It is pointed out that the transition spectra between energy eigen-states of time periodic two level systems manifesting a Berry phase (BP) have two-peaked structures. These are similar to the twin peaks described by the author in Englman [J. Chem. Phys. 144, 024103 (2016)] for the “Molecular Aharonov-Bohm effect,” but are now of unequal heights depending on the values of the BP. A rotation-directional reversal protocol of the precessing field allows a novel, spectroscopic (not interferometric or phase-probing) determination of the dynamic and topological phases from the peak-to-peak line shape distances, here worked out for noiseless BP systems.
REFERENCES
1.
M. V.
Berry
, Proc. R. Soc. A
392
, 45
(1984
).2.
J. E.
Avron
, L.
Sadun
, J.
Segert
, and B.
Simon
, Phys. Rev. Lett.
61
, 1329
(1988
).3.
L.
Fu
, C. L.
Kane
, and E. J.
Mele
, Phys. Rev. Lett.
98
, 106803
(2007
).4.
A. L.
Potter
and P. A.
Lee
, Phys. Rev. B
85
, 094516
(2012
).5.
M.
Aidelsburger
, M.
Lohse
, C.
Schweitzer
, M.
Atala
, J. T.
Barreira
, S.
Nascimbene
, N. R.
Cooper
, I.
Bloch
, and N.
Goldman
, Nat. Phys.
11
, 162
(2015
).6.
M.
Hafezi
and J. M.
Taylor
, Phys. Today
67
(5
), 68
(2014
).7.
J.
Anandan
, J.
Christian
, and K.
Wanelik
, Am. J. Phys.
65
, 180
(1997
).8.
R.
Resta
, J. Phys.: Condens. Matter
12
, R107
(2000
).9.
M. S.
Child
, “Early Perspectives on Geometric Phase
,” in The Role of Degenerate States in Chemistry
, Advances in Chemical Physics
Vol. 124
, edited by M.
Baer
and G. D.
Billing
(Wiley-Interscience
, Hoboken, NJ
, 2004
), pp. 1
–38
.10.
The Role of Degenerate States in Chemistry
, edited byM.
Baer
and G. D.
Billing
, Advances in Chemical Physics
Vol. 124
(Wiley-Interscience
, Hoboken, NJ
, 2004
).11.
D.
Xiao
, M.-C.
Chang
, and Q.
Niu
, Rev. Mod. Phys.
82
, 1959
(2010
).12.
N. J.
Nagaosa
, J.
Sinova
, S.
Onoda
, A. H.
MacDonald
, and N. P.
Ong
, Rev. Mod. Phys.
82
, 1539
(2010
).13.
Y.
Zhuang
, Y.-W.
Tan
, H. L.
Stormer
, and P.
Kim
, Nature
438
, 201
(2005
).14.
D. R.
Yarkony
, Rev. Mod. Phys.
68
, 985
(1996
).15.
W.
Domcke
, D.
Yarkony
, and H.
Köppel
, Conical Intersections: Electronic Structure, Dynamics and Spectroscopy
(World Scientific
, Singapore
, 2004
), Vol. 15
.16.
A.
Tomita
and R. Y.
Chiao
, Phys. Rev. Lett.
57
, 937
(1986
).17.
T.
Bitter
and D.
Dubbers
, Phys. Rev. Lett.
59
, 251
(1987
).18.
R.
Tycko
, Phys. Rev. Lett.
58
, 2281
(1987
).19.
D.
Suter
, G.
Chingas
, R. A.
Harris
, and A.
Pines
, Mol. Phys.
61
, 1327
(1987
).20.
R.
Simon
, H. J.
Kimble
, and E. C. G.
Sudarshan
, Phys. Rev. Lett.
61
, 19
(1988
).21.
D. M.
Bird
and A. R.
Preston
, Phys. Rev. Lett.
61
, 2863
(1988
).22.
A. G.
Wagh
, V. C.
Rakhecha
, P.
Fischer
, and A.
Ioffe
, Phys. Rev. Lett.
81
, 1992
(1998
).23.
M.
Tian
, R. R.
Reibel
, Z. W.
Barber
, J. D.
Fischer
, and W. R.
Rabbitt
, Phys. Rev. A
67
, 011403
(2003
).24.
M.
Atala
, M.
Aideslsburger
, J. T.
Barreiro
, D.
Abanin
et al., Nat. Phys.
9
, 795
-803
(2013
).25.
P. J.
Leek
, J. M.
Fink
, A.
Blais
, R.
Bianchetti
, M.
Göppl
, J. M.
Gambetta
, D. I.
Schuster
, L.
Frunzio
, R. J.
Schoelkopf
, and A.
Walraff
, Science
318
, 1889
(2007
).26.
S.
Berger
, M.
Pechal
, A. A.
Abdumalikov
, Jr., C.
Eichler
, L.
Steffen
, A.
Fedorov
, A.
Walraff
, and S.
Filipp
, Phys. Rev. A
87
, 060303(R)
(2013
).27.
S.
Berger
, M.
Pechal
, P.
Kurpiers
, A. A.
Abdumalikov
, Jr., C.
Eichler
, J. A.
Mlynek
, A.
Shnirman
, Y.
Gefen
, A.
Walraff
, and S.
Filipp
, Nat. Commun.
6
, 8757-1
-8757-10
(2015
).28.
G.
De Chiara
and G. M.
Palma
, Phys. Rev. Lett.
91
, 090404
(2003
).29.
A.
Carollo
, I.
Fuentes-Guridi
, M. F.
santos
, and V.
Vedral
, Phys. Rev. Lett.
90
, 160402
(2013
).30.
R. S.
Whitney
, Yu.
Makhlin
, A.
Shnirman
, and Y.
Gefen
, Phys. Rev. Lett.
94
, 070407
(2005
).31.
32.
R.
Englman
, “Non-interferometric determination of phases in noisy Berry-phase and Floquet systems” (unpublished).33.
R.
Englman
, J. Chem. Phys.
144
, 024103
(2016
).34.
Y.
Aharonov
and D.
Bohm
, Phys. Rev.
115
, 485
(1958
).35.
C. A.
Mead
, Chem. Phys.
49
(23
), 33
(1980
);C. A.
Mead
, Rev. Mod. Phys.
64
, 51
(1992
).36.
C.
Mead
and D.
Truhlar
, J. Chem. Phys.
70
, 2284
(1979
);C.
Mead
and D.
Truhlar
, J. Chem. Phys.
77
, 6090
(1982
).37.
S. I.
Chu
and D. A.
Telnov
, Phys. Rep.
390
, 1
(2004
).38.
D.
Linnemann
, H.
Strobel
, W.
Muessel
, J.
Schulz
, R. J.
Lewis-Swan
, K. V.
Kheruntsyan
, and M. K.
Oberthaler
, Phys. Rev. Lett.
117
, 013001
(2016
).© 2016 Author(s).
2016
Author(s)
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