Share This Article:

Work Done on a Coherently Driven Quantum System

Abstract Full-Text HTML XML Download Download as PDF (Size:579KB) PP. 89-102
DOI: 10.4236/jqis.2015.53011    2,979 Downloads   3,360 Views  

ABSTRACT

We calculate the work done by a Landau-Zener-like dynamical field on two- and three-level quantum system by constructing a quantum power operator. We elaborate a general theory applicable to a wide range of closed-quantum system. We consider the dynamics of the system in the time domain ]-tLZ,tLZ[ (where is the LZ transition time in the sudden limit) where the external pulse changes its sign and its action becomes relevant. The statistical work is evaluated in a period [0,T] where T ≤tLZ. Our results are observed to be in good qualitative agreement with known results.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Nsangou, I. and Fai, L. (2015) Work Done on a Coherently Driven Quantum System. Journal of Quantum Information Science, 5, 89-102. doi: 10.4236/jqis.2015.53011.

References

[1] Jarzynski, C. (1997) Nonequilibrium Equality for Free Energy Differences. Physical Review Letter, 78, Article ID: 2690.
http://dx.doi.org/10.1103/PhysRevLett.78.2690
[2] Sagawa, T. and Ueda, M. (2008) Second Law of Thermodynamics with Discrete Quantum Feedback Control. Physical Review Letter, 100, Article ID: 080403.
http://dx.doi.org/10.1103/PhysRevLett.100.080403
[3] Morikuni, Y. and Tasaki, H. (2011) Quantum Jarzynski-Sagawa-Ueda Relations. Journal of Statistical Physical, 143, 1-10.
http://dx.doi.org/10.1007/s10955-011-0153-7
[4] Toyabe, S., Sagawa, T., Ueda, M., Muneyuki, E. and Sano, M. (2010) Experimental Demonstration of Information-to-Energy Conversion and Validation of the Generalized Jarzynski Equality. Nature Physics, 6, 988-992.
http://dx.doi.org/10.1038/nphys1821
[5] Averin, D.V. and Pekola, J.P. (2011) Statistics of the Dissipated Energy in Driven Single-Electron Transitions. Euro Physics Letter, 96, Article ID: 67004.
[6] Küng, B., Rössler, C., Beck, M., Marthaler, M., Golubev, D.S., Utsumi, Y., Ihn, T. and Ensslin, K. (2012) Irreversibility on the Level of Single-Electron Tunneling. Physical Review X, 2, Article ID: 011001.
http://dx.doi.org/10.1103/physrevx.2.011001
[7] Saira, O.-P., Yoon, Y., Tanttu, T., Möttönen, M., Averin, D.V. and Pekola, J.P. (2012) Test of the Jarzynski and Crooks Fluctuation Relations in an Electronic System. Physical Review Letter, 109, Article ID: 180601.
[8] Alemany, A., Ribezzi, M. and Ritort, F. (2011) Recent Progress in Fluctuation Theorems and Free Energy Recovery. AIP Conference Proceedings, 1332, 96.
http://dx.doi.org/10.1063/1.3569489
[9] Hopkins, A., Jacobs, K., Habib, S. and Schwab, K. (2003) Feedback Cooling of a Nano-Mechanical Resonator. Physical Review B, 68, Article ID: 235328.
http://dx.doi.org/10.1103/PhysRevB.68.235328
[10] Steck, D., Jacobs, K., Mabuchi, H., Bhattacharya, T. and Habib, S. (2004) Quantum Feedback Control of Atomic Motion in an Optical Cavity. Physical Review Letter, 92, Article ID: 223004.
http://dx.doi.org/10.1103/physrevlett.92.223004
[11] Crooks, G.E. (1998) Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems. Journal of Statistical Physics, 90, 1481-1487.
[12] Crooks, G.E. (1999) Excursions in Statistical Dynamics. PhD Thesis, University of California, Berkeley.
[13] Campisi, M., Talkner, P. and Hänggi, P. (2010) Fluctuation Theorems for Continuously Monitored Quantum Fluxes. Physical Review Letters, 105, Article ID: 140601.
http://dx.doi.org/10.1103/physrevlett.105.140601
[14] Campisi, M., Hänggi, P. and Talkner, P. (2011) Colloquium. Quantum Fluctuation Relations: Foundations and Applications. Review Modern Physics, 83, 771-791.
http://dx.doi.org/10.1103/revmodphys.83.771
[15] Campisi, M., Talkner, P. and Hänggi, P. (2011) Influence of Measurements on the Statistics of Work Performed on a Quantum System. Physical Review E, 83, Article ID: 041114.
http://dx.doi.org/10.1103/physreve.83.041114
[16] Pekola, J.P., Solinas, P., Shnirman, A. and Averin, D.V. (2013) Calorimetric Measurement of Work in a Quantum System. New Journal of Physics, 15, Article ID: 115006.
http://dx.doi.org/10.1088/1367-2630/15/11/115006
[17] Chernyak, V. and Mukamel, S. (2004) Effect of Quantum Collapse on the Distribution of Work in Driven Single Molecules. Physical Review Letters, 93, Article ID: 048302.
[18] Allahverdyan, A.E. and Nieuwenhuizen, T.M. (2005) Fluctuations of Work from Quantum Subensembles: The Case against Quantum Work-Fluctuation Theorem. Physical Review E, 71, Article ID: 066102.
[19] Solinas, P., Averin, D.V. and Pekola, J.P. (2013) Work and Its Fluctuations in a Driven Quantum System. Physical Review B, 87, Article ID: 060508(R).
[20] Engel, A. and Nolte, R. (2007) Jarzynski Equation for a Simple Quantum System: Comparing Two Definitions of Work. Europhysics Letters, 79, Article ID: 10003.
[21] Talkner, P., Lutz, E. and Hänggi, P. (2007) Fluctuation Theorems: Work Is Not an Observable. Physical Review E, 75, Article ID: 050102.
[22] Esposito, M., Harbola, U. and Mukamel, S. (2009) Nonequilibrium Fluctuations, Fluctuation Theorems, and Counting Statistics in Quantum Systems. Review Modern Physics, 81, 1665-1702.
[23] Landau, L.D. (1932) On the Theory of Transfer of Energy at Collisions II. Physikalische Zeitschrift der Sowjetunion, 2, 46-51.
[24] Zener, C. (1932) Non-Adiabatic Crossing of Energy Levels. Proceedings of the Royal Society of London, Series A, 137, 696-702.
http://dx.doi.org/10.1098/rspa.1932.0165
[25] Stückelberg, E.C.G. (1932) Theory of Inelastic Collisions between Atoms. Helvetica Physica Acta, 5, 369-423.
[26] Majorana, E. (1932) Atoms Oriented in a Variable Magnetic Field. Nuovo Cimento, 9, 43-50.
[27] Pokrovsky, V.L. and Sinitsyn, N.A. (2004) Spin Transitions in Time-Dependent Regular and Random Magnetic Fields. Physical Review B, 69, Article ID: 104414.
http://dx.doi.org/10.1103/physrevb.69.104414
[28] Lifshitz, E.M. and Landau, L.D. (1981) Quantum Mechanics: Non-Relativistic Theory. Butterworth-Heinemann, Oxford.
[29] Vilenkin, N. and Klimyk, A. (1991) Representation of Lie Group and Special Functions. Kluwer, Dordrecht.
http://dx.doi.org/10.1007/978-94-011-3538-2
[30] Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G. (1953) Higher Transcendental Functions. McGraw-Hill, New York.
[31] Kenmoe, M.B., Phien, H.N., Kiselev, M.N. and Fai, L.C. (2013) Effects of Colored Noise on Landau-Zener Transitions. Physical Review B, 87, Article ID: 224301.
[32] Carroll, C.E. and Hioe, F.T. (1986) Generalisation of the Landau-Zener Calculation to Three Levels. Journal of Physics A: Mathematical and General, 19, 1151-1161.
http://dx.doi.org/10.1088/0305-4470/19/7/017

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.