New experimental techniques based on nonlinear ultrafast spectroscopies have been developed over the last few years, and have been demonstrated to provide powerful probes of quantum dynamics in different types of molecular aggregates, including both natural and artificial light harvesting complexes. Fourier transform-based spectroscopies have been particularly successful, yet “complete” spectral information normally necessitates the loss of all information on the temporal sequence of events in a signal. This information though is particularly important in transient or multi-stage processes, in which the spectral decomposition of the data evolves in time. By going through several examples of ultrafast quantum dynamics, we demonstrate that the use of wavelets provide an efficient and accurate way to simultaneously acquire both temporal and frequency information about a signal, and argue that this greatly aids the elucidation and interpretation of physical process responsible for non-stationary spectroscopic features, such as those encountered in coherent excitonic energy transport.

1.
J.
van der Berg
,
Wavelets in Physics
(
Cambridge University Press
,
2004
).
2.
S.
Mallat
and
A.
Wavelet
,
Tour of Signal Processing
(
Academic Press
,
1999
).
3.
J. D.
Hybl
,
A. W.
Albrecht
,
S. M. G.
Faeder
, and
D. M.
Jonas
,
Chem. Phys. Lett.
297
,
307
(
1998
).
4.
T.
Brixner
,
J.
Stenger
,
H. M.
Vaswani
,
M.
Cho
,
R. E.
Blankenship
, and
G. R.
Fleming
,
Nature (London)
434
,
625
(
2005
).
5.
D.
Abramavicius
,
B.
Palmieri
,
D. V.
Voronine
,
F.
Šanda
, and
S.
Mukamel
,
Chem. Rev.
109
,
2350
(
2009
).
6.
N. S.
Ginsberg
,
Y. C.
Cheng
, and
G. R.
Fleming
,
Acc. Chem. Res.
42
,
1352
1363
(
2009
).
7.
K. A.
Fransted
and
G. S.
Engel
,
Chem. Phys.
403
,
59
67
(
2012
).
8.
G. S.
Engel
,
T. R.
Calhoun
,
E. L.
Read
,
T. K.
Ahn
,
T.
Mancal
,
Y. C.
Cheng
,
R. E.
Blankenship
, and
G. R.
Fleming
,
Nature (London)
446
,
782
786
(
2007
).
9.
V.
Tiwari
,
W. K.
Peters
, and
D. M.
Jonas
,
Proc. Natl. Acad. Sci. U.S.A.
110
,
1203
1208
(
2013
).
10.
A. W.
Chin
,
J.
Prior
,
R.
Rosenbach
,
F.
Caycedo-Soler
,
S. F.
Huelga
, and
M. B.
Plenio
,
Nat. Phys.
9
,
113
118
(
2013
).
11.
A. W.
Chin
,
S. F.
Huelga
, and
M. B.
Plenio
,
Philos. Trans. R. Soc. London, Ser. A
370
,
3638
3657
(
2012
).
12.
A.
Kolli
,
E. J.
O'Reilly
,
G. D.
Scholes
, and
A.
Olaya-Castro
,
J. Chem. Phys.
137
,
174109
(
2012
).
13.
M.
Hase
,
M.
Kitajima
,
A. M.
Constantinescu
, and
H.
Petek
,
Nature (London)
426
,
51
(
2003
).
14.
A.
Cohen
and
J.
Kovačevič
,
Proc. IEEE
84
,
514
(
1996
).
15.
P.
Baum
,
S.
Lochbrunner
,
L.
Gallmann
,
G.
Steinmeyer
,
U.
Keller
, and
E.
Riedle
,
Appl. Phys. B: Lasers Opt.
74
,
s219
s224
(
2002
).
16.
P.
Baum
,
S.
Lochbrunner
, and
E.
Riedle
,
Opt. Lett.
29
,
210
212
(
2004
).
17.
C.
Manzoni
,
D.
Polli
, and
G.
Cerullo
,
Rev. Sci. Instrum.
77
,
023103
9
(
2006
).
18.
D. J.
Kane
and
R.
Trebino
,
IEEE J. Quantum Electron.
29
,
571
579
(
1993
).
19.
T.
Kobayashi
and
A.
Baltuska
,
Meas. Sci. Technol.
13
,
1671
1682
(
2002
).
20.
O.
Nahmias
,
O.
Bismuth
,
O.
Shoshana
, and
S.
Ruhman
,
J. Phys. Chem. A
109
,
8246
8253
(
2005
).
21.
R.
Hildner
,
D.
Brinks
,
J. B.
Nieder
,
R. J.
Cogdell
, and
N. F.
van Hulst
,
Science
340
,
1448
1451
(
2013
).
22.
J.
Paye
and
A.
Migus
,
J. Opt. Soc. Am. B
12
,
1480
1490
(
1995
).
23.
S.
Mukamel
,
C.
CiordasCiurdariu
, and
V.
Khidekel
,
IEEE J. Quantum Electron.
32
,
1278
1288
(
1996
).
24.
J.
Paye
,
IEEE J. Quantum Electron.
28
,
2262
2273
(
1992
).
25.
V. S.
Malinovsky
,
C.
Meier
, and
D. J.
Tannor
,
Chem. Phys.
221
,
67
76
(
1997
).
26.
S.
Beyvers
,
Y.
Ohtsuki
, and
P.
Saalfrank
,
J. Chem. Phys.
124
,
234706
234718
(
2006
).
27.
S.
Fechner
,
F.
Dimler
,
T.
Brixner
,
G.
Gerber
, and
D. J.
Tannor
, “
The von Neuman picture: A new representation for ultrashort laser pulses
,”
Opt. Express
15
(
23
),
15387
15401
(
2007
).
28.
F.
Dimler
,
S.
Fechner
,
A.
Rodenberg
,
T.
Brixner
, and
D. J.
Tannor
,
New J. Phys.
11
,
105052
(
2009
).
29.
S.
Ruetzel
,
C.
Stolzenberger
,
S.
Fechner
,
F.
Dimler
,
T.
Brixner
, and
D. J.
Tannor
,
J. Chem. Phys.
133
,
164510
(
2010
).
30.
T.
Kobayashi
,
T.
Saito
, and
H.
Ohtani
,
Nature (London)
414
,
531
(
2001
).
31.
T.
Kobayashi
and
Z.
Wang
,
New J. Phys.
10
,
065015
(
2008
).
32.
C.
Kreisbeck
,
T.
Kramer
, and
A.
Aspuru-Guzik
,
J. Phys. Chem.
117
,
9380
(
2013
).
33.
G. D.
Scholes
,
G. R.
Fleming
,
A.
Olaya-Castro
, and
R.
van Grondelle
,
Nat. Chem.
3
(
10
),
763
(
2011
).
34.
S. G.
Mallat
,
IEEE Trans. Pattern Anal. Mach. Intell.
11
,
674
693
(
1989
).
35.
J. D.
Harrop
,
S. N.
Taraskin
, and
S. R.
Elliot
,
Phys. Rev. E
66
,
026703
(
2002
).
36.
H.
Van Amerongen
,
L.
Valkumas
, and
R.
Van Grondelle
,
Photosynthetic Excitons
(
World Scientific
,
2000
).
37.
U.
Weiss
,
Quantum Dissipative Systems
(
World Scientific
,
1993
).
38.
D. F.
Walls
and
G. J.
Milburn
,
Quantum Optics
(
Springer
,
1994
).
39.
J.
Prior
,
A. W.
Chin
,
S. F.
Huelga
, and
M. B.
Plenio
,
Phys. Rev. Lett.
105
,
050404
(
2010
).
40.
A.
Rivas
and
S. F.
Huelga
,
Open Quantum Systems: An Introduction
(
Springer
,
Heidelberg
,
2011
).
41.
V.
May
and
O.
Kühn
,
Charge and Energy Transfer Dynamics in Molecular Systems
(
Wiley-VCH
,
Weinheim
,
2011
).
42.
J.
Almeida
,
J.
Prior
, and
M. B.
Plenio
,
J. Phys. Chem. Lett.
3
,
2692
2696
(
2012
).
43.
J. N.
Sanders
,
S.
Mostame
,
S. K.
Saikin
,
X.
Andrade
,
J. R.
Widom
,
A. H.
Marcus
, and
A.
Aspuru-Guzik
,
J. Phys. Chem. Lett.
3
,
2697
2702
(
2012
).
44.
For the undamped case, the ratio of contributions is fixed by the total data acquisition time.
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