Laser Physics, Vol. 15, No. 1, 2005, pp. 46–54.
LASER
SPECTROSCOPY
Original Text Copyright © 2005 by Astro, Ltd.
Copyright © 2005 by MAIK “Nauka /Interperiodica” (Russia).
Generation of Continuous Coherent Radiation
at Lyman-a and 1S–2P Spectroscopy of Atomic Hydrogen1
A. Pahl1, 2, P. Fendel1, 2, B. R. Henrich1, 2, J. Walz1, 2, *, T. W. Hänsch1, 2, and K. S. E. Eikema3
1 Max-Planck-Institut
für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
Mänchen, Schellingstraβe 4/III, 80799 München, Germany
3 Laser Center, Vrije Universiteit Amsterdam, Faculty of Sciences, Department of Physics and Astronomy,
De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
2 Ludwig-Maximilians-Universität
*e-mail: Jochen.Walz@mpq.mpg.de
Received May 26, 2004
Abstract—Continuous coherent radiation from wavelengths from 121 to 123 nm in the vacuum ultraviolet
(VUV) was generated by four-wave sum-frequency mixing in mercury vapor. A yield of 20 nW at Lyman-α
(121.57 nm) was achieved. We describe the experimental setup in detail and present a calculation of the nonlinear susceptibility, the phase-matching integral, and the VUV yield. The Lyman-α beam was used to perform
1S–2P spectroscopy in a cold beam of atomic hydrogen. Linewidths of only 120 MHz were observed, which is
close to the natural linewidth.
1
1. INTRODUCTION
cooling is not an option, since collisions are expected to
be negligible due to the small density of atoms [11].
Laser cooling does not rely on high densities and thus
might be the only possibility for cooling trapped antihydrogen atoms.
Laser cooling can be done on the strong Lyman-α
transition from the 1S ground state to the 2P excited
state. The natural linewidth of Γ = 2π × 99.7 MHz corresponds to a Doppler limit of TDoppler = Γ/2kB =
2.4 mK, and the photon recoil gives a temperature limit
of Trecoil = 2k2/kBm = 1.3 mK, where m denotes the
mass of the atom and k = 2π/ λ is the wavevector of radiation at Lyman-α. A closed cycle, which is needed for
efficient laser cooling, exists between 1S1/2 (mJ = 1/2)
and 2P3/2 (mJ = 3/2). Thus, laser cooling down to the
milli-Kelvin range is possible using radiation at
Lyman-α, as has been discussed by several authors
[12–14]. Other schemes have been proposed for the
laser cooling of hydrogen [15, 16], but they are
expected to be far less efficient than Lyman-α laser
cooling.
The first pulsed Lyman-α sources were reported
long ago [17–20], but no continuous source of laser
radiation at Lyman-α was available until recently.
High-power dye lasers with nanosecond pulse duration
have typically been used to generate Lyman-α radiation
by the third-harmonic conversion of 365 nm in krypton
gas, or by frequency mixing using up to three different
fundamental wavelengths in gases and metal vapors.
Using such a pulsed Lyman-α source, the laser cooling
of trapped hydrogen has been demonstrated [1]. Nevertheless, a continuous source has significant advantages
over pulsed sources. As the lifetime of the 2P states is
1.6 ns, sources with nanosecond pulses thus cause at
most a few excitations per pulse, and laser cooling is
effectively limited by the pulse repetition rate. A con-
Laser cooling of atoms has become a mature tool of
modern experimental physics, one which has provided
new foundations for fields like Bose–Einstein condensation, matter waves, and frequency standards. Despite
all this success, only one experiment with laser-cooled
hydrogen atoms has been reported [1]. Hydrogen is difficult to laser cool in practice because of its low mass
and the short wavelength of its laser-cooling transition
at Lyman-α (121.56 nm) in the VUV (vacuum ultraviolet). Renewed interest in radiation at Lyman-α for
laser cooling comes from the recent production of cold
antihydrogen atoms [2–4].
Cold antihydrogen atoms offer fascinating new
opportunities for precise tests of the fundamental CPT
(charge conjugation–parity reversal–time reversal)
symmetry [5] and perhaps even for experiments with
antimatter gravity. One goal of antihydrogen experiments is the comparison of the Doppler-free two-photon 1S–2S transition in antihydrogen with that of ordinary hydrogen, whose absolute frequency has recently
been measured [6] to two parts in 1014. These future
experiments will most likely make use of magnetically
trapped antihydrogen atoms. For precision spectroscopy in a magnetic trap, a residual dependence of
18.6 Hz/G of the 1S–2S transition frequency on the
magnetic field has to be considered, since it will
broaden and shift the line [7, 8]. It will thus be very
important to cool antihydrogen atoms, thereby reducing their spatial extent in the inhomogeneous magnetic
field of the trap. Evaporative cooling has been used to
achieve Bose–Einstein condensation with dense clouds
of spin-polarized hydrogen atoms in a magnetic trap [9,
10]. In the case of antihydrogen, however, evaporative
1 Dedicated
to H. Walter on the occasion of his 70th birthday.
46
GENERATION OF CONTINUOUS COHERENT RADIATION
tinuous source can therefore provide a larger rate for
laser cooling. Furthermore, the spectral bandwidth of a
continuous source can be much lower. This provides
higher selectivity for magnetic substates of atoms in a
trap, thereby reducing losses due to spurious optical
pumping to untrapped magnetic sublevels.
A continuous coherent source in the VUV was first
described in 1979 using resonant four-wave mixing
(FWM) in Sr to generate radiation at a wavelength of
170 nm [21]. Shorter wavelengths, e.g., down to
133 nm [22], were achieved by resonant FWM in metal
vapors (Sr, K, Mg, and Zn). Recently, it was demonstrated [23] that it is possible to generate continuous
coherent radiation from 121 to 123 nm using mercury
vapor as a nonlinear medium. We present here a
detailed account of this Lyman-α source and its application for 1S–2P spectroscopy in hydrogen [24].
E, cm–1
100000
Ionization limit
80000
9ω ω ω ω N
4 π c b ∆k
0
2
1 2 3 4
- ------ χ a
4 = --- ------------------------2 2 6 2 

(3) 2
1 2 3 G ( b∆k ) , (1)
7s
60000 7s
3S
(3)
(i = 4) laser powers, ωi are the laser frequencies, χ a is
the third-order nonlinear susceptibility per atom, b is
the confocal parameter, ∆k is the wavevector mismatch,
and N is the atomic density. The function |G(b∆k)|2
depends on phase-matching conditions. This expression is applicable if there is no linear absorption at any
of the four frequencies and no significant depletion of
the incident waves. Gaussian profiles and equal confoLASER PHYSICS
Vol. 15
No. 1
2005
7p 1P1
7p 3P1
0
1
6p 1P1
399 nm
6p 3P1
40000
121.56 nm
20000
257 nm
6s 1S0
0
Fig. 1. Simplified level scheme of the mercury atom. The
arrows indicate the laser wavelengths involved in the fourwave mixing scheme.
cal parameters are assumed for the three input beams.
The generated beam will then also have a Gaussian profile with the same confocal parameter.
2.1. Nonlinear Susceptibility
Due to the two-photon resonance, the nonlinear susceptibility can be split into three parts [26]:
(3)
χa
1
= ----------S
( ω 1 + ω 2 )χ 12 χ 34 ,
3
0 (2)
with
χ 12 =
∑
n
2
where i are the fundamental (i = 1, 2, 3) and generated
12p 1P1
545 nm
1S
2. FOUR-WAVE MIXING IN MERCURY
The Lyman-α source is based on continuous-wave
four-wave mixing (cw-FWM) in mercury, where the
frequency of the generated wave is the sum frequency
of three incident laser beams. An important requirement for cw-FWM is the resonant enhancement of the
nonlinear susceptibility. A two-photon resonance is
therefore utilized in combination with near one- and
three-photon resonances. Exact one- and three-photon
resonances are in general not desirable, since they
cause absorption of the fundamental and the generated
light, respectively. The FWM scheme for generating
Lyman-α that was used in our experiment is shown in
Fig. 1. Laser light at 257 and 399 nm is used to establish
a two-photon resonance with the 7s 1S0 state. The wavelength of the third laser, 545 nm, is chosen such that the
sum frequency is at the Lyman-α wavelength of
121.57 nm. Note that this FWM scheme is optimal for
low-power cw laser beams only. For pulsed FWM,
where the peak intensities are many orders of magnitude higher, a scheme with resonances would lead to
premature saturation of the VUV yield and to ionization
of the medium.
In the case of tight focusing, the power of the generated VUV light is given by [25]
47
χ 34 =
∑
ν
⟨n|d |6S⟩ ⟨7S|d |n⟩ ⟨n|d |6S⟩ ⟨7S|d |n⟩
--------------------------------------- + --------------------------------------- , (3)
ωn – ω1
ωn – ω2
⟨ν|d |7S⟩ ⟨6S|d |ν⟩ ⟨ν|d |7S⟩ ⟨6S|d |ν⟩
--------------------------------------- + --------------------------------------- , (4)
ων – ω4
ων – ω3
1
S ( ω 1 + ω 2 ) = ---- Z ( ζ ).
w
(5)
Summing over n and ν includes all excited states that
connect to the 6S and 7S level by dipole transitions. In
writing down the dipole operator, d = ez, linear polarization in the z direction of the fundamental beams is
assumed. S(ω1 + ω2) describes the shape of the two-
48
PAHL et al.
photon resonance, and Z(ζ) is the plasma-dispersion
function [27] given by
(7)
v
∆ω D
-,
w = ω 7S ------w = --------------c
2 ln 2
(8)
hom
where ω7S is the frequency of the 6s
20
0
1S
0–7s
1S
0
transi-
tion, ∆ωD is the Gaussian Doppler width, and Γ 7S =
Γ7S + ∆ωpressure is the Lorentzian homogeneous linewidth of the transition, consisting of the natural linewidth Γ7S = 2π × 5.0 MHz and pressure-broadening
∆ωpressure. With these broadening mechanisms included,
S(ω1 + ω2) describes the full line profile of the two-photon resonance enhancement. Since natural mercury is a
mixture of several isotopes, S(ω1 + ω2) has to be calculated for all isotopes and summed according to the relative abundances [28] and isotope shifts [29]. Figure 2
shows the resulting two-photon line profile |S(ω1 + ω2)|2
for ∆ωpressure = 2π × 1.25 GHz and ∆ωD = 2π × 2.15 GHz
at T = 220°C. The positions and relative abundances of
the different isotopes are indicated by the vertical lines
in the graph. If mercury with a single isotope, e.g.,
202Hg, were available, the increase in the two-photon
resonance strength would improve the VUV yield
almost by a factor of ten. A comparison of the resonance shapes between a mixture and isotopically pure
mercury is shown in Fig. 2b for the same experimental
parameters. However, isotopically pure mercury is a
very expensive option and would require a new design
of the vapor cell, since the vapor cell that is presently
used runs on several hundred grams of mercury.
The dipole matrix elements zab = ⟨a|z|b⟩ can be
obtained from the tabulated values [30] of the oscillator
strengths fab using the relation [31]
hom
3( J + 1)
z ab = -------------------2J + 3
f ab
------,
∆E
40
199
198
Γ 7S
ζ =  ω 1 + ω 2 + i ---------– ω 7S /w,


2
60
200
–∞
(6)
201
∫
–x
e
d x -----------,
x–ζ
202
1
Z ( ζ ) = ------π
(a)
80
2
204
+∞
|S(ω1 + ω2)|2, cm–2
(9)
where zab is in atomic units, ∆E is the energy difference
between levels a and b in Rydbergs, and J is the angular
momentum of state a.
Saturation due to ground-state depletion can be estimated based on the two-photon absorption rate [32] in
the focus. The two-photon matrix element is the same
as the partial susceptibility χ12 (Eq. (3)). With a confocal parameter b = 1.6 mm, the rate is 4.3 × 103 s–1 with
Doppler- and pressure-broadenings as above. This
improved estimate takes the line profile properly into
account, which slightly changes the value given before
[24]. Because the two-photon absorption rate is much
(b)
600
400
200
0
–0.4
–0.2
0
0.2
0.4
0.6
∆, cm–1
Fig. 2. Calculated two-photon resonance function |S(ω1 +
ω2)|2. ∆ is the detuning relative to the isotope 202Hg. The
vertical lines indicate the positions of the two-photon resonance for the different isotopes. A comparison of the calculated shape of a single-component 202Hg sample with the
shape of a natural-abundance isotope mixture is shown in (b).
lower than the inverse of the 71S lifetime [33] (32.1 ns),
saturation is not important.
The nonlinear susceptibility can then be calculated
using the functions S(ω1 + ω2), χ12, and χ34. S(ω1 + ω2)
and χ12 are constant, since the sum of the frequencies
ω1 and ω2 is kept resonant in the experiment and only
ω3 is tuned to change in the generated VUV frequency
(3)
ω4. The wavelength dependence of χ a is shown in
the upper part of Fig. 3. The energy levels of mercury
(3)
lead to resonances in the nonlinear susceptibility χ a .
In our calculation, χ34 diverges at resonances because
the natural linewidths of the levels have been neglected
(3)
in Eq. (4). Zeros in χ a arise when terms in Eq. (3) or
Eq. (4) cancel.
2.2. Phase Matching
The wavevector mismatch ∆k is defined as ∆k = k4 –
(k1 + k2 + k3), where ki is the wavevector of the wave at
frequency ωi . In the plane-wave approximation, i.e., for
a confocal parameter b much longer than the length of
the nonlinear medium L, ∆k must equal zero for phase
LASER PHYSICS
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2005
GENERATION OF CONTINUOUS COHERENT RADIATION
2
∞
G ( b∆k )
2
– i∆kz
∫
12 3P
10 1P
11 3P
3
2
1
30
20
10
2
2∆ke
=
dz -------------------------2
 1 + 2i --z-
–∞

b
11 1P
40
(10)
The phase-matching integral |G(b∆k)|2 in Eq. (1) does
not depend on the length of the nonlinear medium in the
case of strong focusing and is given by [25]
4
12 1P
(11)
 0 for b∆k > 0,
=  2
4 b∆k
for b∆k < 0.
 π ( b∆k ) e
Optimal phase matching is achieved at (b∆k) = –4, with
a peak value of |G(b∆k)|2 = 46.28. Phase matching in
the present case is dominated by resonances of mercury, and the influence of buffer gas is negligible.
|G(b∆k)|2 depends on the wavelength and density of the
mercury vapor. The wavelength dependence is shown
in the middle of Fig. 3 for b = 1.6 mm and N = 8.84 ×
1017 cm–3 (T = 220°C), an optimal density for phase
matching at Lyman-α.
0.8
Lyman-α
n, m
2
nm
|G(b∆k)| 2
f nm
∑ ω---------------------.
–ω
P 4, µW
2
Ne
1
(1)
( n – 1 ) = --- Re [ χ ] -------------2
2 0 m e
5
–6
4
–3
|χ(3)
a |[10 (ea0) /cm ]
matching. In contrast, in the tight-focusing limit (b L),
optimal frequency conversion is achieved for ∆k ≠ 0.
For efficient sum-frequency mixing, ∆k must be negative. The reason for this is the Gouy phase shift of π in
the focus of a Gaussian beam. This phase shift is
present three times in the driving polarization, but only
once in the generated wave, hence the phase mismatch
that must be compensated for.
The wavevectors ki = ni ωi /c depend on the index of
refraction ni at frequency ωi , which can be calculated
using the linear susceptibility [34]:
49
0.6
0.4
0.2
121.5 122.0 122.5 123.0
VUV wavelength, nm
(3)
Fig. 3. Calculated nonlinear susceptibility χ a
123.5
, phase-
matching integral |G(b∆k)|2, and VUV yield 4 in the vicinity of Lyman-α.
2.3. Yield at Lyman-α
The VUV yield 4 as a function of wavelength is
shown on the bottom of Fig. 3 for phase-matching conditions that are optimal for Lyman-α. The parameters
used are typical for our experiment: 1 = 0.58 W, 2 =
0.5 W, 3 = 1.2 W, λ1 = 257 nm, λ2 = 399 nm, λ3 =
545 nm, T = 220°C, and b = 0.16 cm. The calculated
yield at Lyman-α is 20 nW with an uncertainty of
approximately 50%, which is mostly due to the uncertainties, typically 20–30%, in the oscillator strengths
[30].
cavity, which is locked to the laser by the Hänsch–
Couillaud technique [35]. From 2.2 W at 514.5 nm, typically 750–800 mW is generated at 257 nm in β-barium
borate (BBO, from Cleveland crystals). The quality of
the crystal is critical, and we have observed that crystals
were damaged within minutes due to the high circulating power in the cavity. Characteristic for this crystal
damage was an instability of the Ar+ laser that was presumably caused by the appearance of a backreflected
beam. The crystal is hygroscopic and is therefore
heated to 50°C to keep the crystal dry. Flushing the
crystal with oxygen prevents optical damage to the
crystal surface.
3. EXPERIMENTAL SETUP
FOR FWM IN MERCURY
The laser setup for FWM in mercury is shown in
Fig. 4. The first fundamental wavelength, at 257 nm, is
obtained by frequency doubling the light of a singlemode Ar+ laser (Spectra 2030). The frequency doubling
is performed using a bowtie four-mirror enhancement
The doubling cavity is formed by two concave
(−75 mm radius of curvature) and two flat mirrors (all
from Laseroptik Garbsen). The curved mirrors and one
of the flat mirrors are highly reflecting for 514 nm (R >
99.7%). The flat mirror through which the fundamental
beam is coupled into the cavity has a reflectivity of
~98%. The second-harmonic beam is coupled out
LASER PHYSICS
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No. 1
2005
50
PAHL et al.
Wavemeter
Nd : YVO
cw Ti : SA
SHG
LBO
798 nm
AC1
TL2
L3
399 nm
TL1
PR
PR
Ar–ion laser
cw dye laser
Singlemode
Ar–ion laser
545 nm
514 nm
SHG
BBO
AC2
DM1
257 nm
PR
TL3
DM2
L3
PH
To mercury
vapor cell
Fig. 4. Schematic of the laser system. Nd:VYO, diodepumped frequency-doubled Nd:VYO4 laser; Ti:Sa, titanium:sapphire laser; SHG, second-harmonic generation;
L1, L2, mode-matching lenses for SHG; AC1, AC2, astigmatism compensation; TL1–3, pairs of telescope lenses;
DM1, DM2, dichroic mirrors; PR, polarization rotation; L3,
lens to focus the fundamental laser beams into the vapor
cell; PH, pinhole.
through one of the curved mirrors (T > 85% at 257 nm).
The Brewster-cut crystal has a length of 11 mm. The
cavity length is 76.1 cm, and the distance between the
curved mirrors is 8.5 cm.
The second fundamental wavelength, at 399 nm, is
produced by frequency doubling a single-mode frequency-stabilized Ti:sapphire laser (Coherent 899-21)
in lithium triborate (LBO, from Photox). The Ti:sapphire laser produces 1.9 W at 798 nm and is pumped
with a frequency-doubled Nd:YVO4 laser (VERDI
V10, Coherent). This results in 600–650 mW at
399 nm. The LBO crystal is flushed with oxygen and
also heated to 45°C. The doubling cavity is very similar
to the 514 nm cavity described above. The curvatures,
transmittances, and reflectivities of the mirrors and the
crystal dimensions are the same. The enhancement factors of both cavities are better than 60.
The lenses L1 ( f = 400 mm) and L2 ( f = 750 mm)
ensure mode matching of the fundamental beams to the
doubling cavities. Astigmatism of the frequency-doubled beams is compensated for by pairs of cylindrical
lenses (AC1: f = 100 and 200 mm; AC2: f = 100 and
700 mm).
The third wavelength required to generate radiation
at Lyman-α is obtained from a frequency-stabilized dye
laser (Coherent 699-21 operating on rhodamine 110),
which is pumped by an Ar+ laser (Coherent Innova
100). With a pump power of 9 W, 1.5 W at 545 nm is
obtained. Scanning the laser from 540 to 580 nm covers
a VUV range between 121 and 123 nm.
The three fundamental beams are focused with the
quartz lens L3 ( fL3 = 150 mm) into the vapor cell. Telescopes with spatial filtering (TL1, f = 50 and 100 mm;
TL2, f = 100 and 400 mm; TL3, f = 100 and 100 mm)
enlarge the beams to ensure tight and equal foci of the
beams in the vapor cell. The average confocal parameter is 1.6 mm. A reflection from the entrance window at
45° is used to prealign the overlap of the fundamental
beams. This alignment is very delicate and is therefore
performed using piezo-driven mirror mounts (New
Focus).
The mercury vapor cell and the vacuum setup are
shown in Fig. 5. The interaction zone with the mercury
vapor is 15 mm long and has a near-rectangular density
profile. The mercury pressure in this specially designed
stainless steel oven can reach up to 46 mbar (220°C),
which is deduced from temperature measurements. A
buffer gas of approximately 70-mbar helium in the
He
Fundamental LN2
laser beams
Cooling
VUV–production
Hydrogen spectroscopy
Helium Argon
Photoncounter
Vacuum
LY–α
filter
PM
L3
PH
g
olin L4
Co
Hg vapor cell
LN2 trap
L5 L6
Aperture
Skimmer
H2
Microwave
dissociation
TMP
TMP
Nozzle
TMP
RVP
Fig. 5. Mercury vapor cell and the vacuum apparatus for hydrogen spectroscopy. L3, quartz lens, PH, pinhole; L4–L6, MgF2 lenses;
LN2, liquid nitrogen; PM, photomultiplier; TMP, turbomolecular pump; RVP, rotary-vane pump.
LASER PHYSICS
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2005
GENERATION OF CONTINUOUS COHERENT RADIATION
oven ensures that the surrounding optics remain free of
mercury. In addition, heating both the lens L4 and the
entrance window to 65°C prevents the condensation of
mercury. The vacuum tubes next to lens L4 are cooled
by liquid nitrogen in order to cryopump residual
organic molecules in the rest gas that could otherwise
stick to the lens. This solved the previously reported
problem [23] of a declining VUV transmission over
time due to contamination of lens L4.
The generated VUV and the fundamental beams are
separated using the chromatic aberration of MgF2 lens
L4 ( fL4 = 130 mm at 120 nm, Acton Research). The
effective focal length for the VUV beam is almost two
times shorter than for the fundamental beams. A small
mirror is placed in the focus of the fundamental beams
to separate them from the generated VUV radiation. It
also casts a small shadow in the VUV beam, reducing
the intensity by 20%.
The two lenses L5 and L6 that follow form a telescope to collimate the Lyman-α beam for hydrogen
spectroscopy, which will be described below. An aperture 0.5 mm in diameter between the two lenses blocks
most of the stray UV light and transmits most (90%) of
the VUV beam. The VUV photons are detected by a
solar blind photomultiplier (Hamamatsu, R1459) and a
photon counter (SR 400, Stanford Research). Two
Lyman-α filters (Acton Research), each with a bandwidth of 15 nm and a measured peak transmission of
18% at Lyman-α in front of the photomultiplier, reduce
the background due to residual UV radiation to about
2000 photons per second. We estimate that the overall
detection efficiency of Lyman-α is about 0.03% due to
the three lenses (each 48%), the small mirror (80%), the
pinhole (90%), the two filters (each 18%), and the
quantum efficiency of the photomultiplier (12%).
4. EXPERIMENTAL RESULTS
OF FWM IN MERCURY
The two-photon resonance enhancement of the
7s 1S0 state strongly depends on the sum of the wavelengths of the two lasers at 257 and 399 nm. The twophoton resonance was observed by scanning the Ti:sapphire laser while counting the generated VUV photons
at Lyman-α. The wavelength of the dye laser was fixed
at 545 nm. The resulting VUV-wavelength change during the scan can be neglected. A measurement of the
two-photon resonance for T = 220°C is shown in Fig. 6.
The smooth line superimposed is the calculated line
profile from Fig. 2a. The pressure-broadening ∆ωpressure
that is used in the calculations is deduced from a fit of
the measured line profile. This measurement demonstrates the necessity of a two-photon resonance: the
VUV yield is strongly enhanced at wavelengths that
satisfy a two-photon resonance condition.
The VUV yield also depends strongly on the generated wavelength due to resonances at three-photon
height. To measure the VUV yield, the laser frequencies
LASER PHYSICS
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2005
51
VUV yield, 105 photons/0.5 s
6
5
4
3
3 GHz
2
1
0
63927.5
63928.0
63928.5
Two photon frequency, cm–1
Fig. 6. Measured two-photon resonance. The smooth line is
the calculated shape of the two-photon resonance from
Fig. 2, assuming a Doppler width of 2.15 GHz.
at 257 and 399 nm were fixed at the two-photon resonance with the 202Hg isotope, and the dye laser was
scanned by turning the internal Lyot filter with a motor.
The measured wavelength dependence is shown in
Fig. 7. The spectral structure of the VUV yield agrees
well with the calculation shown in Fig. 3. The position
of the mercury energy levels is indicated on the top, and
resonances at three-photon height disappear due to the
combination of phase mismatch and absorption. This
scan was performed using a mercury vapor pressure of
46 mbar (220°C) and moderate laser power levels
(approximately 310 mW at 257 nm, 420 mW at
399 nm, and maximum 940 mW for the dye laser in the
vapor cell). With a different laser setup, in which the
Ti:sapphire laser was pumped by an Ar+ laser (more
output power but difficult to maintain), and with a new
BBO crystal, a maximum Lyman-α yield of 1.2 ×
1010 photons/s right after the interaction volume, equivalent to 20 nW, was achieved [24]. The fundamental
laser powers were approximately 570 mW at 257 nm,
500 mW at 399 nm, and 1.2 W at 545 nm in the mercury
vapor cell. This observed yield at Lyman-α of 20 nW
agrees with the calculated yield in Section 2.
In a former version of the vapor cell, an oscillatory
structure of the VUV yield was observed [23]. It was
found to be a result of reabsorption of the generated
VUV light due to the vapor zone being too long. With
the present vapor cell, which has a vapor zone of only
15 mm and a near-rectangular density profile, no oscillations were observed. In addition, the VUV yield has
been improved by a factor of 40 relative to the VUV
yield in the former vapor cell.
52
PAHL et al.
VUV yield, 106 photons/0.5 s
1
6 12 P 3
12 P
111P
113P
2 2P3/2
F' = 2
24 MHz
F' = 1
2 2P1/2
F' = 1
59 MHz
F' = 0
101P
5
4
121.56 nm
3
1 1 2
2
4 2 10
1
F=1
1 2S1/2
0
121.5
122.0
1420 MHz
F=0
122.5
123.0
VUV wavelength, nm
Fig. 7. Continuous four-wave mixing yield as a function of
the VUV wavelength.
Fig. 8. Excitation scheme for 1S–2P spectroscopy of hydrogen, where the numbers indicate the relative transition
strengths.
5. 1S–2P SPECTROSCOPY OF HYDROGEN
WITH CW RADIATION AT LYMAN-α
6. EXPERIMENTAL SETUP OF LYMAN-α
SPECTROSCOPY
Figure 8 shows the 1S and 2P states of hydrogen,
including fine and hyperfine levels. Relative transition
intensities are indicated and will be explained below.
The relative transition intensity for coupled momenta
can be defined as the ratio of the line strength for coupled momenta and for uncoupled momenta [36]:
The experimental setup for hydrogen spectroscopy
is shown on the right in Fig. 5. Atomic hydrogen is produced from molecular hydrogen at 0.3 mbar in an
Evenson-type microwave discharge [37] using 25 W at
2.45 GHz. Hydrogen atoms are guided by a Teflon tubing to the nozzle. This nozzle is cooled with liquid
nitrogen. The velocity distribution of the hydrogen
beam emanating from the nozzle is given by the atomflux corrected distribution [38], i.e., a Maxwell–Boltzmann distribution multiplied by the velocity v :
S ( γIJF; γ'IJ'F ')
S R ( F, F' ) = ---------------------------------------S ( γIJ; γ'IJ' )
(12)
2

( 2F + 1 ) ( 2F' + 1 ) 
= --------------------------------------------  J F I  ,
( 2I + 1 )
 F' J' 1 
2
(13)
where J, I, and F are the eigenvalues of the operators J,
I, and F; J is the total angular momentum, I is the
nuclear spin, and F = I + J is the total spin, which is
taken as the coupled momentum. Primes indicate the
upper level, and curly brackets denote the 6j symbol.
For the 1S1/2–2P3/2 transition, the ratio of relative line
strengths is (F = 0
F' = 1) : (F = 1
F' = 1) :
(F = 1
F' = 2) = 2 : 1 : 5. For the 1S1/2–2P1/2 transition, the ratio of relative line strengths is (F = 0
F' = 1) : (F = 1
F' = 0) : (F = 1
F' = 1) = 1 :
1 : 2. For the fine structure, J = L + S is taken as the
coupled momentum, and the relative line strength can
be calculated as above for the hyperfine structure. L is
the angular momentum, and S is the electron spin. For
the 1S–2P transition, the relative line strengths are (J =
1/2
J' = 1/2) : (J = 1/2
J' = 3/2) = 1 : 2. From
the above discussion, it follows that the 1S1/2(F = 1)
2P3/2(F' = 2) transition is the strongest, as indicated
in Fig. 8.
f (v ) = f 0v e
3
mv
– ------------2k B T
,
(14)
where f0 is the normalization, m is the hydrogen mass,
kB is the Boltzmann constant, and T is the temperature.
For a temperature of 77 K, the most probable velocity
is vw = 1400 m/s with a spread of 1250 m/s. The nozzle
has a diameter of 0.5 mm. With a 0.3-mm slit at a
280-mm distance, this corresponds to a collimation of
approximately 1 : 700; i.e., vz = 700vx . The Lyman-α
beam and the hydrogen beam cross at an angle of 90°.
Due to the velocity spread ∆vx in the direction of the
Lyman-α beam, a residual Doppler broadening of
30 MHz is expected. The divergence of the Lyman-α
beam is minimized by adjusting lens L6 until the
recorded 1S–2P resonance lines show no further narrowing. 1S–2P excitation spectra are recorded by
counting the resulting fluorescence photons with a solar
blind photomultiplier (Hamamatsu R1459) 22 mm
above the interaction zone while scanning the frequency of the dye laser. Blackened guiding tubes
reduce stray light and leave a gap of 16 mm for the
hydrogen beam and fluorescence detection.
LASER PHYSICS
Vol. 15
No. 1
2005
GENERATION OF CONTINUOUS COHERENT RADIATION
53
200
resolved. Figure 8 shows that, from the F = 0 ground
state, only the F' = 1 excited state and, from the F = 1
ground state, mainly the F' = 2 component of the 2P3/2
state are excited. The expected ratio of line strengths is
(F = 0)
(F' = 1) : (F = 1)
(F' = 1, 2) = 1 : 3. As
a result, a double-peak spectrum is expected for excitation to the 2P3/2 state with a splitting of 1400.5 MHz,
20 MHz smaller than the ground-state hyperfine splitting. The observed splitting is 1400.4(4.6) MHz, which
agrees with expectations.
100
8. CONCLUSIONS
Fluorescence, photons/0.5 s
600
F=1
F' = 1, 2
500
400
120 MHz
F=0
300
0
–2
–1
F' = 1
0
1
2
3
Relative frequency, GHz
4
Fig. 9. Spectrum of the 1 2S1/2–2 2P3/2 transition in a beam
of atomic hydrogen measured with continuous coherent
radiation at Lyman-α.
The on-axis photomultiplier for measuring the generated VUV intensity has, as described in Section 3,
two narrow-bandwidth interference filters in front of it.
Most of the VUV is reflected from the filter and may
reach the interaction region. Depending on the angle of
this backreflection, broadening and even ghost spectra
of almost the same strength as the real signal have been
observed. To avoid these effects, the on-axis photomultiplier and Lyman-α filters are mounted on a bellows
and are tilted.
7. EXPERIMENTAL RESULTS FOR LYMAN-α
SPECTROSCOPY
Figure 9 shows a measured excitation spectrum of
the 1S1/2–2P3/2 transition. Two peaks are observed with
a ratio of approximately 3 : 1 and a separation of
approximately 1.4 GHz. The width of the peaks is only
120 MHz, which is very close to the natural linewidth.
The measured spectrum was fitted with Voigt profiles. The width of the Lorenzian contribution was kept
fixed at 99.7 MHz, the natural linewidth of the
2P-states. From the fit, the width of the Gaussian contribution is obtained. Averaging nine spectra gives
58.2(3.0) MHz. This excess transition width is largely
caused by an estimated Doppler broadening of 30 MHz
due to the spread of the hydrogen beam. The residual
Doppler effect due to a small deviation of the intersecting angle of only 0.3° would be sufficient to account for
the remaining width. The bandwidth of the Lyman-α
beam is expected to be on the order of 10 MHz and
hardly contributes. This estimate is based on the bandwidths of the fundamental beams, which are each less
than a few MHz.
The 24-MHz hyperfine splitting of the 2P3/2 level is
smaller than the 99.7-MHz natural linewidth. The
hyperfine splitting of the upper level is thus not
LASER PHYSICS
Vol. 15
No. 1
2005
The first continuous-wave coherent source for
Lyman-α has been described. The power of 20 nW is
almost at the same level as the average power of a
pulsed Lyman-α source that has been used for laser
cooling [1]. The bandwidth of the continuous Lyman-α
source is estimated to be on the order of 10 MHz. Using
this narrow-bandwidth Lyman-α source, the 1S–2P
transition in atomic hydrogen has been observed for the
first time with almost natural linewidth. There is still
much room for further improvement of the conversion
efficiency of such a cw Lyman-α source.
The yield can be enhanced, e.g., by tighter focusing.
This would require an increased mercury density to
maintain phase matching, which in turn causes more
Doppler and pressure broadening of the two-photon
resonance. Nevertheless, this effect is overcompensated
by the higher VUV yield for tighter focusing. Replacing lens L3, e.g., by a f = 100 mm lens, the power is
expected to increase by more than a factor of two. In the
current vapor cell, tighter focusing is not possible due
to geometric constraints.
Another method for improving the VUV yield
employs electromagnetically induced transparency
(EIT) [39]. The frequency ω1 of the first laser has to be
resonant with the 6s 1S0–6p 3P0 transition (253.7 nm) in
such a scheme. The power of the second laser (then
automatically resonant with the 6p 3P0–7s 1S0 transition
at 408 nm to maintain the two-photon resonance condition) has to be high enough so that the Autler–Townes
splitting exceeds the linewidth of the 6p 3P1 level. The
medium should then be transparent for ω1 but should
still show a significant nonlinear susceptibility. For a
splitting of 3 GHz, a power of 0.53 W at 408 nm is
needed, which appears to be feasible. For an experimental realization of cw FWM using EIT, the frequency-doubled fixed-wavelength Ar+ laser has to be
replaced by a frequency-doubled tunable dye laser.
Yet another way of increasing the VUV output is to
use an enhancement cavity for the fundamental beams
[40]. If each of the fundamental beams is enhanced by
a (moderate) factor of ten, the VUV output would
improve by three orders of magnitude. Saturation due
to one- and two-photon absorption is expected not be a
problem. At present (with 580 mW at 257 nm and
54
PAHL et al.
500 mW at 399 nm), the one-photon absorption rate is
380 s–1, and the two-photon absorption rate is 4.3 ×
103 s–1. With a tenfold enhancement of the powers, the
rates are still much lower than the inverses of the lifetimes of the 6p 3P0 and 7s 1S0 states, respectively, so that
ground-state depletion can be neglected.
ACKNOWLEDGMENTS
This work was supported by the German Federal
Minister for Education and Research (BMBF).
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2005