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A kinetic energy reduction technique and characterizations of the ground states of spin-1 Bose-Einstein condensates
1. | Institute of Mathematics, Academia Sinica, Taipei, 10617, Taiwan |
2. | Department of Applied Mathematics and Center of Mathematical Modeling, and Scientific Computing, National Chiao Tung University, Hsinchu, 30010, Taiwan |
References:
[1] |
M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman and E. A. Cornell, Observation of Bose-Einstein condensation in a dilute atomic vapor, Science, 269 (1995), 198-201.
doi: 10.1126/science.269.5221.198. |
[2] |
W. Bao and Y. Cai, Ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junction, East Asian J. Appl. Math, 1 (2011), 49-81.
doi: 10.4208/eajam.190310.170510a. |
[3] |
W. Bao and F. Y. Lim, Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow, SIAM J. Sci. Comput., 30 (2008), 1925-1948.
doi: 10.1137/070698488. |
[4] |
M. D. Barrett, J. A. Sauer and M. S. Chapman, All-optical formation of an atomic Bose-Einstein condensate, Phys. Rev. Lett., 87 (2001), 010404. |
[5] |
F. Bethuel and X. Zheng, Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Anal., 80 (1988), 60-75.
doi: 10.1016/0022-1236(88)90065-1. |
[6] |
J. Bourgain, H. Brezis and P. Mironescu, Lifting in Sobolev spaces, Journal d'Analyse Mathématique, 80 (2000), 37-86.
doi: 10.1007/BF02791533. |
[7] |
C. C. Bradley, C. A. Sackett, J. J. Tollett and R. G. Hulet, Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions, Phys. Rev. Lett., 75 (1995), 1687-1690.
doi: 10.1103/PhysRevLett.75.1687. |
[8] |
D. Cao, I.-L. Chern and J. Wei, On ground state of spinor Bose-Einstein condensates, NoDEA Nonlinear Differential Equations Appl., 18 (2011), 427-445.
doi: 10.1007/s00030-011-0102-9. |
[9] |
J.-H. Chen, I.-L. Chern and W. Wang, Exploring ground states and excited states of spin-1 Bose-Einstein condensates by continuation methods, J. Comput. Phys., 230 (2011), 2222-2236.
doi: 10.1016/j.jcp.2010.11.048. |
[10] |
F. Dalfovo, S. Giorgini, L. P. Pitaevskii and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys., 71 (1999), 463-512.
doi: 10.1103/RevModPhys.71.463. |
[11] |
K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn and W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett., 75 (1995), 3969-3973.
doi: 10.1103/PhysRevLett.75.3969. |
[12] |
L.-M. Duan, J. I. Cirac and P. Zoller, Quantum entanglement in spinor Bose-Einstein condensates, Phys. Rev. A, 65 (2002), 033619.
doi: 10.1103/PhysRevA.65.033619. |
[13] |
E. V. Goldstein and P. Meystre, Quantum theory of atomic four-wave mixing in Bose-Einstein condensates, Phys. Rev. A, 59 (1999), 3896-3901.
doi: 10.1103/PhysRevA.59.3896. |
[14] |
A. Görlitz, T. L. Gustavson, A. E. Leanhardt, R. Löw, A. P. Chikkatur, S. Gupta, S. Inouye, D. E. Pritchard and W. Ketterle, Sodium Bose-Einstein condensates in the $f=2$ state in a large-volume optical trap, Phys. Rev. Lett., 90 (2003), 090401. |
[15] |
E. P. Gross, Structure of a quantized vortex in boson systems, Il Nuovo Cimento Series 10, 20 (1961), 454-477.
doi: 10.1007/BF02731494. |
[16] |
T.-L. Ho, Spinor bose condensates in optical traps, Phys. Rev. Lett., 81 (1998), 742-745.
doi: 10.1103/PhysRevLett.81.742. |
[17] |
T.-L. Ho and S. K. Yip, Fragmented and single condensate ground states of spin-1 bose gas, Phys. Rev. Lett., 84 (2000), 4031-4034.
doi: 10.1103/PhysRevLett.84.4031. |
[18] |
C. K. Law, H. Pu and N. P. Bigelow, Quantum spins mixing in spinor Bose-Einstein condensates, Phys. Rev. Lett., 81 (1998), 5257-5261.
doi: 10.1103/PhysRevLett.81.5257. |
[19] |
E. H. Lieb and M. Loss, Analysis, vol. 14 of Graduate Studies in Mathematics, 2nd edition, American Mathematical Society, Providence, RI, 2001. |
[20] |
E. H. Lieb, R. Seiringer and J. Yngvason, Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional, Phys. Rev. A, 61 (2000), 043602.
doi: 10.1103/PhysRevA.61.043602. |
[21] |
L.-R. Lin, Mass Redistribution and Its Applications to the Ground States of Spin-1 Bose-Einstein Condensates, Ph.D thesis, National Taiwan University, 2013. |
[22] |
H.-J. Miesner, D. M. Stamper-Kurn, J. Stenger, S. Inouye, A. P. Chikkatur and W. Ketterle, Observation of metastable states in spinor Bose-Einstein condensates, Phys. Rev. Lett., 82 (1999), 2228-2231.
doi: 10.1103/PhysRevLett.82.2228. |
[23] |
T. Ohmi and K. Machida, Bose-Einstein condensation with internal degrees of freedom in alkali atom gases, Journal of the Physical Society of Japan, 67 (1998), 1822-1825.
doi: 10.1143/JPSJ.67.1822. |
[24] |
L. P. Pitaevskii, Vortex lines in an imperfect Bose gas, Soviet Phys. JETP, 13 (1961), 451-454. |
[25] |
H. Pu, C. K. Law and N. P. Bigelow, Complex quantum gases: spinor Bose-Einstein condensates of trapped atomic vapors, Physica B: Condensed Matter, 280 (2000), 27-31.
doi: 10.1016/S0921-4526(99)01429-5. |
[26] |
H. Pu, C. K. Law, S. Raghavan, J. H. Eberly and N. P. Bigelow, Spin-mixing dynamics of a spinor Bose-Einstein condensate, Phys. Rev. A, 60 (1999), 1463-1470.
doi: 10.1103/PhysRevA.60.1463. |
[27] |
D. M. Stamper-Kurn, M. R. Andrews, A. P. Chikkatur, S. Inouye, H.-J. Miesner, J. Stenger and W. Ketterle, Optical confinement of a Bose-Einstein condensate, Phys. Rev. Lett., 80 (1998), 2027-2030.
doi: 10.1103/PhysRevLett.80.2027. |
[28] |
J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. Miesner, A. P. Chikkatur and W. Ketterle, Spin domains in ground-state Bose-Einstein condensates, Nature, 396 (1998), 345-348. |
[29] |
S. Yi, O. E. Müstecapliǧlu, C. P. Sun and L. You, Single-mode approximation in a spinor-1 atomic condensate, Phys. Rev. A, 66 (2002), 011601.
doi: 10.1103/PhysRevA.66.011601. |
show all references
References:
[1] |
M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman and E. A. Cornell, Observation of Bose-Einstein condensation in a dilute atomic vapor, Science, 269 (1995), 198-201.
doi: 10.1126/science.269.5221.198. |
[2] |
W. Bao and Y. Cai, Ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junction, East Asian J. Appl. Math, 1 (2011), 49-81.
doi: 10.4208/eajam.190310.170510a. |
[3] |
W. Bao and F. Y. Lim, Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow, SIAM J. Sci. Comput., 30 (2008), 1925-1948.
doi: 10.1137/070698488. |
[4] |
M. D. Barrett, J. A. Sauer and M. S. Chapman, All-optical formation of an atomic Bose-Einstein condensate, Phys. Rev. Lett., 87 (2001), 010404. |
[5] |
F. Bethuel and X. Zheng, Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Anal., 80 (1988), 60-75.
doi: 10.1016/0022-1236(88)90065-1. |
[6] |
J. Bourgain, H. Brezis and P. Mironescu, Lifting in Sobolev spaces, Journal d'Analyse Mathématique, 80 (2000), 37-86.
doi: 10.1007/BF02791533. |
[7] |
C. C. Bradley, C. A. Sackett, J. J. Tollett and R. G. Hulet, Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions, Phys. Rev. Lett., 75 (1995), 1687-1690.
doi: 10.1103/PhysRevLett.75.1687. |
[8] |
D. Cao, I.-L. Chern and J. Wei, On ground state of spinor Bose-Einstein condensates, NoDEA Nonlinear Differential Equations Appl., 18 (2011), 427-445.
doi: 10.1007/s00030-011-0102-9. |
[9] |
J.-H. Chen, I.-L. Chern and W. Wang, Exploring ground states and excited states of spin-1 Bose-Einstein condensates by continuation methods, J. Comput. Phys., 230 (2011), 2222-2236.
doi: 10.1016/j.jcp.2010.11.048. |
[10] |
F. Dalfovo, S. Giorgini, L. P. Pitaevskii and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys., 71 (1999), 463-512.
doi: 10.1103/RevModPhys.71.463. |
[11] |
K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn and W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett., 75 (1995), 3969-3973.
doi: 10.1103/PhysRevLett.75.3969. |
[12] |
L.-M. Duan, J. I. Cirac and P. Zoller, Quantum entanglement in spinor Bose-Einstein condensates, Phys. Rev. A, 65 (2002), 033619.
doi: 10.1103/PhysRevA.65.033619. |
[13] |
E. V. Goldstein and P. Meystre, Quantum theory of atomic four-wave mixing in Bose-Einstein condensates, Phys. Rev. A, 59 (1999), 3896-3901.
doi: 10.1103/PhysRevA.59.3896. |
[14] |
A. Görlitz, T. L. Gustavson, A. E. Leanhardt, R. Löw, A. P. Chikkatur, S. Gupta, S. Inouye, D. E. Pritchard and W. Ketterle, Sodium Bose-Einstein condensates in the $f=2$ state in a large-volume optical trap, Phys. Rev. Lett., 90 (2003), 090401. |
[15] |
E. P. Gross, Structure of a quantized vortex in boson systems, Il Nuovo Cimento Series 10, 20 (1961), 454-477.
doi: 10.1007/BF02731494. |
[16] |
T.-L. Ho, Spinor bose condensates in optical traps, Phys. Rev. Lett., 81 (1998), 742-745.
doi: 10.1103/PhysRevLett.81.742. |
[17] |
T.-L. Ho and S. K. Yip, Fragmented and single condensate ground states of spin-1 bose gas, Phys. Rev. Lett., 84 (2000), 4031-4034.
doi: 10.1103/PhysRevLett.84.4031. |
[18] |
C. K. Law, H. Pu and N. P. Bigelow, Quantum spins mixing in spinor Bose-Einstein condensates, Phys. Rev. Lett., 81 (1998), 5257-5261.
doi: 10.1103/PhysRevLett.81.5257. |
[19] |
E. H. Lieb and M. Loss, Analysis, vol. 14 of Graduate Studies in Mathematics, 2nd edition, American Mathematical Society, Providence, RI, 2001. |
[20] |
E. H. Lieb, R. Seiringer and J. Yngvason, Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional, Phys. Rev. A, 61 (2000), 043602.
doi: 10.1103/PhysRevA.61.043602. |
[21] |
L.-R. Lin, Mass Redistribution and Its Applications to the Ground States of Spin-1 Bose-Einstein Condensates, Ph.D thesis, National Taiwan University, 2013. |
[22] |
H.-J. Miesner, D. M. Stamper-Kurn, J. Stenger, S. Inouye, A. P. Chikkatur and W. Ketterle, Observation of metastable states in spinor Bose-Einstein condensates, Phys. Rev. Lett., 82 (1999), 2228-2231.
doi: 10.1103/PhysRevLett.82.2228. |
[23] |
T. Ohmi and K. Machida, Bose-Einstein condensation with internal degrees of freedom in alkali atom gases, Journal of the Physical Society of Japan, 67 (1998), 1822-1825.
doi: 10.1143/JPSJ.67.1822. |
[24] |
L. P. Pitaevskii, Vortex lines in an imperfect Bose gas, Soviet Phys. JETP, 13 (1961), 451-454. |
[25] |
H. Pu, C. K. Law and N. P. Bigelow, Complex quantum gases: spinor Bose-Einstein condensates of trapped atomic vapors, Physica B: Condensed Matter, 280 (2000), 27-31.
doi: 10.1016/S0921-4526(99)01429-5. |
[26] |
H. Pu, C. K. Law, S. Raghavan, J. H. Eberly and N. P. Bigelow, Spin-mixing dynamics of a spinor Bose-Einstein condensate, Phys. Rev. A, 60 (1999), 1463-1470.
doi: 10.1103/PhysRevA.60.1463. |
[27] |
D. M. Stamper-Kurn, M. R. Andrews, A. P. Chikkatur, S. Inouye, H.-J. Miesner, J. Stenger and W. Ketterle, Optical confinement of a Bose-Einstein condensate, Phys. Rev. Lett., 80 (1998), 2027-2030.
doi: 10.1103/PhysRevLett.80.2027. |
[28] |
J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. Miesner, A. P. Chikkatur and W. Ketterle, Spin domains in ground-state Bose-Einstein condensates, Nature, 396 (1998), 345-348. |
[29] |
S. Yi, O. E. Müstecapliǧlu, C. P. Sun and L. You, Single-mode approximation in a spinor-1 atomic condensate, Phys. Rev. A, 66 (2002), 011601.
doi: 10.1103/PhysRevA.66.011601. |
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