We apply the chirped-pulse millimeter-wave (CPmmW) technique to transitions between Rydberg states in calcium atoms. The unique feature of Rydberg–Rydberg transitions is that they have enormous electric dipole transition moments (∼5 kiloDebye at n* ∼ 40, where n* is the effective principal quantum number), so they interact strongly with the mm-wave radiation. After polarization by a mm-wave pulse in the 70–84 GHz frequency region, the excited transitions re-radiate free induction decay (FID) at their resonant frequencies, and the FID is heterodyne-detected by the CPmmW spectrometer. Data collection and averaging are performed in the time domain. The spectral resolution is ∼100 kHz. Because of the large transition dipole moments, the available mm-wave power is sufficient to polarize the entire bandwidth of the spectrometer (12 GHz) in each pulse, and high-resolution survey spectra may be collected. Both absorptive and emissive transitions are observed, and they are distinguished by the phase of their FID relative to that of the excitation pulse. With the combination of the large transition dipole moments and direct monitoring of transitions, we observe dynamics, such as transient nutations from the interference of the excitation pulse with the polarization that it induces in the sample. Since the waveform produced by the mm-wave source may be precisely controlled, we can populate states with high angular momentum by a sequence of pulses while recording the results of these manipulations in the time domain. We also probe the superradiant decay of the Rydberg sample using photon echoes. The application of the CPmmW technique to transitions between Rydberg states of molecules is discussed.

1.
The effective principal quantum number, n*, is defined as
$n^* \equiv \protect \sqrt{{R\over I-E}}\break = n - \delta$
n*RIE=nδ
, where R is the Rydberg constant, I is the ionization limit, E is the energy of the state, n is the principal quantum number, and δ is the quantum defect.
2.
T. F.
Gallagher
,
Rydberg Atoms
(
Cambridge University Press
,
Cambridge
,
1994
).
3.
H.
Lefebvre-Brion
and
R. W.
Field
,
The Spectra and Dynamics of Diatomic Molecules
(
Elsevier Academic
,
2004
), p.
352
.
4.
C.
Fabre
,
S.
Haroche
, and
P.
Goy
,
Phys. Rev. A
18
,
229
(
1978
).
5.
L.
Moi
,
C.
Fabre
,
P.
Goy
,
M.
Gross
,
S.
Haroche
,
P.
Encrenaz
,
G.
Beaudin
, and
B.
Lazareff
,
Opt. Commun.
33
,
47
(
1980
).
6.
P.
Goy
,
J. M.
Raimond
,
G.
Vitrant
, and
S.
Haroche
,
Phys. Rev. A
26
,
2733
(
1982
).
7.
T. R.
Gentile
,
B. J.
Hughey
,
D.
Kleppner
, and
T. W.
Ducas
,
Phys. Rev. A
42
,
440
(
1990
).
8.
F.
Merkt
and
H.
Schmutz
,
J. Chem. Phys.
108
,
10033
(
1998
).
9.
W.
Li
,
I.
Mourachko
,
M. W.
Noel
, and
T. F.
Gallagher
,
Phys. Rev. A
67
,
052502
(
2003
).
10.
F.
Merkt
and
A.
Osterwalder
,
Int. Rev. Phys. Chem.
21
,
385
(
2002
).
11.
A.
Osterwalder
,
R.
Seiler
, and
F.
Merkt
,
J. Chem. Phys.
113
,
7939
(
2000
).
12.
A.
Osterwalder
,
S.
Willitsch
, and
F.
Merkt
,
J. Mol. Struct.
599
,
163
(
2001
).
13.
A.
Osterwalder
,
A.
Wüest
,
F.
Merkt
, and
C.
Jungen
,
J. Chem. Phys.
121
,
11810
(
2004
).
14.
S. R.
Lundeen
, in
Advances in Atomic, Molecular, and Optical Physics
, edited by
P. R.
Berman
, and
C. C.
Lin
(
Elsevier Academic
,
Amsterdam
,
2005
), Vol.
52
, pp.
161
208
.
15.
G. G.
Brown
,
B. C.
Dian
,
K. O.
Douglass
,
S. M.
Geyer
,
S. T.
Shipman
, and
B. H.
Pate
,
Rev. Sci. Instrum.
79
,
053103
(
2008
).
16.
G. G.
Brown
,
B. C.
Dian
,
K. O.
Douglass
,
S. M.
Geyer
, and
B. H.
Pate
,
J. Mol. Spectrosc.
238
,
200
(
2006
).
17.
B. C.
Dian
,
G. G.
Brown
,
K. O.
Douglass
, and
B. H.
Pate
,
Science
320
,
924
(
2008
).
18.
G. B.
Park
,
A. H.
Steeves
,
K.
Kuyanov-Prozument
,
J. L.
Neill
, and
R. W.
Field
,
J. Chem. Phys.
135
,
024202
(
2011
).
19.
K.
Prozument
,
A. P.
Colombo
,
Y.
Zhou
,
G. B.
Park
,
V. S.
Petrović
,
S. L.
Coy
, and
R. W.
Field
,
Phys. Rev. Lett.
107
,
143001
(
2011
).
20.
K.
Müller-Dethlefs
and
E. W.
Schlag
,
Annu. Rev. Phys. Chem.
42
,
109
(
1991
).
22.
F. X.
Campos
,
Y.
Jiang
, and
E. R.
Grant
,
J. Chem. Phys.
93
,
2308
(
1990
).
23.
A. M.
Lyyra
,
W. T.
Luh
,
L.
Li
,
H.
Wang
, and
W. C.
Stwalley
,
J. Chem. Phys.
92
,
43
(
1990
).
24.
S.
Guizard
,
N.
Shafizadeh
,
M.
Horani
, and
D.
Gauyacq
,
J. Chem. Phys.
94
,
7046
(
1991
).
25.
S. T.
Pratt
,
J. L.
Dehmer
,
P. M.
Dehmer
, and
W. A.
Chupka
,
J. Chem. Phys.
101
,
882
(
1994
).
26.
Z. J.
Jakubek
and
R. W.
Field
,
Phys. Rev. Lett.
72
,
2167
(
1994
).
27.
K.
Siglow
,
R.
Neuhauser
, and
H. J.
Neusser
,
J. Chem. Phys.
110
,
5589
(
1999
).
28.
P.
Bell
,
F.
Aguirre
,
E. R.
Grant
, and
S. T.
Pratt
,
J. Chem. Phys.
119
,
10146
(
2003
).
29.
J. J.
Kay
,
D. S.
Byun
,
J. O.
Clevenger
,
X.
Jiang
,
V. S.
Petrović
,
R.
Seiler
,
J. R.
Barchi
,
A. J.
Merer
, and
R. W.
Field
,
Can. J. Chem.
82
,
791
(
2004
).
30.
K.
Afrousheh
,
P.
Bohlouli-Zanjani
,
D.
Vagale
,
A.
Mugford
,
M.
Fedorov
, and
J. D. D.
Martin
,
Phys. Rev. Lett.
93
,
233001
(
2004
).
32.
T.
Wang
,
S. F.
Yelin
,
R.
Côté
,
E. E.
Eyler
,
S. M.
Farooqi
,
P. L.
Gould
,
M.
Koštrun
,
D.
Tong
, and
D.
Vrinceanu
,
Phys. Rev. A
75
,
33802
(
2007
).
33.
N. J. A.
Jones
,
R. S.
Minns
,
R.
Patel
, and
H. H.
Fielding
,
J. Phys. B
41
,
185102
(
2008
).
34.
H.
Park
,
P. J.
Tanner
,
B. J.
Claessens
,
E. S.
Shuman
, and
T. F.
Gallagher
,
Phys. Rev. A
84
,
22704
(
2011
).
35.
S. D.
Hogan
,
J. A.
Agner
,
F.
Merkt
,
T.
Thiele
,
S.
Filipp
, and
A.
Wallraff
,
Phys. Rev. Lett.
108
,
063004
(
2012
).
36.
Reference 5, where superradiant emission of a sodium transition in a cavity was heterodyne-detected, is one example.
37.
J.
Sugar
and
C.
Corliss
,
J. Phys. Chem. Ref. Data
14
,
1
(
1985
).
38.
W. R. S.
Garton
and
K.
Codling
,
Proc. Phys. Soc.
86
,
1067
(
1965
).
39.
C. M.
Brown
,
S. G.
Tilford
, and
M. L.
Ginter
,
J. Opt. Soc. Am.
63
,
1454
(
1973
).
40.
J. A.
Armstrong
,
P.
Esherick
, and
J. J.
Wynne
,
Phys. Rev. A
15
,
180
(
1977
).
41.
S. A.
Borgström
and
J. R.
Rubbmark
,
J. Phys. B
10
,
3607
(
1977
).
42.
A. G.
Vaidyanathan
,
W. P.
Spencer
,
J. R.
Rubbmark
,
H.
Kuiper
,
C.
Fabre
,
D.
Kleppner
, and
T. W.
Ducas
,
Phys. Rev. A
26
,
3346
(
1982
).
43.
The paperback version of Ref. 3 serves as a 25-dB attenuator from 70 to 84 GHz.
44.
T. F.
Gallagher
and
P.
Pillet
, in
Advances in Atomic, Molecular, and Optical Physics
, edited by
E.
Arimondo
,
P. R.
Berman
, and
C. C.
Lin
(
Elsevier Academic
,
Amsterdam
,
2008
), Vol.
56
, pp.
161
218
.
45.
J. M.
Raimond
,
G.
Vitrant
, and
S.
Haroche
,
J. Phys. B
14
,
L655
(
1981
).
46.
W. R.
Anderson
,
J. R.
Veale
, and
T. F.
Gallagher
,
Phys. Rev. Lett.
80
,
249
(
1998
).
47.
I.
Mourachko
,
D.
Comparat
,
F.
de Tomasi
,
A.
Fioretti
,
P.
Nosbaum
,
V. M.
Akulin
, and
P.
Pillet
,
Phys. Rev. Lett.
80
,
253
(
1998
).
48.
J.
Stanojevic
,
R.
Côté
,
D.
Tong
,
E. E.
Eyler
, and
P. L.
Gould
,
Phys. Rev. A
78
,
052709
(
2008
).
49.
P. J.
Tanner
,
J.
Han
,
E. S.
Shuman
, and
T. F.
Gallagher
,
Phys. Rev. Lett.
100
,
043002
(
2008
).
50.
51.
N.
Skribanowitz
,
I. P.
Herman
,
J. C.
MacGillivray
, and
M. S.
Feld
,
Phys. Rev. Lett.
30
,
309
(
1973
).
52.
J. C.
MacGillivray
and
M. S.
Feld
,
Phys. Rev. A
14
,
1169
(
1976
).
53.
F.
Gounand
,
M.
Hugon
,
P. R.
Fournier
, and
J.
Berlande
,
J. Phys. B
12
,
547
(
1979
).
54.
M.
Gross
,
P.
Goy
,
C.
Fabre
,
S.
Haroche
, and
J. M.
Raimond
,
Phys. Rev. Lett.
43
,
343
(
1979
).
56.
For values of the Rydberg constant and the ionization limit that may be used to compute n* in calcium, see, for example, Ref. 7.
57.
J. C.
McGurk
,
T. G.
Schmalz
, and
W. H.
Flygare
,
J. Chem. Phys.
60
,
4181
(
1974
).
58.
H. C.
Torrey
,
Phys. Rev.
76
,
1059
(
1949
).
59.
J. C.
McGurk
,
R. T.
Hofmann
, and
W. H.
Flygare
,
J. Chem. Phys.
60
,
2922
(
1974
).
60.
D. W.
Posener
,
J. Magn. Reson.
14
,
121
(
1974
).
61.
L.
Chen
,
C. E.
Cottrell
, and
A. G.
Marshall
,
Chemom. Intell. Lab. Syst.
1
,
51
(
1986
).
62.
For a linearly chirped excitation, the nonresonant contributions to the phase above and below the resonance frequency cancel, and the phase of the excitation at the resonance frequency determines the phase of the FID.
63.
V. M.
Akulin
and
N. V.
Karlov
,
Intense Resonant Interactions in Quantum Electronics
, Texts and Monographs in Physics (
Springer-Verlag
,
Berlin
,
1992
).
64.
Ē. Kup
$\breve{\rm c}$
c˘
e and
R.
Freeman
,
J. Magn. Reson., Ser. A
117
,
246
(
1995
).
65.
J.
Baum
,
R.
Tycko
, and
A.
Pines
,
Phys. Rev. A
32
,
3435
(
1985
).
66.
M. H.
Levitt
and
R.
Freeman
,
J. Magn. Reson.
33
,
473
(
1979
).
67.
R.
Freeman
,
S. P.
Kempsell
, and
M. H.
Levitt
,
J. Magn. Reson.
38
,
453
(
1980
).
68.
J. K.
Messer
and
F. C.
De Lucia
,
Phys. Rev. Lett.
53
,
2555
(
1984
).
69.
S. E.
Maxwell
,
N.
Brahms
,
R.
deCarvalho
,
D. R.
Glenn
,
J. S.
Helton
,
S. V.
Nguyen
,
D.
Patterson
,
J.
Petricka
,
D.
DeMille
, and
J. M.
Doyle
,
Phys. Rev. Lett.
95
,
173201
(
2005
).
70.
D.
Patterson
and
J. M.
Doyle
,
J. Chem. Phys.
126
,
154307
(
2007
).
71.
M. O.
Scully
and
A. A.
Svidzinsky
,
Science
328
,
1239
(
2010
).
72.
J. J.
Kay
,
S. L.
Coy
,
V. S.
Petrović
,
B. M.
Wong
, and
R. W.
Field
,
J. Chem. Phys.
128
,
194301
(
2008
).
You do not currently have access to this content.