Quantum Entanglement in Coupled Lossy Waveguides Using SU(2) and SU(1, 1) Thermo-Algebras
Affiliation(s)
1 School of Physics, University of Hyderabad, Hyderabad, India. 2 Department of Physics, BITS-Pilani, Hyderabad Campus, Hyderabad, India.
1 School of Physics, University of Hyderabad, Hyderabad, India. 2 Department of Physics, BITS-Pilani, Hyderabad Campus, Hyderabad, India.
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.
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
Coupled Waveguides, Thermofield Dynamics, Master Equation, Lie Algebras, Entanglement, Decoherence
Cite this paper
Mogurampally, N. , Chaitanya, K. and Bambah, B. (2015) Quantum Entanglement in Coupled Lossy Waveguides Using SU(2) and SU(1, 1) Thermo-Algebras. Journal of Modern Physics, 6, 1554-1571. doi: 10.4236/jmp.2015.611158.
Mogurampally, N. , Chaitanya, K. and Bambah, B. (2015) Quantum Entanglement in Coupled Lossy Waveguides Using SU(2) and SU(1, 1) Thermo-Algebras. Journal of Modern Physics, 6, 1554-1571. doi: 10.4236/jmp.2015.611158.
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.
[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.