Mm2020 b
0 likes57 views
The document discusses molecular dipole moments and their role in driving the dynamics of vibrational polaritons in the strong and ultrastrong coupling regimes. It provides the motivation for studying quantum fields and polaritonic photodynamics. It also presents the light-matter Hamiltonian that describes the system and mentions the dipole moment operator.
![NON-POLAR and POLAR MOLECULES
Permanent Dipoles
Permanent Dipoles
W(CO)6<latexit sha1_base64="kZpBIPZ4xIDudROdTCGwtrhjnjE=">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</latexit>
CO2<latexit sha1_base64="qMKaj1hvRB11RttmxmkQqTAQSYE=">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</latexit>
H2O<latexit sha1_base64="S4dCWUQtv4udDHCHuZMwwdAkb5Y=">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</latexit>
HF<latexit sha1_base64="eNc/osTEaPvbmlWBRfxNaBPb2go=">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</latexit>
Non-Polar
Polar
qe q [a.u.]
0.0
袖(q)
qe q [a.u.]
0.0
袖(q)
0 2 4 6 8 10 12 14 16 18 20 22
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
hi|袖(q)|ii
0 2 4 6 8 10 12 14 16 18 20 22
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
hi|袖(q)|ii](https://image.slidesharecdn.com/mm2020b-200324163414/85/Mm2020-b-4-320.jpg)
![BOND DISTANCE EVOLUTION
Non-Polar
| gc(0)i = | = 0i e ||2
/2
X
n
n
p
n!
|n = 0i
<latexit sha1_base64="rVhK+kPdFjkJtOJa1dYspiuhEVA=">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</latexit>
0 100 200 300 400
t [fs]
0.9
1.0
1.1
1.2
1.3
1.4
hqi/qe
hqi( = 14)
hqi( = 0)
g = 0.375!10
Permanent
No Permanent
Polar
0 100 200 300 400
t [fs]
0.9
1.0
1.1
1.2
1.3
1.4
hqi/qe
hqi( = 14)
hqi( = 0)
g = 0.375!10
Permanent
No Permanent](https://image.slidesharecdn.com/mm2020b-200324163414/85/Mm2020-b-7-320.jpg)
![PHOTON NUMBER EVOLUTION
Non-Polar
| gv(0)i = | = 0i |n = 0i<latexit sha1_base64="DunSLkiP8yXXNjlqoUgKMt6e2wk=">AAACIXicbVDLSgMxFM34rPVVdekmWIS6KTNV0E2l6MZlBfuATimZ9LYNzWSGJFMo036N/oziQtSN+DNm6iDaelfnnnPCzTleyJnStv1hLS2vrK6tZzaym1vbO7u5vf26CiJJoUYDHsimRxRwJqCmmebQDCUQ3+PQ8IbXid4YgVQsEHd6HELbJ33BeowSbahO7nLiVhXrxK5P9ED6cX80nRbsE1cS0edQnrgiKtvp5gaa+aDwRPxQnVzeLtqzwYvASUEepVPt5J7dbkAjH4SmnCjVcuxQt2MiNaMcplk3UhASOiR9aBkoiDnYjmc5p/i4F0isB4Bn+29vTHylxr5nPEkQNa8l5H9aK9K9i3bMRBhpENRYjNaLONYBTurCXSaBaj42gFDJzC8xHRBJqDalZk18Zz7sIqiXis5psXR7lq9cpUVk0CE6QgXkoHNUQTeoimqIogf0hN7Qu3VvPVov1uu3dclK3xygP2N9fgH/Y6SO</latexit>
Polar
0 100 200 300 400
t [fs]
10 3
10 2
10 1
100
101
hni
g = 0.125!10
0 100 200 300 400
t [fs]
10 3
10 2
10 1
100
101
hni
g = 0.125!10](https://image.slidesharecdn.com/mm2020b-200324163414/85/Mm2020-b-8-320.jpg)
![Polar
| gv(0)i = | = 0i |n = 0i<latexit sha1_base64="DunSLkiP8yXXNjlqoUgKMt6e2wk=">AAACIXicbVDLSgMxFM34rPVVdekmWIS6KTNV0E2l6MZlBfuATimZ9LYNzWSGJFMo036N/oziQtSN+DNm6iDaelfnnnPCzTleyJnStv1hLS2vrK6tZzaym1vbO7u5vf26CiJJoUYDHsimRxRwJqCmmebQDCUQ3+PQ8IbXid4YgVQsEHd6HELbJ33BeowSbahO7nLiVhXrxK5P9ED6cX80nRbsE1cS0edQnrgiKtvp5gaa+aDwRPxQnVzeLtqzwYvASUEepVPt5J7dbkAjH4SmnCjVcuxQt2MiNaMcplk3UhASOiR9aBkoiDnYjmc5p/i4F0isB4Bn+29vTHylxr5nPEkQNa8l5H9aK9K9i3bMRBhpENRYjNaLONYBTurCXSaBaj42gFDJzC8xHRBJqDalZk18Zz7sIqiXis5psXR7lq9cpUVk0CE6QgXkoHNUQTeoimqIogf0hN7Qu3VvPVov1uu3dclK3xygP2N9fgH/Y6SO</latexit>
0 100 200 300 400
t [fs]
10 3
10 2
10 1
100
101
hni
g = 0.125!10
g = 0.250!10
g = 0.375!10
PHOTON NUMBER EVOLUTION](https://image.slidesharecdn.com/mm2020b-200324163414/85/Mm2020-b-9-320.jpg)
![REAL MOLECULAR EXAMPLES
CO2-Asymmetric Mode
Non Polar
HF
Polar
0.6 0.4 0.2 0.0 0.2 0.4 q
0.0
0.1
0.2
0.3
0.4
V(q)[a.u.]
1.0
0.5
0.0
0.5
1.0
袖(q)[a.u.]
t [fs]
0.2
0.1
0.0
0.1
0.2
hqi(t)
20 60 100 140 180 220 260 300 340 t [fs]
0
0.2
0.4
0.6
0.8
1.0
hni(t)
1.0 2.0 3.0 4.0 5.0 6.0 7.0 q/qe [a.u.]
0.1
0.2
0.3
0.4
V(q)[a.u.]
0.0
0.2
0.4
0.6
0.8
1.0
袖(q)[a.u.]
t [fs]
0.9
1.0
1.1
1.2
1.3
1.4
hqi(t)
20 60 100 140 180 220 260 300 340 t [fs]
0
3
6
9
12
15
hni(t)](https://image.slidesharecdn.com/mm2020b-200324163414/85/Mm2020-b-10-320.jpg)
![REFERENCES
Johan F. Triana, F. J. Hern叩ndez and F. Herrera, The Shape of the
Electric Dipole Function Determines the Sub-Picosecond Dynamics of
Anharmonic Vibrational Polaritons, arXiv:2003.07783
F. J. Hern叩ndez and F. Herrera, Multi-level quantum Rabi model for
anharmonic vibrational polaritons, J. Chem. Phys. 151, 144116 (2019)
J. F. Triana and J. L. Sanz-Vicario, Revealing the Presence of Potential
Crossings in Diatomics Induced by Quantum Cavity Radiation, Phys.
Rev. Lett. 122, 063603 (2019)
F. Herrera and J. Owrutsky, Molecular polaritons for controlling
chemistry with quantum optics, arXiv:1911.05017 [Accepted in JCP]](https://image.slidesharecdn.com/mm2020b-200324163414/85/Mm2020-b-12-320.jpg)
Mm2020 b
- 1. Molecular dipole moment drives the dynamics of vibrational polaritons in the strong and ultrastrong coupling regimes Johan F. Triana In collaboration with Federico Hern叩ndez and Felipe Herrera March Meeting March 2-6, 2020 Denver, Colorado Universidad de Santiago de Chile
- 2. MOTIVATION Quantum Fields Polaritonic Photodynamics J. George and T. Ebbesen et.al., Angew. Chem. Int. Ed. 55, 11462 (2016) Strong and Ultra-Strong Coupling Regime Si<latexit sha1_base64="6Y0lNV7kXAQQBn2nrtvZtn37514=">AAAB6nicdVDLTgJBEJzFF+IL9ehlIjHxtNlFiHAjevGIUR4GNmR2aGDC7CMzvUay4Sf0ZNSbn+MP+DcOiIkarVN1VXXS1X4shUbHebcyS8srq2vZ9dzG5tb2Tn53r6mjRHFo8EhGqu0zDVKE0ECBEtqxAhb4Elr++Hzmt25BaRGF1ziJwQvYMBQDwRka6aaLcIfplZj28gXHrjolt1ykju3MMSPlYrVcoe5CKZAF6r38W7cf8SSAELlkWndcJ0YvZQoFlzDNdRMNMeNjNoSOoSELQHvp/OApPRpEiuII6Hz+nk1ZoPUk8E0mYDjSv72Z+JfXSXBQ8VIRxglCyE3EeINEUozorDftCwUc5cQQxpUwV1I+YopxNN/JmfpfHen/pFm03RO7eFkq1M4Wj8iSA3JIjolLTkmNXJA6aRBOAvJAnsmLJa1769F6+oxmrMXOPvkB6/UDXs2OdA==</latexit> Reactant Product +<latexit sha1_base64="V8dctJPwJeb2hUoh1bkNUWY2S18=">AAAB4nicbZDNSgMxFIXv1L9a/6ou3QSLIAhlpgq6LLpx2YL9gXYomfROG5rMDElGKENfQFei7nwkX8C3Ma2z0Naz+nLPCdxzg0RwbVz3yymsrW9sbhW3Szu7e/sH5cOjto5TxbDFYhGrbkA1Ch5hy3AjsJsopDIQ2Akmd3O/84hK8zh6MNMEfUlHEQ85o8aOmheDcsWtuguRVfByqECuxqD82R/GLJUYGSao1j3PTYyfUWU4Ezgr9VONCWUTOsKexYhK1H62WHRGzsJYETNGsnj/zmZUaj2Vgc1IasZ62ZsP//N6qQlv/IxHSWowYjZivTAVxMRk3pcMuUJmxNQCZYrbLQkbU0WZsVcp2frectlVaNeq3mW11ryq1G/zQxThBE7hHDy4hjrcQwNawADhGd7g3Rk6T86L8/oTLTj5n2P4I+fjG2mhikg=</latexit> F<latexit sha1_base64="dy7aSraGYg/b2Z8ae4cP/HYXKnI=">AAAB63icbVDLSgNBEOyNrxhfUY9eFoPgKexGQY9BQTxGMA9MljA76SRDZmaXmVkhLPkKPYl682/8Af/G2bgHTaxTdVc1VHUYc6aN5305hZXVtfWN4mZpa3tnd6+8f9DSUaIoNmnEI9UJiUbOJDYNMxw7sUIiQo7tcHKd6e1HVJpF8t5MYwwEGUk2ZJQYu3roCWLGSqQ3s3654lW9Odxl4uekAjka/fJnbxDRRKA0lBOtu74XmyAlyjDKcVbqJRpjQidkhF1LJRGog3SeeOaeDCPlmjG68/m3NyVC66kIrSfLphe1bPmf1k3M8DJImYwTg5Jai9WGCXdN5GbF3QFTSA2fWkKoYjalS8dEEWrse0q2vr9Ydpm0alX/rFq7O6/Ur/JHFOEIjuEUfLiAOtxCA5pAQcIzvMG7I5wn58V5/bEWnPzmEP7A+fgGtIaOmg==</latexit> Si<latexit sha1_base64="tlEhcFROwY1l3iX8OilWExcfXJ4=">AAAB7HicbVDLSgNBEOz1GeMr6tHLYBA8hd0o6DHoxWNE84DNEmYnk2TIPJaZWSEs+Qs9iXrza/wB/8bZuAdNrFN1VzVUdZxwZqzvf3krq2vrG5ulrfL2zu7efuXgsG1UqgltEcWV7sbYUM4kbVlmOe0mmmIRc9qJJze53nmk2jAlH+w0oZHAI8mGjGDrVmFPYDvWIrtns36l6tf8OdAyCQpShQLNfuWzN1AkFVRawrExYeAnNsqwtoxwOiv3UkMTTCZ4RENHJRbURNk88gydDpVGdkzRfP7tzbAwZipi58nDmUUtX/6nhakdXkUZk0lqqSTO4rRhypFVKG+OBkxTYvnUEUw0cykRGWONiXX/Kbv6wWLZZdKu14LzWv3uotq4Lh5RgmM4gTMI4BIacAtNaAEBBc/wBu+e9J68F+/1x7riFTdH8AfexzeNwo8a</latexit>
- 3. H = 1 2m @2 @qq + V (q) | {z } HM 1 2 @2 @x2 + 1 2 !2 c x2 | {z } HF + p 2!cE0 x袖(q) | {z } HI LIGHT-MATTER HAMILTONIAN H = HM + HF + HI<latexit sha1_base64="7MfyPJxU4rnPvVgcXiWXsyf3OCc=">AAACKXicbVDLSsNAFJ3UV62vqEs3g0UQhJJUQTdCUSh1IVSwD2hCmEwnzdDJg5mJUEK+SD/Fja587fwRJzULbXs2c+acc+Ge68aMCmkY71ppaXllda28XtnY3Nre0Xf3uiJKOCYdHLGI910kCKMh6UgqGenHnKDAZaTnjq9zv/dAuKBReC8nMbEDNAqpRzGSSnL0puUjmbayy+J1UitA0udBeptlJ3Nic5F4k2WOXjVqxhRwnpgFqYICbUd/toYRTgISSsyQEAPTiKWdIi4pZiSrWIkgMcJjNCIDRUMUEGGn074ZPPIiDqVP4PT/N5uiQIhJ4KpMvpyY9XJxkTdIpHdhpzSME0lCrCLK8xIGZQTzs8Eh5QRLNlEEYU7VlhD7iCMs1XErqr45W3aedOs187RWvzurNq6KQ5TBATgEx8AE56ABWqANOgCDJ/AKPsGX9qi9aG/ax2+0pBUz++AftO8f5Supbw==</latexit> H = X !|ih| + !ca a + X X 0 g0(|0 ih| + |ih0 |)(a + a) <latexit sha1_base64="TZjy9b+YqNZ0ETvYGdOc3FTKk3M=">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</latexit> Hilbert Space - Multi-level Quantum Rabi Model F. Hern叩ndez and F. Herrera, J. Chem. Phys. 151, 144116 (2019) Coordinate Space M. Kowalewski, Bennett, Mukamel, J. Phys. Chem. Lett., 7, 2050 (2016) 袖(q)<latexit sha1_base64="MryHYFmwqLgJhCGFCKhmwnXOOl0=">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</latexit> g0<latexit sha1_base64="2w6FCzmiJbDznPnaHQMzvcQ4n/o=">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</latexit>
- 4. NON-POLAR and POLAR MOLECULES Permanent Dipoles Permanent Dipoles W(CO)6<latexit sha1_base64="kZpBIPZ4xIDudROdTCGwtrhjnjE=">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</latexit> CO2<latexit sha1_base64="qMKaj1hvRB11RttmxmkQqTAQSYE=">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</latexit> H2O<latexit sha1_base64="S4dCWUQtv4udDHCHuZMwwdAkb5Y=">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</latexit> HF<latexit sha1_base64="eNc/osTEaPvbmlWBRfxNaBPb2go=">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</latexit> Non-Polar Polar qe q [a.u.] 0.0 袖(q) qe q [a.u.] 0.0 袖(q) 0 2 4 6 8 10 12 14 16 18 20 22 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 hi|袖(q)|ii 0 2 4 6 8 10 12 14 16 18 20 22 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 hi|袖(q)|ii
- 5. VIBRATIONAL POLARITONS: Polariton spectrum and Expectation values Non-Polar 0.0 0.1 0.2 0.3 g/!10 0.0 0.5 1.0 1.5 2.0 2.5 (EE0)/!10 Permanent No Permanent 0.975 1.000 1.025 | GSi hqi/qe 0.0 0.1 0.2 0.3 g/!10 0.0 0.5 1.0 | GSi hni Polar 0.0 0.1 0.2 0.3 g/!10 0.0 0.5 1.0 1.5 2.0 2.5 (EE0)/!10 Permanent No Permanent 0.9 1.0 1.1 | GSi hqi/qe 0.0 0.1 0.2 0.3 g/!10 0 5 10 | GSi hni
- 6. QUANTUM DESCRIPTION OF NUCLEAR DYNAMICS Multiconfigurational Time Dependent Hartree - MCTDH Beck, J辰gckle, Worth, Meyer, Physics Reports 324, 1-105 (2000) Solving TDSE 脹~ d dt (R, x, t) = H (R, x, t) <latexit sha1_base64="fv1M6ac9wuMpQuctrQ5bVDufM6s=">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</latexit> (R, x, t) = n1X j1=1 揃 揃 揃 np X jp=1 Aj1揃揃揃jp (t) fY k=1 ' (k) jk (Qk, t) <latexit sha1_base64="284SpDh6RYQ6Lue/vcZv9HY7wPM=">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</latexit>
- 7. BOND DISTANCE EVOLUTION Non-Polar | gc(0)i = | = 0i e ||2 /2 X n n p n! |n = 0i <latexit sha1_base64="rVhK+kPdFjkJtOJa1dYspiuhEVA=">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</latexit> 0 100 200 300 400 t [fs] 0.9 1.0 1.1 1.2 1.3 1.4 hqi/qe hqi( = 14) hqi( = 0) g = 0.375!10 Permanent No Permanent Polar 0 100 200 300 400 t [fs] 0.9 1.0 1.1 1.2 1.3 1.4 hqi/qe hqi( = 14) hqi( = 0) g = 0.375!10 Permanent No Permanent
- 8. PHOTON NUMBER EVOLUTION Non-Polar | gv(0)i = | = 0i |n = 0i<latexit sha1_base64="DunSLkiP8yXXNjlqoUgKMt6e2wk=">AAACIXicbVDLSgMxFM34rPVVdekmWIS6KTNV0E2l6MZlBfuATimZ9LYNzWSGJFMo036N/oziQtSN+DNm6iDaelfnnnPCzTleyJnStv1hLS2vrK6tZzaym1vbO7u5vf26CiJJoUYDHsimRxRwJqCmmebQDCUQ3+PQ8IbXid4YgVQsEHd6HELbJ33BeowSbahO7nLiVhXrxK5P9ED6cX80nRbsE1cS0edQnrgiKtvp5gaa+aDwRPxQnVzeLtqzwYvASUEepVPt5J7dbkAjH4SmnCjVcuxQt2MiNaMcplk3UhASOiR9aBkoiDnYjmc5p/i4F0isB4Bn+29vTHylxr5nPEkQNa8l5H9aK9K9i3bMRBhpENRYjNaLONYBTurCXSaBaj42gFDJzC8xHRBJqDalZk18Zz7sIqiXis5psXR7lq9cpUVk0CE6QgXkoHNUQTeoimqIogf0hN7Qu3VvPVov1uu3dclK3xygP2N9fgH/Y6SO</latexit> Polar 0 100 200 300 400 t [fs] 10 3 10 2 10 1 100 101 hni g = 0.125!10 0 100 200 300 400 t [fs] 10 3 10 2 10 1 100 101 hni g = 0.125!10
- 9. Polar | gv(0)i = | = 0i |n = 0i<latexit sha1_base64="DunSLkiP8yXXNjlqoUgKMt6e2wk=">AAACIXicbVDLSgMxFM34rPVVdekmWIS6KTNV0E2l6MZlBfuATimZ9LYNzWSGJFMo036N/oziQtSN+DNm6iDaelfnnnPCzTleyJnStv1hLS2vrK6tZzaym1vbO7u5vf26CiJJoUYDHsimRxRwJqCmmebQDCUQ3+PQ8IbXid4YgVQsEHd6HELbJ33BeowSbahO7nLiVhXrxK5P9ED6cX80nRbsE1cS0edQnrgiKtvp5gaa+aDwRPxQnVzeLtqzwYvASUEepVPt5J7dbkAjH4SmnCjVcuxQt2MiNaMcplk3UhASOiR9aBkoiDnYjmc5p/i4F0isB4Bn+29vTHylxr5nPEkQNa8l5H9aK9K9i3bMRBhpENRYjNaLONYBTurCXSaBaj42gFDJzC8xHRBJqDalZk18Zz7sIqiXis5psXR7lq9cpUVk0CE6QgXkoHNUQTeoimqIogf0hN7Qu3VvPVov1uu3dclK3xygP2N9fgH/Y6SO</latexit> 0 100 200 300 400 t [fs] 10 3 10 2 10 1 100 101 hni g = 0.125!10 g = 0.250!10 g = 0.375!10 PHOTON NUMBER EVOLUTION
- 10. REAL MOLECULAR EXAMPLES CO2-Asymmetric Mode Non Polar HF Polar 0.6 0.4 0.2 0.0 0.2 0.4 q 0.0 0.1 0.2 0.3 0.4 V(q)[a.u.] 1.0 0.5 0.0 0.5 1.0 袖(q)[a.u.] t [fs] 0.2 0.1 0.0 0.1 0.2 hqi(t) 20 60 100 140 180 220 260 300 340 t [fs] 0 0.2 0.4 0.6 0.8 1.0 hni(t) 1.0 2.0 3.0 4.0 5.0 6.0 7.0 q/qe [a.u.] 0.1 0.2 0.3 0.4 V(q)[a.u.] 0.0 0.2 0.4 0.6 0.8 1.0 袖(q)[a.u.] t [fs] 0.9 1.0 1.1 1.2 1.3 1.4 hqi(t) 20 60 100 140 180 220 260 300 340 t [fs] 0 3 6 9 12 15 hni(t)
- 11. CONCLUSIONS AND OUTLOOK Low energy polaritons created with polar molecules can have high mean vibrational energy and high mean photon number. Knowing the molecular dipole moment function helps us to design different types of polaritonic systems with different reactivities. We are extending the models including dissipative effects and considering molecular ensembles.
- 12. REFERENCES Johan F. Triana, F. J. Hern叩ndez and F. Herrera, The Shape of the Electric Dipole Function Determines the Sub-Picosecond Dynamics of Anharmonic Vibrational Polaritons, arXiv:2003.07783 F. J. Hern叩ndez and F. Herrera, Multi-level quantum Rabi model for anharmonic vibrational polaritons, J. Chem. Phys. 151, 144116 (2019) J. F. Triana and J. L. Sanz-Vicario, Revealing the Presence of Potential Crossings in Diatomics Induced by Quantum Cavity Radiation, Phys. Rev. Lett. 122, 063603 (2019) F. Herrera and J. Owrutsky, Molecular polaritons for controlling chemistry with quantum optics, arXiv:1911.05017 [Accepted in JCP]