Appl. Phys. B (2014) 117:957–967
DOI 10.1007/s00340-014-5914-y

Generation of vacuum ultraviolet radiation by intracavity
high-harmonic generation toward state detection of single
trapped ions
Kentaro Wakui • Kazuhiro Hayasaka •Tetsuya Ido

Received: 21 June 2014 / Accepted: 13 August 2014 / Published online: 3 September 2014
Ó Springer-Verlag Berlin Heidelberg 2014

Abstract Vacuum ultraviolet (VUV) radiation around
159 nm is obtained toward direct excitation of a single
trapped 115 Inþ ion. An efficient fluoride-based VUV output
coupler is employed for intracavity high-harmonic generation of a Ti:S oscillator. Using this coupler, where wemeasured its reflectance to be about 90 %, an average
power reaching 6.4 lW is coupled out from a modest
fundamental power of 650 mW. When a single comb
component out of 1.9  105 teeth is resonant to the atomic
transition, 100s of fluorescence photons per second will be
detectable under a realistic condition.

1 Introduction
Optical clocks based on trapped single ions and neutral
atoms in optical lattices have reached frequency uncertainties in the order of 1018 [1–3]. This level of accuracy
brings strong impact to applications in science and technology, such as precise determination of physical constants, tests of fundamental physics theories, network
synchronization, geodesy, and redefinition of the second.
Many of the optical clocks use atoms and ions with twoouter electrons as the optical frequency reference according
to the original proposal by Dehmelt [4]. The idea of singleion clocks has been extended to optical lattice clocks where
K. Wakui (&)  K. Hayasaka  T. Ido
National Institute of Information and Communications
Technology, 4-2-1 Nukui-kitamachi, Koganei, Tokyo 184-8795,
Japane-mail: wakui@nict.go.jp
T. IdoPRESTO, Japan Science and Technology Agency, Honcho,
Saitama 223-0012, Japan

multiple neutral atoms are confined in the Lamb–Dicke
regime [5]. Energy levels of such atomic species (Bþ ; Alþ ;Gaþ ; Inþ ; Tlþ , Sr, Yb, Hg) are shown in Fig. 1a with Inþas an example. Their weakly allowed 1 S0 –3 P0 transitions
with linewidth smaller than 1 Hz are used as clock transitions. The clock transitions are observed using the 1 S0 –1
P1 transitions as follows: excitation of the 1 S0 –1 P1 transition after the interrogation of an atom with clock lasers
results in a lot of fluorescent photons when the clock laser
is off-resonant from the 1 S0 –3 P0 transition, and results inthe absence of photons when it is resonant. This method
called ‘‘electron shelving’’ is relatively easily implemented
to lattice clocks since the 1 S0 –1 P1 transition lies in visible
wavelength. In contrast, application to the ions is intractable, because the 1 S0 –1 P1 transitions locate in the vacuum
ultraviolet (VUV) region as is exemplified in Fig. 1a,
where generation of coherent radiation is challenging. The
VUV radiation is also expected to laser-cool the ion, andthis demands the VUV radiation to be continuous wave(CW).
The solution to overcome this difficulty has been provided by quantum logic spectroscopy (QLS), in whichanother ion with a convenient energy level structure istrapped simultaneously and serves as a coolant ion as well
as a quantum-state probe [6]. By this way, the Alþ clock
has been realized without the need for VUV radiation to
excite the 1 S0 –1 P1 transition at 167 nm. The smallest
inaccuracy of single-ion clocks has been reported with theAlþ clock [1], but the implementation of QLS seems
technically demanding since no other demonstrations are
so far reported.
Here, we propose an alternative approach for the ionclock, in which VUV radiation is generated via high-harmonic generation (HHG) [7, 8], and is used only for

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a

K. Wakui et al.

b

Fig. 1 a Relevant energy levels and transitions of Inþ . b Images ofInþ sympathetically cooled with Caþ observed by resonant fluorescence of Caþ at 397 nm. The Inþ is identified as the dark site in theion chainsquantum-state detection of single ions. Cooling of the ionsis supplied by sympathetic cooling, and therefore, a singlemode CW radiation is not required. Detection of single
ions might be feasible with a quasi-CW radiation which isactually a singled-out mode in ‘‘VUV combs’’ generated
via intracavity HHG [9, 10]. Sympathetically cooled ionsare relatively easily prepared [11, 12], and an example ofsuch ion arrays including an Inþ is shown in Fig. 1b.
Besides this main advantage of simpleness, our method has
another advantage of scaling to multi-ion systems for
improved stability [12]. Although the current protocol of
QLS is limited to systems with one target ion, the state
detection using VUV radiation is applicable to systems
with multiple target ions. Such a quasi-CW beam in the
VUV region might be used as a clock laser that interrogatesa thorium nucleus for realizing a more accurate opticalclock [13–17]. Several methods which might be applicable
to direct excitation of VUV transitions have been developed as follows. Triply-resonant four-wave mixing is
implemented to generate 121 nm light [18]. KBBF crystals
are used to demonstrate generation of 156-nm radiation by
sum-frequency mixing [19] and generation of 153-nm
radiation via frequency conversion [20]. Raman-resonant
four-wave mixing in parahydrogen has been proposed more
recently to generate 120- to 200-nm VUV radiation [21].
In Sect. 2, we discuss the feasibility of detecting the1
S0 –1 P1 fluorescent photons at 159 nm from a single Inþion excited with a quasi-CW beam obtained via intracavity
HHG. Section 3 describes experiments to generate the
VUV radiation as the fifth harmonic of femtosecond (fs)frequency combs peaked at 795 nm. We conclude thiswork and discuss the future prospects in Sect. 4.

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2 Single-ion detection with a quasi-CW VUV beam
In this section, we discuss on the possibility of detecting
the quantum state of a single trapped ion by direct excitation using a quasi-CW beam generated as VUV combs.
Our target is the 115 Inþ , which is one of the candidates for
single-ion optical clocks included in Dehmelt’s original
proposal [4]. Recent proposals on the Inþ optical clocks
estimate fractional frequency inaccuracy of 1018 levelowing to its small black body radiation shift [11, 12].
Previously, implementation of the Inþ clock has been
investigated using relatively weak 1 S0 –3 P1 transition at
230 nm for detection, but its performance was limited to1013 level [22, 23]. If the direct excitation of the 1 S0 –1 P1transition at 159 nm is possible, roughly 500 times more
fluorescent photons are emitted from a single Inþ , and it
makes much faster quantum-state detection than that withthe 1 S0 –3 P1 transition. Combined with robust trapping of
the ions by sympathetic cooling, the VUV detection
scheme will enable an easier implementation of the opticalclock. The same method might be applicable not only to a
multi-Inþ clock, but also to a single Alþ clock as well as tomulti-Alþ clock, where the 1 S0 –1 P1 transition lies at
167 nm.
We assume a setup depicted in Fig. 2 for direct excitation of a single Inþ with a VUV beam generated from
HHG. The whole optical path between the VUV source andthe detector is evacuated to avoid absorption by air. The
VUV source and the ion trap will be deployed in separate
vacuum chambers for their different vacuum levels andwill possibly be connected through a high-transmittance
fluoride window. We focus on the case of single ion in thispaper, but extension to multiple ions might be possible byupgrading the optics for simultaneous illumination of ions.
The VUV comb is incident on a grating, and modes aroundthe 1 S0 –1 P1 transition are chosen by a slit to avoid detrimental influence by excess modes such as increased
background photons due to scattering and charging of
insulating materials due to photoelectric effect. The quasiCW beam generated in this way is focused onto the Inþ
sympathetically cooled with two Caþ : Fluorescent photons
emitted from the Inþ are imaged onto the detector using asingle lens. Quantum-state detection of the single ions isenabled by sufficient number of fluorescent photons
detected with a photomultiplier tube (PMT) or a imageintensified charge-coupled device (CCD) camera.
In order to assess the feasibility of the VUV detection
method, it is crucial to know the total average power P0(W) of the VUV comb required for detecting n0 [counts per
second (cps)] fluorescent photons with the detector. Roughestimation is made on P0 by considering the steps of thedirect excitation of single ion consisting of generation ofGeneration of vacuum ultraviolet radiation

959

Fig. 2 Setup for observing a
sympathetically cooled Inþ bydirect excitation using a quasiCW beam generated from the
VUV comb

the quasi-CW beam focused to the ion, fluorescent photon
scattering by the single ion, and collection and detection by
the detector. The VUV comb is incident on the grating, andonly the mode interacting with the ion is transmitted
through the slit and is focused with a curved mirror onto
the ion. After this step, the quasi-CW power Peff which
effectively contributes to excitation of the ion is given by
Peff ¼ gprop  P0

ð1Þ

where gprop ¼ gG gW gS gM gf is the total propagation efficiency to the ion, in which gG , gW , gS , gM . and gf denote,
respectively, grating efficiency, window transmittance,
power ratio of the target comb-mode relative to the whole
spectrum, reflectance of the focusing mirror, and focusing
efficiency to the spot with a radius of r0 . The ion emits
fluorescent photons with a rate ofnfl ¼

Peff C;
Aspot 2Isð2Þwhere C is the spontaneous emission rate and Is is thesaturation intensity, respectively, of the 1 S0 –1 P1 transition.
Aspot ¼ pr02 is the spot size. The photons are imaged onto a
detector with a quantum efficiency of gD by a single lens
which spans a solid angle covering gX of the whole solid
angle and has a transmittance of gL . Then, the count rate
n0 ¼ gdet  nfl (cps) is obtained by the detector, wheregdet ¼ gX gL gD is an overall efficiency in the detection side.
Thus, the photon counting rate per the average VUV-comb
power can be estimated by the following expression:
n0 gprop  gdet C
¼
:
2IS
P0
Aspot

ð3Þ

Now we proceed with estimation on P0 required for the
single-ion detection with realistic experimental parameters.

The spontaneous emission rate of the 1 S0 –1 P1 transition islately revised to be C ¼ 2p  204 (MHz) [24]. The saturation intensity of the transition is calculated fromIs ¼ phcC=3k3 , where h ¼ 6:63  1034 Js is the Planck
constant and c is the speed of light. Using the above valueof C and wavelength k ¼ 158:6 nm, the saturation intensity
is Is ¼ 6:67 W/cm2 . The advantage of sympatheticallycooled ions is that even the invisible ion can be localized
within a known region much smaller than micrometerscale. Localization of a Caþ Doppler-cooled in a conventional linear trap after a routine procedure of micromotion
compensation was measured to be as small as 16 nm (fullwidth at half maximum) along the trap axis direction [25].
The wave packet size of the Inþ cooled by this Caþ ispﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
estimated 115=40 times larger due to the dependence ofpﬃﬃﬃﬃ
the axial secular frequency on mass ð/ 1= mÞ, but the
localization is still in the order of tens of nanometers. This
allows targeting the ion with the smallest spot size possible
with focusing optics. Here, we consider a simple case inwhich a collimated Gaussian beam is tightly focused by aconcave mirror (denoted as ‘‘focusing mirror’’ in Fig. 2).
When we take a mirror diameter D ¼ 25 mm and a radiusof curvature R ¼ 50 mm as an example, the effective
diameter of the focused Gaussian spot is estimated to bed  Rk=D  0:32 lm. Thus, we assume that the VUVradiation is focusable to the spot radius, e.g., r0 ¼ 0:5 lm,
which is more than three times larger than d=2. We also
estimated the focusing efficiency gf ¼ 0:85, which denotes
the reduction of intensity from the ideal focusing. Later we
discuss on derivation of gf in some detail. Grating efficiency of gG ¼ 0:34 was realized at 160 nm [26]. We
estimated that the intensity ratio of the target comb-mode
to the whole spectrum, namely spectrum occupancy, is
gS ¼ 5:3  106 , which is an important issue and is

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discussed in detail later. Mirror reflectance gM is estimatedto be 95 %, because such a high-reflection coating isavailable at the wavelengths longer than 150 nm [27]. For
collection of fluorescent photons, we assume a use of a lenswith a focal length of f ¼ 30 mm in 25 mm diameter madeof MgF2 . This gives photon collection efficiency ofgX ¼ 0:045. A typical transmittance of 85 % was realized with a 3-mm-thick MgF2 [27], and thus, we use a lenstransmission efficiency of gL ¼ 0:85. Note this value isalso used for the window transmittance gW . The quantum
efficiency of our image-intensified CCD camera (PI-MAX
3, Princeton Instruments) is 0.15 at 159 nm, which issimilar to the maximum efficiency of PMTs. Therefore, wetake this value as the detector efficiency gD :Next we estimate the focusing efficiency gf in detail. We
take account of aberration caused by the focusing mirror
which reflects the VUV radiation originally generated as a
Gaussian beam, because the accuracy of mirror surface isclosely related to the beam-focusing efficiency. Surface
accuracy is usually measured at 633 nm (typically using ahelium–neon laser), and k=10 (=63.3 nm) can be easily
achievable for the mirror diameter D  25 mm. The accuracy of 63.3 nm corresponds to phase aberration of A ¼ 2:5
rad at 159 nm. Then, one can evaluate the Strehl ratio of a
Gaussian beam, S ¼ expðr2U Þ, which represents the ratioof the central irradiance of point-spread function before
and after being affected by aberrations [28]. r2U is thevariance of the phase aberration in a Gaussian beam. Dueto the fact that surface roughness of a polished mirror isusually below a few angstroms and that spatial frequencyof surface irregularity is not high, we consider monochromatic primary aberrations, e.g., spherical aberration
ðrU ¼ A=6:20Þ, coma ðrU ¼ A=6:08Þ, and astigmatismðrU ¼ A=6:59Þ [28]. In each case, the Strehl ratio of around
85 % can be maintained. In other words, roughly 85 %power in the reflected VUV beam is not blurred and will becorrectly focused even with aberration which may becaused by the practical surface accuracy. Note, further
improvements of the Strehl ratio are possible by combining and balancing several aberrations [28]. In contrast
to the focusing mirror described above, the beam quality
would not be affected as much by a surface irregularity ofa dichroic beam splitter which should be placed inadvance of the beam input in Fig. 2 and separates fundamental and high-harmonic beams. As shown later inthis paper, the beam diameter at the splitter is normally assmall as 1 mm. The corresponding primary aberrations
caused by that small area is much smaller than that in thecase of the concave focusing mirror ðD  25 mmÞ because
spherical aberration, coma, and astigmatism vary with thefourth, third, and second power, respectively, of radial
distance from the beam axis. Thus, the Strehl ratio for the123

K. Wakui et al.

splitter is estimated to be near unity. Note that surface
accuracy of k=10 is commercially available in substrates
with the thickness and the diameter of 1 and 5 mm,
respectively.
Finally, we estimate the spectrum occupancy gS as follows. Nonlinear optical processes in the HHG can be categorized as perturbative, intermediate, and strong-fieldregimes according to the strength of fundamental electricfield interacting with atoms [7]. As we show in Sect. 3.2,
the peak intensity Ipeak of fundamental fs pulses in our
setup is estimated to be around 2  1013 W/cm2 , which ispresumably within the perturbative regime. In fact, we
calculated the scale parameters in the Ref. [7] as follows,
abb ¼ eEa aB =hD  1:1  103 and abf ¼ eEa aB =hx 
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ0ﬃ
4:5  103 . Here, e ¼ 1:6  1019 C, Ea ¼ 2Z0 Ipeak 
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1:3  108 V/cm, and aB ¼ h= 2mWXe  5:6  1011 m,
denote, respectively, the elementary charge, electric fieldstrength, and the Bohr radius of Xe atoms used as nonlinear
media for HHG. We also used m ¼ 9:11  1031 kg,
Z0 ¼ 377 V/A, and WXe ¼ 12:13 eV, representing theelectron rest mass, the impedance of vacuum, and theionization potential of the Xe atoms [24], respectively. h¼
h=2p is the reduced Planck constant and hx0 ¼ 1:57 eV isa photon energy at 795 nm. 1=D ¼ 1=jx159nm  x0 j 
0:1 fs/rad is a response time of induced atomic dipole
moment. Thus, we confirmed that the following condition
is fulfilled as abb  1 and abf  1, that is the definition of
the perturbative regime [7]. This may allow us to describe
electric field for the nth harmonic as en ðtÞ / ½eF ðtÞn , whereeF ðtÞ denotes the electric field at fundamental wavelength.
If we assume a transform-limited pulse, e.g., with aGaussian temporal envelope whose width is characterized
by r, simple Fourier transform analysis reveals that the
spectral width for the nth harmonic in the frequency
pﬃﬃﬃ
domain becomesn times broader than that for
the fundamental: en ðtÞ / expðnt2 =2r2 Þ ! En ðxÞ /expðnr2 x2 =2Þ. As we show in Sect. 3.2, a spectral
bandwidth of the fundamental fs pulses is BF ¼ 9:5 THz(20 nm centered at 795 nm). This may yield B5th ¼
pﬃﬃﬃ
5 BF ¼ 21:2 THz (159 0:9 nm) for the fifth harmonic.
gS ¼ ðB5th =frep Þ1  5:3  106 is obtained as an inverseof the number of VUV-comb teeth ð1.9 105 Þ. Here,
we introduced an experimental repetition rate of our fs
frequency comb as frep ¼ 111:5 MHz.
In summary, the photon counting rate per the average
VUV-comb power, n0 =P0 , is estimated to be roughly
87 cps/lW, using the above parameters summarized inTable 1. According to the previous report in which single
Inþ is detected using the 1 S0 –3 P1 transition at 230 nm [23],the quantum-state detection was demonstrated with aphoton counting rate of 500 cps. This rate is obtained with

Generation of vacuum ultraviolet radiation

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Table 1 Assumption on numbers for estimating the requirement
for total average power
Description

SymbolEstimation

Spontaneous emission rateC

2p  204 MHz

Saturation intensity

Is

6:67 W/cm2

Spot radiusr0

0:5 lmGrating efficiency
Window transmittance

gG
gW

0.34
0.85

Spectrum occupancygS

5:3  106

Mirror reflectance

gM

0.95

Focusing efficiency

gf

0.85

Photon collection efficiency

gX

0.045

Imaging lens transmission

gL

0.85

Detector quantum efficiency

gD

0.15

The details are described in the text

P0 ¼ 5:8 lW in our scheme. In the following Sect. 3, we
experimentally confirmed that this level of power can begenerated using our existing setup.

3 Intracavity high-harmonic generation using VUVOC
HHG has been intensively studied for generation of radiation whose wavelengths are shorter than 190 nm VUVregion, in order to realize attosecond pulses enabling one toprobe and control electron dynamics in the time domain[8]. The Ti–sapphire (Ti:S) based system is convenient fora tool of spectroscopy because it can generate various
wavelength. The HHG process, however, requires verystrong laser intensities ([1013 W/cm2 ). Though chirped
pulse amplification of Ti:S oscillator has been widely used
to realize such a condition, its repetition rate cannot easily
exceed 20 kHz [7]. Alternatively, intracavity HHG using fs
frequency combs has also realized such a strong intensity
by using a passive fs enhancement cavity (fsEC), while it
can maintain a repetition rate of 100 MHz level. The intracavity HHG thus realized frequency combs in the VUVand extreme ultraviolet (XUV) region [9, 10]. Morerecently, direct frequency comb spectroscopy using such
VUV or XUV combs have been implemented for probingtransition frequencies in argon at 82 nm and in neon at
63 nm [29], or in xenon at 147 nm [30]. The XUV combs
may also be useful for testing bound-state quantum electrodynamics in a single helium ion [31].
Considering to apply the direct state detection scheme toan Inþ clock being developed in our institute [11], we built
a setup of an intracavity HHG and reported VUV-comb
generation centered at 159 nm [32]. But further power-

scaling is needed in order to realize such a VUV detectionof single trapped ions. One of the straightforward ways toscale-up the harmonic yield would be just to enlarge fundamental power of the fs frequency combs [33, 34] for
HHG. The outcoupling method of high harmonics from thefsEC is also the key to scale-up their yield. Several
methods were previously demonstrated using, e.g., a bulk
sapphire window as a Brewster plate [9, 10], a diffraction
grating ruled onto a fsEC mirror surface [35], a diffraction
nanograting [36], an anti-reflection-coated grazing incidence plate [37], a VIS/IR-XUV beamsplitter [38], aBrewster plate made of MgO substrate with a dielectric
coating for VUV [30], and a pierced fsEC mirror [39].
In this section, we report a novel efficient VUV output
coupler (VUV-OC) for the fifth harmonic of Ti:S oscillator.
The VUV-OC consisting of a thin SiO2 substrate andfluoride-multilayer coating works as a Brewster plate
which can be inserted in the fsEC driven at a fundamental
near-infrared (NIR) wavelength, and at the same timeworks as a high reflector at the VUV wavelength. In fact,
we demonstrated an efficient outcoupling of the VUVcomb generated at around 159 nm, and obtained an average
power of 6.4 lW measured with a calibrated detector. This
VUV power is almost ten times larger than that obtained in
our previous experiment [32].
3.1 Development of fluoride-multilayer-coatedBrewster plate (VUV-OC)
The design and performance of the VUV-OC is described
here. The substrate of our VUV-OC is a SiO2 glass platewith thickness of 100 lm. The Brewster angle of thesubstrate is 55 at 795 nm. On one surface, we deposited ahigh-reflection coating at 159 nm, which is a multilayer
quarter-wave stack consisting of AlF3 and GdF3 for lowand high-refractive-index materials, respectively. The
VUV-OC reflectance RVUV
is designed to be [80 % atOC
153–163 nm wavelengths and [90 % at 159 nm forp-polarized VUV light. The VUV-OC was made by SigmaKoki. An average reflectance of the VUV-OC at NIR
wavelengths from 760 to 840 nm is measured as
RNIR
0:005 %. This is mainly caused by the
OC ¼ 0:1150
fluoride-coating layer and may act as a major loss inside
the fsEC. Note, because our VUV-OC is thin, its groupdelay dispersion (GDD) is small enough in the above NIR
range.
In order to evaluate the reflectance of VUV-OC for
p-polarization in the VUV range, we carried out reflectancemeasurement using a synchrotron light source at UVSOR
facility (Okazaki, Japan) [40]. First, incident VUV powerfrom the storage ring is calibrated by a photodiode(AXUV100, IRD). Then, the reflection from the VUV-OC,

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which was placed on a rotation stage, was measured by thesame photodiode. Thus, we measured the absolute reflectance shown in Fig. 3 at several incident angles (45 , 50 ,
55 , 60 , and 65 ). Wavelength was changed with amonochromator in the beamline from 140 to 190 nm with awavelength step of 0.5 nm. At the Brewster angle of 55 ,the reflectance of 86.9 0.4 % was obtained at 159 nm,
and [80 % was achieved from 155 to 161.5 nm. We foundthat the maximum reflectance is higher at the smaller
incident angles: 90.3 0.6 % at 161 nm (50 ) and92.4 0.5 % at 164 nm (45 ). Furthermore, the maximum
reflectance at 65 incidence is still as high as 74 % ataround 153 nm. Thus, this VUV-OC technique is useful insuch a broadband VUV range and can be applicable tooutcoupling, e.g., the seventh harmonic at around 150 nm
generated from Yb-fiber combs at 1,040–1,060 nm.
3.2 Experimental results of intracavity HHG
We deployed our VUV-OC in our experimental intracavity HHG setup shown in Fig. 4. A homemade Ti:S
oscillator consists of a linear cavity including a prism
pair. The center wavelength of fundamental fs combs istuned to be 795 nm. The repetition rate ðfrep Þ, spectral
bandwidth, pulse width, and average power are
111.5 MHz, 20 nm, 65 fs and 650 mW, respectively.
After dispersion compensation by a pair of SF10 prisms,
fs combs are guided into the fsEC placed inside a vacuum
chamber. The fsEC consists of six broadband, low-GDD
mirrors: an input coupler with a reflectance of
RIC  99:5 %, three planar high reflectors (HRs), and two
concave HRs with radius of curvatures of 100 mm.

Fig. 3 VUV-OC reflectance measured at 140–190 nm. From left toright, five splined curves correspond to the incident angles of 65(cyan), 60 (magenta), 55 (blue), 50 (green), and 45 (red). For
reference, the purple dotted horizontal and vertical lines indicate
reflectance of 0.869 and wavelength of 159 nm, respectively

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Although horizontal and vertical beam waist sizes
between the two concave mirrors are slightly different
because of aberration caused by the finite folding angle inbow tie configuration, both of them are evaluated to beabout 5 lm by beam propagation parameters measured
outside the fsEC. The reflection from the input coupler isguided to a diffraction grating. The zeroth-order diffraction from the grating is fiber-coupled and introduced intoa spectrometer (USB4000, Ocean Optics) to evaluate
reflection spectra from the fsEC. Then, the first-orderdiffraction is used for Hänsch–Couillaud [41] locking
technique (referred to as ‘‘Polarization locking’’ inFig. 4), which adjusts frep of the Ti:S oscillator to that of
the fsEC. The carrier-envelope-offset frequency fceo of the
fs comb is controlled so that power inside the fsEC ismaximum. Cavity leakage allows us to estimate the power
as well as the spectrum of cavity field. The average circulating power inside the fsEC was estimated to be 120 W(maximum), which corresponds to the peak intensity of2  1013 W/cm2 . Xe gas was used as nonlinear media andintroduced to the beam waist through a gas-jet nozzle(100 lm diameter). We observed visible plasma via ionization of the Xe gas. The VUV-OC is placed at the
Brewster angle of incidence right after the major focus of
the fsEC. Generated VUV power was measured by asolar-blind phototube (R1187 [42], Hamamatsu). The
phototube was calibrated at Hamamatsu, and the sensitivity to light at 160.8 nm was measured to be 9 mA/W.
Typical intensity spectra for the fundamental frequency
combs are plotted in Fig. 5. The red and blue solid curves inFig. 5a are spectra of the Ti:S oscillator and the fsECtransmission (leakage), respectively. The bandwidth oftransmitted spectrum is about 20 nm, which we used toevaluate gS as described in Sect. 2. The blue (red) solid
curve in Fig. 5b is a reflection spectrum from the fsEC
which is on-resonant (off-resonant). We roughly evaluate
the frequency-averaged enhancement factor for the fsEC
pﬃﬃﬃﬃﬃ[43]: E ¼ ð1  RIC Þ=ð1 þ R  2 RÞ; obtained withneglecting a frequency-dependent round-trip phase term.
Here, R ¼ RIC ð1  RNIR
OC Þ Rr ; where Rr denotes residualreflectance in which we sum up reflectance for all the othermirrors except for the VUV-OC and the fsEC input coupler.
We assume that VUV-OC and input coupler are lossless.
From the experimentally observed enhancement factor of
350, we estimated Rr to be 99.97 % for all the other five
HR mirrors for fsEC. Note, we neglect the GDD effectwhich might be caused by the VUV-OC. Further precise
measurement about frequency-resolved intracavity GDD
and/or losses is possible by using several methods [44–46].
We then measured the time variation of average powerin the VUV comb as shown in Fig. 6a. We tested the two
positions of the VUV-OC: (red) 15 mm and (blue) 25 mm

Generation of vacuum ultraviolet radiation

963

Fig. 4 Experimental setup for intracavity HHG using VUV-OC.
HWP half-wave plate, QWP quarter-wave plate, PBS polarization
beam splitter, PD photo detector, HR broadband high reflector withlow group-delay dispersion. frep -PZT and fceo -PZT correspond to fast
Fig. 5 a Spectra of red Ti:S
oscillator and blue fsECtransmission. b Reflection
spectra when the fsEC is red
off-resonant and blue onresonantpiezoelectric transducers on which cavity mirrors for the Ti:S
oscillator are mounted and feedback controlledabaway from the fsEC focus. As seen in the figure, the closer
VUV-OC position resulted in the faster decay. The decay
constants are fitted by using f ðtÞ ¼ A0 expððt  t0 Þ=sÞ,and we obtained (green) s15mm ¼ 12:0 0:7 s, and (cyan)
s25mm ¼ 750:0 9:3 s. This decay is associated with the
reduction of fundamental power inside the fsEC as can beseen from the Fig. 6b. In contrast, we did not observe any
power reduction (shown as the magenta curve) without Xegas, namely in the absence of high harmonics. One of thepossible reasons for the degradation in the harmonic yield
is VUV-induced IR absorption in our VUV-OC. VUVillumination may cause defects in the VUV-OC which canabsorb intense IR beam. This may change GDD in the
VUV-OC via accumulation of heat, which is not easily
dissipated in vacuum. This degradation was not permanent,
and the harmonic yield was recovered after certain hours of

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Fig. 6 Time variation of
a VUV power and b normalized
fundamental power. VUV-OC
was placed at 15 or 25 mm
away from the fsEC focus. The
fundamental and VUV power at
the same VUV-OC position are
synchronously sampled every
 0.3 s. Time variation of afundamental power in theabsence of high harmonics is
also shown as a magenta curvein b. c Yield of the fifth
harmonic as a function of
fundamental power in the two
VUV-OC positions. Green
curves are obtained by linear
least squares fitting using
y ¼ ax5 , resulting in lefta ¼ ð1:533 0:047Þ  107 ,and right
a ¼ ð1:538 0:006Þ  107 .
Deviation of the harmonic yieldat the same fundamental poweris caused by slower response of
the phototube compared to thatof the power meter

K. Wakui et al.

a

b

c

break time. The similar reversible degradation at IR
wavelength has been reported for oxide mirrors illuminatedby UV radiation in free electron laser systems [47].
The yield of the fifth harmonic as a function of fundamental power is shown in Fig. 6c. In both cases of (left)
15 mm and (right) 25 mm distance, data are fitted well to
y ¼ ax5 as was predicted in Sect. 2. We measured theaverage power of fifth harmonic outcoupled from the fsEC
to be 6.4 lW at maximum with a nozzle back pressure ofabout 1.4 atm. The HHG chamber was evacuated and thepressure inside the chamber was below 10 mTorr when Xe

123

gas was supplied. We previously reported 0.67 lW [32]using a diffraction-grating mirror as demonstrated in [35].
Thus, our VUV-OC outperforms our previous setup andincreased the final yield for nearly ten times. Further
optimization of HHG conditions [48–52] might yield
power increase of the VUV combs.
Finally, we measured a spatial-mode profile of VUVradiation outcoupled from the fsEC via visible fluorescenceemission from a phosphor screen covered with sodium
salicylate (Scintillator window, McPherson). The fluorescence emission is peaked at 420 nm [53]. Because theGeneration of vacuum ultraviolet radiation

965

Fig. 7 a CCD image of fluorescence intensity excited by VUV radiation at a phosphor screen. b 3D surface plot of the fluorescence intensity

Fig. 8 Experimental results ofintensity distributions obtained
from CCD images. a The left
(right) figure is a horizontal(vertical) cross section of thefluorescence intensity
distribution (shown in Fig. 7).
b The left (right) figure is ahorizontal (vertical) crosssection of an intensity
distribution for fundamental
light scattered at the same
phosphor screen. In each case,the horizontal (vertical) axis iscoincident with the major(minor) axis of an elliptic
Gaussianab

VUV radiation is generated at the intracavity focus andreflected by the simple dichroic beamsplitter, the outcoupled VUV radiation should presumably be a clean Gaussianbeam. This feature must be one of the indispensable prerequisites so as to realize tight focusing onto a trapped ion.
A snapshot of fluorescence intensity observed by a CCD
camera (PL-B953U, PixeLINK) is shown in Fig. 7. The
measured intensity distribution is a slightly asymmetrictwo-dimensional (2D) Gaussian. We then fitted the fluorescence intensity and evaluated the spatial-mode profile of
the VUV radiation, based on the fact that a quantum efficiency of sodium salycilate is high in the VUV region [54]and is almost flat over that wavelength range [55, 56]. We
also assume that the sodium salycilate layer was not saturated due to the faint (lW-level) average VUV power. The
fitting results by using a Gaussian function f ðxÞ ¼
I expð2ðx  x0 Þ2 =w2 Þ þ I0 are shown in Fig. 8a. We
0:01 mm and (right) w5th
obtained (left) w5thh ¼ 2:00
v ¼
1:29 0:01 mm as a beam radius at the phosphor screen,
which is placed at about 140 mm away from the fsEC
focus. Thus, a beam diameter of the fifth harmonic on the
VUV-OC is estimated to be about 1 mm in the case of
25 mm distance. We also evaluated a beam radius of

123

966

K. Wakui et al.

fundamental light by the same CCD camera observing thefundamental light scattered at the same phosphor screen.
The fitting results are shown in Fig. 8b, resulting in (left)wFh ¼ 4:72 0:02 mm and (right) wFv ¼ 2:97 0:01 mm. In
such a way, we obtained a beam divergence ratio of theFfifth harmonic compared to the fundamental as w5th
h =wh F
0:42 and w5th
theoreticalv =wv  0:43. According to the p
ﬃﬃﬃ
prediction [39], the ratio is expected to be 1= 5  0:45,
which is in good agreement with the above experimental
observation. Thus, we confirmed that only the fifth harmonic was successfully outcoupled from the fsEC as theGaussian beam using our VUV-OC.

rate of more than 4,000 cps from an Inþ . This counting rate
could dramatically reduce the detection time. Further
increase of the fundamental fs comb power can be achieved
using an injection locking amplifier [33], but the scaling of
the VUV power does not follow the perturbative approximation any more. Nevertheless, increase in the VUV poweris expected, as has been reported in Ref. [51], in whichXUV radiation of 77 lW at 72 nm has been generated as
the 11th harmonic of the amplified Ti:S oscillator. In such
power level of tens of microwatt, instead of focusing thequasi-CW beam tightly to a single ion, the beam could beloosely focused to illuminate a chain of multiple ions
simultaneously along the trapping axis. This might provide
a novel detection method for multi-ion optical clocks.

4 Conclusion

Acknowledgments The authors thank H. Hachisu, A. Yamaguchi,
Y. Li, S. Nagano, H. Ishijima, M. Kumagai, M. Kajita, Y. Hanado,
and M. Sasaki for discussions and support, and E. Sasaki for technicalsupport. Part of this work was supported by the Use-of-UVSOR
Facility Program (BL5B, No. 25-568) of the Institute for Molecular
Science.

In conclusion, we have reported a feasibility study on
detection of a single trapped Inþ at 159 nm VUV wavelength. We estimated a fluorescence photon counting rate
per the average VUV power to be n0 =P0  87 cps=lW in arealistic experimental condition, in which the ion is irradiated by a quasi-CW VUV beam generated via intracavity
HHG. This suggests that an average VUV power ofmicrowatt level suffices for detecting an Inþ ion. Toward
this goal, we have built an intracavity HHG setup for
generating VUV radiation using a novel efficient output
coupler (VUV-OC). Reflectance of the VUV-OC at anincident angle of 55 was measured to be 86:9 0:4 % at
159 nm and was achieved [80 % from 155 to 161.5 nm.
Our HHG setup with the VUV-OC has provided an output
of 6.4-lW VUV combs around 159 nm with an unexpected
exponential decay in power. This power level will yield
more than 500 cps detection of fluorescent photons, indicating that quantum-state discrimination of the ion is feasible with our present setup, provided that the power decay
problem is properly addressed.
With minor modifications and further improvements,
our HHG setup can be deployed to a wider range ofapplications to optical clocks based on ions with two outerelections. A Ti:S oscillator centered at 835 nm can be used
for generating VUV radiation at 167 nm as the fifth harmonic in a setup similar to ours, and our VUV-OC
approach provides efficient output coupling also at thiswavelength as shown in Fig. 3. The 167-nm radiation
generated in this way can be used for probing the 1 S0 –1 P1transition of Alþ . Boosting of the fundamental power up to
1 W is possible with commercially available fs combs, andit gives a peak intensity of 3  1013 W/cm2 in our setup. In
this perturbative regime [10], the HHG power scaling canbe roughly estimated based on our experimental data
shown in Fig. 6c. An average VUV-comb power of 50 lW
is estimated for the 1 W input, corresponding to a detection

123

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