The conservative system of \(N\) atoms coupled with one photon. (English) Zbl 1360.81346
Summary: In this work the conservative system of \(N\) identical two-level atoms coupled with a quantized electromagnetic field, prepared via a single photon Fock state, is investigated. The non-zero initial detuning of the Fock state is under consideration. The present paper reveals and investigates the certain fundamental problems concerning the application of the dipole approximation for the “interaction” of the quantized electromagnetic field with the many-body system. Here, we do not restrict ourselves to any boundary conditions and do not apply the “Weisskopf-Wigner” and “Markovian” approximations. We developed technique to estimate the most “problematic” integral expressions appearing in the quantum optic theory of a photon scattering by a polyatomic system. The Laplace transformation was applied in order to solve the corresponding \(N\)-particle evolution equations. It was shown, the dipole approximation, that is determined by a gauge non-invariant Hamiltonian, can result in certain irreversible processes during the system evolution with time. Namely, possible collective (coherent) modes for the probability amplitudes decay with time. At the same time, the mode corresponding to the field detuning frequency does not vanish. However, the ability to decay vanishes for the collective (coherent) modes, when the used inverse Laplace transformation undergoes a commutation in the specific limits of the problem. The investigated here structure of the solutions for the evolution equations therefore raises the fundamental problem about the correct representation of a damping phenomena in the commonly accepted approximations. The corresponding \(N\)-particle state amplitudes are calculated for the several space configurations of the closed conservative system. The elaborated theory allows to describe analytically the evolution of the system components with time for any space configurations, including the cases with relative distances between atoms shorter or larger than the emission wavelength.
MSC:
81V70 | Many-body theory; quantum Hall effect |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
11C20 | Matrices, determinants in number theory |
11D72 | Diophantine equations in many variables |
15A06 | Linear equations (linear algebraic aspects) |
15A09 | Theory of matrix inversion and generalized inverses |
44A10 | Laplace transform |
45A05 | Linear integral equations |
45F05 | Systems of nonsingular linear integral equations |
45F15 | Systems of singular linear integral equations |
References:
[1] | Kudryavtsev, I. K.; Lambrecht, A.; Moya-Cessa, H.; Knight, P. L., J. Mod. Opt., 40, 1605 (2014) |
[2] | Khalil, E. M., Int. J. Light Electron Opt., 124, 1820 (2013) |
[3] | Svidzinsky, A. A., Phys. Rev. A, 85, 013821 (2012) |
[4] | Wu, Jing-Nuo; Huang, Chih-Hsien; Cheng, Szu-Cheng; Hsieh, Wen-Feng, Phys. Rev. A, 81, 023827 (2010) |
[5] | Lax, M., Phys. Rev., 145, 110 (1966) |
[6] | Klauder, John R.; Sudarshan, E. C.G., Fundamentals of Quantum Optics (2006), Dover Publications, Inc. Mineola: Dover Publications, Inc. Mineola New York |
[7] | Scully, M.; Lamb, W. E., Phys. Rev. Lett., 16, 853 (1966) |
[8] | Schleich, Wolfgang P., Quantum Optics in Phase Space, 507-549 (2001), WILEY-VCH Verlag Berlin GmbH: WILEY-VCH Verlag Berlin GmbH Berlin (Federal Republic of Germany) · Zbl 0961.81136 |
[9] | Dicke, R. H., Phys. Rev., 93, 99 (1954) · Zbl 0055.21702 |
[10] | Wiegner, R.; von Zanthier, J.; Agarwal, G. S., Phys. Rev. A, 84, 023805 (2011) |
[11] | Berman, P. R.; Le Gouët, J. L., Phys. Rev. A, 83, 035804 (2011) |
[12] | Eisaman, M. D.; Childress, L.; Andre, A.; Massou, F.; Zibrov, A. S.; Lukin, M. D., Phys. Rev. Lett., 93, 233602 (2004) |
[13] | Men’shikov, L. I., Phys.-Usp., 42, 107 (1999) |
[14] | Sizhuk, A. S.; Yezhov, S. M., Ukr. J. Phys., 58, 10, 1009-1015 (2013) |
[15] | Scully, Marlan O.; Fry, Edward S.; Raymond Ooi, C. H.; Wódkievic, Krzysztof, Phys. Rev. Lett., 96, 010501 (2006) |
[16] | Scully, M. O.; Svidzinsky, A. A., Science, 325, 1510 (2009) |
[17] | Chang, Juntao, Characteristics of Cooperative Spontaneous Emission with Applications to Atom Microscopy and Coherent xuv Radiation Generation (2008), Dissertation: Texas AM University |
[18] | Skribanowitz, N.; Herman, I. P.; Mac Gillivray, J. C.; Feld, M. S., Phys. Rev. Lett., 30, 309 (1973) |
[19] | Gross, M.; Haroche, S., Phys. Rep., 93, 301 (1982) |
[20] | Röhlsberger, Ralf; Schlage, Kai; Sahoo, Balaram; Couet, Sebastien; Rüffer, Rudolf, Science, 328, 1248 (2010) · Zbl 1355.81178 |
[21] | Stephen, M. J., J. Chem. Phys., 40, 669 (1964) |
[22] | Lehmberg, R. H., Phys. Rev. A, 2, 889 (1970) |
[23] | DeVoe, R. G.; Brewer, R. G., Phys. Rev. Lett., 76, 2049 (1996) |
[24] | Ficek, Z.; Tanas, R., Phys. Rep., 372, 369 (2002) · Zbl 0999.81009 |
[25] | Yu, T.; Eberly, J. H., Phys. Rev. Lett., 93, 140404 (2004) |
[26] | von Zanthier, J.; Bastin, T.; Agarwal, G. S., Phys. Rev. A, 74, 061802(R) (2006) |
[27] | Raymond Ooi, C. H.; Kim, Byung-Gyu; Lee, Hai-Woong, Phys. Rev. A, 75, 063801 (2007) |
[28] | Das, S.; Agarwal, G. S.; Scully, M. O., Phys. Rev. Lett., 101, 153601 (2008) |
[29] | Milonni, P. W., Fast Light, Slow Light and Left Handed Light, 64-68 (2004), CRC Press, Technology and Engineerig |
[30] | Scully, Marlan O.; Suhail Zubairy, M., Quantum Optics (2002), Cambridge University Pressig: Cambridge University Pressig United Kingdom |
[31] | Svidzinsky, A. V., (Mathematical Methods in Theoretical Physics (in Ukrainian language), N. N. Bogolyubov Institute of Theoretical Physics, Kiev, Vol. 2 (2009)) · Zbl 1198.45016 |
[34] | Sizhuk, Andrii S.; Yezhov, Stanislav M., Nanos. Res. Lett., 9, 203 (2014) |
[35] | Sizhuk, A. S.; Yezhov, S. M., Ukr. J. Phys., 57, 6, 670 (2012) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.