Abstract

In standard lasers, light amplification requires population inversion between an upper and a lower state to break the reciprocity between absorption and stimulated emission. However, in a medium prepared in a specific superposition state, quantum interference may fully suppress absorption while leaving stimulated emission intact, opening the possibility of lasing without inversion. Here we show that lasing without inversion arises naturally during propagation of intense femtosecond laser pulses in air. It is triggered by the combination of molecular ionization and molecular alignment, both unavoidable in intense light fields. The effect could enable inversionless amplification of broadband radiation in many molecular gases, opening unusual opportunities for remote sensing.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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  55. S. I. Mitryukovskiy, Y. Liu, A. Houard, and A. Mysyrowicz, “Re-evaluation of the peak intensity inside a femtosecond laser filament in air,” J. Phys. B 48, 094003 (2015).
    [Crossref]

2020 (2)

Q. Zhang, H. Xie, G. Li, X. Wang, H. Lei, J. Zhao, Z. Chen, J. Yao, Y. Cheng, and Z. Zhao, “Sub-cycle coherent control of ionic dynamics via transient ionization injection,” Communications Phys. 3, 50 (2020).
[Crossref]

P. M. Solyankin, I. A. Nikolaeva, A. A. Angeluts, D. E. Shipilo, N. V. Minaev, N. A. Panov, A. V. Balakin, Y. Zhu, O. G. Kosareva, and A. P. Shkurinov, “THz generation from laser-induced breakdown in pressurized molecular gases: on the way to terahertz remote sensing of the atmospheres of Mars and Venus,” New J. Phys. 22, 013039 (2020).
[Crossref]

2019 (8)

Y. Zhang, E. Lötstedt, and K. Yamanouchi, “Mechanism of population inversion in laser-driven ${\rm N}^+_2$N2+,” J. Phys. B 52, 055401 (2019).
[Crossref]

A. Mysyrowicz, R. Danylo, A. Houard, V. Tikhonchuk, X. Zhang, Z. Fan, Q. Liang, S. Zhuang, L. Yuan, and Y. Liu, “Lasing without population inversion in ${\rm N}^+_2$N2+,” APL Photon. 4, 110807 (2019).
[Crossref]

M. Britton, M. Lytova, P. Laferrière, P. Peng, F. Morales, D. H. Ko, M. Richter, P. Polynkin, D. M. Villeneuve, C. Zhang, M. Ivanov, M. Spanner, L. Arissian, and P. B. Corkum, “Short- and long-term gain dynamics in N2+air lasing,” Phys. Rev. A 100, 013406 (2019).
[Crossref]

H. Li, Q. Song, J. Yao, Z. Liu, J. Chen, B. Xu, K. Lin, J. Qiang, B. He, H. Xu, Y. Cheng, H. Zeng, and J. Wu, “Air lasing from singly ionized N2 driven by bicircular two-color fields,” Phys. Rev. A 99, 053413 (2019).
[Crossref]

T. Ando, E. Lötstedt, A. Iwasaki, H. Li, Y. Fu, S. Wang, H. Xu, and K. Yamanouchi, “Rotational, vibrational, and electronic modulations in ${\rm N}^+_2$N2+ lasing at 391 nm: evidence of coherent ${\rm B}^2{\Sigma}^+_u - {\rm X}^2{\Sigma}^+_g - {\rm A}^2{\Pi}_u$ B2Σu+−X2Σg+−A2Πu coupling,” Phys. Rev. Lett. 123, 203201 (2019).
[Crossref]

H. Li, M. Hou, H. Zang, Y. Fu, E. Lötstedt, T. Ando, A. Iwasaki, K. Yamanouchi, and H. Xu, “Significant enhancement of N2+lasing by polarization-modulated ultrashort laser pulses,” Phys. Rev. Lett. 122, 013202 (2019).
[Crossref]

A. Zhang, Q. Liang, M. Lei, L. Yuan, Y. Liu, Z. Fan, X. Zhang, S. Zhuang, C. Wu, Q. Gong, and H. Jiang, “Coherent modulation of superradiance from nitrogen ions pumped with femtosecond pulses,” Opt. Express 27, 12638–12646 (2019).
[Crossref]

A. Zhang, M. Lei, J. Gao, C. Wu, Q. Gong, and H. Jiang, “Subfemtosecond-resolved modulation of superfluorescence from ionized nitrogen molecules by 800-nm femtosecond laser pulses,” Opt. Express 27, 14922–14930 (2019).
[Crossref]

2018 (4)

B. Xu, S. Jiang, J. Yao, J. Chen, Z. Liu, W. Chu, Y. Wan, F. Zhang, L. Qiao, R. Lu, Y. Cheng, and Z. Xu, “Free-space ${\rm N}^+_2$N2+ lasers generated strong laser fields: the role of molecular vibration,” Opt. Express 26, 13331–13339 (2018).
[Crossref]

X. Zhong, Z. Miao, L. Zhang, H. Jiang, Y. Liu, Q. Gong, and C. Wu, “Optimizing the 391-nm lasing intensity from ionized nitrogen molecules in 800-nm femtosecond laser fields,” Phys. Rev. A 97, 033409 (2018).
[Crossref]

L. Arissian, B. Kamer, A. Rastegari, D. M. Villeneuve, and J.-C. Diels, “Transient gain from ${\rm N}^+_2$N2+ in light filaments,” Phys. Rev. A 98, 053438 (2018).
[Crossref]

M. Britton, P. Laferrière, D. H. Ko, Z. Li, F. Kong, G. Brown, A. Naumov, C. Zhang, L. Arissian, and P. B. Corkum, “Testing the role of recollision in ${\rm N}^+_2$N2+ air lasing,” Phys. Rev. Lett. 120, 133208 (2018).
[Crossref]

2017 (5)

A. Azarm, P. Corkum, and P. Polynkin, “Optical gain in rotationally excited nitrogen molecular ions,” Phys. Rev. A 96, 051401 (2017).
[Crossref]

M. Lei, C. Wu, A. Zhang, Q. Gong, and H. Jiang, “Population inversion in the rotational levels of the superradiant N2+ pumped by femtosecond laser pulses,” Opt. Express 25, 4535–4541 (2017).
[Crossref]

X. Zhong, Z. Miao, L. Zhang, Q. Liang, M. Lei, H. Jiang, Y. Liu, Q. Gong, and C. Wu, “Vibrational and electronic excitation of ionized nitrogen molecules in intense laser fields,” Phys. Rev. A 96, 043422 (2017).
[Crossref]

H. Xu, E. Lötstedt, T. Ando, A. Iwasaki, and K. Yamanouchi, “Alignment-dependent population inversion in ${\rm N}^+_2$N2+ in intense few-cycle laser fields,” Phys. Rev. A 96, 041401 (2017).
[Crossref]

Y. Liu, P. Ding, N. Ibrakovic, S. Bengtsson, S. Chen, R. Danylo, E. R. Simpson, E. W. Larsen, X. Zhang, Z. Fan, A. Houard, J. Mauritsson, A. L’Huillier, C. L. Arnold, S. Zhuang, V. Tikhonchuk, and A. Mysyrowicz, “Unexpected sensitivity of nitrogen ions superradiant emission on pump laser wavelength and duration,” Phys. Rev. Lett. 119, 203205 (2017).
[Crossref]

2016 (1)

J. Yao, S. Jiang, W. Chu, B. Zeng, C. Wu, R. Lu, Z. Li, H. Xie, G. Li, C. Yu, Z. Wang, H. Jiang, Q. Gong, and Y. Cheng, “Population redistribution among multiple electronic states of molecular nitrogen ions in strong laser fields,” Phys. Rev. Lett. 116, 143007 (2016).
[Crossref]

2015 (4)

S. I. Mitryukovskiy, Y. Liu, A. Houard, and A. Mysyrowicz, “Re-evaluation of the peak intensity inside a femtosecond laser filament in air,” J. Phys. B 48, 094003 (2015).
[Crossref]

S. Mitryukovskiy, Y. Liu, P. Ding, A. Houard, A. Couairon, and A. Mysyrowicz, “Plasma luminescence from femtosecond filaments in air: evidence for impact excitation with circularly polarized light pulses,” Phys. Rev. Lett. 114, 063003 (2015).
[Crossref]

Y. Liu, P. Ding, G. Lambert, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, “Recollision-induced superradiance of ionized nitrogen molecules,” Phys. Rev. Lett. 115, 133203 (2015).
[Crossref]

H. Xu, E. Lötstedt, A. Iwasaki, and K. Yamanouchi, “Sub-10-fs population inversion in N2+ air lasing through multiple state coupling,” Nat. Commun. 6, 8347 (2015).
[Crossref]

2014 (1)

G. Li, C. Jing, B. Zeng, H. Xie, J. Yao, W. Chu, J. Ni, H. Zhang, H. Xu, Y. Cheng, and Z. Xu, “Signature of superradiance from a nitrogen-gas plasma channel produced by strong-field ionization,” Phys. Rev. A 89, 033833 (2014).
[Crossref]

2013 (5)

J. Ni, W. Chu, C. Jing, H. Zhang, B. Zeng, J. Yao, G. Li, H. Xie, C. Zhang, H. Xu, S.-L. Chin, Y. Cheng, and Z. Xu, “Identification of the physical mechanism of generation of coherent emissions in air by femtosecond laser excitation,” Opt. Express 21, 8746–8752 (2013).
[Crossref]

H. Zhang, C. Jing, J. Yao, G. Li, B. Zeng, W. Chu, J. Ni, H. Xie, H. Xu, S. L. Chin, K. Yamanouchi, Y. Cheng, and Z. Xu, “Rotational coherence encoded in an “air-laser” spectrum of nitrogen molecular ions in an intense laser field,” Phys. Rev. X 3, 041009 (2013).
[Crossref]

J. Yao, G. Li, C. Jing, B. Zeng, W. Chu, J. Ni, H. Zhang, H. Xie, C. Zhang, H. Li, H. Xu, S. L. Chin, Y. Cheng, and Z. Xu, “Remote creation of coherent emissions in air with two-color ultrafast laser pulses,” New J. Phys. 15, 023046 (2013).
[Crossref]

Y. Liu, Y. Brelet, G. Point, A. Houard, and A. Mysyrowicz, “Self-seeded lasing in ionized air pumped by 800 nm femtosecond laser pulses,” Opt. Express 21, 22791–22798 (2013).
[Crossref]

W. Chu, G. Li, H. Xie, J. Ni, J. Yao, B. Zeng, H. Zhang, C. Jing, H. Xu, Y. Cheng, and Z. Xu, “A self-induced white light seeding laser in a femtosecond laser filament,” Laser Phys. Lett. 11, 015301 (2013).
[Crossref]

2012 (1)

S. Xu, J. Bernhardt, M. Sharifi, W. Liu, and S. L. Chin, “Intensity clamping during laser filamentation by TW level femtosecond laser in air and argon,” Laser Phys. 22, 195–202 (2012).
[Crossref]

2011 (1)

J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A 84, 051802 (2011).
[Crossref]

2009 (2)

M. Spanner and S. Patchkovskii, “One-electron ionization of multielectron systems in strong nonresonant laser fields,” Phys. Rev. A 80, 063411 (2009).
[Crossref]

M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett. 103, 043901 (2009).
[Crossref]

2007 (2)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[Crossref]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

2005 (1)

2003 (2)

P. W. Dooley, I. V. Litvinyuk, K. F. Lee, D. M. Rayner, M. Spanner, D. M. Villeneuve, and P. B. Corkum, “Direct imaging of rotational wave-packet dynamics of diatomic molecules,” Phys. Rev. A 68, 023406 (2003).
[Crossref]

Q. Luo, W. Liu, and S. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76, 337–340 (2003).
[Crossref]

2000 (1)

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[Crossref]

1999 (1)

T. Seideman, “Revival structure of aligned rotational wave packets,” Phys. Rev. Lett. 83, 4971–4974 (1999).
[Crossref]

1995 (2)

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995).
[Crossref]

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
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1994 (1)

M. O. Scully and M. Fleischhauer, “Lasers without inversion,” Science 263, 337–338 (1994).
[Crossref]

1993 (3)

A. Nottelmann, C. Peters, and W. Lange, “Inversionless amplification of picosecond pulses due to Zeeman coherence,” Phys. Rev. Lett. 70, 1783–1786 (1993).
[Crossref]

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S.-Y. Zhu, “Atomic coherence effects within the sodium d1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[Crossref]

W. E. van der Veer, R. J. J. van Diest, A. Dönszelmann, and H. B. van Linden van den Heuvell, “Experimental demonstration of light amplification without population inversion,” Phys. Rev. Lett. 70, 3243–3246 (1993).
[Crossref]

1992 (2)

O. Kocharovskaya, “Amplification and lasing without inversion,” Phys. Rep. 219, 175–190 (1992).
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M. O. Scully, “From lasers and masers to phaseonium and phasers,” Phys. Rep. 219, 191–201 (1992).
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1990 (1)

1989 (2)

M. O. Scully, S.-Y. Zhu, and A. Gavrielides, “Degenerate quantum-beat laser: lasing without inversion and inversion without lasing,” Phys. Rev. Lett. 62, 2813–2816 (1989).
[Crossref]

S. E. Harris, “Lasers without inversion: interference of lifetime-broadened resonances,” Phys. Rev. Lett. 62, 1033–1036 (1989).
[Crossref]

1988 (1)

O. A. Kocharovskaya and Y. I. Khanin, “Coherent amplification of an ultrashort pulse in a three-level medium without a population inversion,” Pis’ma Zh. Eksp. Teor. Fiz. 48, 581 (1988).

Ališauskas, S.

D. Kartashov, S. Haessler, S. Ališauskas, G. Andriukaitis, A. Pugžlys, A. Baltuška, J. Möhring, D. Starukhin, M. Motzkus, A. Zheltikov, M. Richter, F. Morales, O. Smirnova, M. Y. Ivanov, and M. Spanner, “Transient inversion in rotationally aligned nitrogen ions in a femtosecond filament,” in Research in Optical Sciences, OSA Technical Digest (online) (Optical Society of America, 2014), paper HTh4B.5.

Ando, T.

T. Ando, E. Lötstedt, A. Iwasaki, H. Li, Y. Fu, S. Wang, H. Xu, and K. Yamanouchi, “Rotational, vibrational, and electronic modulations in ${\rm N}^+_2$N2+ lasing at 391 nm: evidence of coherent ${\rm B}^2{\Sigma}^+_u - {\rm X}^2{\Sigma}^+_g - {\rm A}^2{\Pi}_u$ B2Σu+−X2Σg+−A2Πu coupling,” Phys. Rev. Lett. 123, 203201 (2019).
[Crossref]

H. Li, M. Hou, H. Zang, Y. Fu, E. Lötstedt, T. Ando, A. Iwasaki, K. Yamanouchi, and H. Xu, “Significant enhancement of N2+lasing by polarization-modulated ultrashort laser pulses,” Phys. Rev. Lett. 122, 013202 (2019).
[Crossref]

H. Xu, E. Lötstedt, T. Ando, A. Iwasaki, and K. Yamanouchi, “Alignment-dependent population inversion in ${\rm N}^+_2$N2+ in intense few-cycle laser fields,” Phys. Rev. A 96, 041401 (2017).
[Crossref]

Andriukaitis, G.

D. Kartashov, S. Haessler, S. Ališauskas, G. Andriukaitis, A. Pugžlys, A. Baltuška, J. Möhring, D. Starukhin, M. Motzkus, A. Zheltikov, M. Richter, F. Morales, O. Smirnova, M. Y. Ivanov, and M. Spanner, “Transient inversion in rotationally aligned nitrogen ions in a femtosecond filament,” in Research in Optical Sciences, OSA Technical Digest (online) (Optical Society of America, 2014), paper HTh4B.5.

Angeluts, A. A.

P. M. Solyankin, I. A. Nikolaeva, A. A. Angeluts, D. E. Shipilo, N. V. Minaev, N. A. Panov, A. V. Balakin, Y. Zhu, O. G. Kosareva, and A. P. Shkurinov, “THz generation from laser-induced breakdown in pressurized molecular gases: on the way to terahertz remote sensing of the atmospheres of Mars and Venus,” New J. Phys. 22, 013039 (2020).
[Crossref]

Arissian, L.

M. Britton, M. Lytova, P. Laferrière, P. Peng, F. Morales, D. H. Ko, M. Richter, P. Polynkin, D. M. Villeneuve, C. Zhang, M. Ivanov, M. Spanner, L. Arissian, and P. B. Corkum, “Short- and long-term gain dynamics in N2+air lasing,” Phys. Rev. A 100, 013406 (2019).
[Crossref]

L. Arissian, B. Kamer, A. Rastegari, D. M. Villeneuve, and J.-C. Diels, “Transient gain from ${\rm N}^+_2$N2+ in light filaments,” Phys. Rev. A 98, 053438 (2018).
[Crossref]

M. Britton, P. Laferrière, D. H. Ko, Z. Li, F. Kong, G. Brown, A. Naumov, C. Zhang, L. Arissian, and P. B. Corkum, “Testing the role of recollision in ${\rm N}^+_2$N2+ air lasing,” Phys. Rev. Lett. 120, 133208 (2018).
[Crossref]

Arnold, C. L.

Y. Liu, P. Ding, N. Ibrakovic, S. Bengtsson, S. Chen, R. Danylo, E. R. Simpson, E. W. Larsen, X. Zhang, Z. Fan, A. Houard, J. Mauritsson, A. L’Huillier, C. L. Arnold, S. Zhuang, V. Tikhonchuk, and A. Mysyrowicz, “Unexpected sensitivity of nitrogen ions superradiant emission on pump laser wavelength and duration,” Phys. Rev. Lett. 119, 203205 (2017).
[Crossref]

Azarm, A.

A. Azarm, P. Corkum, and P. Polynkin, “Optical gain in rotationally excited nitrogen molecular ions,” Phys. Rev. A 96, 051401 (2017).
[Crossref]

Balakin, A. V.

P. M. Solyankin, I. A. Nikolaeva, A. A. Angeluts, D. E. Shipilo, N. V. Minaev, N. A. Panov, A. V. Balakin, Y. Zhu, O. G. Kosareva, and A. P. Shkurinov, “THz generation from laser-induced breakdown in pressurized molecular gases: on the way to terahertz remote sensing of the atmospheres of Mars and Venus,” New J. Phys. 22, 013039 (2020).
[Crossref]

Baltuška, A.

D. Kartashov, S. Haessler, S. Ališauskas, G. Andriukaitis, A. Pugžlys, A. Baltuška, J. Möhring, D. Starukhin, M. Motzkus, A. Zheltikov, M. Richter, F. Morales, O. Smirnova, M. Y. Ivanov, and M. Spanner, “Transient inversion in rotationally aligned nitrogen ions in a femtosecond filament,” in Research in Optical Sciences, OSA Technical Digest (online) (Optical Society of America, 2014), paper HTh4B.5.

Bengtsson, S.

Y. Liu, P. Ding, N. Ibrakovic, S. Bengtsson, S. Chen, R. Danylo, E. R. Simpson, E. W. Larsen, X. Zhang, Z. Fan, A. Houard, J. Mauritsson, A. L’Huillier, C. L. Arnold, S. Zhuang, V. Tikhonchuk, and A. Mysyrowicz, “Unexpected sensitivity of nitrogen ions superradiant emission on pump laser wavelength and duration,” Phys. Rev. Lett. 119, 203205 (2017).
[Crossref]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Bernhardt, J.

S. Xu, J. Bernhardt, M. Sharifi, W. Liu, and S. L. Chin, “Intensity clamping during laser filamentation by TW level femtosecond laser in air and argon,” Laser Phys. 22, 195–202 (2012).
[Crossref]

Braun, A.

Brelet, Y.

Britton, M.

M. Britton, M. Lytova, P. Laferrière, P. Peng, F. Morales, D. H. Ko, M. Richter, P. Polynkin, D. M. Villeneuve, C. Zhang, M. Ivanov, M. Spanner, L. Arissian, and P. B. Corkum, “Short- and long-term gain dynamics in N2+air lasing,” Phys. Rev. A 100, 013406 (2019).
[Crossref]

M. Britton, P. Laferrière, D. H. Ko, Z. Li, F. Kong, G. Brown, A. Naumov, C. Zhang, L. Arissian, and P. B. Corkum, “Testing the role of recollision in ${\rm N}^+_2$N2+ air lasing,” Phys. Rev. Lett. 120, 133208 (2018).
[Crossref]

Brown, G.

M. Britton, P. Laferrière, D. H. Ko, Z. Li, F. Kong, G. Brown, A. Naumov, C. Zhang, L. Arissian, and P. B. Corkum, “Testing the role of recollision in ${\rm N}^+_2$N2+ air lasing,” Phys. Rev. Lett. 120, 133208 (2018).
[Crossref]

Chen, J.

H. Li, Q. Song, J. Yao, Z. Liu, J. Chen, B. Xu, K. Lin, J. Qiang, B. He, H. Xu, Y. Cheng, H. Zeng, and J. Wu, “Air lasing from singly ionized N2 driven by bicircular two-color fields,” Phys. Rev. A 99, 053413 (2019).
[Crossref]

B. Xu, S. Jiang, J. Yao, J. Chen, Z. Liu, W. Chu, Y. Wan, F. Zhang, L. Qiao, R. Lu, Y. Cheng, and Z. Xu, “Free-space ${\rm N}^+_2$N2+ lasers generated strong laser fields: the role of molecular vibration,” Opt. Express 26, 13331–13339 (2018).
[Crossref]

Chen, S.

Y. Liu, P. Ding, N. Ibrakovic, S. Bengtsson, S. Chen, R. Danylo, E. R. Simpson, E. W. Larsen, X. Zhang, Z. Fan, A. Houard, J. Mauritsson, A. L’Huillier, C. L. Arnold, S. Zhuang, V. Tikhonchuk, and A. Mysyrowicz, “Unexpected sensitivity of nitrogen ions superradiant emission on pump laser wavelength and duration,” Phys. Rev. Lett. 119, 203205 (2017).
[Crossref]

Chen, Z.

Q. Zhang, H. Xie, G. Li, X. Wang, H. Lei, J. Zhao, Z. Chen, J. Yao, Y. Cheng, and Z. Zhao, “Sub-cycle coherent control of ionic dynamics via transient ionization injection,” Communications Phys. 3, 50 (2020).
[Crossref]

Cheng, Y.

Q. Zhang, H. Xie, G. Li, X. Wang, H. Lei, J. Zhao, Z. Chen, J. Yao, Y. Cheng, and Z. Zhao, “Sub-cycle coherent control of ionic dynamics via transient ionization injection,” Communications Phys. 3, 50 (2020).
[Crossref]

H. Li, Q. Song, J. Yao, Z. Liu, J. Chen, B. Xu, K. Lin, J. Qiang, B. He, H. Xu, Y. Cheng, H. Zeng, and J. Wu, “Air lasing from singly ionized N2 driven by bicircular two-color fields,” Phys. Rev. A 99, 053413 (2019).
[Crossref]

B. Xu, S. Jiang, J. Yao, J. Chen, Z. Liu, W. Chu, Y. Wan, F. Zhang, L. Qiao, R. Lu, Y. Cheng, and Z. Xu, “Free-space ${\rm N}^+_2$N2+ lasers generated strong laser fields: the role of molecular vibration,” Opt. Express 26, 13331–13339 (2018).
[Crossref]

J. Yao, S. Jiang, W. Chu, B. Zeng, C. Wu, R. Lu, Z. Li, H. Xie, G. Li, C. Yu, Z. Wang, H. Jiang, Q. Gong, and Y. Cheng, “Population redistribution among multiple electronic states of molecular nitrogen ions in strong laser fields,” Phys. Rev. Lett. 116, 143007 (2016).
[Crossref]

G. Li, C. Jing, B. Zeng, H. Xie, J. Yao, W. Chu, J. Ni, H. Zhang, H. Xu, Y. Cheng, and Z. Xu, “Signature of superradiance from a nitrogen-gas plasma channel produced by strong-field ionization,” Phys. Rev. A 89, 033833 (2014).
[Crossref]

H. Zhang, C. Jing, J. Yao, G. Li, B. Zeng, W. Chu, J. Ni, H. Xie, H. Xu, S. L. Chin, K. Yamanouchi, Y. Cheng, and Z. Xu, “Rotational coherence encoded in an “air-laser” spectrum of nitrogen molecular ions in an intense laser field,” Phys. Rev. X 3, 041009 (2013).
[Crossref]

W. Chu, G. Li, H. Xie, J. Ni, J. Yao, B. Zeng, H. Zhang, C. Jing, H. Xu, Y. Cheng, and Z. Xu, “A self-induced white light seeding laser in a femtosecond laser filament,” Laser Phys. Lett. 11, 015301 (2013).
[Crossref]

J. Ni, W. Chu, C. Jing, H. Zhang, B. Zeng, J. Yao, G. Li, H. Xie, C. Zhang, H. Xu, S.-L. Chin, Y. Cheng, and Z. Xu, “Identification of the physical mechanism of generation of coherent emissions in air by femtosecond laser excitation,” Opt. Express 21, 8746–8752 (2013).
[Crossref]

J. Yao, G. Li, C. Jing, B. Zeng, W. Chu, J. Ni, H. Zhang, H. Xie, C. Zhang, H. Li, H. Xu, S. L. Chin, Y. Cheng, and Z. Xu, “Remote creation of coherent emissions in air with two-color ultrafast laser pulses,” New J. Phys. 15, 023046 (2013).
[Crossref]

J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A 84, 051802 (2011).
[Crossref]

Chin, S.

Q. Luo, W. Liu, and S. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76, 337–340 (2003).
[Crossref]

Chin, S. L.

J. Yao, G. Li, C. Jing, B. Zeng, W. Chu, J. Ni, H. Zhang, H. Xie, C. Zhang, H. Li, H. Xu, S. L. Chin, Y. Cheng, and Z. Xu, “Remote creation of coherent emissions in air with two-color ultrafast laser pulses,” New J. Phys. 15, 023046 (2013).
[Crossref]

H. Zhang, C. Jing, J. Yao, G. Li, B. Zeng, W. Chu, J. Ni, H. Xie, H. Xu, S. L. Chin, K. Yamanouchi, Y. Cheng, and Z. Xu, “Rotational coherence encoded in an “air-laser” spectrum of nitrogen molecular ions in an intense laser field,” Phys. Rev. X 3, 041009 (2013).
[Crossref]

S. Xu, J. Bernhardt, M. Sharifi, W. Liu, and S. L. Chin, “Intensity clamping during laser filamentation by TW level femtosecond laser in air and argon,” Laser Phys. 22, 195–202 (2012).
[Crossref]

J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A 84, 051802 (2011).
[Crossref]

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[Crossref]

Chin, S.-L.

Chu, W.

B. Xu, S. Jiang, J. Yao, J. Chen, Z. Liu, W. Chu, Y. Wan, F. Zhang, L. Qiao, R. Lu, Y. Cheng, and Z. Xu, “Free-space ${\rm N}^+_2$N2+ lasers generated strong laser fields: the role of molecular vibration,” Opt. Express 26, 13331–13339 (2018).
[Crossref]

J. Yao, S. Jiang, W. Chu, B. Zeng, C. Wu, R. Lu, Z. Li, H. Xie, G. Li, C. Yu, Z. Wang, H. Jiang, Q. Gong, and Y. Cheng, “Population redistribution among multiple electronic states of molecular nitrogen ions in strong laser fields,” Phys. Rev. Lett. 116, 143007 (2016).
[Crossref]

G. Li, C. Jing, B. Zeng, H. Xie, J. Yao, W. Chu, J. Ni, H. Zhang, H. Xu, Y. Cheng, and Z. Xu, “Signature of superradiance from a nitrogen-gas plasma channel produced by strong-field ionization,” Phys. Rev. A 89, 033833 (2014).
[Crossref]

H. Zhang, C. Jing, J. Yao, G. Li, B. Zeng, W. Chu, J. Ni, H. Xie, H. Xu, S. L. Chin, K. Yamanouchi, Y. Cheng, and Z. Xu, “Rotational coherence encoded in an “air-laser” spectrum of nitrogen molecular ions in an intense laser field,” Phys. Rev. X 3, 041009 (2013).
[Crossref]

J. Ni, W. Chu, C. Jing, H. Zhang, B. Zeng, J. Yao, G. Li, H. Xie, C. Zhang, H. Xu, S.-L. Chin, Y. Cheng, and Z. Xu, “Identification of the physical mechanism of generation of coherent emissions in air by femtosecond laser excitation,” Opt. Express 21, 8746–8752 (2013).
[Crossref]

W. Chu, G. Li, H. Xie, J. Ni, J. Yao, B. Zeng, H. Zhang, C. Jing, H. Xu, Y. Cheng, and Z. Xu, “A self-induced white light seeding laser in a femtosecond laser filament,” Laser Phys. Lett. 11, 015301 (2013).
[Crossref]

J. Yao, G. Li, C. Jing, B. Zeng, W. Chu, J. Ni, H. Zhang, H. Xie, C. Zhang, H. Li, H. Xu, S. L. Chin, Y. Cheng, and Z. Xu, “Remote creation of coherent emissions in air with two-color ultrafast laser pulses,” New J. Phys. 15, 023046 (2013).
[Crossref]

J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A 84, 051802 (2011).
[Crossref]

Corkum, P.

A. Azarm, P. Corkum, and P. Polynkin, “Optical gain in rotationally excited nitrogen molecular ions,” Phys. Rev. A 96, 051401 (2017).
[Crossref]

Corkum, P. B.

M. Britton, M. Lytova, P. Laferrière, P. Peng, F. Morales, D. H. Ko, M. Richter, P. Polynkin, D. M. Villeneuve, C. Zhang, M. Ivanov, M. Spanner, L. Arissian, and P. B. Corkum, “Short- and long-term gain dynamics in N2+air lasing,” Phys. Rev. A 100, 013406 (2019).
[Crossref]

M. Britton, P. Laferrière, D. H. Ko, Z. Li, F. Kong, G. Brown, A. Naumov, C. Zhang, L. Arissian, and P. B. Corkum, “Testing the role of recollision in ${\rm N}^+_2$N2+ air lasing,” Phys. Rev. Lett. 120, 133208 (2018).
[Crossref]

P. W. Dooley, I. V. Litvinyuk, K. F. Lee, D. M. Rayner, M. Spanner, D. M. Villeneuve, and P. B. Corkum, “Direct imaging of rotational wave-packet dynamics of diatomic molecules,” Phys. Rev. A 68, 023406 (2003).
[Crossref]

Couairon, A.

S. Mitryukovskiy, Y. Liu, P. Ding, A. Houard, A. Couairon, and A. Mysyrowicz, “Plasma luminescence from femtosecond filaments in air: evidence for impact excitation with circularly polarized light pulses,” Phys. Rev. Lett. 114, 063003 (2015).
[Crossref]

M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett. 103, 043901 (2009).
[Crossref]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[Crossref]

Danylo, R.

A. Mysyrowicz, R. Danylo, A. Houard, V. Tikhonchuk, X. Zhang, Z. Fan, Q. Liang, S. Zhuang, L. Yuan, and Y. Liu, “Lasing without population inversion in ${\rm N}^+_2$N2+,” APL Photon. 4, 110807 (2019).
[Crossref]

Y. Liu, P. Ding, N. Ibrakovic, S. Bengtsson, S. Chen, R. Danylo, E. R. Simpson, E. W. Larsen, X. Zhang, Z. Fan, A. Houard, J. Mauritsson, A. L’Huillier, C. L. Arnold, S. Zhuang, V. Tikhonchuk, and A. Mysyrowicz, “Unexpected sensitivity of nitrogen ions superradiant emission on pump laser wavelength and duration,” Phys. Rev. Lett. 119, 203205 (2017).
[Crossref]

Diels, J.-C.

L. Arissian, B. Kamer, A. Rastegari, D. M. Villeneuve, and J.-C. Diels, “Transient gain from ${\rm N}^+_2$N2+ in light filaments,” Phys. Rev. A 98, 053438 (2018).
[Crossref]

Ding, P.

Y. Liu, P. Ding, N. Ibrakovic, S. Bengtsson, S. Chen, R. Danylo, E. R. Simpson, E. W. Larsen, X. Zhang, Z. Fan, A. Houard, J. Mauritsson, A. L’Huillier, C. L. Arnold, S. Zhuang, V. Tikhonchuk, and A. Mysyrowicz, “Unexpected sensitivity of nitrogen ions superradiant emission on pump laser wavelength and duration,” Phys. Rev. Lett. 119, 203205 (2017).
[Crossref]

S. Mitryukovskiy, Y. Liu, P. Ding, A. Houard, A. Couairon, and A. Mysyrowicz, “Plasma luminescence from femtosecond filaments in air: evidence for impact excitation with circularly polarized light pulses,” Phys. Rev. Lett. 114, 063003 (2015).
[Crossref]

Y. Liu, P. Ding, G. Lambert, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, “Recollision-induced superradiance of ionized nitrogen molecules,” Phys. Rev. Lett. 115, 133203 (2015).
[Crossref]

Dönszelmann, A.

W. E. van der Veer, R. J. J. van Diest, A. Dönszelmann, and H. B. van Linden van den Heuvell, “Experimental demonstration of light amplification without population inversion,” Phys. Rev. Lett. 70, 3243–3246 (1993).
[Crossref]

Dooley, P. W.

P. W. Dooley, I. V. Litvinyuk, K. F. Lee, D. M. Rayner, M. Spanner, D. M. Villeneuve, and P. B. Corkum, “Direct imaging of rotational wave-packet dynamics of diatomic molecules,” Phys. Rev. A 68, 023406 (2003).
[Crossref]

Du, D.

Fan, Z.

A. Mysyrowicz, R. Danylo, A. Houard, V. Tikhonchuk, X. Zhang, Z. Fan, Q. Liang, S. Zhuang, L. Yuan, and Y. Liu, “Lasing without population inversion in ${\rm N}^+_2$N2+,” APL Photon. 4, 110807 (2019).
[Crossref]

A. Zhang, Q. Liang, M. Lei, L. Yuan, Y. Liu, Z. Fan, X. Zhang, S. Zhuang, C. Wu, Q. Gong, and H. Jiang, “Coherent modulation of superradiance from nitrogen ions pumped with femtosecond pulses,” Opt. Express 27, 12638–12646 (2019).
[Crossref]

Y. Liu, P. Ding, N. Ibrakovic, S. Bengtsson, S. Chen, R. Danylo, E. R. Simpson, E. W. Larsen, X. Zhang, Z. Fan, A. Houard, J. Mauritsson, A. L’Huillier, C. L. Arnold, S. Zhuang, V. Tikhonchuk, and A. Mysyrowicz, “Unexpected sensitivity of nitrogen ions superradiant emission on pump laser wavelength and duration,” Phys. Rev. Lett. 119, 203205 (2017).
[Crossref]

Fleischhauer, M.

M. O. Scully and M. Fleischhauer, “Lasers without inversion,” Science 263, 337–338 (1994).
[Crossref]

Fry, E. S.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S.-Y. Zhu, “Atomic coherence effects within the sodium d1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[Crossref]

Fu, Y.

T. Ando, E. Lötstedt, A. Iwasaki, H. Li, Y. Fu, S. Wang, H. Xu, and K. Yamanouchi, “Rotational, vibrational, and electronic modulations in ${\rm N}^+_2$N2+ lasing at 391 nm: evidence of coherent ${\rm B}^2{\Sigma}^+_u - {\rm X}^2{\Sigma}^+_g - {\rm A}^2{\Pi}_u$ B2Σu+−X2Σg+−A2Πu coupling,” Phys. Rev. Lett. 123, 203201 (2019).
[Crossref]

H. Li, M. Hou, H. Zang, Y. Fu, E. Lötstedt, T. Ando, A. Iwasaki, K. Yamanouchi, and H. Xu, “Significant enhancement of N2+lasing by polarization-modulated ultrashort laser pulses,” Phys. Rev. Lett. 122, 013202 (2019).
[Crossref]

Gaarde, M. B.

M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett. 103, 043901 (2009).
[Crossref]

Gao, J.

Gavrielides, A.

M. O. Scully, S.-Y. Zhu, and A. Gavrielides, “Degenerate quantum-beat laser: lasing without inversion and inversion without lasing,” Phys. Rev. Lett. 62, 2813–2816 (1989).
[Crossref]

Gong, Q.

A. Zhang, Q. Liang, M. Lei, L. Yuan, Y. Liu, Z. Fan, X. Zhang, S. Zhuang, C. Wu, Q. Gong, and H. Jiang, “Coherent modulation of superradiance from nitrogen ions pumped with femtosecond pulses,” Opt. Express 27, 12638–12646 (2019).
[Crossref]

A. Zhang, M. Lei, J. Gao, C. Wu, Q. Gong, and H. Jiang, “Subfemtosecond-resolved modulation of superfluorescence from ionized nitrogen molecules by 800-nm femtosecond laser pulses,” Opt. Express 27, 14922–14930 (2019).
[Crossref]

X. Zhong, Z. Miao, L. Zhang, H. Jiang, Y. Liu, Q. Gong, and C. Wu, “Optimizing the 391-nm lasing intensity from ionized nitrogen molecules in 800-nm femtosecond laser fields,” Phys. Rev. A 97, 033409 (2018).
[Crossref]

M. Lei, C. Wu, A. Zhang, Q. Gong, and H. Jiang, “Population inversion in the rotational levels of the superradiant N2+ pumped by femtosecond laser pulses,” Opt. Express 25, 4535–4541 (2017).
[Crossref]

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J. Yao, G. Li, C. Jing, B. Zeng, W. Chu, J. Ni, H. Zhang, H. Xie, C. Zhang, H. Li, H. Xu, S. L. Chin, Y. Cheng, and Z. Xu, “Remote creation of coherent emissions in air with two-color ultrafast laser pulses,” New J. Phys. 15, 023046 (2013).
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J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A 84, 051802 (2011).
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Zeng, H.

H. Li, Q. Song, J. Yao, Z. Liu, J. Chen, B. Xu, K. Lin, J. Qiang, B. He, H. Xu, Y. Cheng, H. Zeng, and J. Wu, “Air lasing from singly ionized N2 driven by bicircular two-color fields,” Phys. Rev. A 99, 053413 (2019).
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Zhang, C.

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Supplementary Material (1)

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» Supplement 1       Details of simulations

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Figures (3)

Fig. 1.
Fig. 1. Schematic of a rotational quantum beat laser without inversion in the time domain using the example of ${\rm N}_2^ +$. Calculations are performed for a 23 fs, 800 nm, ${10^{14}}\,\,{\rm W}/{{\rm cm}^2}$ pump pulse and room temperature (298 K); see text and Supplement 1 for details. The 3D shapes in panels (a),(b) sketch the angular distributions of the rotating molecular ensembles. (a) Field-free molecular alignment of ${{\rm N}_2}$ at 298 K induced by the intense femtosecond pump pulse. (b) Field-free rotational dynamics in the two vibronic states $|X,{\nu ^{{\prime \prime}}} = 0\rangle$ and $|B,{\nu ^\prime} = 0\rangle$ of ${\rm N}_2^ +$ induced by the same pump. (c) ${P_X}{\langle {\cos}^2 \theta \rangle _X}(\tau)$ (blue), ${P_B}{\langle {\cos}^2 \theta \rangle _B}(\tau)$ (red), and ${P_X}{\langle {\cos}^2 \theta \rangle _X}(\tau) - {P_B}{\langle {\cos}^2 \theta \rangle _B}(\tau)$ (green). Gain windows (at ${\tau _1} \simeq 4.4\; {\rm ps}$ and ${\tau _2} \simeq 13.0\; {\rm ps}$) without population inversion at a parallel transition between the two vibronic states are enabled by the different angular distribution geometries of the rotating molecular ensembles in the upper and lower state; no coherence between the two rotational manifolds is required.
Fig. 2.
Fig. 2. Rotational quantum beat lasing without inversion in the frequency domain using the example of ${\rm N}_2^ +$. Calculations are performed for the same pump pulse and temperature as in Fig. 1 and a 20 fs, 391 nm, ${10^{11}}\,\,{\rm W}/{{\rm cm}^2}$ probe pulse; see text and Supplement 1 for details. (a) Full simulation of the frequency-resolved gain (red) and loss (blue) of the weak probe interacting with the pumped system as a function of pump-probe delay. (b) Rotational distributions in the ground vibrational levels of the $X$ and $B$ states of ${\rm N}_2^ +$ formed at the end of the interaction with the intense femtosecond pump pulse. (c) Four-level system controlling absorption and emission at the $|X,{\nu ^{{\prime \prime}}} = 0,J\rangle \to |B,{\nu ^\prime} = 0,J + 1\rangle$ transition. (d) Absorption (blue) and emission (negative absorption) (red) integrated over all frequencies follow the alignment dynamics in Fig. 1(b). The total gain-loss balance integrated over all frequencies (green) follows the pattern of ${P_X}{\langle {\cos}^2 \theta \rangle _X} - {P_B}{\langle {\cos}^2 \theta \rangle _B}$ in Fig. 1(c), showing the same gain windows for the inversionless medium (${P_X} \gt {P_B}$).
Fig. 3.
Fig. 3. Rotational quantum beat lasing in ${\rm N}_2^ +$ for different intensities realistic in femtosecond laser filamentation experiments. Calculations are performed for a 23 fs, 800 nm pump pulse and the same probe pulse and temperature as in Fig. 2. (a) and (b) Same as Fig. 2(a), but for pump intensities of (a) $I = 5.0 \times {10^{13}}\,\,{\rm W}/{{\rm cm}^2}$ and (b) $I = 1.5 \times {10^{14}}\,\,{\rm W}/{{\rm cm}^2}$. (c) Gain-loss balance for $I = 1.5 \times {10^{14}}\,\,{\rm W}/{{\rm cm}^2}$ integrated over the frequency windows (bins) indicated in panel (b). For both intensities, gain windows also emerge for the total gain-loss balance integrated over all frequencies, analogue to Fig. 2(d). Gain windows emerge without population inversion of the medium (${P_X} \gt {P_B}$).