玻色—爱因斯坦凝聚中相位相干性及含时系统中布居局域化研究
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摘要
本文主要内容包括以下几个方面。首先，我们讨论了玻色—爱因斯坦凝聚体(BEC)的相位控制。目前由弱耦合双组分BEC所构成的玻色约瑟夫森结(BJJ)成为研究热点，在平均场理论基础上预言了许多有趣的现象如宏观量子自捕获(MQST)，和π-位相态(结间量子位相差的时间平均值为π)。我们用等效量子自旋模型的势场描述方法得到了弱耦合双组分BEC精确量子相位模型(EQPM)。我们发现依据不同的实验参数，π-位相态既可能是简并基态、亚稳态，也可能是非稳定态。对于亚稳的π-位相态，我们利用瞬子技术计算了它的衰变率或寿命。此外，我们获得了由于量子隧穿导致的简并基态能级劈裂，计算了低能能谱的带宽，在此基础上讨论了玻色—约瑟夫森振荡的相干特性。
在本文的第二大部分中，我们研究了原子或电子的局域化控制。外场驱动下原子或分子跃迁的理论或实验研究已相当广泛和深入。这里考虑激光驱动的三能级原子的布居数反转。利用含时规范变换理论得到系统的精确解，我们用时间演化算符同时得到文献中分别采用π-位相法和STIRAP(受激拉曼散射)方法得到的结果，因而更具有普遍性。同时，我们也讨论了实现布居绝热转换的条件，并给出更为普遍的表达形式，得到了一种新的实现完全布居绝热转换的条件。
鉴于量子点系统中电子局域化控制在量子计算和量子信息处理中的广泛应用，人们迫切希望对此动力学系统能有更深入细致的了解。通过对外驱动场的调控达到控制相邻阱间隧穿的目的，可以成为电子自旋输运或局域化的理论基础。我们探讨在稳恒磁场和旋转磁场的作用下，双量子点中的电子自旋动力学。我们利用SU(2)自旋相干态获得包括库仑相互作用Hubbard模型的时间演化算符，得到解析的含时自旋流。
This paper is of two folds. Firstly, we investigate the relative quantum phase control of two-component Bose-Einstain condanste(BEC). A boson Josephson junction(BJJ) formed in a weakly coupled double-BEC has been discussed intensively. Based on mean-field theory (MFT), which gives rise to the Gross-Pitaevskii equation, interesting phenomena such as macroscopic quantum self-trapping(MQST), and n -phase state, where the time-averaged quantum phase difference across the junction equals n have been predicted. We rederive the EQPM, however, with the potential field description of the effective quantum spin modeled from weakly linked two-component BECs. We find that the n -phase state can be either the degenerate ground state or metastable, even unstable state depending on experimental parameters ofBECs.
The life time of the metastable n -phase state is evaluated explicitly in term of the instanton method. Moreover, we obtain the energy band structure, and the band width of the low-lying energy spectrum of the BECs due to the quantum tunneling between degenerate ground states. Thus we are able to investigate the coherent properties of the Bose-Josephson oscillations.
Localization control of atoms or electrons is discussed in the second part. Transport of atoms or molecules driven by laser beams through a mesoscopic device have continued to receive considerable attention in recent years. Using Lewis-Riesenfeld theory, we obtain exact solutions of the time-dependent system, then we recover both n -pulse method based on time-evolution operator of the system and STIRAP method in terms of instantaneous eigenstates with the help of time-dependent gauge transformation. Moreover, adiabatic conditions of these two schemes which have been widely investigated and generalized in many papers are discussed. A strict formulation of adiabatic conditions is given, and a new adiabatic condition to induce complete population transfer is found.
It is extremely desirable to have a better understanding of the quantum dot (QD) dynamics and to develop a technique to control the localization of electrons which is of possible application in quantum computation and quantum information processing. Tuning of the driving field thus provides a simple mechanism to localize or move spin polarization within an array of quantum dots by adjusting the tunnelling rate between adjacent dots. We study the dynamical spin separation of two interacting electrons confined in the double QDs driven by a static and a rotating magnetic fields. We use an two-site model of Hubbard-type to describe the dynamical system including the Coulomb interaction. With the time-evolution operator obtained by means of SU(2) spin coherent states we are able to derive analytic time-evolution of spin probability-current between the two quantum dots for various initial states.
在本文的第二大部分中，我们研究了原子或电子的局域化控制。外场驱动下原子或分子跃迁的理论或实验研究已相当广泛和深入。这里考虑激光驱动的三能级原子的布居数反转。利用含时规范变换理论得到系统的精确解，我们用时间演化算符同时得到文献中分别采用π-位相法和STIRAP(受激拉曼散射)方法得到的结果，因而更具有普遍性。同时，我们也讨论了实现布居绝热转换的条件，并给出更为普遍的表达形式，得到了一种新的实现完全布居绝热转换的条件。
鉴于量子点系统中电子局域化控制在量子计算和量子信息处理中的广泛应用，人们迫切希望对此动力学系统能有更深入细致的了解。通过对外驱动场的调控达到控制相邻阱间隧穿的目的，可以成为电子自旋输运或局域化的理论基础。我们探讨在稳恒磁场和旋转磁场的作用下，双量子点中的电子自旋动力学。我们利用SU(2)自旋相干态获得包括库仑相互作用Hubbard模型的时间演化算符，得到解析的含时自旋流。
This paper is of two folds. Firstly, we investigate the relative quantum phase control of two-component Bose-Einstain condanste(BEC). A boson Josephson junction(BJJ) formed in a weakly coupled double-BEC has been discussed intensively. Based on mean-field theory (MFT), which gives rise to the Gross-Pitaevskii equation, interesting phenomena such as macroscopic quantum self-trapping(MQST), and n -phase state, where the time-averaged quantum phase difference across the junction equals n have been predicted. We rederive the EQPM, however, with the potential field description of the effective quantum spin modeled from weakly linked two-component BECs. We find that the n -phase state can be either the degenerate ground state or metastable, even unstable state depending on experimental parameters ofBECs.
The life time of the metastable n -phase state is evaluated explicitly in term of the instanton method. Moreover, we obtain the energy band structure, and the band width of the low-lying energy spectrum of the BECs due to the quantum tunneling between degenerate ground states. Thus we are able to investigate the coherent properties of the Bose-Josephson oscillations.
Localization control of atoms or electrons is discussed in the second part. Transport of atoms or molecules driven by laser beams through a mesoscopic device have continued to receive considerable attention in recent years. Using Lewis-Riesenfeld theory, we obtain exact solutions of the time-dependent system, then we recover both n -pulse method based on time-evolution operator of the system and STIRAP method in terms of instantaneous eigenstates with the help of time-dependent gauge transformation. Moreover, adiabatic conditions of these two schemes which have been widely investigated and generalized in many papers are discussed. A strict formulation of adiabatic conditions is given, and a new adiabatic condition to induce complete population transfer is found.
It is extremely desirable to have a better understanding of the quantum dot (QD) dynamics and to develop a technique to control the localization of electrons which is of possible application in quantum computation and quantum information processing. Tuning of the driving field thus provides a simple mechanism to localize or move spin polarization within an array of quantum dots by adjusting the tunnelling rate between adjacent dots. We study the dynamical spin separation of two interacting electrons confined in the double QDs driven by a static and a rotating magnetic fields. We use an two-site model of Hubbard-type to describe the dynamical system including the Coulomb interaction. With the time-evolution operator obtained by means of SU(2) spin coherent states we are able to derive analytic time-evolution of spin probability-current between the two quantum dots for various initial states.
引文
[1] G. J. Milbum, J. Comey, E. M.Wright, and D. F. Walls, Phys. Rev. A 55(1997), 4318.
[2] A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Phys. Rev. Lett. 79(1997), 4950; S. Raghavan, A. Smerzi, V. M. Kenkre, Phys. Rev. A 60(1999), R1787.
[3] S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, Phys. Rve. A 59(1999), 620.
[4] A. Smerzi and S. Raghavan, Phys. Rve. A 61(2000), 063601-1.
[5] F. Sols, Physica B 194(1994), 1389, P. Villain, M. Lewenstein, Phys. Rve. A 59 (1999), 2250.
[6] M. J. Steel and M. J. Collett, Phys. Rev. A 57(1998), 2920.
[7] J. R. Anglin, P. Drummond, and A. Smerzi, Phys. Rev. A 64(2001), 063605-1.
[8] L. B. Ioffe et al., Nature (London) 398(1999), 679; J. E. Mooij et al., Science 285(1999),1036.
[9] V. V. Ulyanov, O. B. Zaslavskii, Phys. Rep. 216(1992), 179.
[10] M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 275(1997), 637.
[11] WeiDong Li, Yunbo Zhang, J.-Q. Liang, Cond-mat/0305504.
[12] J.-Q. Liang, H. J. W. Muler -Kirsten, Phys. Rev. D 45 (1992) ,2963; J.-Q. Liang, H. J. W. Muler-Kirsten, Phys. Rev. D 51,718 (1995).
[13]郝柏林，中性原子的玻色．爱因斯坦凝聚，物理学进展，(1997)17卷，223．232
[14] G. M. Kavoulakis and C. J. Pethick, Phys. Rev. A, 58 1563 (1998).
[15] S. Stringari, Phys. Rev. A 58, 2385 (1998)
[16] B. Damski, cond-mat/0309421
[17] A.V. Gurevich and L.P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974).
[18] A.V. Gurevich and A.L. Krylov, Soy. Phys. JETP 65,944 (1987).
[19] O. Morsch, M. Cristiani, J.H. Muller, D. Ciampini and E. Arimondo, Phys. Rev. A 66, 021601 (2002).
[20] K. Berg-Srensen and K. Mimer, Phys. Rev. A 58, 1480 (1998).
[21] J. Javanainen, Phys. Rev. A 60, 4902 (1999).
[22] M.L. Chiofalo, M. Polini and M.P. Tosi, Ear. Phys. J. D 11,371 (2000).
[23] D. van Oosten, P. van der Straten, and H. T. C. Stoof, Phys. Rev. A 63, 053601 (2001).
[24] M. Kramer, L. Pitaevskii and S. Stringari, Phys. Rev. Lett. 88, 180404 (2002).
[25] A.M. Rey, K. Bumett, R. Roth, M. Edwards, C.J. Williams, and C.W. Clark, J. Phys. B 36, 825 (2003).
[26] M. Machholm, C.J. Pethick, and H. Smith, Phys. Rev. A 67, 053613 (2003).
[27] E. Taylor and E. Zaremba, Phys. Rev. A 68, 053611 (2003).
[28] A. Smerzi and A. Trombettoni, Phys. Rev. A 68, 023613 (2003).
[29] M. Kramer, C. Menotti, L. Pitaevskii and S. Stringari, Ear. Phys. J. D 27, 247 (2003).
[30] J.-P. Martikainen and H.T.C. Stool, cond-mat/0308626
[31] A. Trombettoni and A. Smerzi, Phys. Rev. Lett. 86, 2353 (2001).
[32]F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, M. Inguscio, Science, 293 843 (2001).
[33]C. Fort, F. S. Cataliotti, L. Fallani, F. Ferlaino, P. Maddaloni, and M. Inguscio, Phys. Rev. Lett. 90, 140405 (2003).
[34]S. N. Bose, Z. Physik,(1924) 261,78.
[35]A. Einstein, Sitzungsber, Kgl. Preuss,Akad. Wiss,(1924)P261 ,( 1925)P3
[36]A. G. Tmscott, K. E. Strecker, W. L. McAlexander, G. B. Partridge, and R. G. Hulet, Science(2001) 291,2570-2572
[37]V. Dunjko, V. Lorent, and M. Olshanii, Phys. Rev. Lett. 86, 5413 (2001)
[38]M.D. Girardeau, E.M. Wright, and J.M. Triscari, Phys. Rev. A 63, 033601 (2001)
[39]F. Dalfovo, S. Giorgini, L.P. Pitaevskii and S. Stringari, Rev. Mod. Phys. 71,463 (1999).
[40]L. Tonks, Phys. Rev. 50, 955 (1936)
[41]S. Stringari, Phys. Rev. Lett. 77, 2360 (1996)
[42]E. Zaremba, Phys. Rev. A 57, 518 (1998)
[43]M.-O. Mewes, et al., Phys. Rev. Lett. 77, 988 (1996)
[44]A. Csordas, R. Graham, Phys. Rev. A 59, 1477 (1999)
[45]S. Stringari, Phys. Rev. A 57, 2385 (1998)
[46]T.-L. Ho and M. Ma, J. Low Temp. Phys. 115, 61 (1999)
[47]A. Minguzzi, P. Vignolo, M.L. Chiofalo, and M.P. Tosi, Phys. Rev. A 64, 033605 (2001)
[48]E.B. Kolomeisky, T.J. Newman, J. P. Straley, Phys. Rev. Lett. 85, 1146 (2000)
[49] A. Gofiitz et al., Phys. Rev. Lett. 87, 130402 (2001)
[50] M. Olshanii, Phys. Rev. Lett. 81,938 (1998)
[51] Bogoliubov, N. Phys.(1974)(Moscow)l 1 23
[52] L.P. Pitaevskii, Soy. Phys. JETP(1961) 13 451-477
[53] P. Bouyer and M. A. Kasevich, Phys. Rev. A(1997)56 R108-R1086
[54] M. J. Holland, Jin D. M. L. Chiofale and J. Cooper, Phys. Rev. Lett. (1997)78 3801
[55] L.V. Hau, B. D. Busch, C. Liu, Z. Dutton, M. M. Burns ang J.A. Golovehenko, Phys. Rev. A(1998)58 R54
[56] Jin D. S, J. R. Enser, M. R. Matthews, C. E. Wieman and E.A. Comell, Phys. Rev. Lett.(1996)77 988
[57] M.-O. Mewes, M. R. Andrews, D.-M. Kuru, D. S. Durfee, C. G.. Townsend and W. Kettele, Phys. Rev. Lett.(1997)78 582
[58] M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch and I Bloch, Nature(2002)415 3
[59] M. P. A. Fisher, P. B. Weichman, G. Grinstein and Daniel S. Fisher, Phys. Rev. B (1989)40 546
[60] H. T. C. Stoof Nature(2002)415 25
[61] C. A. Sackett, H. T. C. Stoofand R.G.. Hulet, Phys. Rev. Lett.(1998)80 2031
[62] Y. Kagan, A. E. Murshev and G. V. Shlyapnikov, Phys. Rev. Lett.(1998)81 933
[63] J. M. Gerton, D. Strekalov, Nature(2002)408 692
[64] B. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Comell and C. E.
Wieman, Nature(2001) 412 295
[65]R. A .Duine et al., Phys. Rev. Lett.(2001)86 1406
[66]M .B. Dahan, E. Peik, J. Reichel, Y. Castin and C. Salomon Phys. Rev. Lett. (1996)76 4508
[67]A. Sorensen, L.-M. Duan, J .Ⅰ. Cirac and P. Zoller, Nature(2001)409 63
[68]C. Liu, Z. Dutton, C. H. Behroozi and L. V. Hau, Nature(2001)409 409
[69]U. Al Khawaja and H. Stoof Nature(2001)411 918
[70]Z.Dutton, M.Budde,C. Slowe, L. V. Hau, Science(2001)293 27
[71]F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, Minguscio, Science(2001)293843
[72]C. Orzel, A. K. Tuchman, M. L. Fenselau, M.Y asuda and M. A. Kasevich, Science (2001) 291 2386
[73]J. R. Anglin and W. Kettefie Nature, (2002)416 211
[74]Chu Steven, Nature (2002)416 206
[75]S. L. Rolston and W. D. Phillips Nature(2002)416 219
[76]K. Brunett, P. S. Jullenne, P. D. Lett. E. Tlesinga and C. J. Williams Nature(2002)416 225
[77]Th. Udem, R, Holzwarth and T. W. Hansc Nature(2002)416 233; C, Monroe Nature(2002)416 238
[78]李卫东，博士论文：玻色-爱因斯坦凝聚凝聚中的相干性研究，中国科学院物理研究所(2002)
[79]P. Pedri, L. Pitaevskii, S. Stringari, et al., Phys. Rev. Lett. (2001) 87 220401
[80]J. R. Anglin, P. Drummond and A. Smerzi, Phys. Rev. A (2001) 64 063605; L. Pitaevskii and S. Stringari, Phys. Rev. Lett. (2001) 87 180402
[81]张礼 葛墨林 《量子力学的前沿问题》2000清华大学出版社
[82]M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, W. Kettede Science (1997) 275 31
[83]W. Hoston and L. You Phys. Rev. A. (1996) 53 4254
[84]M. Naraschewski, H. Walls, A. Schenzle, J. I. Cirac and P. Zoller, Phys..Rev. A. (1996) 54 2185
[85]P. W. Anderson, Rev. Mod. Phys. (1966) 38 298
[86]J. Javanainen and S. M. Yoo Phys. Rev. Lett. (1991) 76 161
[87]Liu W. M., Wu B. and Niu Q. Phys. Rev. Lett.(2000)84 2294
[88]B. P. Anderson and M. A. Kasevich Science(1998)282 1689
[89]Li W. D., X. J. Zhou, Y. Q. Wang, J. Q. Liang and W. M. Liu Phys. Rev. A(2001) 64 015602
[90]Q. H. Park and J. H. Eberly Phys. Rev. Lett.(1999) 85 4195
[91]J.Williams, R. Walser, J. Cooper, E. A. Comell, M. Holland, cond-mat/9904399
[92]A. Sinatra and Y. Castin Eur. Phys. J. D.(2000)8 319
[93]A. Smerzi, S. Fantoni, S. Giovanazzi and S.R. Shenoy Phys. Rev. Lett.(1997)79 4950
[94]S. Raghavan, A. Smerzi, S. Fantoni and S. R. Shenoy Phys. Rev. A(1999)59 620
[95]I. Marino, S. Raghavn, S. Fantoni and S. R. Shenoy and A. Smerzi Phys. Rev. A(1999) 60 487
[96]W. H. Lousisell, Phys. Lett. (1963) 7 60
[97]L. Susskind and J. Glogower Physics (Long Island City, N. Y.)(1964) 1 49
[98]R. Lynch Phys. Rep. (1995)256 367
[99]J. Clarke, A. N. Cleland, M. H. Devoret, D. Estevs, J. M. Martinis Science(1998) 293 992
[100]J. M. Martinis, Michel H. Devoret and J. Clarke Phys. Rev. Lett.(1985) 55 1543
[101]G. Schonand A. D. Zaikin Phys. Rep. (1990)198 237
[102]张云波，博士论文：周期瞬子法及其在磁性宏观量子隧穿中的应用，中国科学院物理研究所(1998)
[103]J.-Q. Liang, H. J. W. Muler-Kirsten, D. K. Park and F. C. Pu, Phys. Rev. B (2000)61 8856
[104]N. L. Manakov, V. D. Ovsiannikov, L. P. Rapoport, Phys. Rep. (1986)141 319
[105]S.-I. Chu, Adv. Chem, Phys. (1986)73 739
[106]G. Casati, B.V. Chirikov, D. L. Shepelyansky, I. Guaned, Phys. Rep. (1987) 154 77
[107]M. Kleber, Phys. Rep. (1994)236 331
[108]H. R. Reiss, Phys. Rev. Lett. (1970) 25 1149
[109]M. Gavrilla, J. Z. Kaminski, Phys. Rev. Lett. (1984)52 614
[110]Q. Su, J. H. Ebedy, Phys. Rev. A (1991)43 5997
[111]D. J. Tannor, S. A. Rice, Adv. Chem. Phys. (1988) 70 441
[112]P. Brumer, M. Shapiro, Ann. Rev. Chem. (1992)43 257
[113]H.R.Lewis Jr, J.Math.Phys. 9,1976(1968)
[114] H.R.Lewis Jr and W.B.Riesenfeld J.Math.Phys. 10,1458(1969)
[115] Y-Z Lai, J-Q Liang, H J W Muller-Kirsten and Jian-Ge Zhou, J.Phys. A:Math. Gen. 29(1996)
[116] J.-Q.Liang and H.J.W.Muller-Kirsten, Ann.Phys.(New York)219, 42(1992)
[117] B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990)
[118] L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover, New York,1987)
[119] J. N. Elgin, Phys. Lett. 80A, 140 (1980).
[120] F. T. Hioe and J. H. Eberly, Phys. Rev. Lett. 47, 838 (1981).
[121] M. D. Crisp, Phys. Rev. A 8, 2128 (1973).
[122] R. M. Whitley, Jr. and C. R. Stroud,, Phys. Rev. A 14, 1498 (1976).
[123] C. M. Bowden and C. C. Sung, Phys. Rev. A 18, 1588 (1978).
[124] B. W. Shore and J. R. Ackerhalt, Phys. Rev. A 15, 1640 (1977).
[125] T. W. Mossberg and S. R. Hartman, Phys. Rev. A23, 1271 (1981).
[126] R. G. Hulet and D. Kleppner, Phys. Rev. Lett. 51, 1430 (1983).
[127] G. L. Peterson, C. D. Cantrell and R. S. Burkey, Opt. Commun. 43, 123 (1982)
[128] R. J. Cook and B. W. Shore, Phys. Rev. A20, 539 (1979).
[129] J. Oreg and S. Goshen, Phys. Rev. A29, 3205 (1984).
[130] F. T. Hioe and J. H. Eberly, Phys. Rev. A29, 1164 (1984).
[134] J. Oreg, G. Hazak, and J. H. Eberly, Phys. Rev. A (1985)32, 2776
[135] J.Oreg, F. T. Hioe, and J. H.Eberly, ibid. (1984)29,690
[136]M.V.Berry, Proc. R. Soc. London, Ser. A (1987)392,45
[137]C. E. Carroll and F. T. Hioe, Phys.Rev.A (1990)42,1522
[138]J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, Phys. Rev. A (1989) 40, 6741
[139]B.W. Shore, K. Bergmann, and J. Oreg, Z. Phys. D (1992)23, 33
[140]U.Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys. (1990)92, 5363
[141]F. T. Hioe and J. H. Eberly, Phys. Rev. A (1982)25, 2168
[142]H. P. W. Gottlieb, Phys. Rev. A (1982) 26, 3713
[143]F. T. Hioe and J. H. Eberly, Phys. Rev. Lett. (1981) 47, 838
[144]F. T. Hioe, Phys. Rev. A(1983) 28, 879
[145]F. T. Hioe, Phys.Rev. A(1984)29,3434
[146]C. E. Carroll and F. T .Hioe, J. Opt. Soc .Am. B(1988) 5,1335
[147]F. T. Hioe, J. Opt. Soc. Am. B4, 1327(1987)
[148]L. Jacak, P. Hawrylak, A. Wojs, Quantum Dots, Springer-Verlag, Berlin Heidelberg 1998
[149]H. Grabert, M. Debpret(Ed), Single Charge Tunneling, Plenum, London, 1992
[150]Y. Nagamune, H. Sakaki, L. P. Kouwenhoven, L.C. Mur, Appl. Phys. Lett. (1994)64 2379
[151]D. P. Divinvenzo in: L. L. Sohn, L. P. Kouwengoven, G. Schon(Ed), Mesoscopic Electron Transport, Kluwer, Dordrecht, 1997
[152]J. I. Cirac, P. Zoller. Phys. Rev. Lett. (1995)74 4091
[153]C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, D. J. Wineland, Phys. Rev. Lett. (1995)4714
[154]T. Sleator, Weinfurter, Phys. Rev. Lett.(1995)74 4087
[155]Q.-A. Truchette, C. J. Hood, W. Lang, H, Marbuchi, H. J. Kimble, Phys. Rev. Lett.(1995) 75 4710
[156]D. G. Cory, A. F. Fahmy, T. F. Havel, Proc. Natl. Acad. Sci. U. S. A.(1997)94 1634
[157]J. A. Jones, M. Mosca, R. H. Hansen, Nature (1998)393 344
[158]A. Shnirman, G. Schon, Z. Henmon, Phys. Rev. Lett. (1997) 79 2371
[159]Y. Maklin, G. Schon, A. Shnirman, Nature (1999)398 305
[160]D. Loss, D. P. DiVincenzo, Phys. Rev. A(1998)57 120
[161]D. P. DiVencenzo, D. Bacon, J. Kempe, G. Burkard, K. B. Whaley, Nature(2000)408 339
[162]N. H. Bonedeo, J. Erland, D. Gammon, D. S. Katzer, D. Park, D. G. Steel, Science(1998) 282 1473
[163]B. E. Kane, Nature (1998)393 133
[164]S. Schiemann, A. Kuhn, S. Stenerwald and K. Bergmann, Phys. Rev. Lett. (1993) 71, 3637
[165]E.R. Mucciolo, C. Chamon, and C. Marcus, Phys. Rev. Lett. 89, (2002) 1468020
[166]T. Aono, cond-mat/0205395.
[167]B. Wang, J. Wang, and H. Guo, cond-mat/0208475.
[168]S. K. Waston et al., cond-mat/0302492
[169]Q.-E Sun, H. Guo. and J. Wang, cond-mat/0212293.
[170]R. M. Potok et al., Phys. Rev. Lett. 89, (2002) 266602.
[171]R. M. Potok et al. cond-mat/0303152
[172]L. Kouwenhoven and L. Glazrnan, Physics World 14, (2001) 33
[173]Ping Zhang, Qi-Kun Xue, and X. C. Xie, cond-mat/0304597
[174]Lin Tian, P. Zoller quant-ph/0306085
[175]Florian Meier, Jeremy Levy, Daniel Loss, Phys. Rev. B (2003)68, 134417
[176]Z. Kis, F. Renzoni Phys. Rev A 65, 032318 (2002)
[2] A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Phys. Rev. Lett. 79(1997), 4950; S. Raghavan, A. Smerzi, V. M. Kenkre, Phys. Rev. A 60(1999), R1787.
[3] S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, Phys. Rve. A 59(1999), 620.
[4] A. Smerzi and S. Raghavan, Phys. Rve. A 61(2000), 063601-1.
[5] F. Sols, Physica B 194(1994), 1389, P. Villain, M. Lewenstein, Phys. Rve. A 59 (1999), 2250.
[6] M. J. Steel and M. J. Collett, Phys. Rev. A 57(1998), 2920.
[7] J. R. Anglin, P. Drummond, and A. Smerzi, Phys. Rev. A 64(2001), 063605-1.
[8] L. B. Ioffe et al., Nature (London) 398(1999), 679; J. E. Mooij et al., Science 285(1999),1036.
[9] V. V. Ulyanov, O. B. Zaslavskii, Phys. Rep. 216(1992), 179.
[10] M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 275(1997), 637.
[11] WeiDong Li, Yunbo Zhang, J.-Q. Liang, Cond-mat/0305504.
[12] J.-Q. Liang, H. J. W. Muler -Kirsten, Phys. Rev. D 45 (1992) ,2963; J.-Q. Liang, H. J. W. Muler-Kirsten, Phys. Rev. D 51,718 (1995).
[13]郝柏林，中性原子的玻色．爱因斯坦凝聚，物理学进展，(1997)17卷，223．232
[14] G. M. Kavoulakis and C. J. Pethick, Phys. Rev. A, 58 1563 (1998).
[15] S. Stringari, Phys. Rev. A 58, 2385 (1998)
[16] B. Damski, cond-mat/0309421
[17] A.V. Gurevich and L.P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974).
[18] A.V. Gurevich and A.L. Krylov, Soy. Phys. JETP 65,944 (1987).
[19] O. Morsch, M. Cristiani, J.H. Muller, D. Ciampini and E. Arimondo, Phys. Rev. A 66, 021601 (2002).
[20] K. Berg-Srensen and K. Mimer, Phys. Rev. A 58, 1480 (1998).
[21] J. Javanainen, Phys. Rev. A 60, 4902 (1999).
[22] M.L. Chiofalo, M. Polini and M.P. Tosi, Ear. Phys. J. D 11,371 (2000).
[23] D. van Oosten, P. van der Straten, and H. T. C. Stoof, Phys. Rev. A 63, 053601 (2001).
[24] M. Kramer, L. Pitaevskii and S. Stringari, Phys. Rev. Lett. 88, 180404 (2002).
[25] A.M. Rey, K. Bumett, R. Roth, M. Edwards, C.J. Williams, and C.W. Clark, J. Phys. B 36, 825 (2003).
[26] M. Machholm, C.J. Pethick, and H. Smith, Phys. Rev. A 67, 053613 (2003).
[27] E. Taylor and E. Zaremba, Phys. Rev. A 68, 053611 (2003).
[28] A. Smerzi and A. Trombettoni, Phys. Rev. A 68, 023613 (2003).
[29] M. Kramer, C. Menotti, L. Pitaevskii and S. Stringari, Ear. Phys. J. D 27, 247 (2003).
[30] J.-P. Martikainen and H.T.C. Stool, cond-mat/0308626
[31] A. Trombettoni and A. Smerzi, Phys. Rev. Lett. 86, 2353 (2001).
[32]F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, M. Inguscio, Science, 293 843 (2001).
[33]C. Fort, F. S. Cataliotti, L. Fallani, F. Ferlaino, P. Maddaloni, and M. Inguscio, Phys. Rev. Lett. 90, 140405 (2003).
[34]S. N. Bose, Z. Physik,(1924) 261,78.
[35]A. Einstein, Sitzungsber, Kgl. Preuss,Akad. Wiss,(1924)P261 ,( 1925)P3
[36]A. G. Tmscott, K. E. Strecker, W. L. McAlexander, G. B. Partridge, and R. G. Hulet, Science(2001) 291,2570-2572
[37]V. Dunjko, V. Lorent, and M. Olshanii, Phys. Rev. Lett. 86, 5413 (2001)
[38]M.D. Girardeau, E.M. Wright, and J.M. Triscari, Phys. Rev. A 63, 033601 (2001)
[39]F. Dalfovo, S. Giorgini, L.P. Pitaevskii and S. Stringari, Rev. Mod. Phys. 71,463 (1999).
[40]L. Tonks, Phys. Rev. 50, 955 (1936)
[41]S. Stringari, Phys. Rev. Lett. 77, 2360 (1996)
[42]E. Zaremba, Phys. Rev. A 57, 518 (1998)
[43]M.-O. Mewes, et al., Phys. Rev. Lett. 77, 988 (1996)
[44]A. Csordas, R. Graham, Phys. Rev. A 59, 1477 (1999)
[45]S. Stringari, Phys. Rev. A 57, 2385 (1998)
[46]T.-L. Ho and M. Ma, J. Low Temp. Phys. 115, 61 (1999)
[47]A. Minguzzi, P. Vignolo, M.L. Chiofalo, and M.P. Tosi, Phys. Rev. A 64, 033605 (2001)
[48]E.B. Kolomeisky, T.J. Newman, J. P. Straley, Phys. Rev. Lett. 85, 1146 (2000)
[49] A. Gofiitz et al., Phys. Rev. Lett. 87, 130402 (2001)
[50] M. Olshanii, Phys. Rev. Lett. 81,938 (1998)
[51] Bogoliubov, N. Phys.(1974)(Moscow)l 1 23
[52] L.P. Pitaevskii, Soy. Phys. JETP(1961) 13 451-477
[53] P. Bouyer and M. A. Kasevich, Phys. Rev. A(1997)56 R108-R1086
[54] M. J. Holland, Jin D. M. L. Chiofale and J. Cooper, Phys. Rev. Lett. (1997)78 3801
[55] L.V. Hau, B. D. Busch, C. Liu, Z. Dutton, M. M. Burns ang J.A. Golovehenko, Phys. Rev. A(1998)58 R54
[56] Jin D. S, J. R. Enser, M. R. Matthews, C. E. Wieman and E.A. Comell, Phys. Rev. Lett.(1996)77 988
[57] M.-O. Mewes, M. R. Andrews, D.-M. Kuru, D. S. Durfee, C. G.. Townsend and W. Kettele, Phys. Rev. Lett.(1997)78 582
[58] M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch and I Bloch, Nature(2002)415 3
[59] M. P. A. Fisher, P. B. Weichman, G. Grinstein and Daniel S. Fisher, Phys. Rev. B (1989)40 546
[60] H. T. C. Stoof Nature(2002)415 25
[61] C. A. Sackett, H. T. C. Stoofand R.G.. Hulet, Phys. Rev. Lett.(1998)80 2031
[62] Y. Kagan, A. E. Murshev and G. V. Shlyapnikov, Phys. Rev. Lett.(1998)81 933
[63] J. M. Gerton, D. Strekalov, Nature(2002)408 692
[64] B. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Comell and C. E.
Wieman, Nature(2001) 412 295
[65]R. A .Duine et al., Phys. Rev. Lett.(2001)86 1406
[66]M .B. Dahan, E. Peik, J. Reichel, Y. Castin and C. Salomon Phys. Rev. Lett. (1996)76 4508
[67]A. Sorensen, L.-M. Duan, J .Ⅰ. Cirac and P. Zoller, Nature(2001)409 63
[68]C. Liu, Z. Dutton, C. H. Behroozi and L. V. Hau, Nature(2001)409 409
[69]U. Al Khawaja and H. Stoof Nature(2001)411 918
[70]Z.Dutton, M.Budde,C. Slowe, L. V. Hau, Science(2001)293 27
[71]F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, Minguscio, Science(2001)293843
[72]C. Orzel, A. K. Tuchman, M. L. Fenselau, M.Y asuda and M. A. Kasevich, Science (2001) 291 2386
[73]J. R. Anglin and W. Kettefie Nature, (2002)416 211
[74]Chu Steven, Nature (2002)416 206
[75]S. L. Rolston and W. D. Phillips Nature(2002)416 219
[76]K. Brunett, P. S. Jullenne, P. D. Lett. E. Tlesinga and C. J. Williams Nature(2002)416 225
[77]Th. Udem, R, Holzwarth and T. W. Hansc Nature(2002)416 233; C, Monroe Nature(2002)416 238
[78]李卫东，博士论文：玻色-爱因斯坦凝聚凝聚中的相干性研究，中国科学院物理研究所(2002)
[79]P. Pedri, L. Pitaevskii, S. Stringari, et al., Phys. Rev. Lett. (2001) 87 220401
[80]J. R. Anglin, P. Drummond and A. Smerzi, Phys. Rev. A (2001) 64 063605; L. Pitaevskii and S. Stringari, Phys. Rev. Lett. (2001) 87 180402
[81]张礼 葛墨林 《量子力学的前沿问题》2000清华大学出版社
[82]M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, W. Kettede Science (1997) 275 31
[83]W. Hoston and L. You Phys. Rev. A. (1996) 53 4254
[84]M. Naraschewski, H. Walls, A. Schenzle, J. I. Cirac and P. Zoller, Phys..Rev. A. (1996) 54 2185
[85]P. W. Anderson, Rev. Mod. Phys. (1966) 38 298
[86]J. Javanainen and S. M. Yoo Phys. Rev. Lett. (1991) 76 161
[87]Liu W. M., Wu B. and Niu Q. Phys. Rev. Lett.(2000)84 2294
[88]B. P. Anderson and M. A. Kasevich Science(1998)282 1689
[89]Li W. D., X. J. Zhou, Y. Q. Wang, J. Q. Liang and W. M. Liu Phys. Rev. A(2001) 64 015602
[90]Q. H. Park and J. H. Eberly Phys. Rev. Lett.(1999) 85 4195
[91]J.Williams, R. Walser, J. Cooper, E. A. Comell, M. Holland, cond-mat/9904399
[92]A. Sinatra and Y. Castin Eur. Phys. J. D.(2000)8 319
[93]A. Smerzi, S. Fantoni, S. Giovanazzi and S.R. Shenoy Phys. Rev. Lett.(1997)79 4950
[94]S. Raghavan, A. Smerzi, S. Fantoni and S. R. Shenoy Phys. Rev. A(1999)59 620
[95]I. Marino, S. Raghavn, S. Fantoni and S. R. Shenoy and A. Smerzi Phys. Rev. A(1999) 60 487
[96]W. H. Lousisell, Phys. Lett. (1963) 7 60
[97]L. Susskind and J. Glogower Physics (Long Island City, N. Y.)(1964) 1 49
[98]R. Lynch Phys. Rep. (1995)256 367
[99]J. Clarke, A. N. Cleland, M. H. Devoret, D. Estevs, J. M. Martinis Science(1998) 293 992
[100]J. M. Martinis, Michel H. Devoret and J. Clarke Phys. Rev. Lett.(1985) 55 1543
[101]G. Schonand A. D. Zaikin Phys. Rep. (1990)198 237
[102]张云波，博士论文：周期瞬子法及其在磁性宏观量子隧穿中的应用，中国科学院物理研究所(1998)
[103]J.-Q. Liang, H. J. W. Muler-Kirsten, D. K. Park and F. C. Pu, Phys. Rev. B (2000)61 8856
[104]N. L. Manakov, V. D. Ovsiannikov, L. P. Rapoport, Phys. Rep. (1986)141 319
[105]S.-I. Chu, Adv. Chem, Phys. (1986)73 739
[106]G. Casati, B.V. Chirikov, D. L. Shepelyansky, I. Guaned, Phys. Rep. (1987) 154 77
[107]M. Kleber, Phys. Rep. (1994)236 331
[108]H. R. Reiss, Phys. Rev. Lett. (1970) 25 1149
[109]M. Gavrilla, J. Z. Kaminski, Phys. Rev. Lett. (1984)52 614
[110]Q. Su, J. H. Ebedy, Phys. Rev. A (1991)43 5997
[111]D. J. Tannor, S. A. Rice, Adv. Chem. Phys. (1988) 70 441
[112]P. Brumer, M. Shapiro, Ann. Rev. Chem. (1992)43 257
[113]H.R.Lewis Jr, J.Math.Phys. 9,1976(1968)
[114] H.R.Lewis Jr and W.B.Riesenfeld J.Math.Phys. 10,1458(1969)
[115] Y-Z Lai, J-Q Liang, H J W Muller-Kirsten and Jian-Ge Zhou, J.Phys. A:Math. Gen. 29(1996)
[116] J.-Q.Liang and H.J.W.Muller-Kirsten, Ann.Phys.(New York)219, 42(1992)
[117] B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990)
[118] L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover, New York,1987)
[119] J. N. Elgin, Phys. Lett. 80A, 140 (1980).
[120] F. T. Hioe and J. H. Eberly, Phys. Rev. Lett. 47, 838 (1981).
[121] M. D. Crisp, Phys. Rev. A 8, 2128 (1973).
[122] R. M. Whitley, Jr. and C. R. Stroud,, Phys. Rev. A 14, 1498 (1976).
[123] C. M. Bowden and C. C. Sung, Phys. Rev. A 18, 1588 (1978).
[124] B. W. Shore and J. R. Ackerhalt, Phys. Rev. A 15, 1640 (1977).
[125] T. W. Mossberg and S. R. Hartman, Phys. Rev. A23, 1271 (1981).
[126] R. G. Hulet and D. Kleppner, Phys. Rev. Lett. 51, 1430 (1983).
[127] G. L. Peterson, C. D. Cantrell and R. S. Burkey, Opt. Commun. 43, 123 (1982)
[128] R. J. Cook and B. W. Shore, Phys. Rev. A20, 539 (1979).
[129] J. Oreg and S. Goshen, Phys. Rev. A29, 3205 (1984).
[130] F. T. Hioe and J. H. Eberly, Phys. Rev. A29, 1164 (1984).
[134] J. Oreg, G. Hazak, and J. H. Eberly, Phys. Rev. A (1985)32, 2776
[135] J.Oreg, F. T. Hioe, and J. H.Eberly, ibid. (1984)29,690
[136]M.V.Berry, Proc. R. Soc. London, Ser. A (1987)392,45
[137]C. E. Carroll and F. T. Hioe, Phys.Rev.A (1990)42,1522
[138]J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, Phys. Rev. A (1989) 40, 6741
[139]B.W. Shore, K. Bergmann, and J. Oreg, Z. Phys. D (1992)23, 33
[140]U.Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys. (1990)92, 5363
[141]F. T. Hioe and J. H. Eberly, Phys. Rev. A (1982)25, 2168
[142]H. P. W. Gottlieb, Phys. Rev. A (1982) 26, 3713
[143]F. T. Hioe and J. H. Eberly, Phys. Rev. Lett. (1981) 47, 838
[144]F. T. Hioe, Phys. Rev. A(1983) 28, 879
[145]F. T. Hioe, Phys.Rev. A(1984)29,3434
[146]C. E. Carroll and F. T .Hioe, J. Opt. Soc .Am. B(1988) 5,1335
[147]F. T. Hioe, J. Opt. Soc. Am. B4, 1327(1987)
[148]L. Jacak, P. Hawrylak, A. Wojs, Quantum Dots, Springer-Verlag, Berlin Heidelberg 1998
[149]H. Grabert, M. Debpret(Ed), Single Charge Tunneling, Plenum, London, 1992
[150]Y. Nagamune, H. Sakaki, L. P. Kouwenhoven, L.C. Mur, Appl. Phys. Lett. (1994)64 2379
[151]D. P. Divinvenzo in: L. L. Sohn, L. P. Kouwengoven, G. Schon(Ed), Mesoscopic Electron Transport, Kluwer, Dordrecht, 1997
[152]J. I. Cirac, P. Zoller. Phys. Rev. Lett. (1995)74 4091
[153]C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, D. J. Wineland, Phys. Rev. Lett. (1995)4714
[154]T. Sleator, Weinfurter, Phys. Rev. Lett.(1995)74 4087
[155]Q.-A. Truchette, C. J. Hood, W. Lang, H, Marbuchi, H. J. Kimble, Phys. Rev. Lett.(1995) 75 4710
[156]D. G. Cory, A. F. Fahmy, T. F. Havel, Proc. Natl. Acad. Sci. U. S. A.(1997)94 1634
[157]J. A. Jones, M. Mosca, R. H. Hansen, Nature (1998)393 344
[158]A. Shnirman, G. Schon, Z. Henmon, Phys. Rev. Lett. (1997) 79 2371
[159]Y. Maklin, G. Schon, A. Shnirman, Nature (1999)398 305
[160]D. Loss, D. P. DiVincenzo, Phys. Rev. A(1998)57 120
[161]D. P. DiVencenzo, D. Bacon, J. Kempe, G. Burkard, K. B. Whaley, Nature(2000)408 339
[162]N. H. Bonedeo, J. Erland, D. Gammon, D. S. Katzer, D. Park, D. G. Steel, Science(1998) 282 1473
[163]B. E. Kane, Nature (1998)393 133
[164]S. Schiemann, A. Kuhn, S. Stenerwald and K. Bergmann, Phys. Rev. Lett. (1993) 71, 3637
[165]E.R. Mucciolo, C. Chamon, and C. Marcus, Phys. Rev. Lett. 89, (2002) 1468020
[166]T. Aono, cond-mat/0205395.
[167]B. Wang, J. Wang, and H. Guo, cond-mat/0208475.
[168]S. K. Waston et al., cond-mat/0302492
[169]Q.-E Sun, H. Guo. and J. Wang, cond-mat/0212293.
[170]R. M. Potok et al., Phys. Rev. Lett. 89, (2002) 266602.
[171]R. M. Potok et al. cond-mat/0303152
[172]L. Kouwenhoven and L. Glazrnan, Physics World 14, (2001) 33
[173]Ping Zhang, Qi-Kun Xue, and X. C. Xie, cond-mat/0304597
[174]Lin Tian, P. Zoller quant-ph/0306085
[175]Florian Meier, Jeremy Levy, Daniel Loss, Phys. Rev. B (2003)68, 134417
[176]Z. Kis, F. Renzoni Phys. Rev A 65, 032318 (2002)