Abstract

Realizing single light bullets and vortices that are stable in high dimensions is a long-standing goal in the study of nonlinear optical physics. The storage and retrieval of such stable high-dimensional optical pulses may offer a variety of applications. Here, we present a scheme to generate such optical pulses in a cold Rydberg atomic gas. By virtue of electromagnetically induced transparency, strong, long-range atom–atom interaction in Rydberg states is mapped to light fields, resulting in a giant, fast-responding nonlocal Kerr nonlinearity and the formation of light bullets and vortices carrying orbital angular momenta, which have extremely low generation power and very slow propagation velocity, and can stably propagate, with the stability provided by the combination of local and nonlocal Kerr nonlinearities. We demonstrate that the light bullets and vortices obtained can be stored and retrieved in the system with high efficiency and fidelity. Our study provides a new route for manipulating high-dimensional nonlinear optical processes via controlled optical nonlinearities in cold Rydberg gases.

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References

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2018 (2)

Q. Y. Liang, A. V. Venkatramani, S. H. Cantu, T. L. Nicholson, M. J. Gullans, A. V. Gorshkov, J. D. Thompson, C. Chin, M. D. Lukin, and V. Vuletić, “Observation of three-photon bound states in a quantum nonlinear medium,” Science 359, 783–786 (2018).
[Crossref]

Q. Zhang, Z. Bai, and G. Huang, “Fast-responding property of electromagnetically induced transparency in Rydberg atoms,” Phys. Rev. A 97, 043821 (2018).
[Crossref]

2017 (3)

C. R. Murray and T. Pohl, “Coherent photon manipulation in interacting atomic ensembles,” Phys. Rev. X 7, 031007 (2017).
[Crossref]

M. J. Gullans, S. Diehl, S. T. Rittenhouse, B. P. Ruzic, J. P. DÍncao, P. Julienne, A. V. Gorshkov, and J. M. Taylor, “Efimov states of strongly interacting photons,” Phys. Rev. Lett. 119, 233601 (2017).
[Crossref]

O. Lahav, O. Kfir, P. Sidorenko, M. Mutzafi, A. Fleischer, and O. Cohen, “Three-dimensional spatiotemporal pulse-train solitons,” Phys. Rev. X 7, 041051 (2017).
[Crossref]

2016 (9)

O. Firstenberg, C. S. Adams, and S. Hofferberth, “Nonlinear quantum optics mediated by Rydberg interactions,” J. Phys. B 49, 152003 (2016).
[Crossref]

L. Yang, B. He, J. Wu, Z. Zhang, and M. Xiao, “Interacting photon pulses in a Rydberg medium,” Optica 3, 1095–1103 (2016).
[Crossref]

E. Distante, A. Padrón-Brito, M. Cristiani, D. Paredes-Barato, and H. de Riedmatten, “Storage enhanced nonlinearities in a cold atomic Rydberg ensemble,” Phys. Rev. Lett. 117, 113001 (2016).
[Crossref]

L. Li and A. Kuzmich, “Quantum memory with strong and controllable Rydberg-level interactions,” Nat. Commun. 7, 13618 (2016).
[Crossref]

H. Busche, P. Huillery, S. Ball, T. Ilieva, M. P. A. Jones, and C. S. Adams, “Contactless nonlinear optics mediated by long-range Rydberg interactions,” Nat. Phys. 13, 655–658 (2016).
[Crossref]

D. Tiarks, S. Schmidt, G. Rempe, and S. Dürr, “Optical π phase shift created with a single-photon pulse,” Sci. Adv. 2, e1600036 (2016).
[Crossref]

H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Fórster resonances,” Nat. Commun. 7, 12480 (2016).
[Crossref]

P. Bienias and H. P. Büchler, “Quantum theory of Kerr nonlinearity with Rydberg slow light polaritons,” New J. Phys. 18, 123026 (2016).
[Crossref]

Z. Bai and G. Huang, “Enhanced third-order and fifth-order Kerr nonlinearities in a cold atomic system via Rydberg-Rydberg interaction,” Opt. Express 24, 4442–4461 (2016).
[Crossref]

2015 (3)

V. Parigi, V. DÁmbrosio, 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]

R. A. De Oliveira, G. C. Borba, W. S. Martins, S. Barreiro, D. Felinto, and J. W. R. Tabosa, “Nonlinear optical memory for manipulation of orbital angular momentum of light,” Opt. Lett. 40, 4939–4942 (2015).
[Crossref]

D. Ding, W. Zhang, Z. Zhou, S. Shi, G. Xiang, X. Wang, Y. Jiang, B. Shi, and G. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 050502 (2015).
[Crossref]

2014 (5)

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
[Crossref]

B. He, A. V. Sharypov, J. Sheng, C. Simon, and M. Xiao, “Two-photon dynamics in coherent Rydberg atomic ensemble,” Phys. Rev. Lett. 112, 133606 (2014).
[Crossref]

S. Baur, D. Tiarks, G. Rempe, and S. Dürr, “Single-photon switch based on Rydberg blockade,” Phys. Rev. Lett. 112, 073901 (2014).
[Crossref]

H. Gorniaczyk, C. Tresp, J. Schmidt, H. Fedder, and S. Hofferberth, “Single-photon transistor media ted by interstate Rydberg interactions,” Phys. Rev. Lett. 113, 053601 (2014).
[Crossref]

Y. Chen, Z. Bai, and G. Huang, “Ultraslow optical solitons and their storage and retrieval in an ultracold ladder-type atomic system,” Phys. Rev. A 89, 023835 (2014).
[Crossref]

2013 (5)

J. D. Pritchard, K. J. Weatherill, and C. S. Adams, “Nonlinear optics using cold Rydberg atoms,” Annu. Rev. Cold At. Mol. 1, 301–350 (2013).
[Crossref]

F. Eilenberger, K. Prater, S. Minardi, R. Geiss, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and T. Pertsch, “Observation of discrete, vortex light bullets,” Phys. Rev. X 3, 041031 (2013).
[Crossref]

D. Maxwell, D. J. Szwer, D. P. Barato, H. Busche, J. D. Pritchard, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Storage and control of optical photons using Rydberg polaritons,” Phys. Rev. Lett. 110, 103001 (2013).
[Crossref]

J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
[Crossref]

L. Veissier, A. Nicolas, L. Giner, D. Maxein, A. S. Sheremet, E. Giacobino, and J. Laurat, “Reversible optical memory for twisted photons,” Opt. Lett. 38, 712–714 (2013).
[Crossref]

2012 (3)

I. Novikova, R. L. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photon. Rev. 6, 333–353 (2012).
[Crossref]

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012).
[Crossref]

R. Löw, H. Weimer, J. Nipper, J. B. Balewski, B. Butscher, H. P. Büchler, and T. Pfau, “An experimental and theoretical guide to strongly interacting Rydberg gases,” J. Phys. B 45, 113001 (2012).
[Crossref]

2011 (3)

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
[Crossref]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

S. Sevinçli, N. Henkel, C. Ates, and T. Pohl, “Nonlocal nonlinear optics in cold Rydberg gases,” Phys. Rev. Lett. 107, 153001 (2011).
[Crossref]

2010 (5)

H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, and M. Weidemüller, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
[Crossref]

A. M. Mateo, V. Delgado, and B. A. Malomed, “Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices,” Phys. Rev. A 82, 053606 (2010).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105, 263901 (2010).
[Crossref]

M. Saffman, T. G. Walker, and K. Molmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

M. Peccianti, I. B. Burgess, G. Assanto, and R. Morandotti, “Space-time bullet trains via modulation instability and nonlocal solitons,” Opt. Express 18, 5934–5941 (2010).
[Crossref]

2009 (3)

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009).
[Crossref]

H. C. Gurgov and O. Cohen, “Spatiotemporal pulse-train solitons,” Opt. Express 17, 7052–7058 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Collisions between discrete surface spatiotemporal solitons in nonlinear waveguide arrays,” Phys. Rev. A 79, 013811 (2009).
[Crossref]

2008 (1)

M. Belić, N. Petrović, W.-P. Zhong, R.-H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
[Crossref]

2007 (2)

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98, 113003 (2007).
[Crossref]

S. Mauger, J. Millen, and M. P. A. Jones, “Spectroscopy of strontium Rydberg states using electromagnetically induced transparency,” J. Phys. B 40, F319 (2007).
[Crossref]

2006 (1)

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[Crossref]

2005 (5)

I. Friedler, D. Petrosyan, M. Fleischhauer, and G. Kurizki, “Long-range interactions and entanglement of slow single-photon pulses,” Phys. Rev. A 72, 043803 (2005).
[Crossref]

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
[Crossref]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53 (2005).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[Crossref]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

2004 (1)

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
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2003 (1)

T. Hong, “Spatial weak-light solitons in an electromagnetically induced nonlinear waveguide,” Phys. Rev. Lett. 90, 183901 (2003).
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2001 (1)

W. Krolikowski, O. Bang, J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
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2000 (1)

S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–382 (2000).
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1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behrrozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
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X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
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1997 (1)

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
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1995 (1)

R. McLeod, K. Wagner, and S. Blair, “(3+1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
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1990 (1)

Adams, C. S.

H. Busche, P. Huillery, S. Ball, T. Ilieva, M. P. A. Jones, and C. S. Adams, “Contactless nonlinear optics mediated by long-range Rydberg interactions,” Nat. Phys. 13, 655–658 (2016).
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O. Firstenberg, C. S. Adams, and S. Hofferberth, “Nonlinear quantum optics mediated by Rydberg interactions,” J. Phys. B 49, 152003 (2016).
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J. D. Pritchard, K. J. Weatherill, and C. S. Adams, “Nonlinear optics using cold Rydberg atoms,” Annu. Rev. Cold At. Mol. 1, 301–350 (2013).
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D. Maxwell, D. J. Szwer, D. P. Barato, H. Busche, J. D. Pritchard, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Storage and control of optical photons using Rydberg polaritons,” Phys. Rev. Lett. 110, 103001 (2013).
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A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98, 113003 (2007).
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Agrawal, G. P.

S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–382 (2000).
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Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2006).

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H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, and M. Weidemüller, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
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D. L. Andrews and M. Babiker, The Angular Momentum of Light (Cambridge Univeristy, 2013).

Arnold, C.

V. Parigi, V. DÁmbrosio, 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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M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012).
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M. Peccianti, I. B. Burgess, G. Assanto, and R. Morandotti, “Space-time bullet trains via modulation instability and nonlocal solitons,” Opt. Express 18, 5934–5941 (2010).
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I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009).
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Ates, C.

S. Sevinçli, N. Henkel, C. Ates, and T. Pohl, “Nonlocal nonlinear optics in cold Rydberg gases,” Phys. Rev. Lett. 107, 153001 (2011).
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Babiker, M.

D. L. Andrews and M. Babiker, The Angular Momentum of Light (Cambridge Univeristy, 2013).

Bai, Z.

Q. Zhang, Z. Bai, and G. Huang, “Fast-responding property of electromagnetically induced transparency in Rydberg atoms,” Phys. Rev. A 97, 043821 (2018).
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Z. Bai and G. Huang, “Enhanced third-order and fifth-order Kerr nonlinearities in a cold atomic system via Rydberg-Rydberg interaction,” Opt. Express 24, 4442–4461 (2016).
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Y. Chen, Z. Bai, and G. Huang, “Ultraslow optical solitons and their storage and retrieval in an ultracold ladder-type atomic system,” Phys. Rev. A 89, 023835 (2014).
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R. Löw, H. Weimer, J. Nipper, J. B. Balewski, B. Butscher, H. P. Büchler, and T. Pfau, “An experimental and theoretical guide to strongly interacting Rydberg gases,” J. Phys. B 45, 113001 (2012).
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Ball, S.

H. Busche, P. Huillery, S. Ball, T. Ilieva, M. P. A. Jones, and C. S. Adams, “Contactless nonlinear optics mediated by long-range Rydberg interactions,” Nat. Phys. 13, 655–658 (2016).
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Bang, O.

W. Krolikowski, O. Bang, J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
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Barato, D. P.

D. Maxwell, D. J. Szwer, D. P. Barato, H. Busche, J. D. Pritchard, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Storage and control of optical photons using Rydberg polaritons,” Phys. Rev. Lett. 110, 103001 (2013).
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Barreiro, S.

Bartelt, H.

F. Eilenberger, K. Prater, S. Minardi, R. Geiss, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and T. Pertsch, “Observation of discrete, vortex light bullets,” Phys. Rev. X 3, 041031 (2013).
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S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105, 263901 (2010).
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Baur, S.

S. Baur, D. Tiarks, G. Rempe, and S. Dürr, “Single-photon switch based on Rydberg blockade,” Phys. Rev. Lett. 112, 073901 (2014).
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Behrrozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behrrozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
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Belic, M.

M. Belić, N. Petrović, W.-P. Zhong, R.-H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
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Bienias, P.

H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Fórster resonances,” Nat. Commun. 7, 12480 (2016).
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P. Bienias and H. P. Büchler, “Quantum theory of Kerr nonlinearity with Rydberg slow light polaritons,” New J. Phys. 18, 123026 (2016).
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J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
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Blair, S.

R. McLeod, K. Wagner, and S. Blair, “(3+1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
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Borba, G. C.

Boyd, R. W.

R. W. Boyd, “Nonlinear Optics,” 3rd Ed. (Academic/Elsevier, 2008).

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P. Bienias and H. P. Büchler, “Quantum theory of Kerr nonlinearity with Rydberg slow light polaritons,” New J. Phys. 18, 123026 (2016).
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H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Fórster resonances,” Nat. Commun. 7, 12480 (2016).
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R. Löw, H. Weimer, J. Nipper, J. B. Balewski, B. Butscher, H. P. Büchler, and T. Pfau, “An experimental and theoretical guide to strongly interacting Rydberg gases,” J. Phys. B 45, 113001 (2012).
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Burgess, I. B.

M. Peccianti, I. B. Burgess, G. Assanto, and R. Morandotti, “Space-time bullet trains via modulation instability and nonlocal solitons,” Opt. Express 18, 5934–5941 (2010).
[Crossref]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009).
[Crossref]

Busche, H.

H. Busche, P. Huillery, S. Ball, T. Ilieva, M. P. A. Jones, and C. S. Adams, “Contactless nonlinear optics mediated by long-range Rydberg interactions,” Nat. Phys. 13, 655–658 (2016).
[Crossref]

D. Maxwell, D. J. Szwer, D. P. Barato, H. Busche, J. D. Pritchard, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Storage and control of optical photons using Rydberg polaritons,” Phys. Rev. Lett. 110, 103001 (2013).
[Crossref]

Butscher, B.

R. Löw, H. Weimer, J. Nipper, J. B. Balewski, B. Butscher, H. P. Büchler, and T. Pfau, “An experimental and theoretical guide to strongly interacting Rydberg gases,” J. Phys. B 45, 113001 (2012).
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Cantu, S. H.

Q. Y. Liang, A. V. Venkatramani, S. H. Cantu, T. L. Nicholson, M. J. Gullans, A. V. Gorshkov, J. D. Thompson, C. Chin, M. D. Lukin, and V. Vuletić, “Observation of three-photon bound states in a quantum nonlinear medium,” Science 359, 783–786 (2018).
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Chen, G.

M. Belić, N. Petrović, W.-P. Zhong, R.-H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
[Crossref]

Chen, Y.

Y. Chen, Z. Bai, and G. Huang, “Ultraslow optical solitons and their storage and retrieval in an ultracold ladder-type atomic system,” Phys. Rev. A 89, 023835 (2014).
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Chin, C.

Q. Y. Liang, A. V. Venkatramani, S. H. Cantu, T. L. Nicholson, M. J. Gullans, A. V. Gorshkov, J. D. Thompson, C. Chin, M. D. Lukin, and V. Vuletić, “Observation of three-photon bound states in a quantum nonlinear medium,” Science 359, 783–786 (2018).
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Cohen, O.

O. Lahav, O. Kfir, P. Sidorenko, M. Mutzafi, A. Fleischer, and O. Cohen, “Three-dimensional spatiotemporal pulse-train solitons,” Phys. Rev. X 7, 041051 (2017).
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H. C. Gurgov and O. Cohen, “Spatiotemporal pulse-train solitons,” Opt. Express 17, 7052–7058 (2009).
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Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
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Cristiani, M.

E. Distante, A. Padrón-Brito, M. Cristiani, D. Paredes-Barato, and H. de Riedmatten, “Storage enhanced nonlinearities in a cold atomic Rydberg ensemble,” Phys. Rev. Lett. 117, 113001 (2016).
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DÁmbrosio, V.

V. Parigi, V. DÁmbrosio, 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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De Oliveira, R. A.

de Riedmatten, H.

E. Distante, A. Padrón-Brito, M. Cristiani, D. Paredes-Barato, and H. de Riedmatten, “Storage enhanced nonlinearities in a cold atomic Rydberg ensemble,” Phys. Rev. Lett. 117, 113001 (2016).
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Delgado, V.

A. M. Mateo, V. Delgado, and B. A. Malomed, “Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices,” Phys. Rev. A 82, 053606 (2010).
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Deng, L.

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
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Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
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DePaola, B. D.

H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, and M. Weidemüller, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
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Diehl, S.

M. J. Gullans, S. Diehl, S. T. Rittenhouse, B. P. Ruzic, J. P. DÍncao, P. Julienne, A. V. Gorshkov, and J. M. Taylor, “Efimov states of strongly interacting photons,” Phys. Rev. Lett. 119, 233601 (2017).
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DÍncao, J. P.

M. J. Gullans, S. Diehl, S. T. Rittenhouse, B. P. Ruzic, J. P. DÍncao, P. Julienne, A. V. Gorshkov, and J. M. Taylor, “Efimov states of strongly interacting photons,” Phys. Rev. Lett. 119, 233601 (2017).
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Ding, D.

D. Ding, W. Zhang, Z. Zhou, S. Shi, G. Xiang, X. Wang, Y. Jiang, B. Shi, and G. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 050502 (2015).
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Distante, E.

E. Distante, A. Padrón-Brito, M. Cristiani, D. Paredes-Barato, and H. de Riedmatten, “Storage enhanced nonlinearities in a cold atomic Rydberg ensemble,” Phys. Rev. Lett. 117, 113001 (2016).
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Dürr, S.

D. Tiarks, S. Schmidt, G. Rempe, and S. Dürr, “Optical π phase shift created with a single-photon pulse,” Sci. Adv. 2, e1600036 (2016).
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S. Baur, D. Tiarks, G. Rempe, and S. Dürr, “Single-photon switch based on Rydberg blockade,” Phys. Rev. Lett. 112, 073901 (2014).
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Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behrrozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
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Eilenberger, F.

F. Eilenberger, K. Prater, S. Minardi, R. Geiss, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and T. Pertsch, “Observation of discrete, vortex light bullets,” Phys. Rev. X 3, 041031 (2013).
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S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105, 263901 (2010).
[Crossref]

Fedder, H.

H. Gorniaczyk, C. Tresp, J. Schmidt, H. Fedder, and S. Hofferberth, “Single-photon transistor media ted by interstate Rydberg interactions,” Phys. Rev. Lett. 113, 053601 (2014).
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Felinto, D.

Firstenberg, O.

O. Firstenberg, C. S. Adams, and S. Hofferberth, “Nonlinear quantum optics mediated by Rydberg interactions,” J. Phys. B 49, 152003 (2016).
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Fleischer, A.

O. Lahav, O. Kfir, P. Sidorenko, M. Mutzafi, A. Fleischer, and O. Cohen, “Three-dimensional spatiotemporal pulse-train solitons,” Phys. Rev. X 7, 041051 (2017).
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Fleischhauer, M.

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
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I. Friedler, D. Petrosyan, M. Fleischhauer, and G. Kurizki, “Long-range interactions and entanglement of slow single-photon pulses,” Phys. Rev. A 72, 043803 (2005).
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M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
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I. Friedler, D. Petrosyan, M. Fleischhauer, and G. Kurizki, “Long-range interactions and entanglement of slow single-photon pulses,” Phys. Rev. A 72, 043803 (2005).
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T. F. Gallagher, Rydberg Atoms (Cambridge University, 2008).

Gauguet, A.

D. Maxwell, D. J. Szwer, D. P. Barato, H. Busche, J. D. Pritchard, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Storage and control of optical photons using Rydberg polaritons,” Phys. Rev. Lett. 110, 103001 (2013).
[Crossref]

Geiss, R.

F. Eilenberger, K. Prater, S. Minardi, R. Geiss, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and T. Pertsch, “Observation of discrete, vortex light bullets,” Phys. Rev. X 3, 041031 (2013).
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Giacobino, E.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
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L. Veissier, A. Nicolas, L. Giner, D. Maxein, A. S. Sheremet, E. Giacobino, and J. Laurat, “Reversible optical memory for twisted photons,” Opt. Lett. 38, 712–714 (2013).
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Giese, C.

H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, and M. Weidemüller, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
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Giner, L.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
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L. Veissier, A. Nicolas, L. Giner, D. Maxein, A. S. Sheremet, E. Giacobino, and J. Laurat, “Reversible optical memory for twisted photons,” Opt. Lett. 38, 712–714 (2013).
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Gorniaczyk, H.

H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Fórster resonances,” Nat. Commun. 7, 12480 (2016).
[Crossref]

H. Gorniaczyk, C. Tresp, J. Schmidt, H. Fedder, and S. Hofferberth, “Single-photon transistor media ted by interstate Rydberg interactions,” Phys. Rev. Lett. 113, 053601 (2014).
[Crossref]

Gorshkov, A. V.

Q. Y. Liang, A. V. Venkatramani, S. H. Cantu, T. L. Nicholson, M. J. Gullans, A. V. Gorshkov, J. D. Thompson, C. Chin, M. D. Lukin, and V. Vuletić, “Observation of three-photon bound states in a quantum nonlinear medium,” Science 359, 783–786 (2018).
[Crossref]

M. J. Gullans, S. Diehl, S. T. Rittenhouse, B. P. Ruzic, J. P. DÍncao, P. Julienne, A. V. Gorshkov, and J. M. Taylor, “Efimov states of strongly interacting photons,” Phys. Rev. Lett. 119, 233601 (2017).
[Crossref]

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
[Crossref]

Grangier, P.

J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
[Crossref]

Gullans, M. J.

Q. Y. Liang, A. V. Venkatramani, S. H. Cantu, T. L. Nicholson, M. J. Gullans, A. V. Gorshkov, J. D. Thompson, C. Chin, M. D. Lukin, and V. Vuletić, “Observation of three-photon bound states in a quantum nonlinear medium,” Science 359, 783–786 (2018).
[Crossref]

M. J. Gullans, S. Diehl, S. T. Rittenhouse, B. P. Ruzic, J. P. DÍncao, P. Julienne, A. V. Gorshkov, and J. M. Taylor, “Efimov states of strongly interacting photons,” Phys. Rev. Lett. 119, 233601 (2017).
[Crossref]

Günter, G.

H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, and M. Weidemüller, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
[Crossref]

Guo, G.

D. Ding, W. Zhang, Z. Zhou, S. Shi, G. Xiang, X. Wang, Y. Jiang, B. Shi, and G. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 050502 (2015).
[Crossref]

Gurgov, H. C.

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behrrozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behrrozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
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L. Yang, B. He, J. Wu, Z. Zhang, and M. Xiao, “Interacting photon pulses in a Rydberg medium,” Optica 3, 1095–1103 (2016).
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B. He, A. V. Sharypov, J. Sheng, C. Simon, and M. Xiao, “Two-photon dynamics in coherent Rydberg atomic ensemble,” Phys. Rev. Lett. 112, 133606 (2014).
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Henkel, N.

S. Sevinçli, N. Henkel, C. Ates, and T. Pohl, “Nonlocal nonlinear optics in cold Rydberg gases,” Phys. Rev. Lett. 107, 153001 (2011).
[Crossref]

Hofferberth, S.

O. Firstenberg, C. S. Adams, and S. Hofferberth, “Nonlinear quantum optics mediated by Rydberg interactions,” J. Phys. B 49, 152003 (2016).
[Crossref]

H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Fórster resonances,” Nat. Commun. 7, 12480 (2016).
[Crossref]

H. Gorniaczyk, C. Tresp, J. Schmidt, H. Fedder, and S. Hofferberth, “Single-photon transistor media ted by interstate Rydberg interactions,” Phys. Rev. Lett. 113, 053601 (2014).
[Crossref]

Hofmann, C. S.

H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, and M. Weidemüller, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
[Crossref]

Hong, T.

T. Hong, “Spatial weak-light solitons in an electromagnetically induced nonlinear waveguide,” Phys. Rev. Lett. 90, 183901 (2003).
[Crossref]

Huang, G.

Q. Zhang, Z. Bai, and G. Huang, “Fast-responding property of electromagnetically induced transparency in Rydberg atoms,” Phys. Rev. A 97, 043821 (2018).
[Crossref]

Z. Bai and G. Huang, “Enhanced third-order and fifth-order Kerr nonlinearities in a cold atomic system via Rydberg-Rydberg interaction,” Opt. Express 24, 4442–4461 (2016).
[Crossref]

Y. Chen, Z. Bai, and G. Huang, “Ultraslow optical solitons and their storage and retrieval in an ultracold ladder-type atomic system,” Phys. Rev. A 89, 023835 (2014).
[Crossref]

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
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Sci. Adv. (1)

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[Crossref]

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The frequency and wave number of the probe field are given by ωp+ω and Kp+K(ω), respectively. Thus, ω=0 corresponds to the center frequency of the probe field.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2006).

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Supplementary Material (1)

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Figures (9)

Fig. 1.
Fig. 1. Rydberg atomic model. (a) EIT level scheme, where the ground state |1, intermediate state |2, and Rydberg state |3 are, respectively, driven by a pulsed probe field (with pulse duration τ0) and a strong control field. State |2 has a large spontaneous decay rate Γ12MHz. The weak decay Γ23KHz from |3 to |2 is also taken into account. The van der Waals interaction V(rr) between the two atoms in Rydberg states, respectively located at r and r, shifts the Rydberg state energy. (b) Geometry of the system. The probe and control laser fields counter-propagate in the Rydberg gas. Depletion of the strong control field is neglected. (c) Storage and retrieval of a (3+1)D light bullet, illustrated by an isosurface plot of the light intensity of the light bullet before storage (z=0), at the beginning of the storage (z=5.4mm), and after the storage (z=10.8mm); see text for details.
Fig. 2.
Fig. 2. Effective atomic interaction potential G2 as functions of r/Rb. We show the local response region (a) with R0=300μm, nonlocal response region; (b) with R0=10μm, and strong nonlocal response region; and (c) with R0=1μm. In all situations, real parts (blue solid line) dominate the imaginary part (orange dashed line). For a better visualization, G2 has been amplified 108 times. We also show the intensity profile of the probe field |U/U0|2 (black dotted-dashed line). The purple dashed line in (c) is for the function G2(0)+[2G2(0)/r2]r2/2. Parameters are Δ2=15Γ12 and Rb=[|C6Δ2|/(2|Ωc|2)]1/6=5.8μm. These parameters guarantee that the system is in the dispersive nonlinearity regime (i.e., |Δ2|Γ12).
Fig. 3.
Fig. 3. Stability of light bullets. (a) Light bullet energy E as a function of the transverse beam width ws. In the region where E/ws<0 (i.e., curve C2), the light bullet is stable; in regions E/ws>0 (i.e., curves C1 and C3), the light bullet is unstable. Panels (b), (c), and (d) are numerical results of E, ws (transverse beam width), and wt (pulse duration) as a functions of z/(2Ldiff), obtained by choosing initial conditions from curves C1, C2, and C3 in panel (a). Stability of parameter set (ws,wt,E) with initial conditions (0.08, 0.06, 1.15) (b), (0.66, 0.41, 0.44) (c), and (1.5, 1.1, 0.55) (d).
Fig. 4.
Fig. 4. Evolution of light bullets and vortices in the nonlocal response region. (a) Evolution of |u|2 with the fundamental mode (LG)00 (i.e., light bullet), as a function of x/Rb and y/Rb when propagating to the distance, respectively, at z/(2Ldiff)=0, 1, 2, 3, and 4 for atomic density Na=3×1010cm3. (b) Evolution of |u|2 with the higher-order mode (LG)01 (i.e., light vortex) for Na=4.95×1010cm3.
Fig. 5.
Fig. 5. Evolution of light vortices corresponding to the mode (LG)12 in the nonlocal response region. Evolution of |u|2 as a function of x/Rb and y/Rb when propagating to the distance at z/(2Ldiff)=0,1,2,3, and 4, respectively. Parameters are R0=1.67Rb, Na=9.9×1010cm3 (a), R0=0.83Rb, Na=1.46×1011cm3 (b), and R0=0.42Rb, Na=5.3×1011cm3 (c) with Rb=6μm. Other system parameters are the same as those used in Fig. 4.
Fig. 6.
Fig. 6. Evolution of light bullets and light vortices in the strongly nonlocal response region. Evolution of |u|2 with (LG)00 mode [panel (a); light bullet] and (LG)12 mode [panel (b); light vortex], obtained based on solving Eq. (3). Isosurface plots of the pulses are shown when propagating to distances s=z/(2Ldiff)=0,1,2,3,4, respectively.
Fig. 7.
Fig. 7. Storage and retrieval of (3+1)D light vortices with the (LG)01 mode in the nonlocal response region. The black dashed line shows the switching on, switching off, and re-switching on of the control field |Ωcτ0|. The curves 1, 2, and 3 are temporal profiles of the probe pulse |Ωpτ0|, respectively, at z=0 (before the storage), z=4Ldiff (at the beginning of the storage), and 8Ldiff (after the storage), with Ldiff=1.36mm; the corresponding isosurface plots for |Ωpτ0|=0.1are also shown. In the calculation, we have set R0=10μm, C62π×81.6GHzμm6, Ωpτ0=27, Δ2τ0=1340, Δ3τ0=1.8, and Ωc0τ0=90 with τ0=9×107s. The control parameters are Ts=0.2τ0, Toff=5τ0, Ton=15τ0.
Fig. 8.
Fig. 8. Memory of light bullets for the case without the Rydberg–Rydberg interaction. Storage and retrieval of (3+1)D LB at z=0(before storage), z=Ldiff (at the beginning of storage), and 2Ldiff (after storage), with Ldiff=1.36mm; the corresponding isosurface plots for |Ωpτ0|=0.1 are also shown.
Fig. 9.
Fig. 9. Storage and retrieval of (3+1)D light bullets and light vortices in the strong nonlocal response region. (a) Memory of the LB [(LG)00 mode]. The black dashed line shows the switching on and off of the control field |Ωcτ0|. Curves 1, 2, and 3 are temporal profiles of the probe pulse |Ωpτ0|, respectively, at z=0 (before storage), z=6Ldiff (at the beginning of storage), and 12Ldiff (after storage), with Ldiff=0.047mm; the corresponding isosurface plots for |Ωpτ0|=0.1 are also shown. (b) The same as (a) but for the memory of the LV with the (LG)12 mode.

Equations (10)

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H^H=α=13ωαS^αα(r,t)[ΩpS^12(r,t)+ΩcS^23(r,t)+h.c.]+Nad3rS^33(r,t)V(rr)S^33(r,t),
i(z+1ct)Ωp+c2ωp2Ωp+κ12ρ21=0,
ρ^t=i[H^H,ρ^]Γ[ρ^],
i(z+α0)U12K22Uτ2+c2ωp2U+W1|U|2U+d2rG2(rr)|U(r,z,τ)|2U(r,z,τ)=0,
ius+(2ξ2+2η2)u+gd2uσ2+g1|u|2u+dξdηN(ξξ,ηη)|u(ξ,η,s,σ)|2u(ξ,η,s,σ)=id0u,
u=A(s)exp[ξ2+η22ws2(s)]sech[σwt(s)]×exp[iCs(s)ξ2+η22ws2(s)iCt(s)σ22+iϕ(s)],
ump=Cmpws[2ξ2+η2ws]|m|exp(ξ2+η2ws2)×Lp|m|[2(ξ2+η2)ws2]sech[σwt(s)]eimϕ,
ius+(2ξ2+2η2)u+gd2σ2u+g1|u|2ug4(ξ2+η2)u=id0u,
VLB1.25×106c,
P¯max0.2nW,