1), P. 117–140.Winterfeldt C., Spielmann C., and Gerber G. Colloquium: Optimal control of high-harmonic generation. Rev. Mod. Phys. 2008, 80(1), P. 117–140.Krausz F., Ivanov M. Attosecond physics. Rev. Mod. Phys., 2009, 81, P. 163–234.Krausz F., Ivanov M. Attosecond physics. Rev. Mod. Phys., 2009, 81, P. 163–234.Nisoli M., Sansone G. New frontiers in attosecond science Author links open overlay panel. Prog. Quant. Electr., 2009, 33, P. 17–59.Nisoli M., Sansone G. New frontiers in attosecond science Author links open overlay panel. Prog. Quant. Electr., 2009, 33, P. 17–59.Kohler M.C., Pfeifer T., Hatsagortsyan K.Z.,Keitel C.H. Frontiers of Atomic High-Harmonic Generation. Advances In Atomic, Molecular, and Optical Physics, 2012, 61, P. 159–208.Kohler M.C., Pfeifer T., Hatsagortsyan K.Z.,Keitel C.H. Frontiers of Atomic High-Harmonic Generation. Advances In Atomic, Molecular, and Optical Physics, 2012, 61, P. 159–208.Strelkov V.V., Platonenko V.T., Sterzhantov A.F. and Ryabikin M.Yu. Attosecond electromagnetic pulses: generation, measurement, and application. Generation of high-order harmonics of an intense laser field for attosecond pulse production. Phys. Uspekhi, 2016, 59(5), P. 425–445.Strelkov V.V., Platonenko V.T., Sterzhantov A.F. and Ryabikin M.Yu. Attosecond electromagnetic pulses: generation, measurement, and application. Generation of high-order harmonics of an intense laser field for attosecond pulse production. Phys. Uspekhi, 2016, 59(5), P. 425–445.de Morisson Faria C. F. and Rost J-M. High-order harmonic generation from a confined atom. Phys. Rev. A, 2000, 62(5), P. 051402(R)/1-4.de Morisson Faria C. F. and Rost J-M. High-order harmonic generation from a confined atom. Phys. Rev. A, 2000, 62(5), P. 051402(R)/1-4.Boyd R.W. Nonlinear Optics.3rd ed., Academic Press, 2007, 613 p.Boyd R.W. Nonlinear Optics.3rd ed., Academic Press, 2007, 613 p.Lewenstein M., Balcou Ph., Ivanov M.Yu., LHuillier A., and Corkum P.B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A, 1994, 49(3), P. 2117–2132.Lewenstein M., Balcou Ph., Ivanov M.Yu., LHuillier A., and Corkum P.B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A, 1994, 49(3), P. 2117–2132.Becker W., Long S. and McIver J.K. Higher-harmonic production in a model atom with short-range potential. Phys. Rev. A, 1990, 41(7), P. 4112–4115.Becker W., Long S. and McIver J.K. Higher-harmonic production in a model atom with short-range potential. Phys. Rev. A, 1990, 41(7), P. 4112–4115.Connerade J.-P., Dolmatov V.K., Lakshmi P.A. and Manson S.T. Electron structure of endohedrally confined atoms: atomic hydrogen in an attractive shell. J. Phys. B, 1999, 32(10), P. L239–L246.Connerade J.-P., Dolmatov V.K., Lakshmi P.A. and Manson S.T. Electron structure of endohedrally confined atoms: atomic hydrogen in an attractive shell. J. Phys. B, 1999, 32(10), P. L239–L246.Connerade J.-P. and Semaoune R. Atomic compressibility and reversible insertion of atoms into solids. J. Phys. B, 2000, 33(17), P. 3467– 3484.Connerade J.-P. and Semaoune R. Atomic compressibility and reversible insertion of atoms into solids. J. Phys. B, 2000, 33(17), P. 3467– 3484.Michels A., de Boer J. and Bijl A. Remarks concerning molecural interaction and their influence on the polarisability. Physica (The Hague), 1937, 4(10), P. 981–994.Michels A., de Boer J. and Bijl A. Remarks concerning molecural interaction and their influence on the polarisability. Physica (The Hague), 1937, 4(10), P. 981–994.Sommerfeld A. and Welker H. Kanstliche grenzbedingungen beim Keplerproblem.¨ Ann. Phys., 1938, 32, P. 56–65.Sommerfeld A. and Welker H. Kanstliche grenzbedingungen beim Keplerproblem.¨ Ann. Phys., 1938, 32, P. 56–65.Suryanarayana D. and Weil J. A. On the hyperfine splitting of the hydrogen atom in a spherical box J. Chem. Phys., 1975, 64(2), P. 510–513.Suryanarayana D. and Weil J. A. On the hyperfine splitting of the hydrogen atom in a spherical box J. Chem. Phys., 1975, 64(2), P. 510–513.Ley-Koo E., Rubinstein S. The hydrogen atom within spherical boxes with penetrable walls. J. Chem. Phys., 1979, 71(1), P. 351–357.Ley-Koo E., Rubinstein S. The hydrogen atom within spherical boxes with penetrable walls. J. Chem. Phys., 1979, 71(1), P. 351–357.Last I. and George Th. F. Light absorption by an atom moving inside a spherical box. Chem. Phys. Lett., 1987, 142(1-2), P. 19–24.Last I. and George Th. F. Light absorption by an atom moving inside a spherical box. Chem. Phys. Lett., 1987, 142(1-2), P. 19–24.Laughlin C., Burrows B. L., Cohen M. A hydrogen-like atom confined within an impenetrable spherical box. J. Phys. B, 2002, 35(3), P. 701–716.Laughlin C., Burrows B. L., Cohen M. A hydrogen-like atom confined within an impenetrable spherical box. J. Phys. B, 2002, 35(3), P. 701–716.Kang Sh., Yang Y-Ch., He J., Xiong F-Q. , Xu N. The hydrogen atom confined in both Debye screening potential and impenetrable spherical box. Cent. Eur. J. Phys., 2013, 11, P. 584–593.Kang Sh., Yang Y-Ch., He J., Xiong F-Q. , Xu N. The hydrogen atom confined in both Debye screening potential and impenetrable spherical box. Cent. Eur. J. Phys., 2013, 11, P. 584–593.Zhou Sh-G. , Zhao J. and E-G. A spherical-box approach for resonances in the presence of the Coulomb interaction. J. Phys. B, 2009, 42(24), P. 245001/1-4.Zhou Sh-G. , Zhao J. and E-G. A spherical-box approach for resonances in the presence of the Coulomb interaction. J. Phys. B, 2009, 42(24), P. 245001/1-4.Burrows B. L., Cohen M. Exact solutions for perturbed confined hydrogen atoms: Polarizabilities and nuclear shielding factors. Phys. Rev. A, 2005, 72(3), P. 032508/1-6.Burrows B. L., Cohen M. Exact solutions for perturbed confined hydrogen atoms: Polarizabilities and nuclear shielding factors. Phys. Rev. A, 2005, 72(3), P. 032508/1-6.Kang S., Liu Q., Meng H-Y., Shi T-Y. Hydrogen atom in ellipsoidal cavity. Phys. Lett. A, 2007, 360(4-5), P. 608–614.Kang S., Liu Q., Meng H-Y., Shi T-Y. Hydrogen atom in ellipsoidal cavity. Phys. Lett. A, 2007, 360(4-5), P. 608–614.Capitelli M. Energy levels of atomic hydrogen in a closed box: A natural cutoff criterion of the electronic partition function. Phys. Rev. A, 2009, 80(3), P. 032113/1-5.Capitelli M. Energy levels of atomic hydrogen in a closed box: A natural cutoff criterion of the electronic partition function. Phys. Rev. A, 2009, 80(3), P. 032113/1-5.Masovic D. R. Unusually kicked dynamics: Hydrogen atom in a spherical box. Cent. Eur. J. Phys., 2012, 10, P. 768–778.Masovic D. R. Unusually kicked dynamics: Hydrogen atom in a spherical box. Cent. Eur. J. Phys., 2012, 10, P. 768–778.Cabrera-Trujillo R., Cruz S. A. Confinement approach to pressure effects on the dipole and the generalized oscillator strength of atomic hydrogen. Phys. Rev. A, 2013, 87(1), P. 012502/1-10.Cabrera-Trujillo R., Cruz S. A. Confinement approach to pressure effects on the dipole and the generalized oscillator strength of atomic hydrogen. Phys. Rev. A, 2013, 87(1), P. 012502/1-10.Lumb S., Lumb S., Prasad V. Laser-induced excitation and ionization of a confined hydrogen atom in an exponential-cosine-screened Coulomb potential. Phys. Rev. A, 2014, 90(3), P. 032505/1-9.Lumb S., Lumb S., Prasad V. Laser-induced excitation and ionization of a confined hydrogen atom in an exponential-cosine-screened Coulomb potential. Phys. Rev. A, 2014, 90(3), P. 032505/1-9.Masovic D. R. High-harmonic generation and spherically confined hydrogen atom. Can. J. Phys., 2015, 93(4), P. 434–444.Masovic D. R. High-harmonic generation and spherically confined hydrogen atom. Can. J. Phys., 2015, 93(4), P. 434–444.Strelkov V. V., Platonenko V. T. and Becker A. High-harmonic generation in a dense medium. Phys. Rev. A, 2005, 71(5), P. 053808/1-8.Strelkov V. V., Platonenko V. T. and Becker A. High-harmonic generation in a dense medium. Phys. Rev. A, 2005, 71(5), P. 053808/1-8.McDonald C. R., Amin K. S., Aalmalki S. and Brabec T. Enhancing High Harmonic Output in Solids through Quantum Confinement. PRL, 2017, 119(18), P. 183902/1-6.McDonald C. R., Amin K. S., Aalmalki S. and Brabec T. Enhancing High Harmonic Output in Solids through Quantum Confinement. PRL, 2017, 119(18), P. 183902/1-6.Heyl C. M., Gudde J. L’Huillier A. and H¨ ofer U. High-order harmonic generation with¨ µJ laser pulses at high repetition rates. J. Phys. B: At. Mol. Opt. Phys., 2012, 45(7), P. 074020/1-9.Heyl C. M., Gudde J. L’Huillier A. and H¨ ofer U. High-order harmonic generation with¨ µJ laser pulses at high repetition rates. J. Phys. B: At. Mol. Opt. Phys., 2012, 45(7), P. 074020/1-9.Topcu T., Bleda E. A. and Altun Z. Drastically enhanced high-order harmonic generation from endofullerenes. Phys. Rev. A, 2019, 100(6), P. 063421/1-12.Topcu T., Bleda E. A. and Altun Z. Drastically enhanced high-order harmonic generation from endofullerenes. Phys. Rev. A, 2019, 100(6), P. 063421/1-12.Friedman N., Khaykovich L., Ozeri R. and Davidson N. Compression of cold atoms to very high densities in a rotating-beam blue-detuned optical trap. Phys. Rev. A, 2000, 61(3), P. 031403(R)/1-4.Friedman N., Khaykovich L., Ozeri R. and Davidson N. Compression of cold atoms to very high densities in a rotating-beam blue-detuned optical trap. Phys. Rev. A, 2000, 61(3), P. 031403(R)/1-4.Burrows B. L., Cohen M. Confined systems within arbitrary enclosed surfaces. J. Phys. B, 2016, 49(12), P. 125001/1-6.Burrows B. L., Cohen M. Confined systems within arbitrary enclosed surfaces. J. Phys. B, 2016, 49(12), P. 125001/1-6.Burrows B. L. and Cohen M. Confined one- and two-center systems. Phys. Rev. A. 2013. 88(5). P. 052511.6p.Burrows B. L. and Cohen M. Confined one- and two-center systems. Phys. Rev. A. 2013. 88(5). P. 052511.6p.Jaskolski W. Confined many-electron systems. Phys. Rep., 1996, 271(1), P. 1-66.Jaskolski W. Confined many-electron systems. Phys. Rep., 1996, 271(1), P. 1-66.Milner V., Hanssen J. L., Campbell W. C. and Raizen M. G. Optical Billiards for Atoms. Phys.Rev.Lett., 2001, 86(8), P. 15141517.Milner V., Hanssen J. L., Campbell W. C. and Raizen M. G. Optical Billiards for Atoms. Phys.Rev.Lett., 2001, 86(8), P. 15141517.Rohwedder B. Quantum billiard atom optics. EPL, 2002, 60(4), P. 505–511.Rohwedder B. Quantum billiard atom optics. EPL, 2002, 60(4), P. 505–511.Friedman N., Kaplan A. Dark optical traps for cold atoms. Adv. At. Mol. Phys., 2002, 48, P. 99–151.Friedman N., Kaplan A. Dark optical traps for cold atoms. Adv. At. Mol. Phys., 2002, 48, P. 99–151.Rakhmonov S., Matrasulov D. and Matveev V. Quantum dynamics of a hydrogen-like atom in a time-dependent box: non-adiabatic regime. Eur. Phys. J. D., 2018, 72, P. 177/1-8.Rakhmonov S., Matrasulov D. and Matveev V. Quantum dynamics of a hydrogen-like atom in a time-dependent box: non-adiabatic regime. Eur. Phys. J. D., 2018, 72, P. 177/1-8.

The authors declare that there are no conflicts of interest present.