PHYSICAL REVIEW LETTERS
PRL 99, 173001 (2007)
week ending
26 OCTOBER 2007
Efficient Coherent Population Transfer among Three States in NO Molecules
by Stark-Chirped Rapid Adiabatic Passage
Martin Oberst,* Holger Münch, and Thomas Halfmann†
Institute for Applied Physics, TU Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany
(Received 6 July 2007; published 25 October 2007)
We present the experimental demonstration of a novel, efficient, and selective technique to prepare
population inversion. The technique is an extension of Stark-chirped rapid adiabatic passage (SCRAP),
i.e., SCRAP among three states. In this process a -type quantum system is driven by two laser pulses, the
pump and Stokes pulses, which are appropriately detuned from transition frequencies. A third laser pulse
induces a dynamic Stark shift in the upper energy level, and the timing of all three pulses is controlled in
order to prepare population inversion between the two lower states in the -type level scheme. Our data
on population transfer in nitric oxide (NO) molecules clearly show that SCRAP among three states
provides an advantageous alternative to such techniques as stimulated Raman adiabatic passage.
DOI: 10.1103/PhysRevLett.99.173001
PACS numbers: 33.55.Be, 33.90.+h, 42.50.Hz
Coherent interactions between light and matter are a
major topic in quantum optics, quantum information processing, atomic interferometry, laser physics, nonlinear
optics, physical chemistry, and many other fields of contemporary laser-based physics [1– 4]. In particular, the
manipulation of population distributions and atomic coherences by interaction of the quantum system with strong,
coherent radiation has attracted significant attention [5,6].
The rich variety of applications requires population transfer techniques which combine efficiency, selectivity, and
robustness. Adiabatic passage techniques are a class of
coherent processes that fulfill all of these requirements.
Examples of such processes are rapid adiabatic passage
(RAP), stimulated Raman adiabatic passage (STIRAP) [5],
vibrational ladder climbing [1,7], and Stark-chirped rapid
adiabatic passage (SCRAP) [8].
SCRAP was developed to drive a two-level quantum
system into population inversion. In SCRAP the transition
between a ground state j1i and an excited state j2i is driven
by a pump laser pulse. The frequency of the pump laser !P
is tuned close to, but not exactly at, the resonance frequency !12 . Another laser pulse, intense but of frequency
far detuned from any atomic resonance, induces dynamic
Stark shifts of the transition frequency !12 . The pump
pulse and Stark pulse are delayed with respect to each
other but still partly overlap in time. The increasing Stark
shift moves the transition frequency through resonance
with the pump laser, which is then turned off before the
Stark shift falls again. If the pump laser is strong enough,
population is driven completely from the ground state j1i
to the excited state j2i in a RAP process. If the total
amplitude of the Stark shift is larger than the inhomogeneous linewidth, SCRAP has the advantage that it is unimpaired by inhomogeneous level broadening. And
SCRAP is effective even if the pump must drive a multiphoton transition instead of a single-photon transition.
While SCRAP has been implemented for two-level systems, many interesting applications arise in multilevel
0031-9007=07=99(17)=173001(4)
systems, such as the vibrationally excited states of molecules. STIRAP, and even nonadiabatic pulses [9], are
well-established tools to drive efficient and selective population transfer between ground and excited molecular vibrational states. These methods lose efficiency in the
presence of inhomogeneous broadening, however, because
they are based on resonant excitation; they are also inefficient for multiphoton transitions [10]. To overcome these
limitations an extension of SCRAP to three-level systems
has recently been proposed: SCRAP among three states
[11]. The technique uses two coupling radiation fields,
referred to as pump field and Stokes field, in a -type
level scheme (see Fig. 1). The pump laser couples the
ground state j1i to an intermediate state j2i, while j2i is
coupled by the Stokes laser to the target state j3i (Fig. 1).
Pump and Stokes fields may drive one-photon or multiphoton processes. A Stark laser pulse, far detuned from any
resonance, induces dynamic Stark shifts.
We consider two options for the timing of the pulse
sequences. The most obvious extension of SCRAP to the
three-state system is sequential double-SCRAP [11], or
‘‘D-SCRAP,’’ in which the pulse sequence is pump-
FIG. 1. Coupling scheme for population transfer by SCRAP
among three states in nitric oxide (NO) molecules.
173001-1
© 2007 The American Physical Society
PRL 99, 173001 (2007)
PHYSICAL REVIEW LETTERS
Stark-Stokes; see Fig. 2. The pump and Stokes pulses
overlap in time with the intermediate Stark pulse, but not
with each other, and the detunings are such that jP j,
jS j 0. This produces two separate, consecutive
SCRAP processes. First, the rising edge of the Stark laser
pulse induces a dynamic Stark shift of the transition frequency !12 between states j1i and j2i, so that !12 is swept
through the pump frequency !P , and population flows
adiabatically from j1i to j2i. Then the falling edge of the
Stark pulse sweeps the transition frequency !23 through
the Stokes frequency !S , and population flows from j2i to
j3i in a second SCRAP process. The obvious limitation of
this trivial version of SCRAP among three states is that, in
order for D-SCRAP to be efficient, the intermediate state
j2i must have a lifetime long compared to the delay between the pump and Stokes pulses.
We have therefore implemented a truly three-state alternative, three-state SCRAP or ‘‘T-SCRAP,’’ in which pump
and Stokes occur simultaneously, within the falling edge of
a longer Stark pulse. (A similar process using the rising
Stark edge is also possible.) The detunings are such that
jP j > jS j. The resulting transfer process can be understood qualitatively as follows. When the pump and Stokes
lasers turn on, in the falling edge of the Stark pulse, both
!12 and !23 are decreasing. Since jP j > jS j, resonance
with the pump laser is again passed first, and population
flows from j1i to j2i. The resonance between !23 and the
Stokes field then follows, and population flows from j2i to
the j3i.
In this qualitative picture, T-SCRAP and D-SCRAP
appear similar, but the important difference is that the
storage time in state j2i is determined by the pulse durations and the Stark shift rate, rather than by the pulse
FIG. 2 (color online). Excitation by D-SCRAP: experimentally
obtained population of the target state j3i, when the pump and
Stokes laser detunings are varied. The solid, white line indicates
the two-photon resonance between the states j1i and j3i.
week ending
26 OCTOBER 2007
timings, and may thus be made much shorter. In fact the
simplified picture of T-SCRAP in terms of consecutive
SCRAP processes is not truly accurate, and the full
three-state dynamics must be considered. However, the
conclusion of the qualitative picture remains valid;
T-SCRAP allows for almost instantaneous population
transfer to the target state, with minimal losses due to
radiative decay [11].
In our experiment, we implemented for the first time
both D-SCRAP and T-SCRAP to populate a highly excited
vibrational state in NO molecules (see Fig. 1). The pump
laser (P 226:2501 nm) couples the rovibrational
ground state j1i X 2 1=2 v00 0; J 1=2 to the intermediate state j2i A2 1=2 v0 0; J 1=2. The lifetime
of the intermediate state is 2 206 ns [12]. The Stokes
laser (S 299:7334 nm) couples the intermediate state
to the target state j3i X2 1=2 v00 6; J 1=2. Stark
shifts are induced by an intense radiation pulse at St 1064:4548 nm. A probe laser pulse (Pr 235:11 nm),
well delayed with respect to the other laser pulses, serves
to monitor the population in the excited state by resonantly enhanced multiphoton ionization via state j4i A2 1=2 v0 4; J 1=2.
The transfer efficiency, as monitored by the probe laser,
is calibrated by comparison with stimulated emission
pumping (SEP). In SEP, the pump laser and the Stokes
laser interact with the molecules, while the Stark laser is
switched off. If both lasers are strong, and if the Stokes
pulse follows the pump pulse (SEP type I), then 25% of the
total population is transferred to the target state. If the laser
pulses are coincident (SEP type II), then 33% of the
population is transferred to the target state. These expectations hold true (i) if the lasers drive the transitions
strongly, i.e., the product of the Rabi frequency and
the interaction time is 1 (the Rabi frequency E=@ is essentially defined as the product of the transition
moment and the electric field E of the laser) or
(ii) intensity variations due to the spatial and temporal
profile of the laser pulses are sufficiently large to permit
averaging of the transfer efficiency to the values, expected
from incoherent excitation. We confirmed that both requirements are met in our experiment.
The pump pulse and Stokes pulse with Fouriertransform limited bandwidth are provided by a laser system, involving pulsed amplification of continuous wave
radiation and subsequent frequency conversion. The Stark
laser pulse is provided by an injection-seeded Nd:YAG
laser. Pulse delays are controlled by optical delay lines.
The probe laser pulse is deduced from a broadband tunable
pulsed dye-laser system. Typical pulse energies for the
pump, Stokes, Stark, and probe lasers are EP 300 J,
ES 600 J, ESt 70 mJ, and EPr 310 J. Pulse durations (FWHM of intensity) are P 5:1 ns, S 3:1 ns,
St 14:4 ns, and Pr 5 ns. The probe pulse is delayed
by 2 s with respect to the other laser pulses. All laser
beams are combined and mildly focused into the interac-
173001-2
PRL 99, 173001 (2007)
PHYSICAL REVIEW LETTERS
tion region of a time-of-flight ion spectrometer. The NO
molecules are provided in a pulsed (repetition rate 20 Hz),
supersonic jet. The supersonic beam was generated by a
pulsed nozzle (General Valve, aperture 0.8 mm).
Figure 2 shows the experimentally obtained population,
driven to the target state j3i vs the laser detunings, for the
case of excitation by D-SCRAP. The laser pulse sequence
is also indicated in Fig. 2. We have determined the values
of the Rabi frequencies by performing complementary
experiments on power broadening and coherent population
trapping. Thus, for the laser intensities in our D-SCRAP
experiment we deduce P 2 0:7 GHz and S 2 0:7 GHz. The pulse areas, defined as P P 22 1 and S S 13 1, indicate strong interaction. We
also performed spectroscopic investigations of the Stark
shifts in NO from which we determine a Stark shift of
StSt 2 4 GHz at the peak of the Stark pulse, i.e., at
time tSt . In Fig. 2 a plateau of almost complete population
transfer to the target state is observed. The calibration of
the transfer efficiency is due to SEP type I. The maximum
obtained transfer efficiency is 91%. The transfer efficiency
does not vary appreciably for broad ranges of laser frequencies. Transfer is observed only for negative detunings,
as expected from the direction of the laser-induced Stark
shift. The plateau extends to frequencies, detuned far from
exact two-photon resonance. The efficiency is also not
affected by pulse-to-pulse intensity fluctuations in the laser
pulses. These features are clear evidence for robust, adiabatic population transfer. The plateau in Fig. 2 shows a
characteristic rectangular shape. In D-SCRAP the population is stored in the intermediate state j2i, before it is
transferred to the target state j3i. For both jP j < jS j
and jP j > jS j maximum population transfer is possible,
if the conditions 0 < jP j < jStP j and 0 < jS j < jStS j
are fulfilled. StP is the effective maximum Stark shift of
the pump laser resonance frequency at time tP . StS is the
effective maximum Stark shift of the Stokes laser resonance frequency at time tS . The conditions define the
plateau, as depicted in Fig. 2. The limits of the plateau
permit a measure for the Stark shifts StP and StS . From
Fig. 2, we deduce jmax
P j StP 2 3:2 GHz and
j
St
2
1:7 GHz. The delay of the Stark
jmax
S
S
pulse to the pump pulse is slightly smaller than the delay of
the Stokes pulse to the Stark pulse (see Fig. 2). Thus, the
Stark shift at the peak of the pump pulse is larger than the
shift at the peak of the Stokes pulse. Therefore, the plateau
exhibits a rectangular shape, i.e., a different dependence of
the transfer efficiency with respect to the two detunings.
The experimental results are confirmed by numerical simulations, based on a density matrix formalism, including
losses and Doppler broadening. For these purposes the
Liouville equation is solved numerically by using a
Runge-Kutta algorithm of fourth order. The simulation
yields beside the characteristic rectangular shape of the
transfer plateau a maximum transfer efficiency of 91%.
This fits very well with the experimentally obtained value.
week ending
26 OCTOBER 2007
In D-SCRAP, population is stored in the intermediate state
j2i during the transfer process. Thus, D-SCRAP suffers
significantly from spontaneous decay of state j2i, if the
delay between pump pulse and Stokes pulse approaches
the radiative lifetime 2 . In our experiment, the lifetime of
the intermediate state (2 206 ns) is much larger than
the pulse delay ( 22 ns) between the pump pulse and
the Stokes pulse. We estimate losses of approximately
10%. For shorter lifetimes or larger pulse delays, radiative losses may prohibit any efficient population transfer by
D-SCRAP.
We also measured the transfer efficiency to the target
state j3i for a pulse sequence according to T-SCRAP. The
calibration of the transfer efficiency is due to SEP type II.
Figure 3 shows the experimentally obtained population in
the target state vs the laser detunings. In the experiment,
the pump pulse and the Stokes pulse are nearly coincident.
Both pulses follow the Stark pulse (see Fig. 3). The Rabi
frequencies are P 2 0:4 GHz and S 2 0:7 GHz. The pulse areas are P P 11 1 and
S S 13 1. Thus, the transitions are strongly driven.
The peak Stark shift is StSt 2 5 GHz. T-SCRAP
shows a plateau of maximum population transfer as well
(see Fig. 3). The maximum transfer efficiency is 95%. The
transfer efficiency does not vary in an extended range of
detunings and is insensitive to pulse-to-pulse intensity
fluctuations. This is clear evidence for robust, adiabatic
evolution. As in the case of D-SCRAP, the insensitivity of
the transfer efficiency with respect to laser detunings allows for the compensation of inhomogeneous line broadenings, e.g., Doppler broadening. If the laser-induced Stark
shifts are larger than the inhomogeneous bandwidth, all
molecules in the ensemble are transferred to the target
FIG. 3 (color online). Excitation by T-SCRAP: experimentally
obtained population of the target state j3i. Compare caption of
Fig. 2.
173001-3
PRL 99, 173001 (2007)
PHYSICAL REVIEW LETTERS
state. In contrast, efficient excitation of inhomogeneously
broadened ensembles by resonant techniques, e.g.,
STIRAP, requires a significant increase in the pump and
Stokes laser intensities in order to compensate the inhomogeneous broadening by power broadening. Efficient
population transfer by pulses is not possible at all.
Figure 3 shows a characteristic triangular shape for the
transfer efficiency vs the detunings. The shape of the
plateau differs significantly from the structure, observed
in the case of D-SCRAP (compare Fig. 2). In T-SCRAP, the
molecules interact with both the pump and the Stokes pulse
in the falling edge of the Stark laser. As discussed above, a
successful implementation of T-SCRAP requires jP j >
jS j. Moreover, the Stark shift must be larger than the
detunings otherwise the resonance condition will not be
met. Thus, 0 < jP j < jStP j and 0 < jS j < jStS j, with
tP tS . These conditions for the detunings define the
triangular shape of the plateau, depicted in Fig. 3. Vice
versa, the limits of the plateau permit a measure for the
laser-induced Stark shift. From Fig. 3 we deduce the Stark
shift at the peak of the pump and Stokes pulse as jmax
P j j
St
2 StP 2 4:2 GHz and jmax
S
S
3:5 GHz. The experimental results are further verified by
numerical simulations (see D-SCRAP). These yield, besides the characteristic triangular shape of the transfer
plateau, a maximum transfer efficiency of 98.7%. This
fits very well with the experimentally obtained value of
95%. In particular, this already exceeds the experimentally
obtained transfer efficiencies of alternative techniques,
e.g., STIRAP.
Hardly any population is stored in the intermediate state
j2i during the T-SCRAP process. Thus the latter technique
experiences only very minor radiative losses. The time
scale of the transfer is determined by the duration of the
pump pulse and/or Stokes pulse, as well as by the rate of
the Stark shift. As the pulse durations are much smaller
than the lifetime 2 and the Stark shift rate additionally
reduces the transfer time, losses are negligible. The Stark
shift rate is an experimentally controllable parameter,
which can (at least in principle) be matched to the lifetime
of any quantum system. Thus, T-SCRAP is applicable to a
larger set of atomic or molecular systems than D-SCRAP.
The transfer efficiency obtained for T-SCRAP is only 4%
higher than that of D-SCRAP. This is due to two aspects.
The first aspect is the smaller pump Rabi frequency in the
case of T-SCRAP. This reduces the overall transfer efficiency of the process. The second aspect is the very long
lifetime of state j2i in NO molecules. Thus, although the
losses from this state reduce the transfer efficiency of DSCRAP, they are not big enough to prohibit efficient
population transfer.
In conclusion, we have demonstrated efficient, selective,
and robust population transfer by two novel techniques,
i.e., sequential double-SCRAP and three-state SCRAP in a
-type three-level system in NO molecules. Both techniques permitted the preparation of almost complete population inversion between the vibrational ground state and
week ending
26 OCTOBER 2007
an highly excited, metastable vibrational state. T-SCRAP is
less affected by the finite lifetime of an intermediate state
than D-SCRAP. We have demonstrated that both techniques are insensitive to variations in the experimental
parameters, i.e., laser intensities and laser detunings,
provided certain constraints are maintained. Both permit the preparation of population inversion also in media
that are subject to inhomogeneous broadening. Moreover,
D-SCRAP and T-SCRAP do not suffer from additional
Stark shifts, which are inevitably induced when multiphoton transitions are driven. These are clear advantages with
respect to alternative techniques such as STIRAP and pulses. Compared to vibrational ladder climbing, the presented techniques show even higher selectivity. All of these
features make D-SCRAP, and especially T-SCRAP, powerful tools to prepare quantum systems in highly excited
metastable states.
We acknowledgevaluable discussions with N. V. Vitanov
(Sofia University), J. Anglin, J. Klein, and K. Bergmann
(University of Kaiserslautern). The work was funded by
the Deutsche Forschungsgemeinschaft and the European
Union.
*Corresponding author.
Current address: Fachbereich Physik, Universität
Kaiserslautern, Postfach 30 49, 67653 Kaiserslautern,
Germany.
[email protected]
†
http://www.quantumcontrol.de
[1] D. J. Maas, D. I. Duncan, A. F. G. van der Meer, W. J. van
der Zande, and L. D. Noordam, Chem. Phys. Lett. 270, 45
(1997).
[2] I. Vrabel and W. Jakubetz, J. Chem. Phys. 118, 7366
(2003).
[3] J. Karczmarek, J. Wright, P. Corkum, and M. Ivanov,
Phys. Rev. Lett. 82, 3420 (1999).
[4] M. Weitz, B. C. Young, and S. Chu, Phys. Rev. Lett. 73,
2563 (1994).
[5] N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 763 (2001).
[6] M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris,
Phys. Rev. Lett. 77, 4326 (1996).
[7] D. J. Maas, D. I. Duncan, R. B. Vrijen, W. J. van der
Zande, and L. D. Noordam, Chem. Phys. Lett. 290, 75
(1998).
[8] T. Rickes, L. P. Yatsenko, S. Steuerwald, T. Halfmann,
B. W. Shore, N. V. Vitanov, and K. Bergmann, J. Chem.
Phys. 113, 534 (2000).
[9] B. W. Shore, The Theory of Coherent Atomic Excitation
(Wiley, New York, 1990).
[10] K. Böhmer, T. Halfmann, L. P. Yatsenko, B. W. Shore, and
K. Bergmann, Phys. Rev. A 64, 023404 (2001).
[11] A. A. Rangelov, N. V. Vitanov, L. P. Yatsenko, B. W.
Shore, T. Halfmann, and K. Bergmann, Phys. Rev. A 72,
053403 (2005).
[12] J. Luque and D. R. Crosley, J. Chem. Phys. 111, 7405
(1999).
173001-4