Optics Communications 264 (2006) 463–470
www.elsevier.com/locate/optcom
Enhanced four-wave mixing in mercury isotopes, prepared by
stark-chirped rapid adiabatic passage
Martin Oberst *, Jens Klein, Thomas Halfmann
Fachbereich Physik, Universität Kaiserslautern, 67653 Kaiserslautern, Germany
Received 19 October 2005; accepted 11 December 2005
Abstract
We demonstrate significant enhancement of four-wave mixing in coherently driven mercury isotopes to generate vacuum-ultraviolet
radiation at 125 nm. The enhancement is accomplished by preparation of the mercury atoms in a state of maximum coherence, i.e.
maximum nonlinear-optical polarization, driven by Stark-chirped rapid adiabatic passage (SCRAP). In this technique, a pump laser at
313 nm excites the two-photon transition between the ground state 6s2 1S0 and the target state 7s 1S0 in mercury. A strong, offresonant radiation field at 1064 nm generates dynamic Stark shifts. These Stark shifts serve to induce a rapid adiabatic passage process on the two-photon transition. During the process a coherent superposition of the two states is established, which enhances the
nonlinear-optical polarization in the medium to the maximum possible value. The maximum coherence permits efficient four-wave
mixing of a pump laser and an additional probe laser at 626 nm. The efficiency is further enhanced, as the SCRAP process allows
to stimulate the complete set of different mercury isotopes to participate in the frequency conversion process. This enlarges the effective
atomic density of the medium. Thus, we observe the generation of vacuum-ultraviolet radiation at 125 nm enhanced by more than one
order of magnitude with respect to conventional frequency conversion. Parallel to the frequency conversion process, we monitored
the evolution of the population in the medium by laser-induced fluorescence. These data demonstrate efficient coherent population
transfer by SCRAP.
Ó 2006 Elsevier B.V. All rights reserved.
1. Introduction
Nonlinear-optical processes in metal vapors attracted
significant interest [2–4] in laser-based physics, as metals
offer large nonlinear susceptibilities and can be easily provided in cells with large densities. These media are of particular interest for efficient frequency conversion processes
to generate short-wavelength, i.e. vacuum-ultraviolet laser
radiation (kVUV < 200 nm). Such radiation finds application in laser spectroscopy, laser lithography or high-resolution microscopy.
Nonlinear-optical crystals would offer larger density,
but such crystals are opaque in the vacuum-ultraviolet
*
Corresponding author. Tel.: +49 631 205 47 18; fax: +49 631 205 39
03.
E-mail address: [email protected] (M. Oberst).
URL: http://www.quantumcontrol.de (T. Halfmann).
0030-4018/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.optcom.2005.12.084
spectral region and do not permit frequency conversion
to short-wavelength radiation. Therefore, atomic or molecular vapors are the only nonlinear-optical media to provide
such short-wavelength radiation. Nevertheless, conventional frequency conversion techniques in gaseous media
suffer from relatively low conversion efficiencies, typically
in the regime of 106–104. Tuning the mixing fields close
to resonances enhances the corresponding nonlinear susceptibilities, but also results in reabsorption of the generated vacuum-ultraviolet radiation.
Several techniques, based on coherent preparation, were
established in the last decade to enhance conversion efficiencies and to reduce reabsorption processes in resonantly
driven nonlinear-optical media in the gas phase (see Ref. [5]
and references therein). To suppress losses due to reabsorption of the generated vacuum-ultraviolet radiation electromagnetically-induced transparency (EIT) serves as the
most efficient technique (see Ref. [6] and references
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M. Oberst et al. / Optics Communications 264 (2006) 463–470
therein). In four-wave mixing processes, supported by EIT,
a pump laser resonantly couples a ground state j1i to an
excited state j2i via a two-photon transition at frequency
x12. An additional dressing laser with frequency x23 resonantly couples state j2i to another excited state j3i. In a
resonantly enhanced four-wave mixing process, involving
two photons from the pump and one photon from the
dressing laser, radiation at x13, i.e. the transition frequency
between the ground state j1i and the excited state j3i, is
generated. Thus, from simple considerations, based on a
purely incoherent interaction, reabsorption was expected
to occur. In contrast, if both lasers exhibit perfect coherence properties, and provided, the transition between the
excited states j2i and j3i is strongly driven, reabsorption
of the generated radiation is cancelled by destructive quantum interference. On the other hand, nonlinear-optical susceptibilities, which are responsible for the frequency
conversion process, are not reduced to zero. Thus, EIT
serves to drive frequency conversion processes even in an
otherwise strongly absorbing medium. Enhancement of
four-wave mixing, mediated by EIT has been theoretically
studied [7–9] and experimentally demonstrated [10–19].
However, though the nonlinear-optical susceptibilities
in media, driven to EIT, are not reduced to zero, they
are significantly lower than the maximum possible values.
A quantum mechanical treatment of the dynamics in a
coherently driven medium reveals, that if the system is
prepared in the state of maximum coherence [1,13,18–
23], the largest value for the nonlinear-optical polarization
can be provided. This state is defined as a coherent superposition of the ground and an excited state with equal
amplitudes. Thus, the amplitudes of two states jii and
jji are jcij2 = 1/2 and jcjj2 = 1/2. The coherence, defined
as the off-diagonal element of the density matrix, i.e.
qij ¼ ci cj , yields jqijj = 1/2. This generates a local oscillator driven at the transition frequency xij. The interaction
of this oscillator and an additional probe laser results in
an efficient nonlinear mixing process. For instance, this
allows the enhanced generation of vacuum-ultraviolet
radiation (see Section 2).
A maximum coherence can be prepared via different
coherent excitation schemes, e.g. coherent population
return (CPR) [1,19,24–33], stimulated Raman adiabatic
passage (STIRAP) [5] or Stark-chirped rapid adiabatic passage (SCRAP) [5,34]. In CPR the ground state j1i and
excited state j2i in a two-level system are coherently coupled by a pump laser. The transition is strongly driven,
i.e. the product of the Rabi frequency X and the interaction
time s is Xs 1. The Rabi frequency X = lE/
h is essentially defined as the product of the transition moment l
and the electric field E of the laser. If the pump laser is
slightly detuned from exact resonance, i.e. with a detuning
D such that X > D > 1/s, population flows from the ground
state to the excited state and back again. Thus, during the
process the population is equally distributed between the
ground and the excited state and therefore a transient maximum coherence is established. This maximum coherence
can be used for efficient frequency conversion. Contrary
to expectations, based on incoherent excitations, CPR permits the largest conversion efficiency slightly detuned from
the resonance.
A transient maximum coherence can also be established
in a three-level system, e.g. by STIRAP. In such coupling
schemes, the ground state j1i is coupled to an intermediate
state j2i by a pump laser. The state j2i is coupled to the target state j3i by a Stokes laser. The two-photon resonance
between ground state j1i and target state j3i has to be
maintained. For a counter-intuitive pulse sequence (i.e.
Stokes laser pulse preceding pump laser pulse) population
is driven completely from the ground to the target state.
During the transfer process a transient maximum coherence is established between the ground and the target state.
Like CPR this also serves to enhance the efficiency of nonlinear-optical processes.
While in principle both CPR and STIRAP permit the
implementation of a maximum coherence and efficient frequency conversion, they suffer from line splitting and line
broadening in the medium. When inhomogeneously (e.g.
Doppler) broadened media are considered, Doppler shifts
limit the efficiency of CPR and STIRAP to a fraction of
the atomic ensemble, i.e. such atoms, which exhibit appropriate detunings. To overcome this effect, the Doppler
width has to be compensated by power broadening, i.e.
an increase in the coupling strengths and therefore laser
intensities. The same holds true for nonlinear-optical media
involving atomic species of different isotopes. Thus, the
medium exhibits isotope splittings and shifts of the relevant
transitions. Only a fraction of the atoms in the medium can
be driven coherently under appropriate conditions for CPR
or STIRAP. If all isotopes in the medium shall be prepared
by CPR or STIRAP to permit efficient frequency conversion, the Rabi frequencies X, i.e. the laser intensities, have
to be larger than the isotope shifts DIS. The conversion efficiency and therefore the strength of the generated electric
field, depends exponentially on the density of the nonlinearoptical medium. Thus, techniques such as CPR and STIRAP will not yield the maximum efficiency, if Doppler
broadening and isotope shifts cannot be compensated by
power broadening.
As already discussed, nonlinear optical processes
demand large atomic densities. These can be provided in
heated cells. Therefore, considerable Doppler broadening
occurs in the medium. Moreover, metal vapors, which
serve as nonlinear-optical media with large nonlinear susceptibilities, often show broad isotope distributions covering several tens of GHz bandwidth. In these media, CPR
and STIRAP cannot be implemented with laser pulses of
realistic intensities, such that the complete ensemble participates in the process.
Stark-chirped rapid adiabatic passage (SCRAP) is a
technique for coherent, adiabatic preparation [5], which
is capable of overcoming the perturbing effects of inhomogeneous broadening [1] or isotope shifts and to provide
maximum coherence in a nonlinear-optical medium with-
M. Oberst et al. / Optics Communications 264 (2006) 463–470
out the need to increase Rabi frequencies, i.e. laser intensities. In SCRAP a ground state j1i and an excited state
j2i are coherently coupled by a pump laser, either on a
one-photon or a multi-photon transition. The pump laser
frequency is slightly detuned from the transition frequency x12. Another strong radiation pulse, in the following referred to as the Stark laser, which is off-resonant
with all transitions in the medium, provides a dynamic
Stark shift of the transition frequency x12. The pump
and the Stark laser pulse are appropriately delayed with
respect to each other. Then, all the population from the
ground state is transferred completely to the excited state
in a rapid adiabatic passage process (RAP) [5]. During the
process a transient maximum coherence is prepared. This
serves to enhance any frequency conversion process, driven in the medium, e.g. by introducing an additional
probe laser to mix with the pump laser [1,35,36]. Provided
the dynamic Stark shift is larger than the isotope shifts
and/or the Doppler broadening of the medium, all atoms
of the sample will participate in the SCRAP process and
frequency conversion.
The capability of SCRAP to provide a large relative
enhancement of third-harmonic generation in the extremeultraviolet spectral region has been demonstrated experimentally [1]. The latter experiment was performed in a
supersonic beam of krypton atoms with relatively low
density and therefore low absolute conversion efficiency.
The SCRAP process also suffered from incoherent losses,
induced by photoionization. In addition, this setup did
not provide tunability of the generated radiation and isotope shifts did not play a role.
In what follows, we will present experimental data on
four-wave mixing in a dense mercury vapor of natural
isotope abundance, prepared by SCRAP in a state of
maximum coherence. Mercury provides large nonlinear
susceptibilities for the generation of vacuum-ultraviolet
radiation with wavelengths close to the Lyman-alpha transition in hydrogen. In this coupling scheme no incoherent
losses due to photoionization occur during the SCRAP
process. As a cell rather than an atomic jet is used, large
products of density and interaction length permit efficient
frequency conversion. In addition to the pump and Stark
shifting laser, a probe laser is used to induce a four-wave
mixing process with the pump laser. Thus, if the probe laser
frequency is varied, the generated vacuum-ultraviolet
radiation will also be tunable.
The work presented in this paper, deals with nonlinear
optics in coherently prepared media. Bruce W. Shore is
one of the pioneers in the field of coherent excitations
[37], which are essential to the processes, discussed in
the following. The technique of Stark-chirped rapid
adiabatic passage (SCRAP), as briefly described above,
was developed in cooperation with Bruce W. Shore [5].
Without this most fundamental and thorough theoretical
work of Bruce W. Shore on coherent interactions, the
experiments, presented here, would not have been possible
at all.
465
2. Coupling scheme in mercury atoms
The coupling scheme for efficient generation of vacuumultraviolet radiation by four-wave mixing in mercury vapor
of natural isotope abundance, prepared by SCRAP, is as
follows (see Fig. 1). The pump laser (kP = 313 nm) couples
the atomic ground state 6s2 1S0 and the excited state 7s 1S0
(lifetime s7s 36 ns [38]) by a two-photon transition,
slightly detuned from exact resonance [34]. A strong laser
pulse (kSt = 1064 nm), off-resonant with all atomic transitions, induces dynamic Stark shifts of the two-photon transition frequency. The pump and Stark laser pulses are
appropriately delayed with respect to each other. An additional probe laser (kPr = 626 nm) interacts with the pump
laser in a four-wave mixing process to yield vacuum-ultraviolet (signal) radiation (kS = 125 nm). The probe laser is
well detuned from any atomic resonance to highly excited
states and thus does not modify the population distribution
in the system. Still, the state 9p 1P1 is close enough to provide a relatively large nonlinear-optical susceptibility for
the four-wave mixing process.
We note, that also a second frequency conversion process occurs during the SCRAP process. In addition to the
vacuum-ultraviolet signal radiation, also radiation at
183 nm is observed in the experiment. This is due to a difference frequency mixing process, induced by the strong
Fig. 1. Coupling scheme for four-wave mixing in mercury atoms,
prepared by SCRAP. All wavelengths are given in nanometers. The
energetic position of the levels and detunings are schematic, i.e. not
calibrated in this figure.
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M. Oberst et al. / Optics Communications 264 (2006) 463–470
Stark and the pump laser. The generated frequency is
2xP xSt.
For a detailed analysis of a sample of mercury atoms in
natural abundance the isotope shifts have to be considered.
Table 1 lists the most prominent isotopes of mercury with
their relative abundance, as well as the isotope shift of the
two-photon transition between the states 6s2 1S0 and 7s 1S0.
The relative abundances are taken from Ref. [38]. The isotope shifts are obtained from measurements of laserinduced fluorescence (LIF) in mercury (see below).
To our knowledge the isotope shifts of the two-photon
transition between the states 6s2 1S0 and 7s 1S0 are measured for the first time via a degenerate two photon process.
Smith et al. (see Ref. [39]) reports a measurement of the isotope shifts of the same transition via a Doppler free nondegenerate two photon process. Our data fit well with the
isotope shifts given in Ref. [39].
The relevant atomic parameters (i.e. the effective twophoton Rabi frequency and the Stark shift of the two-photon transition) are calculated from one-photon dipole
moments and level positions, taken from Refs. [38,40–42].
From these data, the Stark shift of the two-photon transition is calculated according to
!
X jl7s;i j2 jl6s;i j2 E2
St
S¼
;
ð1Þ
2
4D
4D
h
7s;i
6s;i
i
where l6s,i and l7s,i are the one-photon dipole moments
from state 6s2 1S0 and state 7s 1S0 to intermediate states
jii, D6s,i and D7s,i are the detunings from the one-photon
resonances and ESt is the electric field of the Stark laser.
The sum in Eq. (1) includes the mainly contributing intermediate atomic states in mercury up to state 13p 1P1. All
other states will only give negligible contributions to the total Stark shifts. The calculation yields values for the net
Stark shifts induced by the infrared laser at kSt = 1064 nm
(in the following all Stark shifts and Rabi frequencies are in
units of a circular frequency [ns1]):
2
S St ½ns1 ¼ 1852 I St ½GW=cm ;
ð2Þ
where ISt is the intensity of the Stark laser. The Stark shift
caused by the weaker pump laser is
2
S P ½ns1 ¼ 93 I P ½GW=cm ;
ð3Þ
with the intensity IP of the pump laser. The minus indicates
that the orientation of the Stark shift caused by the pump
laser is opposite to the orientation of the Stark shift gener-
Table 1
Relative abundance of mercury isotopes and isotope shifts for the twophoton transition 6s2 1 S0 ! 7s 1S0 (with respect to the resonance for the
mercury isotope 202Hg)
Isotope
Abundance
mP (GHz)
198/199
200/201
202
204
27.1
36.3
29.65
6.85
7.5
3.6
0.0
4.9
ated by the Stark laser. Since the pump laser intensity in the
experiment is always smaller or equal to the Stark laser
intensity, the Stark shift SP is always less than 5% of the
Stark shift generated by the Stark laser and is therefore neglected in the following.
The two-photon Rabi frequency is calculated as:
X l6s;i li;7s
E2P :
ð4Þ
XP ¼
2h2 D6s;i
i
In the sum we included the dipole moments for the onephoton transitions (6s2 1S0 ! 6p,7p 1,3P1) and (6p,7p
1,3
P1 ! 7s 1S0) in mercury, which give the major contributions to the two-photon coupling. The calculation yields
the following equations for the effective two-photon Rabi
frequency:
XP ½ns1 ¼ 38 I P ½GW=cm2 :
ð5Þ
3. Experimental setup
The experimental setup is shown in Fig. 2. A heat pipe
employing mercury as the working fluid provides the nonlinear-optical medium. The basic design of the heat pipe
follows the setup, described in Ref. [40]. The body of the
heat pipe consists of a conical cylinder, made of stainless
steel, with a length of 10 cm, a diameter of 1.2 cm at the
ends and 1.8 cm in the center. Orthogonal to the major axis
of the heat pipe, an additional arm is added with a length
of 5 cm, a diameter of 1.2 cm at the end and 1.8 cm in the
center. This allows the observation of laser-induced fluorescence orthogonal to the propagation direction of the
laser beam. The center of the heat pipe is heated to temperatures up to 440 K. The ends are cooled to 300 K and
sealed with windows, made of MgF2, which is transparent
in the spectral region down to k = 120 nm. A temperature
gradient between the hot part of the cell in the center and
the cooled ends is established. When a small amount of
liquid mercury is deposited in the center of the cell, the
temperature gradient yields a convection stream of mercury vapor. The gaseous mercury condenses at the cooled
parts of the heat pipe close to the windows. The conical
shape of the heat pipe forms a slope towards the center,
which provides gravity recirculation of the condensed
mercury. Argon, with a pressure of 1–2 mbar is added as
a buffer gas, which keeps the ends of the cell, i.e. the
windows, free of mercury. Typically, in our experiments
the center of the cell was heated to 400 K. This yielded
mercury pressures of 1–10 mbar and densities in the order
of 1016 atoms/cm3. At this temperature the effective interaction region, i.e. the region with a constant density of
mercury atoms, spans a range of approximately 5 cm
length along the major axis of the heat pipe. Outside this
region the mercury density drops significantly.
The laser pulses for the experiment are generated as follows: a self-built optical-parametric oscillator (OPO), with
two counter-rotating BBO crystals as the active nonlinearoptical medium, is pumped by the frequency-tripled output
M. Oberst et al. / Optics Communications 264 (2006) 463–470
467
Fig. 2. Experimental setup.
of a pulsed, injection-seeded, single-longitudinal mode
Nd:YAG laser (Rofin Sinar RSY MOPA). The Nd:YAG
laser output and the frequency-tripled radiation show a
nearly Gaussian intensity distribution in space and time.
The bandwidth is Fourier-transform limited. About
25 mJ of the frequency-tripled radiation of the Nd:YAGlaser at 355 nm are used to pump the OPO. The linear
cavity of the OPO is injection-seeded by the output of a
continuous wave, single-longitudinal mode Titanium–
Sapphire laser (Coherent 899-21) at 820 nm. Typically,
several hundred mW of the Titanium–Sapphire laser are
available to seed the OPO. The OPO cavity is stabilized
on the transmission of the seed laser through the cavity,
which is monitored by a photodiode. The transmission
signal is processed in a PC and used to control the cavity
length by a piezo-electric crystal. While the cavity of the
OPO is highly reflective for the infrared idler radiation at
820 nm, in the experiment the visible signal output at
626 nm, with typical pulse energies of 4 mJ and a pulse
duration of approximately 6 ns (FWHM) is used.
As the OPO is injection-seeded and pumped by transform-limited radiation, the output of the OPO also exhibits
transform-limited bandwidth. The signal wave at 626 nm,
which shows a Gaussian intensity distribution in space
and time, is frequency doubled in a BBO crystal to provide
the pump laser pulse for the experiment at a wavelength of
kP = 313 nm with typical pulse energies of 500 lJ and a
pulse duration of approximately 4 ns (FWHM). The signal
radiation, remaining after the frequency doubling process,
serves as the probe pulse in the experiment. The Stark laser
pulse is provided by the radiation of the Nd:YAG laser at
the fundamental wavelength kSt = 1064 nm, that remains
after frequency tripling. Typical energies for the Starkshifting laser pulse in the interaction region are 23 mJ with
a pulse duration of approximately 15 ns (FWHM).
The diameter of the Stark laser is reduced by a telescope
to 840 lm. This corresponds to intensities in the order of
0.28 GW/cm2 for the Stark laser in the interaction region
of the mercury cell. The pump and probe laser beam are
separated after the frequency doubling crystal by a Pellin-
Broca prism. The pump beam is mildly focussed by a
quartz lens (focal length, f = 400 mm) and spatially overlapped with the probe and Stark laser beam. In the interaction region the diameter of the pump laser is 240 lm and
the diameter of the probe laser is 1460 lm. This corresponds to intensities in the order of 0.27 GW/cm2 for the
pump and 0.05 GW/cm2 for the probe laser. We confirmed
experimentally, that the Rayleigh lengths of pump, Stark
and probe laser are substantially longer than the length
of the effective interaction region in the heat pipe, i.e. the
region with high density of mercury atoms (see above).
For the SCRAP process, the Stark laser has to be
delayed with respect to the pump laser [34]. In the current
setup, the Stark laser pulse propagates along an optical
delay line with a length of 2 m, introducing a delay of
6.7 ns. The pump and probe laser pulses are coincident.
The vacuum-ultraviolet radiation at kS = 125 nm, generated by four-wave mixing of the pump and probe laser
pulse in the mercury heat pipe, is separated in an evacuated
spectrometer (Model VM-502, Acton Research, arm-length
20 cm) from the driving radiation fields. The spectrometer
was modified such that the original frequency selective element, a grating, was replaced by a Pellin-Broca prism,
made of MgF2. Thus, the damage threshold of the setup
with respect to the intense Stark laser beam was increased.
After the Pellin-Broca prism the vacuum-ultraviolet radiation is detected in an electron multiplier tube (Hamamatsu,
model R595).
In addition to the detection scheme for the vacuumultraviolet radiation, laser-induced fluorescence (LIF) from
the decay of the excited state 7s 1S0 to state 6p 3P1 at a
wavelength of kF = 408 nm (see Fig. 1) was observed perpendicular to the beam propagation direction. The intensity of the fluorescence is proportional to the population
of the excited state 7s 1S0, thus it can be used to measure
the efficiency of the coherent population transfer. The fluorescence is imaged by a lens (focal length f = 50 mm) on the
entrance slit of a monochromator (Jobin Yvon, DH 10 IR)
and detected by a photo multiplier (Hamamatsu, model
R7400-U04). The output signal of either the electron
468
M. Oberst et al. / Optics Communications 264 (2006) 463–470
multiplier or the photo multiplier is amplified in a fast
broadband amplifier (Femto, DHPVA-100), integrated in
a boxcar gated averager (SRS, model SR250) and processed in a PC.
4. Results and discussion
4.1. Efficient coherent population transfer, driven by SCRAP
In this section, we will discuss the efficiency of coherent
population transfer, driven by SCRAP, as monitored by
laser-induced fluorescence.
Fig. 3 shows the relative intensity of the fluorescence
from the excited state 7s 1S0, when the pump laser is tuned
in the vicinity of the two-photon transition frequency. The
figure compares the relative intensity of the laser-induced
fluorescence if the Stark laser is switched off (Fig. 3, hollow
circles, red line) or on (Fig. 3, solid squares, blue line),
respectively. As only fluorescence is monitored, the probe
laser is switched off in these measurements. The laser intensities are 0.28 GW/cm2 for the pump and 0.28 GW/cm2 for
the Stark laser.
When the Stark laser is switched off (Fig. 3, hollow circles, red line) the spectrum reveals clearly separated lines,
corresponding to the isotope distribution of mercury and
permits the determination of the isotope shifts, as listed
in Table 1. Doppler broadening limits the resolution.
If the pump laser drives the transition strongly on resonance, on the average half of the population of each isotope is driven to the excited state. In terms of incoherent
excitation this would be called ‘‘saturation’’. In the case
of coherent excitation the equivalent for saturation is a
large value of the pulse area, i.e. a large product of the peak
pump Rabi frequency XP and the interaction time sP, thus
XPsP 1. The excitation probability, averaged over the
spatial laser profile, approaches the value obtained in the
case of saturated incoherent excitation, i.e. 50%. We confirmed experimentally that the intensity of the pump laser
was sufficient to drive the two-photon transition strongly.
This is confirmed in the spectrum depicted in Fig. 3, since
the linewidth in the multiplet already exhibits evidence for
power broadening. The experimentally determined total
linewidth of approximately Dm 2.4 GHz exceeds the
Doppler width, which can be calculated to be DmD 1.8 GHz. The difference of 0.6 GHz indicates the onset of
power broadening. The pump laser bandwidth plays a negligible role for the total linewidth. Further, for the laser
intensity applied here, the two-photon Rabi frequency is
estimated to be XP 2p Æ 1.7 GHz, the pulse area is XPsP 44 1. This also confirms that the system is strongly
driven.
If the Stark laser is switched on, the spectrum changes
significantly (Fig. 3, solid squares, blue line). The maximum is shifted by approximately 2p Æ 20 GHz with respect
to the spectrum without the Stark laser. The Stark laser is
delayed 6.7 ns relative to the pump laser. This was found to
be the optimum value for the SCRAP process. In the
shifted spectrum the isotope structure is no longer resolved.
The maximum value of the Stark-shifted spectrum is significantly enhanced with respect to the maximum value of the
spectrum without the Stark laser. The linewidth of the
Stark shifted spectrum exceeds the isotope shift. This indicates, that during the pump pulse the range of the Stark
shift is larger than the isotope shifts. SCRAP addresses
the complete ensemble of mercury atoms. Thus, the coherent process is capable of compensating both Doppler
broadening and isotope shifts. All atoms in the sample
are coherently driven to the excited state 7s 1S0. If only
incoherent excitation was considered, a Stark shift would
shift a spectral line, and reduce the resolution as well as
the peak signal. Thus the enhanced fluorescence signal in
our experiment exhibits a clear proof of coherent population transfer by SCRAP.
The experimentally deduced Stark shift of 2p Æ 20 GHz is
smaller than the calculated, maximum Stark shift of
2p Æ 83 GHz. This is due to the fact that the local intensity
of the larger Stark laser at the position of the much smaller
pump laser beam varies when the overlap of both lasers is
slightly aligned outside the center of the laser beams. Then
the Stark laser profile still covers the pump laser profile
completely, but the two beams are no more centered with
respect to their regions of maximum intensity.
4.2. Four-wave mixing, enhanced by SCRAP
Fig. 3. Intensity of the laser-induced fluorescence in mercury, when the
frequency of the exciting pump laser is varied. The zero point of the
frequency scale is calibrated to the resonance of the mercury isotope
202
Hg. The maximum fluorescence signal obtained is set to unity. When
the Stark laser is switched off, the spectrum exhibits the isotope
distribution of mercury (hollow circles, red line). When the Stark laser is
switched on, the maximum fluorescence signal increases significantly and
the spectrum broadens (solid squares, blue line).
In this section, we will discuss the manipulation of nonlinear-optical processes, i.e. enhanced four-wave mixing,
driven by SCRAP.
Fig. 4 shows the generated vacuum-ultraviolet radiation
at a wavelength of kS = 125 nm, when the frequency of the
pump laser is varied (compare Fig. 3) in the vicinity of the
two-photon resonance and the Stark laser is either switched
on or off. The Stark laser pulse is delayed by 6.7 ns with
M. Oberst et al. / Optics Communications 264 (2006) 463–470
Fig. 4. Relative intensity of the vacuum-ultraviolet radiation, generated in
the four-wave mixing process, when the pump laser frequency is varied in
the vicinity of the two-photon resonance (hollow circles, red line). The
intensity axis is normalized to the peak value of the signal, when the Stark
laser is switched off. The zero of the frequency axis is calibrated to the twophoton resonance for the mercury isotope 202Hg. When the Stark laser is
switched on, and the system is driven to maximum coherence by SCRAP,
the efficiency of the frequency conversion process increases significantly
(solid squares, blue line). The enhancement with respect to the peak value
of the signal when the Stark laser is switched off is more than an order of
magnitude. The inset shows the spectrum when the Stark laser is switched
off.
respect to the pump laser pulse. The pump and probe lasers
are coincident. The laser intensities are 0.09 GW/cm2 for
the pump laser, 0.28 GW/cm2 for the Stark laser and
0.01 GW/cm2 for the probe laser. This corresponds to a
pump Rabi frequency of XP = 2p Æ 0.5 GHz.
If the Stark laser is switched on (Fig. 4, solid squares,
blue line), the spectrum is shifted by approximately
2p Æ 14 GHz with respect to the spectrum without the Stark
laser. This deviates from the maximum theoretically possible value of approximately Smax = 2p Æ 83 GHz for this
Stark laser intensity. The difference is due to the modified
spatial overlap of the laser profiles in the interaction region
(see above).
When the Stark laser is switched off (see Fig. 4, hollow
circles, red line) the spectrum mirrors the different isotopes
of mercury (as with fluorescence) in the efficiency of the frequency conversion process. In contrast to the spectrum
obtained by laser-induced fluorescence (see Fig. 3), the
spectrum of the vacuum-ultraviolet radiation is broader
and exhibits a more complicated structure. This is due to
coherent population return (CPR) and the onset of power
broadening. When a two-level system is driven coherently
by the pump laser pulse alone, the maximum efficiency
for frequency conversion is obtained slightly detuned from
the exact two-photon resonances of the isotopes (CPR
case, see above) [1,43,44]. When power broadening also
starts to show up, the line profile becomes more complicated, as Fig. 4 shows. Although CPR helps to enhance
the efficiency of the frequency conversion process, the
pump laser intensity, i.e. the Rabi frequency of
XP = 2p Æ 0.5 GHz, is not sufficient to cover the isotope
shifts. A Rabi frequency on the order of the isotope shifts
would be necessary to drive the complete atomic ensemble
to maximum coherence by CPR. Thus, the pump laser
469
intensity had to be increased by more than an order of
magnitude.
In contrast, when the Stark laser is switched on, the system is prepared in a state of maximum coherence by
SCRAP and the isotope shifts are covered by the Stark shift
– even for the moderate pump laser intensity, applied in
our experiment. A significant enhancement of the fourwave mixing process is observed. The intensity of the vacuum-ultraviolet radiation increases by more than an order
of magnitude (see Fig. 4, solid squares, blue line). Thus, the
data exhibit a striking proof for the advantages of frequency conversion in a medium, coherently driven by
SCRAP.
5. Conclusion
We have demonstrated the enhancement of four-wave
mixing, i.e. the efficient generation of vacuum-ultraviolet
radiation in a dense medium of mercury atoms with natural
isotope abundance, coherently prepared by Stark-chirped
rapid adiabatic passage (SCRAP). The conversion efficiency was increased by an order of magnitude with respect
to conventional frequency mixing. Despite prominent isotope shifts, the SCRAP process drove a significantly
enlarged atomic ensemble to a state of transient maximum
coherence. Only moderate pump laser intensities are necessary for the SCRAP process, while competing techniques,
e.g. coherent population return (CPR), demand much
higher intensities. When a tunable probe laser is used in
the setup, the generated vacuum-ultraviolet radiation will
also offer tunability. In addition, we monitored the efficiency of the population transfer process by laser-induced
fluorescence. The data also clearly showed an enhancement
in the transfer efficiency and the signature of the SCRAP
process.
Acknowledgements
We acknowledge valuable discussions with B.W. Shore,
A.V. Smith, J.P. Marangos, L.P. Yatsenko and K. Bergmann. The work was funded by the Deutsche Forschungsgemeinschaft.
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