High fidelity and robustness in population inversion is very desirable for many quantum control applications. We expand composite pulse schemes developed for two-level dynamics and present an analytic solution for the coherent evolution of an N-level quantum system with SU(2) symmetry, for achieving high fidelity and robust population inversion. Our approach offers a platform for accurate steering of the population transfer in physical multi-level systems, which is crucial for fidelity in quantum computation and achieving fundamental excitations in nuclear magnetic resonances and atomic physics. We also introduce and discuss the geometrical trajectories of these dynamics on the Majorana sphere as an interpretation, allowing us to gain physical insight on the dynamics of many-body or high-dimensional quantum systems.

1.
M.
Nielsen
and
I.
Chuange
,
Quantum Computation and Quantum Information
(
Cambridge University Press
,
Cambridge
,
2000
).
2.
A.
Sørensen
and
K.
Mølmer
,
Phys. Rev. Lett.
82
,
1971
(
1999
).
3.
L.
Allen
and
J.
Eberly
,
Optical Resonance and Two Level Systems
(
Dover
,
New York
,
1975
).
4.
J.
Gong
and
S. A.
Rice
,
Phys. Rev. A
69
,
063410
(
2004
).
5.
J.
Gong
and
S.
Rice
,
J. Chem. Phys.
120
,
9984
(
2004
).
6.
H.
Suchowski
,
Y.
Silberberg
, and
D. B.
Uskov
,
Phys. Rev. A
84
,
013414
(
2011
).
7.
A.
Yariv
,
IEEE J. Quantum Electron.
9
,
9
(
1973
).
8.
J.
Keeler
,
Understanding NMR
(
John Wiley and Sons
,
New York
,
2005
).
9.
I. I.
Rabi
,
J. R.
Zacharias
,
S.
Millman
, and
P.
Kusch
,
Phys. Rev.
53
,
318
(
1938
).
10.
C.
Zener
,
Proc. R. Soc. London, Ser. A
137
,
696
(
1932
).
11.
N.
Rosen
and
C.
Zener
,
Phys. Rev.
40
,
502
(
1932
).
12.
E. L.
Hahn
,
Phys. Rev.
80
,
580
(
1950
).
13.
H. Y.
Carr
and
E. M.
Purcell
,
Phys. Rev.
94
,
630
(
1954
).
14.
H. M.
Cho
,
R.
Tycko
,
A.
Pines
, and
J.
Guckenheimer
,
Phys. Rev. Lett.
56
,
1905
(
1986
).
15.
H. K.
Cummins
,
G.
Llewellyn
, and
J. A.
Jones
,
Phys. Rev. A
67
,
042308
(
2003
).
16.
M. H.
Levitt
and
R.
Freeman
,
J. Magn. Reson.
33
,
473
(
1979
).
17.
R.
Freeman
,
S. P.
Kempsell
, and
M.
Levitt
,
J. Magn. Reson.
38
,
453
(
1980
).
18.
M. H.
Levitt
,
Prog. Nucl. Magn. Reson. Spectrosc.
18
,
61
(
1986
).
19.
R.
Tycko
,
Phys. Rev. Lett.
51
,
775
(
1983
).
20.
B. T.
Torosov
and
N. V.
Vitanov
,
Phys. Rev. A
83
,
053420
(
2011
).
21.
B. T.
Torosov
,
E. S.
Kyoseva
, and
N. V.
Vitanov
,
Phys. Rev. A
92
,
033406
(
2015
).
22.
M. H.
Levitt
,
D.
Suter
, and
R. R.
Ernst
,
J. Chem. Phys.
80
,
3064
(
1984
).
23.
J. R.
Kuklinski
,
U.
Gaubatz
,
F. T.
Hioe
, and
K.
Bergmann
,
Phys. Rev. A
40
,
6741
(
1989
).
24.
J.
Oreg
,
F. T.
Hioe
, and
J. H.
Eberly
,
Phys. Rev. A
29
,
690
(
1984
).
25.
K.
Bergmann
,
H.
Theuer
, and
B. W.
Shore
,
Rev. Mod. Phys.
70
,
1003
(
1998
).
26.
B. W.
Shore
,
K.
Bergmann
, and
J.
Oreg
,
Z. Phys. D: At., Mol. Clusters
23
,
33
(
1992
).
27.
M.
Fleischauer
,
A.
Imamoglu
, and
J.
Marangos
,
Rev. Mod. Phys.
77
,
633
(
2005
).
28.
N. V.
Vitanov
,
A. A.
Rangelov
,
B. W.
Shore
, and
K.
Bergmann
,
Rev. Mod. Phys.
89
,
015006
(
2017
).
29.
R. J.
Cook
and
B. W.
Shore
,
Phys. Rev. A
20
,
539
(
1979
).
30.
F. T.
Hioe
,
J. Opt. Soc. Am. B
4
,
1327
(
1987
).
31.
E.
Majorana
,
Nuovo Cimento
9
,
43
(
1932
).
32.
F.
Bloch
and
I. I.
Rabi
,
Rev. Mod. Phys.
17
,
237
(
1945
).
33.
H.
Mäkelä
and
A.
Messina
,
Phys. Rev. A
81
,
012326
(
2010
).
34.
H. D.
Liu
and
L. B.
Fu
,
Phys. Rev. A
94
,
022123
(
2016
).
35.
R.
Barnett
,
D.
Podolsky
, and
G.
Refael
,
Phys. Rev. B
80
,
024420
(
2009
).
36.
B.
Lian
,
T.-L.
Ho
, and
H.
Zhai
,
Phys. Rev. A
85
,
051606
(
2012
).
37.
P.
Bruno
,
Phys. Rev. Lett.
108
,
240402
(
2012
).
38.
P.
Ribeiro
,
J.
Vidal
, and
R.
Mosseri
,
Phys. Rev. Lett.
99
,
050402
(
2007
).
39.
P.
Ribeiro
,
J.
Vidal
, and
R.
Mosseri
,
Phys. Rev. E
78
,
021106
(
2008
).
40.
B.
Shore
,
The Theory of Coherent Atomic Excitation
(
Wiley
,
New York
,
1990
), Vol. I.
41.
M.
Born
and
E.
Wolf
,
Principles of Optics
(
Cambridge University Press
,
Cambridge
,
1999
).
42.
F.
Bloch
,
Phys. Rev.
70
,
460
(
1946
).
43.
M.
Hamermesh
,
Group Theory and Its Application to Physical Problems
(
Addison-Wesley
,
Reading, Mass
,
1962
), p.
354
.

Supplementary Material

You do not currently have access to this content.