Quantum Entanglement in Coupled Lossy Waveguides Using SU(2) and SU(1, 1) Thermo-Algebras

Naveen Kumar Mogurampally^1*, K. V. S. Shiv Chaitanya², Bindu A. Bambah¹

¹School of Physics, University of Hyderabad, Hyderabad, India.
²Department of Physics, BITS-Pilani, Hyderabad Campus, Hyderabad, India.

DOI: 10.4236/jmp.2015.611158                

Abstract

In this paper, the master equation for the coupled lossy waveguides is solved using the thermofield dynamics (TFD) formalism. This formalism allows the use of the underlying symmetry algebras SU(2) and SU(1, 1), associated with the Hamiltonian of the coupled lossy waveguides, to compute entanglement and decoherence as a function of time for various input states such as NOON states and thermal states.

Keywords

Coupled Waveguides, Thermofield Dynamics, Master Equation, Lie Algebras, Entanglement, Decoherence

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Christodoulides, D.N., Lederer, F. and Silberberg, Y. (2003) Nature (London), 424, 817-823. http://dx.doi.org/10.1038/nature01936
[2]	Longhi, S. (2009) Physical Review A, 79, Article ID: 023811.
[3]	Longhi, S. (2009) Laser and Photonic Review, 3, 243-261. http://dx.doi.org/10.1002/lpor.200810055
[4]	Rai, A., Das, S. and Agarwal, G.S. (2010) Optics Express, 18, 6241-6254. http://dx.doi.org/10.1364/OE.18.006241
[5]	Politi, A., Cryan, M.J., Rarity, J.G., Yu, S. and O’Brien, J.L. (2008) Science, 320, 646-649. http://dx.doi.org/10.1126/science.1155441
[6]	Rozema, L.A., Bateman, J.D., Mahler, D.H., et al. (2014) Physical Review Letters, 112, Article ID: 223602(5).
[7]	Zurek, W.H. (2003) Reviews of Modern Physics, 75, 715-775. http://dx.doi.org/10.1103/RevModPhys.75.715
[8]	Umezawa, H., Matsumoto, H. and Tachiki, M. (1982) Thermofield Dynamics and Condenced States. North-Holland Publishing Company, Amsterdam.
[9]	Laplae, L., Mancini, F. and Umezawa, H. (1974) Physical Review C, 10, 151.
[10]	Takahashi, Y. and Umezawa, H. (1975) Collective Phenomenon, 2, 55-80.
[11]	Ojima, I. (1981) Annals of Physics, 137, 1-32. http://dx.doi.org/10.1016/0003-4916(81)90058-0
[12]	Umezawa, H. (1993) Equilibrium and Non-Equilibrium Thermal Physics. Proceedings of the 3rd Workshop on Thermofield Theories and Their Applications, Banff, World Scientific, Singapore.
[13]	Chaturvedi, S. and Srinivasan, V. (1991) Journal of Modern Optics, 38, 777-783. http://dx.doi.org/10.1080/09500349114550761
[14]	Chaturvedi, S. and Srinivasan, V. (1991) Physical Review A, 43, 4054-4057. http://dx.doi.org/10.1103/PhysRevA.43.4054
[15]	Shanta, P., Chaturvedi, S., Srinivasan, V. and Kapoor, A.K. (1996) International Journal of Modern Physics B, 10, 1573-1584. http://dx.doi.org/10.1142/S0217979296000672
[16]	Shanta, P., Chaturvedi, S. and Srinivasan, V. (1986) Modern Physics Letters A, 11, 2381-2396.
[17]	Chaturvedi, S., Srinivasan, V. and Agarwal, G.S. (1999) Journal of Physics A: Mathematical and General, 32, 1909-1926. http://dx.doi.org/10.1088/0305-4470/32/10/009
[18]	Perelomov, A. (1986) Generalized Coherent States and Their Applications. Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-3-642-61629-7
[19]	Fujii, K. (2002) Introduction to Coherent States and Quantum Information Theory. http://arxiv.org/abs/quant-ph/0112090
[20]	Agarwal, G.S. and Biswas, A. (2005) Journal of Optics B: Quantum Semiclassical Optics, 7, 350-354. http://dx.doi.org/10.1088/1464-4266/7/11/006
[21]	Vidal, G. and Werner, R.F. (2002) Physical Review A, 65, Article ID: 032314. http://arxiv.org/abs/quant-ph/0102117
[22]	Hong, C.K., Ou, Z.Y. and Mandel, L. (1987) Physical Review Letters, 59, 2044-2046. http://dx.doi.org/10.1103/PhysRevLett.59.2044
[23]	Afek, I., Ambar, O. and Silberberg, Y. (2010) Science, 328, 879-881. http://dx.doi.org/10.1126/science.1188172
[24]	Simon, R. (2000) Physical Review Letters, 84, 2726-2729. http://dx.doi.org/10.1103/PhysRevLett.84.2726
[25]	Hashizume, Y. and Suzuki, M. (2013) Physica A: Statistical Mechanics and Its Applications, 392, 3518-3530.