Two-photon spectroscopy of atomic cesium confined and cooled in a magneto-optical trap is reported. The hyperfine structure of the 6D_(5/2) state is determined with 1% accuracy. New capabilities for studying ac Stark shifts and kinetic transport for cold atoms are suggested

Georgiades, N. Ph.

Kimble, H. J.

Polzik, E. S.

English

Caltech Authors - Main

1474 OPTICS LETTERS / Vol. 19, No. 18 / September 15, 1994
Two-photon spectroscopy of the 6S1/2 - 6D5 /2
transition of trapped atomic cesium
N. Ph. Georgiades, E. S. Polzik,* and H. J. Kimble
Norman Bridge Laboratory of Physics, California Institute of Technology, Pasadena, California 91125
Received March 9, 1994
Two-photon spectroscopy of atomic cesium confined and cooled in a magneto-optical trap is reported. The
hyperfine structure of the 6D&2 state is determined with 1% accuracy. New capabilities for studying ac Stark
shifts and kinetic transport for cold atoms are suggested.
Cold atoms confined in a magneto-optical trap'
(MOT) are becoming a powerful tool for high-
resolution spectroscopy. 2 5 The almost-Doppler-free
environment and the high atomic density in a MOT
are compelling advantages for using trapped atoms
as a sample for spectroscopy. For example, by use
of this method high-precision Doppler-less mea-
surements of hyperfine structure in sodium were
performed in the research reported in Ref. 4, and
two-step excitation in trapped rubidium and cesium
was studied in Ref. 5. Following this theme, in this
Letter we report the results of two-photon spec-
troscopy for Cs atoms trapped in a MOT. The transi-
tion we have studied is the 6S/2 - 6D5/2 transition
excited by two-photon absorption at AO = 883 nm.
Regarding usual Doppler-free two-photon spec-
troscopy in an atomic vapor,6 note that the use of
atoms in a MOT mitigates the residual Doppler
broadening associated with the strong focusing re-
quired for most two-photon processes, which usually
have relatively small cross sections and hence re-
quire rather high intensities.
The atomic energy levels for Cs relevant to our in-
vestigation are shown in Fig. 1. Together with the
trapping beams for the MOT that are quasi-resonant
to the 6SV2 - 6P3 /2 transition at AT = 852 nm, the
scheme for two-photon excitation effectively forms a
V system including the ground state and the two ex-
cited states 6P3/2 and 6D5/2. By monitoring the fluo-
rescence from the decay of the excited 6D5/2 state to
the intermediate 6P3/2 level at AF = 917 nm as a func-
tion of excitation frequency near Ao, we determine the
excited-state structure of the 6D5/2 level and hence
the magnetic dipole (a) hyperfine structure parame-
ter with an accuracy of -1%. With respect to earlier
research we recall that Tai et a1.7 measured the mag-
netic dipole coefficient (a) by means of magnetic-level
crossing in a vapor cell with an accuracy of 30%.8 In
addition to the determination of the excited-state hy-
perfine structure, we have also used the two-photon
transition as a probe to observe ac Stark shifts and
power broadening of the ground state caused by the
presence of the trapping beams and to record some
dynamical effects of thermal motion.
In our experiment we employ a homemade
Ti:sapphire laser to produce the radiation Po at
AO = 883 nm for two-photon excitation of the 6D5 /2
state. The laser is frequency stabilized relative to
a reference cavity9 (Fig. 2). The reference cavity
itself is locked to the fluorescent signal (6D 5 /2 -
6P3/2) generated by Doppler-free two-photon absorp-
tion (6SV2 - 6D5 /2) obtained from an auxiliary Cs
vapor cell. Before reaching the Cs cell the locking
beam is double passed through two acousto-optic
modulators (AOM's). By changing the rf drive
frequency to one acousto-optic modulator with an
HP8644A synthesized signal generator we can scan
the laser frequency by ±40 MHz near AO, corre-
sponding to AfQ = ±80 MHz detuning for the two-
photon transition.
To trap the Cs atoms, we use a MOT in a vapor
cell, as first implemented by Monroe et al.1 The
trap is sustained by five intersecting laser beams
of circular polarization with three in the horizontal
plane at 1200 separation and two counterpropagating
in the vertical (z) direction. A pair of anti-Helmholtz
coils aligned along the z axis generates the necessary
magnetic-field gradient for the MOT (Fig. 2). The
trapping laser PT is an external-cavity semiconductor
diode laser1 0 that is frequency locked at -10 MHz
below the 6S,12, F = 4 - 6P3 /2, F = 5 transition
at AT = 852 nm through saturated absorption in an
133
Cs
6D 5/2 , F-21
> F_4 1~~~~~~~93.8 MHZ
\ <F = 9X7 nm 
x0 -8
83nmX % 6P3/Z F_4
- 883,nm | 852nm
SI5/2 - F-4 93W:1: t9193 MHZ
Fig. 1. Relevant energy levels of 133Cs for trapping and
for two-photon excitation.
0146-9592/94/181474-03$6.00/0 © 1994 Optical Society of America
September 15, 1994 / Vol. 19, No. 18 / OPTICS LETTERS 1475
Fig. 2. Diagram of the experimental setup.
auxiliary Cs cell (not shown in Fig. 2). The waist for
each beam is fixed at 0)T = 4 mm. A second diode
laser, PR, is operated without an external cavity and
is manually tuned into resonance with the 6S112, F =
3 - 6P3/2, F = 3 or 4 transition to prevent depletion
of the F = 4 ground state. The trap diameter is of
the order of 0.5 mm.
We obtain spectroscopic information about the
structure of the 6D5 /2 level by observing the fluo-
rescence from the 6D512 - 6 P3/2 transition at AF =
917 nm as a function of excitation frequency near
AO = 883 nm. To optimize the signal without sat-
urating the two-photon transition, we must make
sure in the excitation and imaging systems to match
the Rayleigh length for the excitation beam to the
size of the volume that is imaged. More explicitly,
recall that the total fluorescence signal IF for un-
saturated excitation with Gaussian beam is given
by IF = (2F2Po2 na.6/AO)arctan(L/2zo), where na is the
atomic density, Po is the excitation power at AO, e
is the overall collection and detection efficiency, L is
the length of the imaged volume, and z, = g7ro02/AO
is the Rayleigh length. Here r2 is the two-photon
cross section, defined by R2 = r2o02 , with R2 the rate
of two-photon excitation for an intensity Io.
In our experiment the waist size of the excitation
laser is chosen to be -7 Jum and L -150 ,um so that
arctan(L/2z 0) - 0.4. The saturation power with this
geometry for the two-photon transition is measured
to be -10 mW, which permits Po = 2-4 mW. Fluo-
rescence at AF is collected by a telescope system con-
sisting of two lenses with N.A. = 0.25 (opening angle
30°) and is focused with 1:1 imaging onto the surface
of an avalanche photodiode (APD) with an active area
of 150 ,um X 150 /um. Two identical interference fil-
ters centered at 920 nm protect the avalanche photo-
diode from the stray light that is mainly at 852 nm.
The electrical pulses from the avalanche photodiode
are counted by an SR400 photon counter that is in-
terfaced with a personal computer (PC).
To observe the spectra unperturbed by the trap-
ping beams (while also recording the effect of this
perturbation), we mechanically chop the trapping
and repumping beams at 4 kHz and observe two-
photon excitation spectra with the trapping beams
both on and off. By gating the photon counting
system accordingly, we are then able to obtain in
a single-scan excitation spectra with the trapping
beams both on and off. Excitation spectra are ac-
quired by variation of the drive frequency to the
acousto-optic modulator (and hence the laser fre-
quency) to scan across the entire hyperfine struc-
ture of the 6D5/2 level at a rate of typically 0.05 Hz.
An example of such a spectrum is shown in Fig. 3,
in which two-photon excitation proceeds from the
F = 4 component of the ground 6SI/2 level to five
hyperfine components with F = 6,5,4,3,2 of the
excited 6D5/2 level. Note that the two-photon exci-
tation spectra taken in the on state permit observa-
tion of the effect of the strong trapping beams on the
Cs ground state, complementing nicely other types of
trapped-atom spectroscopy.2 5
The magnetic dipole a and electric quadruple b
coefficients of the 6D5/2 state are determined from
spectra similar to those in Fig. 3 recorded over a
range of experimental conditions for the trapping
beams, the atomic density, and the excitation power
Po at AO. Spectra with the trapping and repump-
ing lasers chopped off are fitted to multi-Lorenzian
functions to extract line positions, amplitudes, and
widths for each of the observed hyperfine compo-
nents. From the fitted splittings of the hyperfine
peaks [see, e.g., Eq. (1) of Ref. 7] we then calculate
with a least-squares procedure the coefficients a =
-4.69 ± 0.04 MHz and b = 0.18 ± 0.73MHz, which
are to be compared with those of Ref. 7, namely,
a = -3.6 ± 1.0 MHz and no evidence for a nonzero
value of b. Within our quoted uncertainties no
observable dependence of the splittings on the
intensity of the trapping beams has been found for
single-beam intensities between 0.8 and 3 mW/cm2.
To address the issue of possible Zeeman shifts of
the line positions, we have compared splittings of
the various 6D5 /2 hyperfine components and have
also measured hyperfine splittings at two different
magnetic-field gradients (6.2 and 4.8 G/cm in the z
direction) and again have found no changes within
our stated uncertainty.
7500
6000
6 4500
_C
0 3000
1500
0
70 90 110 130
Q ( MHz)
Fig. 3. Two-photon excitation spectra for P0 = 3.3 mW
showing the fluorescence IF at AF versus excitation
frequency fl (cycles/s) near AO = 883 nm with the
trapping and repumping beams chopped on (circles) and
off (squares). Stark shifts and power broadening of the
ground state resulting from the presence of the trapping
beams are clearly evident, here with a total trapping
power of 3.1 mW. Note that 0 refers to the two-photon
detuning (i.e., twice the actual frequency change near Ao).
-. - ~~~I I I 
-F-6
A SF-
9 F-4
~~~~ ~~~F-3
/ F.~~~~~~-2-
LI~~~~~~~~~~. 4
1476 OPTICS LETTERS / Vol. 19, No. 18 / September 15, 1994
6
N
M0
61
5
4
3
0 10 15 20
Power ( Pe ) ( mW )
Fig. 4. Linewidths (FWHM) of the F = 6, 5, 4 hyperfine
components of the 6D5/2 level versus the excitation power
P0 with the trapping beams off and the repumping beam
either off (solid curves) or on (dashed curves).
I.OX1O4
0.8x10
4
'0 0.6x10
4
C0
01 0.4X10
4
0.2X10
4
0
0 20 40 60 80
Q ( MHz)
Fig. 5. Two-photon excitation spectra for Po = 16 mW
showing fluorescence Ip versus detuning fl obtained with
the repumping and trapping beams off (squares) and
with the repumping beam on and the trapping beam off
(circles).
In addition to line positions, the peak widths have
been measured as a function of excitation power
P0, with the broadening exhibited in Fig. 4 due to
saturation of the two-photon transition. At low
power the widths of the resonances extrapolate to
3.2 ± 0.2 MHz. Considering residual Doppler broad-
ening from the finite trap temperature, assumed to
be the Doppler cooling limit TD = 120 /K, we obtain
a value for the natural linewidth of 3.1 ± 0.2 MHz.
The discrepancy between our measurement and the
theoretical prediction of 2.5 MHz (Ref. 11) may be
attributable to fluctuations in laser frequency
(linewidth -500 kHz), to inhomogeneities in the trap
environment (especially spatially dependent Zeeman
splittings), to temperatures in excess of TD, and/or
to uncertainties of the theoretical value itself. One
interesting feature of our measurements in Fig. 4 is
the dependence of the line broadening of the F = 4
and F = 5 states on the presence or absence of the
repumping beam, whereas the widths of the F = 6
state seem insensitive to this.
To investigate this point further, we show in Fig. 5
two spectra, one obtained with the repumping beam
on and the other with the repumping beam off. The
difference in relative heights of the F = 5, 4,3 compo-
nents between the two curves is due to the fact that,
without the repumping beam, the F = 4 component
of 6S1X2 is depleted as a result of the decay of the F =
5,4,3,2 components of 6D5/2 to the F = 3 component
of 6S,/2. Indeed, without the repumping beam the
transitions with F = 5,4,3,2 should normally have
near-zero amplitudes since the time to deplete the
F = 4 ground level under the conditions of Fig. 5 is
only -10-6 s, compared with the 10 -s interval of the
off cycle during which the spectra are acquired. That
significant amplitudes are observed in Fig. 5 without
the repumping beam is principally because of ther-
mal motion, which brings fresh atoms from the trap
into the small excitation volume. Further studies of
spectra such as those in Fig. 5 with systematic vari-
ations in trap parameters as well as in the size of the
excitation volume might be of interest in providing a
relatively nonintrusive probe of the trap kinetics.
In conclusion, we have investigated two-photon
spectroscopy of cold trapped Cs atoms and have de-
termined the a coefficient for the 6D5/2 state with
1% accuracy, which represents a 30-fold improvement
over the results of Ref. 7. We have observed ac Stark
shifts for the ground state of cold atoms (Fig. 3) and
have demonstrated a possible avenue for exploring
transport processes in the trap (Figs. 4 and 5).
We gratefully acknowledge contributions of H.
Tsuchida and correspondence from S. Svanberg.
This study was funded in part by the U.S. Army Re-
search Office and the National Science Foundation.
E. S. Polzik acknowledges support from Aarhus
University.
*Present address, Institute of Physics and As-
tronomy, Aarhus University, Aarhus C, DK-8000,
Denmark.
References
1. E. L. Raab, M. Prentiss, A. Cable, S. Chu, and
D. Pritchard, Phys. Rev. Lett. 59, 2631 (1987);
C. Monroe, W. Swann, H. Robinson, and
C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
2. J. W. R. Tobosa, G. Chen, Z. Hu, R. B. Lee, and H. J.
Kimble, Phys. Rev. Lett. 66, 3245 (1991); D. Grison,
B. Lounis, C. Salomon, J. Y. Courtis, and G. Grynberg,
Europhys. Lett. 15, 149 (1991).
3. For a recent summary of spectroscopic measurements
in optical lattices see Phys. Today 46(6), 17 (1993).
4. M. Zhu, C. W. Oates, and J. L. Hall, Opt. Lett. 18,
1186 (1993).
5. R. W. Fox, S. L. Gilbert, L. Hollberg, and J. H.
Marquardt, Opt. Lett. 18, 1456 (1993).
6. L. S. Vasilenko, V. P. Chebotaev, and A. V. Shishaev,
Sov. Phys. JETP Lett. 12, 13 (1970).
7. C. Tai, W. Happer, and R. Guta, Phys. Rev. A 12,723
(1975).
8. For work on other excited states in Cs see G. Belin,
L. Holmgren, and S. Svanberg, Phys. Scr. 14, 39
(1976).
9. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. K.
Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl.
Phys. B 31, 97 (1983).
10. K. Libbrecht and J. L. Hall, Rev. Sci. Instrum. 64,
2133 (1993).
11. 0. S. Heavens, J. Opt. Soc. Am. 51, 1058 (1961).
. .. . . . Il I I ,, I ,, r-I -
F- 4
'F-5
I . . . . I . I I . . . . I . . , -
F-S6II . 7
F-5
I ,
I I F-4
I I I
II II F-
I II
I i
I I I~~~~~~~~~~*


Two-photon spectroscopy of the 6S_(1/2) → 6D_(5/2) transition of trapped atomic cesium

1474 OPTICS LETTERS / Vol. 19, No. 18 / September 15, 1994
Two-photon spectroscopy of the 6S1/2 - 6D5 /2
transition of trapped atomic cesium
N. Ph. Georgiades, E. S. Polzik,* and H. J. Kimble
Norman Bridge Laboratory of Physics, California Institute of Technology, Pasadena, California 91125
Received March 9, 1994
Two-photon spectroscopy of atomic cesium confined and cooled in a magneto-optical trap is reported. The
hyperfine structure of the 6D&2 state is determined with 1% accuracy. New capabilities for studying ac Stark
shifts and kinetic transport for cold atoms are suggested.
Cold atoms confined in a magneto-optical trap'
(MOT) are becoming a powerful tool for high-
resolution spectroscopy. 2 5 The almost-Doppler-free
environment and the high atomic density in a MOT
are compelling advantages for using trapped atoms
as a sample for spectroscopy. For example, by use
of this method high-precision Doppler-less mea-
surements of hyperfine structure in sodium were
performed in the research reported in Ref. 4, and
two-step excitation in trapped rubidium and cesium
was studied in Ref. 5. Following this theme, in this
Letter we report the results of two-photon spec-
troscopy for Cs atoms trapped in a MOT. The transi-
tion we have studied is the 6S/2 - 6D5/2 transition
excited by two-photon absorption at AO = 883 nm.
Regarding usual Doppler-free two-photon spec-
troscopy in an atomic vapor,6 note that the use of
atoms in a MOT mitigates the residual Doppler
broadening associated with the strong focusing re-
quired for most two-photon processes, which usually
have relatively small cross sections and hence re-
quire rather high intensities.
The atomic energy levels for Cs relevant to our in-
vestigation are shown in Fig. 1. Together with the
trapping beams for the MOT that are quasi-resonant
to the 6SV2 - 6P3 /2 transition at AT = 852 nm, the
scheme for two-photon excitation effectively forms a
V system including the ground state and the two ex-
cited states 6P3/2 and 6D5/2. By monitoring the fluo-
rescence from the decay of the excited 6D5/2 state to
the intermediate 6P3/2 level at AF = 917 nm as a func-
tion of excitation frequency near Ao, we determine the
excited-state structure of the 6D5/2 level and hence
the magnetic dipole (a) hyperfine structure parame-
ter with an accuracy of -1%. With respect to earlier
research we recall that Tai et a1.7 measured the mag-
netic dipole coefficient (a) by means of magnetic-level
crossing in a vapor cell with an accuracy of 30%.8 In
addition to the determination of the excited-state hy-
perfine structure, we have also used the two-photon
transition as a probe to observe ac Stark shifts and
power broadening of the ground state caused by the
presence of the trapping beams and to record some
dynamical effects of thermal motion.
In our experiment we employ a homemade
Ti:sapphire laser to produce the radiation Po at
AO = 883 nm for two-photon excitation of the 6D5 /2
state. The laser is frequency stabilized relative to
a reference cavity9 (Fig. 2). The reference cavity
itself is locked to the fluorescent signal (6D 5 /2 -
6P3/2) generated by Doppler-free two-photon absorp-
tion (6SV2 - 6D5 /2) obtained from an auxiliary Cs
vapor cell. Before reaching the Cs cell the locking
beam is double passed through two acousto-optic
modulators (AOM's). By changing the rf drive
frequency to one acousto-optic modulator with an
HP8644A synthesized signal generator we can scan
the laser frequency by ±40 MHz near AO, corre-
sponding to AfQ = ±80 MHz detuning for the two-
photon transition.
To trap the Cs atoms, we use a MOT in a vapor
cell, as first implemented by Monroe et al.1 The
trap is sustained by five intersecting laser beams
of circular polarization with three in the horizontal
plane at 1200 separation and two counterpropagating
in the vertical (z) direction. A pair of anti-Helmholtz
coils aligned along the z axis generates the necessary
magnetic-field gradient for the MOT (Fig. 2). The
trapping laser PT is an external-cavity semiconductor
diode laser1 0 that is frequency locked at -10 MHz
below the 6S,12, F = 4 - 6P3 /2, F = 5 transition
at AT = 852 nm through saturated absorption in an
133Cs
6D 5/2 , F-21
> F_4 1~~~~~~~93.8 MHZ
\ <F = 9X7 nm 
x0 -883nmX % 6P3/Z F_4
- 883,nm | 852nm
SI5/2 - F-4 93W:1: t9193 MHZ
Fig. 1. Relevant energy levels of 133Cs for trapping and
for two-photon excitation.
0146-9592/94/181474-03$6.00/0 © 1994 Optical Society of America
September 15, 1994 / Vol. 19, No. 18 / OPTICS LETTERS 1475
Fig. 2. Diagram of the experimental setup.
auxiliary Cs cell (not shown in Fig. 2). The waist for
each beam is fixed at 0)T = 4 mm. A second diode
laser, PR, is operated without an external cavity and
is manually tuned into resonance with the 6S112, F =
3 - 6P3/2, F = 3 or 4 transition to prevent depletion
of the F = 4 ground state. The trap diameter is of
the order of 0.5 mm.
We obtain spectroscopic information about the
structure of the 6D5 /2 level by observing the fluo-
rescence from the 6D512 - 6 P3/2 transition at AF =
917 nm as a function of excitation frequency near
AO = 883 nm. To optimize the signal without sat-
urating the two-photon transition, we must make
sure in the excitation and imaging systems to match
the Rayleigh length for the excitation beam to the
size of the volume that is imaged. More explicitly,
recall that the total fluorescence signal IF for un-
saturated excitation with Gaussian beam is given
by IF = (2F2Po2 na.6/AO)arctan(L/2zo), where na is the
atomic density, Po is the excitation power at AO, e
is the overall collection and detection efficiency, L is
the length of the imaged volume, and z, = g7ro02/AO
is the Rayleigh length. Here r2 is the two-photon
cross section, defined by R2 = r2o02 , with R2 the rate
of two-photon excitation for an intensity Io.
In our experiment the waist size of the excitation
laser is chosen to be -7 Jum and L -150 ,um so that
arctan(L/2z 0) - 0.4. The saturation power with this
geometry for the two-photon transition is measured
to be -10 mW, which permits Po = 2-4 mW. Fluo-
rescence at AF is collected by a telescope system con-
sisting of two lenses with N.A. = 0.25 (opening angle
30°) and is focused with 1:1 imaging onto the surface
of an avalanche photodiode (APD) with an active area
of 150 ,um X 150 /um. Two identical interference fil-
ters centered at 920 nm protect the avalanche photo-
diode from the stray light that is mainly at 852 nm.
The electrical pulses from the avalanche photodiode
are counted by an SR400 photon counter that is in-
terfaced with a personal computer (PC).
To observe the spectra unperturbed by the trap-
ping beams (while also recording the effect of this
perturbation), we mechanically chop the trapping
and repumping beams at 4 kHz and observe two-
photon excitation spectra with the trapping beams
both on and off. By gating the photon counting
system accordingly, we are then able to obtain in
a single-scan excitation spectra with the trapping
beams both on and off. Excitation spectra are ac-
quired by variation of the drive frequency to the
acousto-optic modulator (and hence the laser fre-
quency) to scan across the entire hyperfine struc-
ture of the 6D5/2 level at a rate of typically 0.05 Hz.
An example of such a spectrum is shown in Fig. 3,
in which two-photon excitation proceeds from the
F = 4 component of the ground 6SI/2 level to five
hyperfine components with F = 6,5,4,3,2 of the
excited 6D5/2 level. Note that the two-photon exci-
tation spectra taken in the on state permit observa-
tion of the effect of the strong trapping beams on the
Cs ground state, complementing nicely other types of
trapped-atom spectroscopy.2 5
The magnetic dipole a and electric quadruple b
coefficients of the 6D5/2 state are determined from
spectra similar to those in Fig. 3 recorded over a
range of experimental conditions for the trapping
beams, the atomic density, and the excitation power
Po at AO. Spectra with the trapping and repump-
ing lasers chopped off are fitted to multi-Lorenzian
functions to extract line positions, amplitudes, and
widths for each of the observed hyperfine compo-
nents. From the fitted splittings of the hyperfine
peaks [see, e.g., Eq. (1) of Ref. 7] we then calculate
with a least-squares procedure the coefficients a =
-4.69 ± 0.04 MHz and b = 0.18 ± 0.73MHz, which
are to be compared with those of Ref. 7, namely,
a = -3.6 ± 1.0 MHz and no evidence for a nonzero
value of b. Within our quoted uncertainties no
observable dependence of the splittings on the
intensity of the trapping beams has been found for
single-beam intensities between 0.8 and 3 mW/cm2.
To address the issue of possible Zeeman shifts of
the line positions, we have compared splittings of
the various 6D5 /2 hyperfine components and have
also measured hyperfine splittings at two different
magnetic-field gradients (6.2 and 4.8 G/cm in the z
direction) and again have found no changes within
our stated uncertainty.
7500
6000
6 4500
_C
0 3000
1500
0
70 90 110 130
Q ( MHz)
Fig. 3. Two-photon excitation spectra for P0 = 3.3 mW
showing the fluorescence IF at AF versus excitation
frequency fl (cycles/s) near AO = 883 nm with the
trapping and repumping beams chopped on (circles) and
off (squares). Stark shifts and power broadening of the
ground state resulting from the presence of the trapping
beams are clearly evident, here with a total trapping
power of 3.1 mW. Note that 0 refers to the two-photon
detuning (i.e., twice the actual frequency change near Ao).
-. - ~~~I I I 
-F-6
A SF-
9 F-4
~~~~ ~~~F-3
/ F.~~~~~~-2-
LI~~~~~~~~~~. 4
1476 OPTICS LETTERS / Vol. 19, No. 18 / September 15, 1994
6
N
M0
61
5
4
3
0 10 15 20
Power ( Pe ) ( mW )
Fig. 4. Linewidths (FWHM) of the F = 6, 5, 4 hyperfine
components of the 6D5/2 level versus the excitation power
P0 with the trapping beams off and the repumping beam
either off (solid curves) or on (dashed curves).
I.OX1O4
0.8x104
'0 0.6x104
C0
01 0.4X10
4
0.2X104
0
0 20 40 60 80
Q ( MHz)
Fig. 5. Two-photon excitation spectra for Po = 16 mW
showing fluorescence Ip versus detuning fl obtained with
the repumping and trapping beams off (squares) and
with the repumping beam on and the trapping beam off
(circles).
In addition to line positions, the peak widths have
been measured as a function of excitation power
P0, with the broadening exhibited in Fig. 4 due to
saturation of the two-photon transition. At low
power the widths of the resonances extrapolate to
3.2 ± 0.2 MHz. Considering residual Doppler broad-
ening from the finite trap temperature, assumed to
be the Doppler cooling limit TD = 120 /K, we obtain
a value for the natural linewidth of 3.1 ± 0.2 MHz.
The discrepancy between our measurement and the
theoretical prediction of 2.5 MHz (Ref. 11) may be
attributable to fluctuations in laser frequency
(linewidth -500 kHz), to inhomogeneities in the trap
environment (especially spatially dependent Zeeman
splittings), to temperatures in excess of TD, and/or
to uncertainties of the theoretical value itself. One
interesting feature of our measurements in Fig. 4 is
the dependence of the line broadening of the F = 4
and F = 5 states on the presence or absence of the
repumping beam, whereas the widths of the F = 6
state seem insensitive to this.
To investigate this point further, we show in Fig. 5
two spectra, one obtained with the repumping beam
on and the other with the repumping beam off. The
difference in relative heights of the F = 5, 4,3 compo-
nents between the two curves is due to the fact that,
without the repumping beam, the F = 4 component
of 6S1X2 is depleted as a result of the decay of the F =
5,4,3,2 components of 6D5/2 to the F = 3 component
of 6S,/2. Indeed, without the repumping beam the
transitions with F = 5,4,3,2 should normally have
near-zero amplitudes since the time to deplete the
F = 4 ground level under the conditions of Fig. 5 is
only -10-6 s, compared with the 10 -s interval of the
off cycle during which the spectra are acquired. That
significant amplitudes are observed in Fig. 5 without
the repumping beam is principally because of ther-
mal motion, which brings fresh atoms from the trap
into the small excitation volume. Further studies of
spectra such as those in Fig. 5 with systematic vari-
ations in trap parameters as well as in the size of the
excitation volume might be of interest in providing a
relatively nonintrusive probe of the trap kinetics.
In conclusion, we have investigated two-photon
spectroscopy of cold trapped Cs atoms and have de-
termined the a coefficient for the 6D5/2 state with
1% accuracy, which represents a 30-fold improvement
over the results of Ref. 7. We have observed ac Stark
shifts for the ground state of cold atoms (Fig. 3) and
have demonstrated a possible avenue for exploring
transport processes in the trap (Figs. 4 and 5).
We gratefully acknowledge contributions of H.
Tsuchida and correspondence from S. Svanberg.
This study was funded in part by the U.S. Army Re-
search Office and the National Science Foundation.
E. S. Polzik acknowledges support from Aarhus
University.
*Present address, Institute of Physics and As-
tronomy, Aarhus University, Aarhus C, DK-8000,
Denmark.
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. .. . . . Il I I ,, I ,, r-I -
F- 4
'F-5
I . . . . I . I I . . . . I . . , -
F-S6II . 7
F-5
I ,
I I F-4
I I I
II II F-
I II
I i
I I I~~~~~~~~~~*


For a recent summary of spectroscopic measurements in optical lattices see Phys.

For work on other excited states in Cs see

http://authors.library.caltech.edu/29383/1/GEOol94.pdf

Two-photon spectroscopy of the 6S_(1/2) → 6D_(5/2) transition of trapped atomic cesium

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