Abstract

We present a novel approach for the optical manipulation of neutral atoms in annular light structures produced by the phenomenon of conical refraction occurring in biaxial optical crystals. For a beam focused to a plane behind the crystal, the focal plane exhibits two concentric bright rings enclosing a ring of null intensity called the Poggendorff ring. We demonstrate both theoretically and experimentally that the Poggendorff dark ring of conical refraction is confined in three dimensions by regions of higher intensity. We derive the positions of the confining intensity maxima and minima and discuss the application of the Poggendorff ring for trapping ultra-cold atoms using the repulsive dipole force of blue-detuned light. We give analytical expressions for the trapping frequencies and potential depths along both the radial and the axial directions. Finally, we present realistic numerical simulations of the dynamics of a 87Rb Bose-Einstein condensate trapped inside the Poggendorff ring which are in good agreement with corresponding experimental results.

© 2015 Optical Society of America

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References

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  5. J.A. Stickney, D. Z. Anderson, and A. A. Zozulya, “Transistorlike behavior of a Bose-Einstein condensate in a triple-well potential,” Phys. Rev. A 75, 013608 (2007).
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    [Crossref]
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  33. T. Kalkandjiev and M. Bursukova, “Conical refraction: an experimental introduction,” Proc. SPIE 6994, 69940B (2008).
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  37. A. Turpin, Yu. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Free-space optical polarization demultiplexing and multiplexing by means of conical refraction,” Opt. Lett. 37, 4197–4199 (2012).
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  38. Yu. V. Loiko, A. Turpin, T. K. Kalkandjiev, E. U. Rafailov, and J. Mompart, “Generating a three-dimensional dark focus from a single conically refracted light beam,” Opt. Lett. 38, 4648–4651 (2013).
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    [Crossref] [PubMed]
  42. R. Grimm and M. Weidemüller, “Optical dipole traps for neutral atoms,” Adv. At. Mol. Opt. Phy. 42, 95–170 (2000).
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  43. A. Ashkin, “Trapping of Atoms by Resonance Radiation Pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
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  46. R. T. Darcy, D. McCloskey, K. E. Ballantine, B. D. Jennings, J. G. Lunney, P. R. Eastham, and J. F. Donegan, “White light conical diffraction,” Opt. Express 21, 20394–20403 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  51. L. Amico, A. Osterloh, and F. Cataliotti, “Quantum Many Particle Systems in Ring-Shaped Optical Lattices,” Phys. Rev. Lett. 95, 063201 (2005).
    [Crossref] [PubMed]
  52. M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems, (Oxford, 2012).
    [Crossref]
  53. Yu. V. Loiko, V. Ahufinger, R. Menchon-Enrich, G. Birkl, and J. Mompart, “Coherent injecting, extracting, and velocity-filtering of neutral atoms in a ring trap via spatial adiabatic passage,” Eur. Phys. J. D 68, 147 (2014).
    [Crossref]
  54. O. Morizot, Y. Colombe, V. Lorent, H. Perrin, and B. M. Garraway, “Ring trap for ultracold atoms,” Phys. Rev. A 74, 023617 (2006).
    [Crossref]
  55. D. Aghamalyan, L. Amico, and L. C. Kwek, “Effective dynamics of cold atoms flowing in two ring shaped optical potentials with tunable tunneling,” Phys. Rev. A 88, 063627 (2013).
    [Crossref]

2014 (6)

S Eckel, Jeffrey G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, “Hysteresis in a quantized superfluid atomtronic circuit,” Nature 506, 200–204 (2014).
[Crossref] [PubMed]

L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weintenberg, S. Nascimbène, J. Dalibard, and J. Beugnon, “Quench-induced supercurrents in an annular two-dimensional Bose gas,” Phys. Rev. Lett. 113, 135302 (2014).
[Crossref]

C. Ryu, K. C. Henderson, and M. G. Boshier, “Creation of matter wave Bessel beams and observation of quantized circulation in a BoseEinstein condensate,” New J. Phys. 16, 013046 (2014).
[Crossref]

Yu. V. Loiko, V. Ahufinger, R. Menchon-Enrich, G. Birkl, and J. Mompart, “Coherent injecting, extracting, and velocity-filtering of neutral atoms in a ring trap via spatial adiabatic passage,” Eur. Phys. J. D 68, 147 (2014).
[Crossref]

R. T. Darcy, D. McCloskey, K. E. Ballantine, J. G. Lunney, P. R. Eastham, and J. F. Donegan, “Conical diffraction intensity profiles generated using a top-hat input beam,” Opt. Express 22, 11290–11300 (2014).
[Crossref] [PubMed]

A. Turpin, Yu. V. Loiko, T. K. Kalkandjiev, H. Tomizawa, and J. Mompart, “Super-Gaussian conical refraction beam,” Opt. Lett. 39, 4349–4352 (2014).
[Crossref] [PubMed]

2013 (9)

A. Turpin, Yu. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Wave-vector and polarization dependence of conical refraction,” Opt. Express 21, 4503–4511 (2013).
[Crossref] [PubMed]

A. Turpin, Yu. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Multiple rings formation in cascaded conical refraction,” Opt. Lett. 38, 1455–1457 (2013).
[Crossref] [PubMed]

R. T. Darcy, D. McCloskey, K. E. Ballantine, B. D. Jennings, J. G. Lunney, P. R. Eastham, and J. F. Donegan, “White light conical diffraction,” Opt. Express 21, 20394–20403 (2013).
[Crossref] [PubMed]

A. Turpin, V. Shvedov, C Hnatonsky, Yu. V. Loiko, J. Mompart, and W. Krolikowski, “Optical vault: a reconfigurable bottle beam based on conical refraction of light,” Opt. Express,  21, 26335–26340 (2013).
[Crossref] [PubMed]

Yu. V. Loiko, A. Turpin, T. K. Kalkandjiev, E. U. Rafailov, and J. Mompart, “Generating a three-dimensional dark focus from a single conically refracted light beam,” Opt. Lett. 38, 4648–4651 (2013).
[Crossref] [PubMed]

D. Aghamalyan, L. Amico, and L. C. Kwek, “Effective dynamics of cold atoms flowing in two ring shaped optical potentials with tunable tunneling,” Phys. Rev. A 88, 063627 (2013).
[Crossref]

K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, “Driving Phase Slips in a Superfluid Atom Circuit with a Rotating Weak Link,” Phys. Rev. Lett. 110, 025302 (2013).
[Crossref] [PubMed]

C. Ryu, P. W. Blackburn, A. A. Blinova, and M. G. Boshier, “Experimental Realization of Josephson Junctions for an Atom SQUID,” Phys. Rev. Lett. 111, 205301 (2013).
[Crossref] [PubMed]

A. I. Yakimenko, Yu. M. Bidasyuk, O. O. Prikhodko, S. I. Vilchinskii, E. A. Ostrovskaya, and Yu. S. Kivshar, “Optical tweezers for vortex rings in Bose-Einstein condensates,” Phys. Rev. A 88, 043637 (2013).
[Crossref]

2012 (1)

2011 (3)

V. Peet, “Conical refraction and formation of multiring focal image with Laguerre–Gauss light beams,” Opt. Lett. 36, 2913–2915 (2011).
[Crossref] [PubMed]

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Observation of Persistent Flow of a Bose-Einstein Condensate in a Toroidal Trap,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

T. Lauber, J. Küber, O. Wille, and G. Birkl, “Optimized Bose-Einstein-condensate production in a dipole trap based on a 1070-nm multifrequency laser: Influence of enhanced two-body loss on the evaporation process,” Phys. Rev. A 84, 043641 (2011).
[Crossref]

2010 (2)

M.V. Berry, “Conical diffraction from an N-crystal cascade,” J. of Optics,  12, 075704 (2010).
[Crossref]

M.R. Dennis, R.P. King, B. Jack, K. O. Holleran, and M.J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[Crossref]

2009 (2)

R. A. Pepino, J. Cooper, D. Z. Anderson, and M. J. Holland, “Atomtronic Circuits of Diodes and Transistors,” Phys. Rev. Lett. 103, 140405 (2009).
[Crossref] [PubMed]

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009) and the references therein.
[Crossref]

2008 (4)

J. J. Thorn, E. A. Schoene, T. Li, and D. A. Steck, “Experimental Realization of an Optical One-Way Barrier for Neutral Atoms,” Phys. Rev. Lett. 100, 240407 (2008).
[Crossref] [PubMed]

T. Kalkandjiev and M. Bursukova, “Conical refraction: an experimental introduction,” Proc. SPIE 6994, 69940B (2008).
[Crossref]

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B: At. Mol. Opt. Phys. 41, 211001 (2008).
[Crossref]

S. K. Schnelle, E. D. van Ooijen, M. J. Davis, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Versatile two-dimensional potentials for ultra-cold atoms,” Opt. Express 16, 1405–1412 (2008).
[Crossref] [PubMed]

2007 (6)

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Öhberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express 15, 8619–8625 (2007).
[Crossref] [PubMed]

B. T. Seaman, M. Krämer, D. Z. Anderson, and M. J. Holland, “Atomtronics: Ultracold-atom analogs of electronic devices,” Phys. Rev. A 75, 023615 (2007).
[Crossref]

J.A. Stickney, D. Z. Anderson, and A. A. Zozulya, “Transistorlike behavior of a Bose-Einstein condensate in a triple-well potential,” Phys. Rev. A 75, 013608 (2007).
[Crossref]

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, “Holographic quantum states,”Phys. Rev. Lett. 99, 260401 (2007).
[Crossref]

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[Crossref]

S. E. Olson, M. L. Terraciano, M. Bashkansky, and F. K. Fatemi, “Cold-atom confinement in an all-optical dark ring trap,” Phys. Rev. A 76, 061404 (2007).
[Crossref]

2006 (2)

E. Courtade, O. Houde, J.-F. Clément, P. Verkerk, and D. Hennequin, “Dark optical lattice of ring traps for cold atoms,” Phys. Rev. A 74, 031403 (2006).
[Crossref]

O. Morizot, Y. Colombe, V. Lorent, H. Perrin, and B. M. Garraway, “Ring trap for ultracold atoms,” Phys. Rev. A 74, 023617 (2006).
[Crossref]

2005 (1)

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum Many Particle Systems in Ring-Shaped Optical Lattices,” Phys. Rev. Lett. 95, 063201 (2005).
[Crossref] [PubMed]

2004 (2)

M. V. Berry, “Conical diffraction asymptotics: Fine structure of Poggendorff rings and axial spike,” J. Opt. A: Pure Appl. Opt. 6, 289–300 (2004).
[Crossref]

A. Ruschhaupt and J. G. Muga, “Atom diode: A laser device for a unidirectional transmission of ground-state atoms,” Phys. Rev. A 70, 061604 (2004).
[Crossref]

2002 (1)

T. Freegarde and K. Dholakia, “Cavity-enhanced toroidal dipole force traps for dark-field seeking species,” Opt. Commun. 201, 99 (2002).
[Crossref]

2001 (3)

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. Lond. A 457, 2251–2263 (2001).
[Crossref]

M. Barrett, J. Sauer, and M. S. Chapman, “All-Optical Formation of an Atomic Bose-Einstein Condensate,” Phys. Rev. Lett. 87, 010404 (2001).
[Crossref] [PubMed]

G. Birkl, F. B. J. Buchkremer, R. Dumke, and W. Ertmer, “Atom optics with microfabricated optical elements,” Opt. Commun. 191, 67–81 (2001);;T. Müther, J. Nes, A.-L. Gehrmann, M. Volk, W. Ertmer, G. Birkl, M. Gruber, and J. Jahns, “Atomic quantum systems in optical micro-structures,” J. Phys. Conf. Ser. 19, 97–101 (2005).
[Crossref]

2000 (3)

E. M. Wright, J. Arlt, and K. Dholakia, “Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams,” Phys. Rev. A 63, 013608 (2000).
[Crossref]

R. Grimm and M. Weidemüller, “Optical dipole traps for neutral atoms,” Adv. At. Mol. Opt. Phy. 42, 95–170 (2000).
[Crossref]

A. Belafhal, “Theoretical intensity distribution of internal conical refraction,” Opt. Commun. 178, 257–265 (2000).
[Crossref]

1999 (2)

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of coherent light beams,” Opt. Commun. 167, 1–5 (1999).
[Crossref]

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750 (1999).
[Crossref]

1998 (1)

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, 2027 (1998).
[Crossref]

1978 (2)

A. Ashkin, “Trapping of Atoms by Resonance Radiation Pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
[Crossref]

A. M. Belskii and A. P. Khapalyuk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. (USSR) 44, 436–439 (1978).

1837 (2)

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1837).

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals, Trans. R. Irish Acad. 17, 145–158 (1837).

Aghamalyan, D.

D. Aghamalyan, L. Amico, and L. C. Kwek, “Effective dynamics of cold atoms flowing in two ring shaped optical potentials with tunable tunneling,” Phys. Rev. A 88, 063627 (2013).
[Crossref]

Ahufinger, V.

Yu. V. Loiko, V. Ahufinger, R. Menchon-Enrich, G. Birkl, and J. Mompart, “Coherent injecting, extracting, and velocity-filtering of neutral atoms in a ring trap via spatial adiabatic passage,” Eur. Phys. J. D 68, 147 (2014).
[Crossref]

M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems, (Oxford, 2012).
[Crossref]

Amico, L.

D. Aghamalyan, L. Amico, and L. C. Kwek, “Effective dynamics of cold atoms flowing in two ring shaped optical potentials with tunable tunneling,” Phys. Rev. A 88, 063627 (2013).
[Crossref]

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum Many Particle Systems in Ring-Shaped Optical Lattices,” Phys. Rev. Lett. 95, 063201 (2005).
[Crossref] [PubMed]

Andersen, M. F.

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A. Turpin, Yu. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Multiple rings formation in cascaded conical refraction,” Opt. Lett. 38, 1455–1457 (2013).
[Crossref] [PubMed]

Yu. V. Loiko, A. Turpin, T. K. Kalkandjiev, E. U. Rafailov, and J. Mompart, “Generating a three-dimensional dark focus from a single conically refracted light beam,” Opt. Lett. 38, 4648–4651 (2013).
[Crossref] [PubMed]

A. Turpin, Yu. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Wave-vector and polarization dependence of conical refraction,” Opt. Express 21, 4503–4511 (2013).
[Crossref] [PubMed]

A. Turpin, Yu. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Free-space optical polarization demultiplexing and multiplexing by means of conical refraction,” Opt. Lett. 37, 4197–4199 (2012).
[Crossref] [PubMed]

T. Lauber, J. Küber, F. Schmaltz, J. Mompart, and G. Birkl, “Coherent transport of Bose-Einstein condensates in a mesoscopic storage ring,” submitted for publication.

Morizot, O.

O. Morizot, Y. Colombe, V. Lorent, H. Perrin, and B. M. Garraway, “Ring trap for ultracold atoms,” Phys. Rev. A 74, 023617 (2006).
[Crossref]

Muga, J. G.

A. Ruschhaupt and J. G. Muga, “Atom diode: A laser device for a unidirectional transmission of ground-state atoms,” Phys. Rev. A 70, 061604 (2004).
[Crossref]

Muniz, S. R.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Observation of Persistent Flow of a Bose-Einstein Condensate in a Toroidal Trap,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Murray, N.

S Eckel, Jeffrey G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, “Hysteresis in a quantized superfluid atomtronic circuit,” Nature 506, 200–204 (2014).
[Crossref] [PubMed]

Nascimbène, S.

L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weintenberg, S. Nascimbène, J. Dalibard, and J. Beugnon, “Quench-induced supercurrents in an annular two-dimensional Bose gas,” Phys. Rev. Lett. 113, 135302 (2014).
[Crossref]

Natarajan, V.

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, “Holographic quantum states,”Phys. Rev. Lett. 99, 260401 (2007).
[Crossref]

Öhberg, P.

Olson, S. E.

S. E. Olson, M. L. Terraciano, M. Bashkansky, and F. K. Fatemi, “Cold-atom confinement in an all-optical dark ring trap,” Phys. Rev. A 76, 061404 (2007).
[Crossref]

Osterloh, A.

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum Many Particle Systems in Ring-Shaped Optical Lattices,” Phys. Rev. Lett. 95, 063201 (2005).
[Crossref] [PubMed]

Ostrovskaya, E. A.

A. I. Yakimenko, Yu. M. Bidasyuk, O. O. Prikhodko, S. I. Vilchinskii, E. A. Ostrovskaya, and Yu. S. Kivshar, “Optical tweezers for vortex rings in Bose-Einstein condensates,” Phys. Rev. A 88, 043637 (2013).
[Crossref]

Ozeri, R.

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750 (1999).
[Crossref]

Padgett, M. J.

Padgett, M.J.

M.R. Dennis, R.P. King, B. Jack, K. O. Holleran, and M.J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[Crossref]

Peet, V.

Pepino, R. A.

R. A. Pepino, J. Cooper, D. Z. Anderson, and M. J. Holland, “Atomtronic Circuits of Diodes and Transistors,” Phys. Rev. Lett. 103, 140405 (2009).
[Crossref] [PubMed]

Perrin, H.

O. Morizot, Y. Colombe, V. Lorent, H. Perrin, and B. M. Garraway, “Ring trap for ultracold atoms,” Phys. Rev. A 74, 023617 (2006).
[Crossref]

Phillips, W. D.

S Eckel, Jeffrey G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, “Hysteresis in a quantized superfluid atomtronic circuit,” Nature 506, 200–204 (2014).
[Crossref] [PubMed]

K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, “Driving Phase Slips in a Superfluid Atom Circuit with a Rotating Weak Link,” Phys. Rev. Lett. 110, 025302 (2013).
[Crossref] [PubMed]

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Observation of Persistent Flow of a Bose-Einstein Condensate in a Toroidal Trap,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, “Holographic quantum states,”Phys. Rev. Lett. 99, 260401 (2007).
[Crossref]

Prikhodko, O. O.

A. I. Yakimenko, Yu. M. Bidasyuk, O. O. Prikhodko, S. I. Vilchinskii, E. A. Ostrovskaya, and Yu. S. Kivshar, “Optical tweezers for vortex rings in Bose-Einstein condensates,” Phys. Rev. A 88, 043637 (2013).
[Crossref]

Pritchard, D. E.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009) and the references therein.
[Crossref]

Rafailov, E. U.

Ramanathan, A.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Observation of Persistent Flow of a Bose-Einstein Condensate in a Toroidal Trap,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Riis, E.

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B: At. Mol. Opt. Phys. 41, 211001 (2008).
[Crossref]

Rubinsztein-Dunlop, H.

Ruschhaupt, A.

A. Ruschhaupt and J. G. Muga, “Atom diode: A laser device for a unidirectional transmission of ground-state atoms,” Phys. Rev. A 70, 061604 (2004).
[Crossref]

Ryu, C.

C. Ryu, K. C. Henderson, and M. G. Boshier, “Creation of matter wave Bessel beams and observation of quantized circulation in a BoseEinstein condensate,” New J. Phys. 16, 013046 (2014).
[Crossref]

C. Ryu, P. W. Blackburn, A. A. Blinova, and M. G. Boshier, “Experimental Realization of Josephson Junctions for an Atom SQUID,” Phys. Rev. Lett. 111, 205301 (2013).
[Crossref] [PubMed]

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, “Holographic quantum states,”Phys. Rev. Lett. 99, 260401 (2007).
[Crossref]

Sanpera, A.

M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems, (Oxford, 2012).
[Crossref]

Sauer, J.

M. Barrett, J. Sauer, and M. S. Chapman, “All-Optical Formation of an Atomic Bose-Einstein Condensate,” Phys. Rev. Lett. 87, 010404 (2001).
[Crossref] [PubMed]

Schmaltz, F.

T. Lauber, J. Küber, F. Schmaltz, J. Mompart, and G. Birkl, “Coherent transport of Bose-Einstein condensates in a mesoscopic storage ring,” submitted for publication.

Schmiedmayer, J.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009) and the references therein.
[Crossref]

Schnelle, S. K.

Schoene, E. A.

J. J. Thorn, E. A. Schoene, T. Li, and D. A. Steck, “Experimental Realization of an Optical One-Way Barrier for Neutral Atoms,” Phys. Rev. Lett. 100, 240407 (2008).
[Crossref] [PubMed]

Seaman, B. T.

B. T. Seaman, M. Krämer, D. Z. Anderson, and M. J. Holland, “Atomtronics: Ultracold-atom analogs of electronic devices,” Phys. Rev. A 75, 023615 (2007).
[Crossref]

Shvedov, V.

Stamper-Kurn, D. M.

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, 2027 (1998).
[Crossref]

Steck, D. A.

J. J. Thorn, E. A. Schoene, T. Li, and D. A. Steck, “Experimental Realization of an Optical One-Way Barrier for Neutral Atoms,” Phys. Rev. Lett. 100, 240407 (2008).
[Crossref] [PubMed]

Stenger, J.

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, 2027 (1998).
[Crossref]

Stepanov, M. A.

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of coherent light beams,” Opt. Commun. 167, 1–5 (1999).
[Crossref]

Stickney, J.A.

J.A. Stickney, D. Z. Anderson, and A. A. Zozulya, “Transistorlike behavior of a Bose-Einstein condensate in a triple-well potential,” Phys. Rev. A 75, 013608 (2007).
[Crossref]

Terraciano, M. L.

S. E. Olson, M. L. Terraciano, M. Bashkansky, and F. K. Fatemi, “Cold-atom confinement in an all-optical dark ring trap,” Phys. Rev. A 76, 061404 (2007).
[Crossref]

Thorn, J. J.

J. J. Thorn, E. A. Schoene, T. Li, and D. A. Steck, “Experimental Realization of an Optical One-Way Barrier for Neutral Atoms,” Phys. Rev. Lett. 100, 240407 (2008).
[Crossref] [PubMed]

Tomizawa, H.

Turpin, A.

van Ooijen, E. D.

Verkerk, P.

E. Courtade, O. Houde, J.-F. Clément, P. Verkerk, and D. Hennequin, “Dark optical lattice of ring traps for cold atoms,” Phys. Rev. A 74, 031403 (2006).
[Crossref]

Vilchinskii, S. I.

A. I. Yakimenko, Yu. M. Bidasyuk, O. O. Prikhodko, S. I. Vilchinskii, E. A. Ostrovskaya, and Yu. S. Kivshar, “Optical tweezers for vortex rings in Bose-Einstein condensates,” Phys. Rev. A 88, 043637 (2013).
[Crossref]

Weidemüller, M.

R. Grimm and M. Weidemüller, “Optical dipole traps for neutral atoms,” Adv. At. Mol. Opt. Phy. 42, 95–170 (2000).
[Crossref]

Weintenberg, C.

L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weintenberg, S. Nascimbène, J. Dalibard, and J. Beugnon, “Quench-induced supercurrents in an annular two-dimensional Bose gas,” Phys. Rev. Lett. 113, 135302 (2014).
[Crossref]

Wille, O.

T. Lauber, J. Küber, O. Wille, and G. Birkl, “Optimized Bose-Einstein-condensate production in a dipole trap based on a 1070-nm multifrequency laser: Influence of enhanced two-body loss on the evaporation process,” Phys. Rev. A 84, 043641 (2011).
[Crossref]

Wright, A. J.

Wright, E. M.

E. M. Wright, J. Arlt, and K. Dholakia, “Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams,” Phys. Rev. A 63, 013608 (2000).
[Crossref]

Wright, K. C.

K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, “Driving Phase Slips in a Superfluid Atom Circuit with a Rotating Weak Link,” Phys. Rev. Lett. 110, 025302 (2013).
[Crossref] [PubMed]

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Observation of Persistent Flow of a Bose-Einstein Condensate in a Toroidal Trap,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Yakimenko, A. I.

A. I. Yakimenko, Yu. M. Bidasyuk, O. O. Prikhodko, S. I. Vilchinskii, E. A. Ostrovskaya, and Yu. S. Kivshar, “Optical tweezers for vortex rings in Bose-Einstein condensates,” Phys. Rev. A 88, 043637 (2013).
[Crossref]

Zelan, M.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Observation of Persistent Flow of a Bose-Einstein Condensate in a Toroidal Trap,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Zozulya, A. A.

J.A. Stickney, D. Z. Anderson, and A. A. Zozulya, “Transistorlike behavior of a Bose-Einstein condensate in a triple-well potential,” Phys. Rev. A 75, 013608 (2007).
[Crossref]

Adv. At. Mol. Opt. Phy. (1)

R. Grimm and M. Weidemüller, “Optical dipole traps for neutral atoms,” Adv. At. Mol. Opt. Phy. 42, 95–170 (2000).
[Crossref]

Eur. Phys. J. D (1)

Yu. V. Loiko, V. Ahufinger, R. Menchon-Enrich, G. Birkl, and J. Mompart, “Coherent injecting, extracting, and velocity-filtering of neutral atoms in a ring trap via spatial adiabatic passage,” Eur. Phys. J. D 68, 147 (2014).
[Crossref]

J. of Optics (1)

M.V. Berry, “Conical diffraction from an N-crystal cascade,” J. of Optics,  12, 075704 (2010).
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J. Opt. A: Pure Appl. Opt. (1)

M. V. Berry, “Conical diffraction asymptotics: Fine structure of Poggendorff rings and axial spike,” J. Opt. A: Pure Appl. Opt. 6, 289–300 (2004).
[Crossref]

J. Phys. B: At. Mol. Opt. Phys. (1)

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B: At. Mol. Opt. Phys. 41, 211001 (2008).
[Crossref]

Nat. Phys. (1)

M.R. Dennis, R.P. King, B. Jack, K. O. Holleran, and M.J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[Crossref]

Nature (1)

S Eckel, Jeffrey G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, “Hysteresis in a quantized superfluid atomtronic circuit,” Nature 506, 200–204 (2014).
[Crossref] [PubMed]

New J. Phys. (1)

C. Ryu, K. C. Henderson, and M. G. Boshier, “Creation of matter wave Bessel beams and observation of quantized circulation in a BoseEinstein condensate,” New J. Phys. 16, 013046 (2014).
[Crossref]

Opt. Commun. (4)

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of coherent light beams,” Opt. Commun. 167, 1–5 (1999).
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A. Belafhal, “Theoretical intensity distribution of internal conical refraction,” Opt. Commun. 178, 257–265 (2000).
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T. Freegarde and K. Dholakia, “Cavity-enhanced toroidal dipole force traps for dark-field seeking species,” Opt. Commun. 201, 99 (2002).
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G. Birkl, F. B. J. Buchkremer, R. Dumke, and W. Ertmer, “Atom optics with microfabricated optical elements,” Opt. Commun. 191, 67–81 (2001);;T. Müther, J. Nes, A.-L. Gehrmann, M. Volk, W. Ertmer, G. Birkl, M. Gruber, and J. Jahns, “Atomic quantum systems in optical micro-structures,” J. Phys. Conf. Ser. 19, 97–101 (2005).
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Opt. Express (6)

Opt. Lett. (5)

Opt. Spectrosc. (USSR) (1)

A. M. Belskii and A. P. Khapalyuk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. (USSR) 44, 436–439 (1978).

Phys. Rev. A (11)

E. Courtade, O. Houde, J.-F. Clément, P. Verkerk, and D. Hennequin, “Dark optical lattice of ring traps for cold atoms,” Phys. Rev. A 74, 031403 (2006).
[Crossref]

A. I. Yakimenko, Yu. M. Bidasyuk, O. O. Prikhodko, S. I. Vilchinskii, E. A. Ostrovskaya, and Yu. S. Kivshar, “Optical tweezers for vortex rings in Bose-Einstein condensates,” Phys. Rev. A 88, 043637 (2013).
[Crossref]

S. E. Olson, M. L. Terraciano, M. Bashkansky, and F. K. Fatemi, “Cold-atom confinement in an all-optical dark ring trap,” Phys. Rev. A 76, 061404 (2007).
[Crossref]

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750 (1999).
[Crossref]

E. M. Wright, J. Arlt, and K. Dholakia, “Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams,” Phys. Rev. A 63, 013608 (2000).
[Crossref]

B. T. Seaman, M. Krämer, D. Z. Anderson, and M. J. Holland, “Atomtronics: Ultracold-atom analogs of electronic devices,” Phys. Rev. A 75, 023615 (2007).
[Crossref]

A. Ruschhaupt and J. G. Muga, “Atom diode: A laser device for a unidirectional transmission of ground-state atoms,” Phys. Rev. A 70, 061604 (2004).
[Crossref]

J.A. Stickney, D. Z. Anderson, and A. A. Zozulya, “Transistorlike behavior of a Bose-Einstein condensate in a triple-well potential,” Phys. Rev. A 75, 013608 (2007).
[Crossref]

T. Lauber, J. Küber, O. Wille, and G. Birkl, “Optimized Bose-Einstein-condensate production in a dipole trap based on a 1070-nm multifrequency laser: Influence of enhanced two-body loss on the evaporation process,” Phys. Rev. A 84, 043641 (2011).
[Crossref]

O. Morizot, Y. Colombe, V. Lorent, H. Perrin, and B. M. Garraway, “Ring trap for ultracold atoms,” Phys. Rev. A 74, 023617 (2006).
[Crossref]

D. Aghamalyan, L. Amico, and L. C. Kwek, “Effective dynamics of cold atoms flowing in two ring shaped optical potentials with tunable tunneling,” Phys. Rev. A 88, 063627 (2013).
[Crossref]

Phys. Rev. Lett. (11)

K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, “Driving Phase Slips in a Superfluid Atom Circuit with a Rotating Weak Link,” Phys. Rev. Lett. 110, 025302 (2013).
[Crossref] [PubMed]

C. Ryu, P. W. Blackburn, A. A. Blinova, and M. G. Boshier, “Experimental Realization of Josephson Junctions for an Atom SQUID,” Phys. Rev. Lett. 111, 205301 (2013).
[Crossref] [PubMed]

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum Many Particle Systems in Ring-Shaped Optical Lattices,” Phys. Rev. Lett. 95, 063201 (2005).
[Crossref] [PubMed]

J. J. Thorn, E. A. Schoene, T. Li, and D. A. Steck, “Experimental Realization of an Optical One-Way Barrier for Neutral Atoms,” Phys. Rev. Lett. 100, 240407 (2008).
[Crossref] [PubMed]

R. A. Pepino, J. Cooper, D. Z. Anderson, and M. J. Holland, “Atomtronic Circuits of Diodes and Transistors,” Phys. Rev. Lett. 103, 140405 (2009).
[Crossref] [PubMed]

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, 2027 (1998).
[Crossref]

M. Barrett, J. Sauer, and M. S. Chapman, “All-Optical Formation of an Atomic Bose-Einstein Condensate,” Phys. Rev. Lett. 87, 010404 (2001).
[Crossref] [PubMed]

A. Ashkin, “Trapping of Atoms by Resonance Radiation Pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
[Crossref]

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, “Holographic quantum states,”Phys. Rev. Lett. 99, 260401 (2007).
[Crossref]

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Observation of Persistent Flow of a Bose-Einstein Condensate in a Toroidal Trap,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weintenberg, S. Nascimbène, J. Dalibard, and J. Beugnon, “Quench-induced supercurrents in an annular two-dimensional Bose gas,” Phys. Rev. Lett. 113, 135302 (2014).
[Crossref]

Proc. R. Soc. Lond. A (1)

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. Lond. A 457, 2251–2263 (2001).
[Crossref]

Proc. SPIE (1)

T. Kalkandjiev and M. Bursukova, “Conical refraction: an experimental introduction,” Proc. SPIE 6994, 69940B (2008).
[Crossref]

Prog. Opt. (1)

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[Crossref]

Rev. Mod. Phys. (1)

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009) and the references therein.
[Crossref]

Trans. R. Irish Acad. (2)

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1837).

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals, Trans. R. Irish Acad. 17, 145–158 (1837).

Other (3)

J. G. Lee and W. T. Hill, “Spatial shaping for generating arbitrary optical dipoles traps for ultracold degenerate gases,” arXiv:1406.4084.

T. Lauber, J. Küber, F. Schmaltz, J. Mompart, and G. Birkl, “Coherent transport of Bose-Einstein condensates in a mesoscopic storage ring,” submitted for publication.

M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems, (Oxford, 2012).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Intensity and polarization distribution (depicted with yellow double arrows) of conical refraction with input beams of circular (a) and linear vertical (b) polarization. The dark ring between the two bright ones is known as the Poggendorff dark ring (PDR).

Fig. 2
Fig. 2

Normalized CR intensity for a CP Gaussian input beam as given by Eq. (11) along the radial direction (a) at the focal plane and (b) along the axial direction at the radial position of the PDR (ξ = ξ0). Blue solid circles represent experimental data with an experimental uncertainty of 5 % along both axis.

Fig. 3
Fig. 3

(a) Normalized light intensity in three dimensions near the PDR. (b) 2D contour density plot near the PDR of the normalized light intensity calculated from Eqs. (9) and (11) and for ρ0 = R0/w0 = 20. Color map: black = null intensity, white = high intensity.

Fig. 4
Fig. 4

(a) Profile of the trapping potential at Z = 0, i.e. at the focal plane (dashed curve), and at Z = 4 (solid curve) where the inner and the outer bright rings of CR have equal maximum intensity. (b) Coefficient Ar as a function of Z. The analytical expression for the Ar(Z) is given by Eq. (15).

Fig. 5
Fig. 5

(a) Plot of the atomic density from the numerical simulation of a trapped 87Rb BEC after 30ms of expansion in the ring V r = 1 2 m ω r 2 ( r ( R 0 0.541 w 0 ) ) 2, with the frequency ωr = 2π × 265Hz being calculated using the harmonic approximation. Parameter values used for the simulation: R0 = 170μm, w0 = 18μm, P = 27mW, wz = 2π × 500Hz, as = 5.45nm and N = 12000 atoms. (b) Experimental density distribution of a trapped 87Rb BEC in the CR ring potential using the same experimental parameters as for the numerical simulation, with the exception of the axial confinement, that was made using a red-detuned Gaussian beam focused with a cylindrical lens, providing a measured trapping frequency of w z exp = 2 π × ( 169 ± 2 ) Hz. The measured radial trapping frequency provided by the CR PDR was ω r exp = 2 π × ( 300 ± 20 ) Hz. (c) Numerical simulation under the same conditions as in (a) but including the scattering induced by the position spreading during detection. Each Fig. is 600μm × 600μm. Color map: dark blue (red) corresponds to null (high) intensity. White dashed lines in (c) indicate the position of the cross-dipole trap with respect to the PDR, being both of them orthogonal to the gravity field. The waist radius of each beam from the cross-dipole trap is 25μm.

Fig. 6
Fig. 6

Radial sections of the atomic density of the BEC (a) before and (b) after 30ms of azimuthal expansion of the BEC trapped in the harmonic potential V r = 1 2 m ω r 2 ( r ( R 0 0.541 w 0 ) ) 2 (black-dashed line) and in the Poggendroff dark ring of CR (red-solid line). Black-dashed and red-dotted lines are the corresponding trapping potentials. Parameter values: R0 = 170μm, w0 = 18μm, P = 27mW, wr = 2π × 265Hz, wz = 2π × 500Hz, as = 5.45nm and N = 12000 atoms. The ground state (a) is obtained by adding an extra confinement (wazi = 2π × 265Hz) in the azimuthal direction in order to reproduce the loading of the BEC in the CR ring trap.

Tables (1)

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Table 1 Positions of the Poggendorff dark ring and of the maxima in the radial (ξ±) and axial (Z±) directions.

Equations (18)

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E ( ρ , Z ) = ( B C + C S S B C C ) e 0 ,
B C ( ρ , Z ) = 1 2 π 0 η a ( η ) e i Z 4 η 2 cos ( η ρ 0 ) J 0 ( η ρ ) d η ,
B S ( ρ , Z ) = 1 2 π 0 η a ( η ) e i Z 4 η 2 sin ( η ρ 0 ) J 1 ( η ρ ) d η ,
I CP = | B C | 2 + | B S | 2 ,
I LP = I CP + 2 Re [ B C B S * ] cos ( 2 Φ ( φ + ϕ 0 ) ) ,
E ( ξ , Z , φ ) = f ( ξ , Z ) E 0 ( e CR e 0 ) e CR ,
f ( ξ , Z ) = 1 8 π 3 ρ 0 0 d η η a ( η ) e i Z 4 η 2 cos ( η ξ π 4 ) ,
e CR = ( cos φ + φ 0 2 sin φ + φ 0 2 ) .
I CP a ( ξ , Z ) = | f ( ξ , Z ) | 2 ,
I LP a ( ξ , Z , φ ) = I CP a cos 2 ( Φ φ + φ 0 2 ) .
f ( ξ , Z ) = P ( w Z ) 3 / 4 2 π 2 w 0 2 ρ 0 [ Γ ( 3 4 ) F 1 1 ( 3 4 ; 1 2 ; ξ 2 w Z ) + 2 ξ w Z Γ ( 5 4 ) F 1 1 ( 5 4 ; 3 2 ; ξ 2 w Z ) ] ,
U ˜ 0 = π c 2 2 [ Γ D 2 ω D 2 3 ( 2 ω D 2 ω L ) + Γ D 1 ω D 1 3 ( 1 ω D 1 ω L ) ] ,
ω r , z = A r , z U ˜ 0 P π 2 m w 0 4 ρ 0 ,
U ( ξ ± , 0 ) = C ± U ˜ 0 P 4 π 2 w 0 2 ρ 0 ,
A r ( Z ) = 0.051 + 8.817 1.873 + 2.307 Z 2 .
U ( ξ 0 , Z ) = U ˜ 0 P 4 π 2 w 0 2 ρ 0 Z 2 .
U ( ξ 0 , Z ± ) = 0.17 U ˜ 0 P 4 π 2 w 0 2 ρ 0 .
i h ¯ t Ψ ( r , t ) = ( h ¯ 2 2 m 2 + V ext ( r ) + g 2 D | Ψ ( r , t ) | 2 ) Ψ ( r , t ) ,

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