Abstract

Spinor Bose–Einstein condensates (BECs) and singular optical systems have both recently served as sandboxes to create and study analogs of phenomena from other fields of physics that are otherwise difficult to create and control experimentally. Interfacing singular optics and spinor BECs allows us to take advantage of and build on the foundations of singular optics to create and describe complex spin textures in BECs that serve as analogs of other systems. Here, the complete BEC wavefunctions are precisely engineered via a two-photon Raman interaction to contain π-symmetric (lemon, star) or 2π-symmetric (saddle, spiral) C-point singularities. The optical Raman beams are singular optical beams that contain these singularities and transfer them to the condensate, thereby creating vector-vortex spin textures—the spinor counterparts to scalar vortices—in pseudo-spin-1/2 BECs. With a version of atom-optic polarimetry, we can measure the Stokes parameters of the atomic cloud and characterize the singularities by the patterns present in their ellipse fields or by the C-point index. In the low density limit, these spin textures are analogs of optical vector vortices and should have dynamics driven by a matter-wave Gouy phase. With precise tuning of Raman beam parameters, we can create full Bloch BECs that contain every possible superposition between two states in the atomic cloud. Full Bloch BECs are similar to topologically stable magnetic skyrmions such as those created in thin metal films and nanowires, which may prove useful for atom-spintronics and topological quantum processes.

© 2016 Optical Society of America

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2016 (1)

J. T. Schultz, A. Hansen, J. D. Murphree, M. Jayaseelan, and N. P. Bigelow, “Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate,” J. Mod. Opt. 63, 1–9 (2016).
[Crossref]

2015 (4)

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
[Crossref]

X. Zhang, M. Ezawa, and Y. Zhou, “Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions,” Sci. Rep. 5, 9400 (2015).
[Crossref]

T. Mawson, G. Ruben, and T. Simula, “Route to non-Abelian quantum turbulence in spinor Bose-Einstein condensates,” Phys. Rev. A 91, 063630 (2015).
[Crossref]

S. W. Seo, S. Kang, W. J. Kwon, and Y. Shin, “Half-quantum vortices in an antiferromagnetic spinor Bose-Einstein condensate,” Phys. Rev. Lett. 115, 015301 (2015).
[Crossref]

2014 (6)

V. Kumar and N. K. Viswanathan, “Topological structures in vector-vortex beam fields,” J. Opt. Soc. Am. B 31, A40–A45 (2014).
[Crossref]

Editorial, “The power of analogies,” Nat. Photonics 8, 1 (2014).

M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, “Observation of Dirac monopoles in a synthetic magnetic field,” Nature 505, 657–660 (2014).
[Crossref]

R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Quantum entanglement of complex photon polarization patterns in vector beams,” Phys. Rev. A 89, 060301(R) (2014).
[Crossref]

J. T. Schultz, A. Hansen, and N. P. Bigelow, “A Raman waveplate for spinor Bose-Einstein condensates,” Opt. Lett. 39, 4271–4273 (2014).
[Crossref]

E. J. Galvez, B. L. Rojec, V. Kumar, and N. K. Viswanathan, “Generation of isolated asymmetric umbilics in light’s polarization,” Phys. Rev. A 89, 031801R (2014).
[Crossref]

2013 (6)

D. Lopez-Mago, B. Perez-Garcia, A. Yepiz, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “Dynamics of polarization singularities in composite optical vortices,” J. Opt. 15, 044028 (2013).
[Crossref]

N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, “Writing and deleting single magnetic skyrmions,” Science 341, 636–639 (2013).
[Crossref]

V. Kumar and N. K. Viswanathan, “The Pancharatnam-Berry phase in polarization singular beams,” J. Opt. 15, 044026 (2013).
[Crossref]

V. P. Lukin, O. V. Angelski, L. A. Bolbasova, E. A. Kopylov, M. V. Tuev, and V. V. Nosov, “Comparison of singular-optical and statistical approaches for investigations of turbulence tasks,” Proc. SPIE 9066, 906612 (2013).
[Crossref]

J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, “Observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture,” Phys. Rev. Lett. 111, 245301 (2013).
[Crossref]

R. D. Ramkhalawon, T. G. Brown, and M. A. Alonso, “Imaging the polarization of a light field,” Opt. Express 21, 4106–4115 (2013).
[Crossref]

2012 (8)

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photon. News 23(4), 25–29 (2012).
[Crossref]

J. Choi, W. J. Kwon, and Y. Shin, “Observation of topologically stable 2D skyrmions in an antiferromagnetic spinor Bose-Einstein condensate,” Phys. Rev. Lett. 108, 035301 (2012).
[Crossref]

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam-Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
[Crossref]

C. Vo, S. Riedl, S. Baur, G. Rempe, and S. Dürr, “Coherent logic gate for light pulses based on storage in a Bose–Einstein condensate,” Phys. Rev. Lett. 109, 263602 (2012).
[Crossref]

G. M. Philip, V. Kumar, G. Milione, and N. K. Viswanathan, “Manifestation of the Gouy phase in vector-vortex beams,” Opt. Lett. 37, 2667–2669 (2012).
[Crossref]

M. O. Borgh and J. Ruostekoski, “Topological interface engineering and defect crossing in ultracold atomic gases,” Phys. Rev. Lett. 109, 015302 (2012).
[Crossref]

E. J. Galvez, S. Khadka, W. H. Schubert, and S. Nomoto, “Poincaré-beam patterns produced by nonseparable superpositions of Laguerre-Gauss and polarization modes of light,” Appl. Opt. 51, 2925–2934 (2012).
[Crossref]

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[Crossref]

2011 (6)

Y. Kawaguchi and M. Ueda, “Symmetry classification of spinor Bose-Einstein condensates,” Phys. Rev. A 84, 053616 (2011).
[Crossref]

I. G. da Paz, P. L. Saldanha, M. C. Nemes, and J. G. Peixoto de Faria, “Experimental proposal for measuring the Gouy phase of matter waves,” New J. Phys. 13, 125005 (2011).
[Crossref]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Colloquium: artificial gauge potential for neutral atoms,” Rev. Mod. Phys. 83, 1523–1543 (2011).
[Crossref]

Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, “Spin-orbit-coupled Bose-Einstein condensates,” Nature 471, 83–86 (2011).
[Crossref]

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).
[Crossref]

2010 (1)

2009 (6)

K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, “Sculpting the vortex state of a spinor BEC,” Phys. Rev. Lett. 102, 030405 (2009).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

J. A. M. Huhtamäki, T. P. Simula, M. Kobayashi, and K. Machida, “Stable fractional vortices in the cyclic states of Bose-Einstein condensates,” Phys. Rev. A 80, 051601(R) (2009).
[Crossref]

Y.-J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[Crossref]

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, “Creation and detection of skyrmions in a Bose-Einstein condensate,” Phys. Rev. Lett. 103, 250401 (2009).
[Crossref]

M. Kobayashi, Y. Kawaguchi, M. Nitta, and M. Ueda, “Collision dynamics and rung formation of non-Abelian vortices,” Phys. Rev. Lett. 103, 115301 (2009).
[Crossref]

2008 (4)

C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083–1159 (2008).
[Crossref]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, “Raman coupling of Zeeman sublevels in an alkali-metal Bose-Einstein condensate,” Phys. Rev. A 78, 053412 (2008).
[Crossref]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, “Optical control of the internal and external angular momentum of a Bose-Einstein condensate,” Phys. Rev. A 77, 041601 (2008).
[Crossref]

M. R. Dennis, “Polarization singularity anisotropy: determining monstardom,” Opt. Lett. 33, 2572–2574 (2008).
[Crossref]

2007 (5)

A. Y. Bekshaeva and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial beams with singularities,” Opt. Commun. 271, 332–348 (2007).
[Crossref]

A. K. Spilman and T. G. Brown, “Stress birefringent, space-variant wave plates for vortex illumination,” Appl. Opt. 46, 61–66 (2007).
[Crossref]

G. W. Semenoff and F. Zhou, “Discrete symmetries and 1/3-quantum vortices in condensates of F = 2 cold atoms,” Phys. Rev. Lett. 98, 100401 (2007).
[Crossref]

E. Brion, L. H. Pedersen, and K. Mølmer, “Adiabatic elimination in a lambda system,” J. Phys. A 40, 1033–1043 (2007).
[Crossref]

A. Ardavan, “Exploiting the Poincaré-Bloch symmetry to design high-fidelity broadband composite linear retarders,” New J. Phys. 9, 24–32 (2007).
[Crossref]

2006 (1)

L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate,” Nature 443, 312–315 (2006).
[Crossref]

2005 (2)

M. P. Fewell, “Adiabatic elimination, the rotating-wave approximation and two-photon transitions,” Opt. Commun. 253, 125–137 (2005).
[Crossref]

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose–Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95, 173601 (2005).
[Crossref]

2003 (3)

J. Ruostekoski and J. R. Anglin, “Monopole core instability and Alice rings in spinor Bose-Einstein condensates,” Phys. Rev. Lett. 91, 190402 (2003).
[Crossref]

C. M. Savage and J. Ruostekoski, “Dirac monopoles and dipoles in ferromagnetic spinor Bose-Einstein condensates,” Phys. Rev. A 68, 043604 (2003).
[Crossref]

A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, “Coreless vortex formation in a spinor Bose-Einstein condensate,” Phys. Rev. Lett. 90, 140403 (2003).
[Crossref]

2002 (3)

L.-M. Kuang, J.-H. Li, and B. Hu, “Polarization and decoherence in a two-component Bose-Einstein condensate,” J. Opt. B 4, 295–299 (2002).
[Crossref]

I. Freund, M. S. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
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M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
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2001 (1)

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
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1999 (1)

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
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1998 (1)

T. Ohmi and K. Machida, “Bose-Einstein condensation with internal degrees of freedom in alkali atom gases,” J. Phys. Soc. Jpn. 67, 1822–1825 (1998).
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1983 (1)

J. F. Nye, “Lines of circular polarization in electromagnetic wave fields,” Proc. R. Soc. London A 389, 279–290 (1983).
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1977 (1)

M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
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1936 (2)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
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A. H. S. Holbourn, “Angular momentum of circularly polarized light,” Nature 137, 31 (1936).
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Alfano, R. R.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam-Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
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G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
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Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Alonso, M. A.

Anderson, B. P.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
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Angelski, O. V.

V. P. Lukin, O. V. Angelski, L. A. Bolbasova, E. A. Kopylov, M. V. Tuev, and V. V. Nosov, “Comparison of singular-optical and statistical approaches for investigations of turbulence tasks,” Proc. SPIE 9066, 906612 (2013).
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Angelsky, O. V.

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photon. News 23(4), 25–29 (2012).
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J. Ruostekoski and J. R. Anglin, “Monopole core instability and Alice rings in spinor Bose-Einstein condensates,” Phys. Rev. Lett. 91, 190402 (2003).
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F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).
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Ardavan, A.

A. Ardavan, “Exploiting the Poincaré-Bloch symmetry to design high-fidelity broadband composite linear retarders,” New J. Phys. 9, 24–32 (2007).
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Arnold, C.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
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Baur, S.

C. Vo, S. Riedl, S. Baur, G. Rempe, and S. Dürr, “Coherent logic gate for light pulses based on storage in a Bose–Einstein condensate,” Phys. Rev. Lett. 109, 263602 (2012).
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Beckley, A. M.

Bekshaeva, A. Y.

A. Y. Bekshaeva and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial beams with singularities,” Opt. Commun. 271, 332–348 (2007).
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Berry, M. V.

M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
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Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
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Bickel, J. E.

N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, “Writing and deleting single magnetic skyrmions,” Science 341, 636–639 (2013).
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Bigelow, N. P.

J. T. Schultz, A. Hansen, J. D. Murphree, M. Jayaseelan, and N. P. Bigelow, “Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate,” J. Mod. Opt. 63, 1–9 (2016).
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J. T. Schultz, A. Hansen, and N. P. Bigelow, “A Raman waveplate for spinor Bose-Einstein condensates,” Opt. Lett. 39, 4271–4273 (2014).
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K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, “Sculpting the vortex state of a spinor BEC,” Phys. Rev. Lett. 102, 030405 (2009).
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L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, “Creation and detection of skyrmions in a Bose-Einstein condensate,” Phys. Rev. Lett. 103, 250401 (2009).
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K. C. Wright, L. S. Leslie, and N. P. Bigelow, “Optical control of the internal and external angular momentum of a Bose-Einstein condensate,” Phys. Rev. A 77, 041601 (2008).
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K. C. Wright, L. S. Leslie, and N. P. Bigelow, “Raman coupling of Zeeman sublevels in an alkali-metal Bose-Einstein condensate,” Phys. Rev. A 78, 053412 (2008).
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A. Hansen, J. T. Schultz, and N. P. Bigelow, “Full Bloch Bose-Einstein condensates,” in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper LTu1I.2.

A. Hansen, J. T. Schultz, and N. P. Bigelow, “Measuring the Gouy phase of matter waves using full Bloch Bose–Einstein condensates,” in The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement Meeting, OSA Technical Digest (Optical Society of America, 2013), paper M6.64.

Bolbasova, L. A.

V. P. Lukin, O. V. Angelski, L. A. Bolbasova, E. A. Kopylov, M. V. Tuev, and V. V. Nosov, “Comparison of singular-optical and statistical approaches for investigations of turbulence tasks,” Proc. SPIE 9066, 906612 (2013).
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M. O. Borgh and J. Ruostekoski, “Topological interface engineering and defect crossing in ultracold atomic gases,” Phys. Rev. Lett. 109, 015302 (2012).
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Brown, T. G.

Cardano, F.

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J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, “Observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture,” Phys. Rev. Lett. 111, 245301 (2013).
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J. Choi, W. J. Kwon, and Y. Shin, “Observation of topologically stable 2D skyrmions in an antiferromagnetic spinor Bose-Einstein condensate,” Phys. Rev. Lett. 108, 035301 (2012).
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Y.-J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
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Cornell, E. A.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
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D’Ambrosio, V.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
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I. G. da Paz, P. L. Saldanha, M. C. Nemes, and J. G. Peixoto de Faria, “Experimental proposal for measuring the Gouy phase of matter waves,” New J. Phys. 13, 125005 (2011).
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J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Colloquium: artificial gauge potential for neutral atoms,” Rev. Mod. Phys. 83, 1523–1543 (2011).
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Das Sarma, S.

C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083–1159 (2008).
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de Lisio, C.

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
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M. R. Dennis, “Polarization singularity anisotropy: determining monstardom,” Opt. Lett. 33, 2572–2574 (2008).
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M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
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Deutsch, B. M.

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, “Creation and detection of skyrmions in a Bose-Einstein condensate,” Phys. Rev. Lett. 103, 250401 (2009).
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Dowling, J. P.

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose–Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95, 173601 (2005).
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Dürr, S.

C. Vo, S. Riedl, S. Baur, G. Rempe, and S. Dürr, “Coherent logic gate for light pulses based on storage in a Bose–Einstein condensate,” Phys. Rev. Lett. 109, 263602 (2012).
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Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Evans, S.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam-Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
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Ezawa, M.

X. Zhang, M. Ezawa, and Y. Zhou, “Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions,” Sci. Rep. 5, 9400 (2015).
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Felde, C. V.

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photon. News 23(4), 25–29 (2012).
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Fewell, M. P.

M. P. Fewell, “Adiabatic elimination, the rotating-wave approximation and two-photon transitions,” Opt. Commun. 253, 125–137 (2005).
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Fickler, R.

R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Quantum entanglement of complex photon polarization patterns in vector beams,” Phys. Rev. A 89, 060301(R) (2014).
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Freedman, M.

C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083–1159 (2008).
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Freund, I.

I. Freund, M. S. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
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Galvez, E. J.

E. J. Galvez, B. L. Rojec, V. Kumar, and N. K. Viswanathan, “Generation of isolated asymmetric umbilics in light’s polarization,” Phys. Rev. A 89, 031801R (2014).
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E. J. Galvez, S. Khadka, W. H. Schubert, and S. Nomoto, “Poincaré-beam patterns produced by nonseparable superpositions of Laguerre-Gauss and polarization modes of light,” Appl. Opt. 51, 2925–2934 (2012).
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Gerbier, F.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Colloquium: artificial gauge potential for neutral atoms,” Rev. Mod. Phys. 83, 1523–1543 (2011).
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Gutiérrez-Vega, J. C.

D. Lopez-Mago, B. Perez-Garcia, A. Yepiz, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “Dynamics of polarization singularities in composite optical vortices,” J. Opt. 15, 044028 (2013).
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Haljan, P. C.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
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Hall, D. S.

M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, “Observation of Dirac monopoles in a synthetic magnetic field,” Nature 505, 657–660 (2014).
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M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

Hannay, J. H.

M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[Crossref]

Hanneken, C.

N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, “Writing and deleting single magnetic skyrmions,” Science 341, 636–639 (2013).
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Hansen, A.

J. T. Schultz, A. Hansen, J. D. Murphree, M. Jayaseelan, and N. P. Bigelow, “Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate,” J. Mod. Opt. 63, 1–9 (2016).
[Crossref]

J. T. Schultz, A. Hansen, and N. P. Bigelow, “A Raman waveplate for spinor Bose-Einstein condensates,” Opt. Lett. 39, 4271–4273 (2014).
[Crossref]

K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, “Sculpting the vortex state of a spinor BEC,” Phys. Rev. Lett. 102, 030405 (2009).
[Crossref]

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, “Creation and detection of skyrmions in a Bose-Einstein condensate,” Phys. Rev. Lett. 103, 250401 (2009).
[Crossref]

A. Hansen, J. T. Schultz, and N. P. Bigelow, “Full Bloch Bose-Einstein condensates,” in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper LTu1I.2.

A. Hansen, J. T. Schultz, and N. P. Bigelow, “Measuring the Gouy phase of matter waves using full Bloch Bose–Einstein condensates,” in The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement Meeting, OSA Technical Digest (Optical Society of America, 2013), paper M6.64.

Hernandez-Aranda, R. I.

D. Lopez-Mago, B. Perez-Garcia, A. Yepiz, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “Dynamics of polarization singularities in composite optical vortices,” J. Opt. 15, 044028 (2013).
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Higbie, J. M.

L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate,” Nature 443, 312–315 (2006).
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Holbourn, A. H. S.

A. H. S. Holbourn, “Angular momentum of circularly polarized light,” Nature 137, 31 (1936).
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Hu, B.

L.-M. Kuang, J.-H. Li, and B. Hu, “Polarization and decoherence in a two-component Bose-Einstein condensate,” J. Opt. B 4, 295–299 (2002).
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Huhtamäki, J. A. M.

J. A. M. Huhtamäki, T. P. Simula, M. Kobayashi, and K. Machida, “Stable fractional vortices in the cyclic states of Bose-Einstein condensates,” Phys. Rev. A 80, 051601(R) (2009).
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Jayaseelan, M.

J. T. Schultz, A. Hansen, J. D. Murphree, M. Jayaseelan, and N. P. Bigelow, “Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate,” J. Mod. Opt. 63, 1–9 (2016).
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Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, “Spin-orbit-coupled Bose-Einstein condensates,” Nature 471, 83–86 (2011).
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Y.-J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[Crossref]

Juzeliunas, G.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Colloquium: artificial gauge potential for neutral atoms,” Rev. Mod. Phys. 83, 1523–1543 (2011).
[Crossref]

Kandel, S.

M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, “Observation of Dirac monopoles in a synthetic magnetic field,” Nature 505, 657–660 (2014).
[Crossref]

Kang, S.

S. W. Seo, S. Kang, W. J. Kwon, and Y. Shin, “Half-quantum vortices in an antiferromagnetic spinor Bose-Einstein condensate,” Phys. Rev. Lett. 115, 015301 (2015).
[Crossref]

J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, “Observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture,” Phys. Rev. Lett. 111, 245301 (2013).
[Crossref]

Kapale, K. T.

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose–Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95, 173601 (2005).
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Karimi, E.

Kawaguchi, Y.

Y. Kawaguchi and M. Ueda, “Symmetry classification of spinor Bose-Einstein condensates,” Phys. Rev. A 84, 053616 (2011).
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M. Kobayashi, Y. Kawaguchi, M. Nitta, and M. Ueda, “Collision dynamics and rung formation of non-Abelian vortices,” Phys. Rev. Lett. 103, 115301 (2009).
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Ketterle, W.

A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, “Coreless vortex formation in a spinor Bose-Einstein condensate,” Phys. Rev. Lett. 90, 140403 (2003).
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Khadka, S.

Kielpinski, D.

A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, “Coreless vortex formation in a spinor Bose-Einstein condensate,” Phys. Rev. Lett. 90, 140403 (2003).
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Kobayashi, M.

J. A. M. Huhtamäki, T. P. Simula, M. Kobayashi, and K. Machida, “Stable fractional vortices in the cyclic states of Bose-Einstein condensates,” Phys. Rev. A 80, 051601(R) (2009).
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M. Kobayashi, Y. Kawaguchi, M. Nitta, and M. Ueda, “Collision dynamics and rung formation of non-Abelian vortices,” Phys. Rev. Lett. 103, 115301 (2009).
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Kopylov, E. A.

V. P. Lukin, O. V. Angelski, L. A. Bolbasova, E. A. Kopylov, M. V. Tuev, and V. V. Nosov, “Comparison of singular-optical and statistical approaches for investigations of turbulence tasks,” Proc. SPIE 9066, 906612 (2013).
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Kuang, L.-M.

L.-M. Kuang, J.-H. Li, and B. Hu, “Polarization and decoherence in a two-component Bose-Einstein condensate,” J. Opt. B 4, 295–299 (2002).
[Crossref]

Kubetzka, A.

N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, “Writing and deleting single magnetic skyrmions,” Science 341, 636–639 (2013).
[Crossref]

Kumar, V.

V. Kumar and N. K. Viswanathan, “Topological structures in vector-vortex beam fields,” J. Opt. Soc. Am. B 31, A40–A45 (2014).
[Crossref]

E. J. Galvez, B. L. Rojec, V. Kumar, and N. K. Viswanathan, “Generation of isolated asymmetric umbilics in light’s polarization,” Phys. Rev. A 89, 031801R (2014).
[Crossref]

V. Kumar and N. K. Viswanathan, “The Pancharatnam-Berry phase in polarization singular beams,” J. Opt. 15, 044026 (2013).
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G. M. Philip, V. Kumar, G. Milione, and N. K. Viswanathan, “Manifestation of the Gouy phase in vector-vortex beams,” Opt. Lett. 37, 2667–2669 (2012).
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Kwon, W. J.

S. W. Seo, S. Kang, W. J. Kwon, and Y. Shin, “Half-quantum vortices in an antiferromagnetic spinor Bose-Einstein condensate,” Phys. Rev. Lett. 115, 015301 (2015).
[Crossref]

J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, “Observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture,” Phys. Rev. Lett. 111, 245301 (2013).
[Crossref]

J. Choi, W. J. Kwon, and Y. Shin, “Observation of topologically stable 2D skyrmions in an antiferromagnetic spinor Bose-Einstein condensate,” Phys. Rev. Lett. 108, 035301 (2012).
[Crossref]

Lapkiewicz, R.

R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Quantum entanglement of complex photon polarization patterns in vector beams,” Phys. Rev. A 89, 060301(R) (2014).
[Crossref]

Laurat, J.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
[Crossref]

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A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, “Coreless vortex formation in a spinor Bose-Einstein condensate,” Phys. Rev. Lett. 90, 140403 (2003).
[Crossref]

Leslie, L. S.

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, “Creation and detection of skyrmions in a Bose-Einstein condensate,” Phys. Rev. Lett. 103, 250401 (2009).
[Crossref]

K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, “Sculpting the vortex state of a spinor BEC,” Phys. Rev. Lett. 102, 030405 (2009).
[Crossref]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, “Raman coupling of Zeeman sublevels in an alkali-metal Bose-Einstein condensate,” Phys. Rev. A 78, 053412 (2008).
[Crossref]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, “Optical control of the internal and external angular momentum of a Bose-Einstein condensate,” Phys. Rev. A 77, 041601 (2008).
[Crossref]

Leslie, S. R.

L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate,” Nature 443, 312–315 (2006).
[Crossref]

Li, J.-H.

L.-M. Kuang, J.-H. Li, and B. Hu, “Polarization and decoherence in a two-component Bose-Einstein condensate,” J. Opt. B 4, 295–299 (2002).
[Crossref]

Lin, Y.-J.

Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, “Spin-orbit-coupled Bose-Einstein condensates,” Nature 471, 83–86 (2011).
[Crossref]

Y.-J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[Crossref]

Lopez-Mago, D.

D. Lopez-Mago, B. Perez-Garcia, A. Yepiz, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “Dynamics of polarization singularities in composite optical vortices,” J. Opt. 15, 044028 (2013).
[Crossref]

Lukin, V. P.

V. P. Lukin, O. V. Angelski, L. A. Bolbasova, E. A. Kopylov, M. V. Tuev, and V. V. Nosov, “Comparison of singular-optical and statistical approaches for investigations of turbulence tasks,” Proc. SPIE 9066, 906612 (2013).
[Crossref]

Machida, K.

J. A. M. Huhtamäki, T. P. Simula, M. Kobayashi, and K. Machida, “Stable fractional vortices in the cyclic states of Bose-Einstein condensates,” Phys. Rev. A 80, 051601(R) (2009).
[Crossref]

T. Ohmi and K. Machida, “Bose-Einstein condensation with internal degrees of freedom in alkali atom gases,” J. Phys. Soc. Jpn. 67, 1822–1825 (1998).
[Crossref]

Marrucci, L.

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Opt. Express (2)

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Figures (4)

Fig. 1.
Fig. 1.

(a) Bloch sphere. (b) Three-level lambda system.

Fig. 2.
Fig. 2.

Maps of the Stokes parameters. (a) Experiment and (b) theory maps of the Stokes parameters of a coreless vortex where = 2 in the spin state containing the vortex. Maps for each of the Stokes parameters S i are experimentally obtained using an atom-optic polarimetry technique [44] on essentially identical coreless vortices. S 1 and S 2 can be used to reconstruct the relative phase of the spin states. Examples of Stokes maps for = 1 coreless vortices appear in [44]. With this information, we create spin ellipse maps to classify the singularities. These Stokes parameters correspond to a spiral singularity with C -point index I C = 1 . The Stokes parameter S 0 would correspond to the total density of the cloud; in this case, the vortex state ( | ψ ) dominates at the edge of the cloud, so the shape of the spin density ( S 3 ) gives a good indication of the overall atomic density.

Fig. 3.
Fig. 3.

Maps of the local spin ellipses. The orientation of the major axis of the ellipses, ϕ / 2 , is found from maps of the Stokes parameters S 1 and S 2 . The ellipticity is determined by S 3 , and the ellipses are red and blue for right- and left-handed precession of the transverse components of the spin vector, respectively. When the population of the spin states is equal, the spin ellipse becomes a line (drawn in green). Spin lines show how the orientation of the major axes of the spin ellipses changes, revealing a fingerprint of the (a) star, (b) lemon, (c) spiral, and (d) saddle singularities.

Fig. 4.
Fig. 4.

Characterizing singularities by the C -point index. Spin lines representing the local orientation of the major axis of the spin ellipse are plotted over the condensate phase. The singularities here are the same as those in Fig. 3 with a narrowed plot range focused on the singularities. The local spinors in the x y plane are parallel to the major axes of the spin ellipses, and rotate by π and 2 π around the singularity for π - and 2 π -symmetric singularities corresponding to an | I C | of 1/2 [(a), (b)] and 1 [(c), (d)], respectively. The sign of I C is determined by the direction of rotation of the spinor as the contour is followed in a counterclockwise (positive) direction. Both (a) and (d) have negative indices because the spinors rotate clockwise, while in (b) and (c) the spinors rotate counterclockwise corresponding to positive indices. In (c) and (d) the extra singularities near the exterior are artifacts from the edge of the atomic cloud and imperfect separation of the spin components during the Stern–Gerlach operation and therefore do not correspond to actual singularities in the BEC.

Equations (6)

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ψ⃗ t = i 4 Δ [ | Ω A | 2 Ω A * Ω B Ω A Ω B * | Ω B | 2 ] ψ⃗ .
M ( t ) = cos Ω t 2 I + i sin Ω t 2 P ( 2 α , ϕ A B ) ,
P ( 2 α , ϕ A B ) = [ cos 2 α sin 2 α e i ϕ A B sin 2 α e i ϕ A B cos 2 α ]
ψ⃗ ( t ) = n ( ψ ψ ) n e i Φ 2 ( | ψ | e i ϕ 2 | ψ | e i ϕ 2 ) .
Φ = arctan ( tan Ω t 2 cos 2 α ) + π 2 ϕ A B + Ω t 2 ,
I C = 1 4 π ϕ ( r ) · d r ,

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