We use symmetry arguments and simple model systems to describe the conversion of the singlet state of parahydrogen into an oscillating sample magnetization at zero magnetic field. During an initial period of free evolution governed by the scalar-coupling Hamiltonian HJ, the singlet state is converted into scalar spin order involving spins throughout the molecule. A short dc pulse along the z axis rotates the transverse spin components of nuclear species I and S through different angles, converting a portion of the scalar order into vector order. The development of vector order can be described analytically by means of single-transition operators, and it is found to be maximal when the transverse components of I are rotated by an angle of ±π/2 relative to those of S. A period of free evolution follows the pulse, during which the vector order evolves as a set of oscillating coherences. The imaginary parts of the coherences represent spin order that is not directly detectable, while the real parts can be identified with oscillations in the z component of the molecular spin dipole. The dipole oscillations are due to a periodic exchange between Iz and Sz, which have different gyromagnetic ratios. The frequency components of the resulting spectrum are imaginary, since the pulse cannot directly induce magnetization in the sample; it is only during the evolution under HJ that the vector order present at the end of the pulse evolves into detectable magnetization.

1.
C. R.
Bowers
, “
Sensitivity enhancement utilizing parahydrogen
,” in
Encyclopedia of Magnetic Resonance
(
Wiley
,
2007
).
2.
C.
Bowers
and
D.
Weitekamp
,
J. Am. Chem. Soc.
109
,
5541
(
1987
);
C.
Bowers
and
D.
Weitekamp
,
Phys. Rev. Lett.
57
,
2645
(
1986
).
[PubMed]
3.
M.
Pravica
and
D.
Weitekamp
,
Chem. Phys. Lett.
145
,
255
(
1988
).
4.
R. W.
Adams
,
J. A.
Aguilar
,
K. D.
Atkinson
,
M. J.
Cowley
,
P. I. P.
Elliott
,
S. B.
Duckett
,
G. G. R.
Green
,
I. G.
Khazal
,
J.
López-Serrano
, and
D. C.
Williamson
,
Science
323
,
1708
(
2009
).
5.
R. W.
Adams
,
S. B.
Duckett
,
R. A.
Green
,
D. C.
Williamson
, and
G. G. R.
Green
,
J. Chem. Phys.
131
,
194505
(
2009
).
6.
N. M.
Zacharias
,
H. R.
Chan
,
N.
Sailasuta
,
B. D.
Ross
, and
P.
Bhattacharya
,
J. Am. Chem. Soc.
134
,
934
(
2012
);
[PubMed]
E. Y.
Chekmenev
,
J.
Hövener
,
V. A.
Norton
,
K.
Harris
,
L. S.
Batchelder
,
P.
Bhattacharya
,
B. D.
Ross
, and
D. P.
Weitekamp
,
J. Am. Chem. Soc.
130
,
4212
(
2008
);
[PubMed]
K.
Golman
,
O.
Axelsson
,
H.
Jóhannesson
,
S.
Månsson
,
C.
Olofsson
, and
J.
Petersson
,
Magn. Reson. Med.
46
,
1
(
2001
).
[PubMed]
7.
S. B.
Duckett
and
N. J.
Wood
,
Coord. Chem. Rev.
252
,
2278
(
2008
).
8.
M. B.
Franzoni
,
L.
Buljubasich
,
H. W.
Spiess
, and
K.
Münnemann
,
J. Am. Chem. Soc.
134
,
10393
(
2012
).
9.
E.
Vinogradov
and
A. K.
Grant
,
J. Magn. Reson.
194
,
46
(
2008
).
10.
L.
Bouchard
,
S.
Burt
,
M.
Anwar
,
K.
Kovtunov
,
I.
Koptyug
, and
A.
Pines
,
Science
319
,
442
(
2008
).
11.
M. S.
Anwar
,
J. A.
Jones
,
D.
Blazina
,
S. B.
Duckett
, and
H. A.
Carteret
,
Phys. Rev. A
70
,
032324
(
2004
).
12.
T.
Theis
,
P.
Ganssle
,
G.
Kervern
,
S.
Knappe
,
J.
Kitching
,
M. P.
Ledbetter
,
D.
Budker
, and
A.
Pines
,
Nat. Phys.
7
,
571
(
2011
).
13.
T.
Theis
,
M. P.
Ledbetter
,
G.
Kervern
,
J. W.
Blanchard
,
P. J.
Ganssle
,
M. C.
Butler
,
H. D.
Shin
,
D.
Budker
, and
A.
Pines
,
J. Am. Chem. Soc.
134
,
3987
(
2012
).
14.
J. W.
Blanchard
,
M. P.
Ledbetter
,
T.
Theis
,
M. C.
Butler
,
D.
Budker
, and
A.
Pines
,
J. Am. Chem. Soc.
135
,
3607
(
2013
).
15.
M. C.
Butler
,
M. P.
Ledbetter
,
T.
Theis
,
J. W.
Blanchard
,
D.
Budker
, and
A.
Pines
,
J. Chem. Phys.
138
,
184202
(
2013
).
16.
M.
Ledbetter
,
C.
Crawford
,
A.
Pines
,
D.
Wemmer
,
S.
Knappe
,
J.
Kitching
, and
D.
Budker
,
J. Magn. Reson.
199
,
25
(
2009
).
17.
D. B.
Zax
,
A.
Bielecki
,
K. W.
Zilm
,
A.
Pines
, and
D. P.
Weitekamp
,
J. Chem. Phys.
83
,
4877
(
1985
);
D.
Zax
,
A.
Bielecki
,
K.
Zilm
, and
A.
Pines
,
Chem. Phys. Lett.
106
,
550
(
1984
);
D. P.
Weitekamp
,
A.
Bielecki
,
D.
Zax
,
K.
Zilm
, and
A.
Pines
,
Phys. Rev. Lett.
50
,
1807
(
1983
).
18.
D.
Yu
,
N.
Garcia
, and
S.
Xu
,
Concepts Magn. Reson.
34A
,
124
(
2009
).
19.
D.
Budker
and
M.
Romalis
,
Nat. Phys.
3
,
227
(
2007
).
20.
I. M.
Savukov
and
M. V.
Romalis
,
Phys. Rev. Lett.
94
,
123001
(
2005
).
21.
V.
Shah
,
S.
Knappe
,
P. D. D.
Schwindt
, and
J.
Kitching
,
Nat. Photonics
1
,
649
(
2007
).
22.
M.
Goldman
and
H.
Jóhannesson
,
C. R. Phys.
6
,
575
(
2005
);
H.
Jóhannesson
,
O.
Axelsson
, and
M.
Karlsson
,
C. R. Phys.
5
,
315
(
2004
);
M.
Haake
,
J.
Natterer
, and
J.
Bargon
,
J. Am. Chem. Soc.
118
,
8688
(
1996
).
23.
S.
Aime
,
R.
Gobetto
,
F.
Reineri
, and
D.
Canet
,
J. Magn. Reson.
178
,
184
(
2006
).
24.
J.
Natterer
,
O.
Schedletzky
,
J.
Barkemeyer
,
J.
Bargon
, and
S.
Glaser
,
J. Magn. Reson.
133
,
92
(
1998
).
25.
C.
Cohen-Tannoudji
,
B.
Diu
, and
F.
Laloë
,
Quantum Mechanics
(
Wiley
,
New York
,
1977
), pp.
1072
1085
.
26.
M.
Auzinsh
,
D.
Budker
, and
S.
Rochester
,
Optically Polarized Atoms: Understanding Light-Atom Interactions
(
Oxford
,
New York
,
2010
).
27.
C.
Cohen-Tannoudji
,
B.
Diu
, and
F.
Laloë
,
Quantum Mechanics
(
Wiley
,
New York
,
1977
), pp.
1054
1055
.
28.
29.
R. R.
Ernst
,
G.
Bodenhausen
, and
A.
Wokaun
,
Principles of Nuclear Magnetic Resonance in One and Two Dimensions
(
Clarendon Press
,
Oxford
,
1987
), pp.
34
37
.
30.
J.
Natterer
and
J.
Bargon
,
Prog. Nucl. Magn. Reson. Spectrosc.
31
,
293
(
1997
).
31.
See supplementary material in
T.
Theis
,
M. P.
Ledbetter
,
G.
Kervern
,
J. W.
Blanchard
,
P. J.
Ganssle
,
M. C.
Butler
,
H. D.
Shin
,
D.
Budker
, and
A.
Pines
,
J. Am. Chem. Soc.
134
,
3987
(
2012
).
32.
C. J.
Lee
,
D.
Suter
, and
A.
Pines
,
J. Magn. Reson.
75
,
110
(
1987
).
33.
A.
Messiah
,
Quantum Mechanics
(
Wiley
,
New York
,
1959
), Chap. XV.
You do not currently have access to this content.