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A quantum gas of ultracold molecules, with long-range and anisotropic interactions, will enable a series of fundamental studies in physics and chemistry. In particular, samples of ground-state molecules at ultralow temperatures and high number densities will facilitate the explorations of a large number of many-body physical phenomena and applications in quantum information processing. However, due to the lack of efficiently cooling techniques such as laser cooling for atomic gases, high number densities for ultracold molecular samples are not readily attainable. Associating ultracold atoms to weakly bound dimer molecules via Feshbach resonance and subsequently transferring them to a wanted molecular ro-vibronic ground state by a stimulated Raman adiabatic passages (STIRAP) have proved to be an effective way in producing ideal ultracold molecular samples. As a typical illustration, in a recent study (2010 Nat. Phys. 6 265) Danzl et al. experimentally realized the preparation of Cs2 molecule into its ro-vibronic ground state via two different multi-level STIRAPs:one is based on a single conversion route and the others are based on a cascade-connected route (labeled by 4p-STIRAP and s-STIRAP, respectively). In this work, we present a theoretical study for these two STIRAP schemes, focusing on the differences in physical principle and realistic performance between them. On the one hand, according to the theoretical approach of quasi-dark eigenstates, we conclude that a highly efficient population transfer is achievable in both schemes. On the other hand, by systematically studying the influences of the relevant parameters, including the spontaneous decays and the detunings from the intermediate states, and the temporal sequence and the amplitude of the laser pulses, we disclose their respective advantages and weaknesses in the realistic implementation. We theoretically predict that for both schemes their maximal conversion efficiencies each can attain 0.97 as long as the spontaneous decays from the intermediate excited states are sufficiently suppressed. Yet considering the fact that the already implemented efficiency is only around 0.6 for both schemes, there is still room for optimization, e.g. using stable Rydberg energy levels in future experiment. Furthermore, the success of these two schemes can provide a new route to the controllable entanglement preparation, opening more applications in the fields of quantum logic gate and so on.
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Keywords:
- stimulated Raman adiabatic process /
- population transfer /
- adiabatic condition /
- entangled state
[1] Gaubatz U, Rudecki P, Schiemann S, Bergmann K 1990 J. Chem. Phys. 92 5363
[2] Vitanov N V, Rangelov A A, Shore B W, Bergmann K 2017 Rev. Mod. Phys. 89 015006
[3] Yun J, Li C, Chung H, Choi J, Cho M 2015 Chem. Phys. Lett. 627 20
[4] Vewinger F, Heinz M, Garcia-Fernandez R, Vitanov N V, Bergmann K 2003 Phys. Rev. Lett. 91 213001
[5] Toyoda K, Uchida K, Noguchi A, Haze S, Urabe S 2013 Phys. Rev. A 87 052307
[6] Qian J, Zhang W, Ling H Y 2010 Phys. Rev. A 81 013632
[7] Zhai J, Zhang L, Zhang K, Qian J, Zhang W 2015 J. Opt. Soc. Am. B 32 2164
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[9] Jamonneau P, Htet G, Drau, Roch J F, Jacques V 2016 Phys. Rev. Lett. 116 043603
[10] Yale C G, Buckley B B, Christle D, Burkard G, Heremans F J, Bassett L C, Awschalom D D 2013 PNAS 110 7595
[11] Danzl J G, Mark M J, Haller E, Gustavsson M, Hart R, Aldegunde J, Hutson J M Ngerl H C 2010 Nat. Phys. 6 265
[12] Chen T, Zhu S, Li X, Qian J, Wang Y 2014 Phys. Rev. A 89 063402
[13] Mller D, Srensen J L, Thomsen J B, Drewsen M 2007 Phys. Rev. A 76 062321
[14] Webster S C, Weidt S, Lake K, McLoughlin J J, Hensinger W K 2013 Phys. Rev. Lett 111 140501
[15] Theuer H, Bergmann K 1998 Eur. Phys. J. D 2 279
[16] Kulin S, Saubamea B, Peik E, Lawall J, Hijmans T W, Leduc M, Cohen-Tannoudji C 1997 Phys. Rev. Lett. 78 4185
[17] Nlleke C, Neuzner A, Reiserer A, Hahn C, Rempe G, Ritter S 2013 Phys. Rev. Lett. 110 140403
[18] Novikov S, Sweeney T, Robinson J E, Premaratne S P, Suri B, Wellstood F C, Palmer B S 2008 Nat. Phys. 4 622
[19] Ospelkaus S, Pe'Er A, Ni K K, Zirbel J J, Neyenhuis B,Kotochigova S, Jin D S 2008 Nat. Phys. 4 622
[20] Ni K K, Ospelkaus S, de Miranda M H G, Pe'Er A, Neyenhuis B, Zirbel J J, Ye J 2008 Science 322 231
[21] Lang F, Winkler K, Strauss C, Grimm R, Denschlag J H 2008 Phys. Rev. Lett. 101 133005
[22] Stellmer S, Pasquiou B, Grimm R, Schreck F 2012 Phys. Rev. Lett. 109 115302
[23] Shore B W 2011 Manipulating Quantum Structures Using Laser Pulses (Cambridge: Cambridge University Press) pp57-60
[24] Aikawa K, Akamatsu D, Hayashi M, Oasa K, Kobayashi J, Naidon P, Inouye S 2010 Phys. Rev. Lett. 105 203001
[25] Molony P K, Gregory P D, Ji Z, Lu B, Kppinger M P, Le Sueur C R, Cornish S L 2014 Phys. Rev. Lett. 113 255301
[26] Ji Z, Zhang H, Wu J, Yuan J, Yang Y, Zhao Y, Jia S 2012 Phys. Rev. A 85 013401
[27] Park J W, Will S A, Zwierlein M W 2015 Phys. Rev. Lett. 114 205302
[28] Guo M, Zhu B, Lu B, Ye X, Wang F, Vexiau R, Wang D 2016 Phys. Rev. Lett. 116 205303
[29] Ciamei A, Bayerle A, Chen C C, Pasquiou B, Schreck F 2017 Phys. Rev. A 96 013406
[30] Liao W T, Plffy A, Keitel C H 2011 Phys. Lett. B 705 134
[31] Oreg J, Bergmann K, Shore B W, Rosenwaks S 1992 Phys. Rev. A 45 4888
[32] Viteau M, Chotia A, Allegrini M, Bouloufa N, Dulieu O, Comparat D, Pillet P 2008 Science 321 232
[33] Klein J, Beil F, Halfmann T 2007 Phys. Rev. Lett. 99 113003
[34] Du Y X, Liang Z T, Huang W, Yan H, Zhu S L 2014 Phys. Rev. A 90 023821
[35] Pu H, Maenner P, Zhang W, Ling H Y 2007 Phys. Rev. Lett. 98 050406
[36] Meystre P 2001 Atom Optics (New York: Springer Science Business Media) pp4-7
[37] Butscher B, Bendkowsky V, Nipper J, Balewski J B, Kukota L, Lw R, Rost J M 2011 J. Phys. B: At. Mol. Opt. Phys. 44 184004
[38] Bendkowsky V, Butscher B, Nipper J, Shaffer J P, Lw R, Pfau T 2009 Nature 458 1005
[39] Volz J, Weber M, Schlenk D, Rosenfeld W, Vrana J, Saucke K, Weinfurter H 2006 Phys. Rev. Lett. 96 030404
[40] Zhen B Y, Huai Z W, Shi B Z 2010 Chin. Phys. B 19 094205
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[1] Gaubatz U, Rudecki P, Schiemann S, Bergmann K 1990 J. Chem. Phys. 92 5363
[2] Vitanov N V, Rangelov A A, Shore B W, Bergmann K 2017 Rev. Mod. Phys. 89 015006
[3] Yun J, Li C, Chung H, Choi J, Cho M 2015 Chem. Phys. Lett. 627 20
[4] Vewinger F, Heinz M, Garcia-Fernandez R, Vitanov N V, Bergmann K 2003 Phys. Rev. Lett. 91 213001
[5] Toyoda K, Uchida K, Noguchi A, Haze S, Urabe S 2013 Phys. Rev. A 87 052307
[6] Qian J, Zhang W, Ling H Y 2010 Phys. Rev. A 81 013632
[7] Zhai J, Zhang L, Zhang K, Qian J, Zhang W 2015 J. Opt. Soc. Am. B 32 2164
[8] Di Stefano P G, Paladino E, Pope T J, Falci G 2016 Phys. Rev. A 93 051801
[9] Jamonneau P, Htet G, Drau, Roch J F, Jacques V 2016 Phys. Rev. Lett. 116 043603
[10] Yale C G, Buckley B B, Christle D, Burkard G, Heremans F J, Bassett L C, Awschalom D D 2013 PNAS 110 7595
[11] Danzl J G, Mark M J, Haller E, Gustavsson M, Hart R, Aldegunde J, Hutson J M Ngerl H C 2010 Nat. Phys. 6 265
[12] Chen T, Zhu S, Li X, Qian J, Wang Y 2014 Phys. Rev. A 89 063402
[13] Mller D, Srensen J L, Thomsen J B, Drewsen M 2007 Phys. Rev. A 76 062321
[14] Webster S C, Weidt S, Lake K, McLoughlin J J, Hensinger W K 2013 Phys. Rev. Lett 111 140501
[15] Theuer H, Bergmann K 1998 Eur. Phys. J. D 2 279
[16] Kulin S, Saubamea B, Peik E, Lawall J, Hijmans T W, Leduc M, Cohen-Tannoudji C 1997 Phys. Rev. Lett. 78 4185
[17] Nlleke C, Neuzner A, Reiserer A, Hahn C, Rempe G, Ritter S 2013 Phys. Rev. Lett. 110 140403
[18] Novikov S, Sweeney T, Robinson J E, Premaratne S P, Suri B, Wellstood F C, Palmer B S 2008 Nat. Phys. 4 622
[19] Ospelkaus S, Pe'Er A, Ni K K, Zirbel J J, Neyenhuis B,Kotochigova S, Jin D S 2008 Nat. Phys. 4 622
[20] Ni K K, Ospelkaus S, de Miranda M H G, Pe'Er A, Neyenhuis B, Zirbel J J, Ye J 2008 Science 322 231
[21] Lang F, Winkler K, Strauss C, Grimm R, Denschlag J H 2008 Phys. Rev. Lett. 101 133005
[22] Stellmer S, Pasquiou B, Grimm R, Schreck F 2012 Phys. Rev. Lett. 109 115302
[23] Shore B W 2011 Manipulating Quantum Structures Using Laser Pulses (Cambridge: Cambridge University Press) pp57-60
[24] Aikawa K, Akamatsu D, Hayashi M, Oasa K, Kobayashi J, Naidon P, Inouye S 2010 Phys. Rev. Lett. 105 203001
[25] Molony P K, Gregory P D, Ji Z, Lu B, Kppinger M P, Le Sueur C R, Cornish S L 2014 Phys. Rev. Lett. 113 255301
[26] Ji Z, Zhang H, Wu J, Yuan J, Yang Y, Zhao Y, Jia S 2012 Phys. Rev. A 85 013401
[27] Park J W, Will S A, Zwierlein M W 2015 Phys. Rev. Lett. 114 205302
[28] Guo M, Zhu B, Lu B, Ye X, Wang F, Vexiau R, Wang D 2016 Phys. Rev. Lett. 116 205303
[29] Ciamei A, Bayerle A, Chen C C, Pasquiou B, Schreck F 2017 Phys. Rev. A 96 013406
[30] Liao W T, Plffy A, Keitel C H 2011 Phys. Lett. B 705 134
[31] Oreg J, Bergmann K, Shore B W, Rosenwaks S 1992 Phys. Rev. A 45 4888
[32] Viteau M, Chotia A, Allegrini M, Bouloufa N, Dulieu O, Comparat D, Pillet P 2008 Science 321 232
[33] Klein J, Beil F, Halfmann T 2007 Phys. Rev. Lett. 99 113003
[34] Du Y X, Liang Z T, Huang W, Yan H, Zhu S L 2014 Phys. Rev. A 90 023821
[35] Pu H, Maenner P, Zhang W, Ling H Y 2007 Phys. Rev. Lett. 98 050406
[36] Meystre P 2001 Atom Optics (New York: Springer Science Business Media) pp4-7
[37] Butscher B, Bendkowsky V, Nipper J, Balewski J B, Kukota L, Lw R, Rost J M 2011 J. Phys. B: At. Mol. Opt. Phys. 44 184004
[38] Bendkowsky V, Butscher B, Nipper J, Shaffer J P, Lw R, Pfau T 2009 Nature 458 1005
[39] Volz J, Weber M, Schlenk D, Rosenfeld W, Vrana J, Saucke K, Weinfurter H 2006 Phys. Rev. Lett. 96 030404
[40] Zhen B Y, Huai Z W, Shi B Z 2010 Chin. Phys. B 19 094205
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