# Two-photon excitation and absorption spectroscopy of gaseous and
supercritical xenon

Thilo vom Hövel<EMAIL_ADDRESS>Franz Huybrechts  Eric Boltersdorf
Christian Wahl  Frank Vewinger  Martin Weitz  Institut für Angewandte Physik,
Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany

###### Abstract

Spectroscopy of gases under high-pressure conditions is of interest in various
fields such as plasma physics and astrophysics. Recently, it has also been
proposed to utilize a high-pressure noble gas environment as a thermalization
medium to extend the wavelength range of photon Bose-Einstein condensates to
the vacuum-ultraviolet regime, from the presently accessible visible and near-
infrared spectral regimes. In this work, we report on experimental results of
two-photon spectroscopy of gaseous and supercritical xenon for pressures as
high as $95\text{\,}\mathrm{bar}$, probing the transitions from the $5p^{6}$
electronic ground-state to the $5p^{5}6p$ and $5p^{5}6p^{\prime}$ excited-
state configurations. Aiming at the exploration of possible pumping schemes
for future vacuum-ultraviolet photon condensates, we have recorded degenerate
two-photon excitation spectra of such dense xenon samples. In further
measurements, we have investigated whether irradiation of an auxiliary light
field can enhance the reabsorption of the emission on the second excimer
continuum of xenon, which is subject to a large Stokes shift. To this end,
absorption measurements have been conducted, driving the $5p^{6}\rightarrow
5p^{5}6p$ two-photon transitions nondegenerately.

##  I Introduction

The spectra of gases under high-pressure conditions are known to show a range
of universal features, such as the applicability of the thermodynamic Kennard-
Stepanov relation and Kasha’s rule [1, 2, 3, 4, 5], caused by a thermalization
of internal energy levels induced by frequent collisions between constituent
particles. Accordingly, it seems natural to exploit these universal features
for the thermalization of light [6]. In a thermally equilibrated gas that is
sufficiently cold and dense for the thermal de Broglie wave packets to
spatially overlap, quantum statistical effects emerge. For integer-spin
particles, Bose-Einstein condensation to the lowest-energy eigenstate can then
occur, as has been observed among others for ultracold atomic gases [7, 8],
exciton polaritons [9, 10], and photons confined to optical microcavities [11,
12, 13] or fibers [14].

The centerpiece of a typical experimental platform for photon Bose-Einstein
condensation is a dye solution-filled optical microcavity with a very short
(wavelength-size) mirror spacing, introducing a low-frequency cutoff for
cavity photons, as well as a matterlike (i.e., quadratic) dispersion relation.
Photons in the visible spectral range near $580\text{\,}\mathrm{nm}$
wavelength thermalize by repeated absorption-reemission processes to the
(rovibrational) temperature of the dye molecules, which are at room
temperature. The dye molecules fulfill the Kennard-Stepanov relation, a
Boltzmann-like thermodynamic frequency scaling between the absorption and the
emission spectral profiles. This universal relation applies to systems where
the rovibrational manifolds of both the lower and the upper electronic state
are in thermal equilibrium [15, 16, 5, 17], as is the case in this system due
to frequent collisions of dye molecules with surrounding solvent molecules
occurring on a ${10}^{-14}\text{\,}\mathrm{s}$ timescale, much shorter than
the radiative lifetime of the upper electronic state. In contrast to a usual
laser, no population inversion of the active medium is required to generate
coherent optical emission [18] and spontaneous emission can be retrapped in
the microcavity.

Bose-Einstein condensates of photons are accordingly expected to be an
attractive platform for a coherent light source in the vacuum-ultraviolet
spectral regime (VUV), where the operation of a laser requires high pump
intensities, given the $1/\omega^{3}$ scaling of upper electronic state
lifetimes, with $\omega$ as the optical frequency. Since in this spectral
regime dye molecules cannot be employed as the thermalization medium due to a
lack of suitable transitions, earlier work [19, 20] suggested to use noble
gases exhibiting closed electronic transitions in this wavelength range, e.g.,
around $147\text{\,}\mathrm{nm}$ wavelength for the xenon $5p^{6}\rightarrow
5p^{5}6s$ transition at high pressures. The frequent interatomic collisions
occurring in such dense gas samples can lead to the thermalization of the
quasimolecular collisional manifolds in both ground and electronically excited
states, expected to induce a Kennard-Stepanov frequency scaling between
absorption and emission spectral profiles [5], as necessary to enable the
thermalization of photons. Other than in dilute gases, at pressures in the
$100\text{\,}\mathrm{bar}$ regime, the collisional line broadening of gas
atoms typically becomes comparable to the thermal energy in frequency units
$k_{\text{B}}T/\hbar$, and thermalization of photons can become effective.

A further demand on a thermalization medium is a large reabsorption
probability for radiation in the spectral emission region, such that in future
microcavity-based experiments the confined radiation is absorbed and reemitted
multiple times, as necessary to establish thermal contact between the photons
and the medium. For xenon, a schematic of the quasimolecular potential curves
of the relevant electronic levels in a binary collision picture is shown in
Fig. 1(a). The lowest-energy absorption line ($5p^{6}\rightarrow 5p^{5}6s$) is
near $147\text{\,}\mathrm{nm}$ wavelength [21]. For gas pressures exceeding a
few-hundred millibar, emission is observed on the so-called second excimer
continuum at around $172\text{\,}\mathrm{nm}$ wavelength, subject to a Stokes
shift [22] of about $25\text{\,}\mathrm{nm}$, as understood from the
quasimolecular potential curves. This large energetic gap between absorption
and emission leads to a small reabsorption probability for radiation emitted
on the second excimer continuum. A closing of this energetic gap could be
enabled by an auxiliary light field, facilitating two-photon transitions from
the electronic ground state to the higher-energetic states of the $5p^{5}6p$
or $5p^{5}6p^{\prime}$ configurations with even total angular momentum [Figs.
1(b) and 1(c)]. On a fine-structure level, the $5p^{5}6s$ electronic state
consists of two components: one with $J=1$, linked by an optically allowed
transition to the $5p^{6}$ $(J=0)$ ground state, and a metastable one with
$J=2$, which in the asymptotic limit is the lowest-energetic atomic fine-
structure component. While direct laser excitation of the metastable
$5p^{5}6s$ $(J=2)$ state from the ground state is dipole forbidden, the
metastable level can be populated via potential curve crossings of excited
quasimolecular states in dense gas systems with frequent interconstituent
collisions.

Available spectroscopic data of samples around the regime in between usual gas
and liquid phase conditions, where the collisional spectral line broadening is
of the order of the thermal energy in frequency units, are relatively scarce.
In earlier work, absorption and emission VUV spectra of xenon have been
recorded at pressures of up to $130\text{\,}\mathrm{bar}$ [23, 19, 20]. Two-
photon excitation spectra of the $5p^{6}\rightarrow 5p^{5}6p$ and
$5p^{5}6p^{\prime}$ transitions of xenon have been recorded in a pressure
range of up to $13\text{\,}\mathrm{bar}$ [24, 25, 26, 27, 28], with the
excitation usually detected by monitoring the rates of the second excimer
emission near $172\text{\,}\mathrm{nm}$ wavelength or those of the
intermediate infrared emission. For a fixed excitation wavelength of
$266\text{\,}\mathrm{nm}$, line profiles of the second excimer emission have
been analyzed at xenon pressures as high as $180\text{\,}\mathrm{bar}$ [20].
In the moderate-pressure regime, multiphoton ionization spectroscopy has been
performed for both atomic and diatomic xenon [29].

The aim of the present work is to obtain (V)UV spectroscopic data of such
dense xenon ensembles. We report on the observation of excitation spectra of
degenerate $5p^{6}\rightarrow 5p^{5}6p$ and $5p^{5}6p^{\prime}$ two-photon
transitions of xenon at pressures of up to $95\text{\,}\mathrm{bar}$. While,
in the gaseous regime, the spectral components of the transitions to the
individual upper states of the $5p^{5}6p$ and $5p^{5}6p^{\prime}$
configurations remain spectrally resolved, at higher pressures upon which the
supercritical regime is reached, the observed pressure broadening exceeds the
splitting between the individual configurations. Moreover, we present
$5p^{6}\rightarrow 5p^{5}6p$ two-photon absorption spectra of xenon, driven
nondegenerately [30] with radiation near the second excimer continuum around
$172\text{\,}\mathrm{nm}$ and visible spectral range photons near
$500\text{\,}\mathrm{nm}$ wavelength while monitoring the absorption of the
light field around $172\text{\,}\mathrm{nm}$. Our results suggest that the
large Stokes shift between absorption and emission of the xenon
$5p^{6}\rightarrow 5p^{5}6s$ single-photon transition can be compensated by
irradiation with an auxiliary light field, enabling the reabsorption of
radiation emitted on the excimer transition as required for photon
thermalization.

In the following, Sec. II describes the experimental setup used here and Sec.
III presents two-photon excitation spectroscopy studies of dense xenon
samples. Subsequently, measurements exploring the feasibility of Stokes shift
compensation by irradiation of an auxiliary light field are reported in Sec.
IV. Finally, Sec. V gives conclusions and an outlook.

Figure 1: (a) Schematic of the potential-energy curves in the xenon dimer
system. For the sake of clarity, only relevant states are shown; for a
complete visualization, see [26, 21, 31]. The quasimolecular ground state,
constituted by two colliding xenon atoms in the $5p^{6}$ state, is mostly
repulsive (the inset shows a shallow well around
$4.3\text{\,}\mathrm{\SIUnitSymbolAngstrom}$). The first excited state,
constituted by one atom each in the $5p^{6}$ and $5p^{5}6s$ states, exhibits a
pronounced potential well around $2.9\text{\,}\mathrm{\SIUnitSymbolAngstrom}$,
leading to the formation of bound excimers. For those quasimolecular states of
the higher-lying $5p^{5}6p$ and $5p^{5}6p^{\prime}$ configurations whose exact
potential-energy curve shape is not covered by the literature, horizontal
lines indicate the asymptotic energies. The dotted lines refer to potential
energy curves associated with the metastable $(J=2)$ component of the
$5p^{5}6s$ state. [(b), (c)] Electronic states within the $5p^{5}6p$ and
$5p^{5}6p^{\prime}$ configurations can be excited by two-photon transitions in
a (b) degenerate or (c) nondegenerate manner.

##  II Experimental Environment

Figure 2: (a) Setup for two-photon excitation spectroscopy. The exciting UV
beam is focused into the center of a xenon-filled high-pressure cell and the
resulting fluorescent radiation in the vacuum-ultraviolet spectral regime is
collected with a concave mirror and guided to a grating spectrometer. (b)
Setup for two-photon absorption spectroscopy. Broadband VUV radiation from a
laser-induced plasma is overlapped with a counterpropagating beam of tunable
laser radiation near $500\text{\,}\mathrm{nm}$ wavelength and guided through a
xenon-filled high-pressure cell. The transmitted VUV radiation is analyzed
with a spectrometer comprising an ICCD camera, allowing for time-resolved
detection. The inset shows a spectrum of the VUV beam generated in the laser-
induced plasma as detected by the ICCD-based spectrometer in the absence of
xenon in the high-pressure cell.

Our experimental instrumentation is based on a setup described in earlier work
[19, 20]. The centerpiece of the setup is high-pressure gas cells made from
stainless steel, equipped with MgF2 windows for optical access in the VUV
spectral regime and an optical path length of $2\text{\,}\mathrm{cm}$. For all
measurements described in this work, we use xenon (grade 4.8, Air Liquide).
The high-pressure cell is placed in a vacuum chamber, along with all optics
required to guide VUV radiation to and from the sample. The vacuum chamber is
evacuated to below $5\text{\times}{10}^{-5}\text{\,}\mathrm{mbar}$ to suppress
absorption of short-wavelength radiation by atmospheric gases [32, 33, 34].

To generate tunable UV radiation, we use a Q-switched pulsed laser (Spectra
Physics, model Quanta Ray PRO 250-10), providing radiation near
$1064\text{\,}\mathrm{nm}$ wavelength with a pulse energy of
$1400\text{\,}\mathrm{m}\mathrm{J}$, a pulse length of
$10\text{\,}\mathrm{ns}$, and a repetition rate of $10\text{\,}\mathrm{Hz}$.
After second-harmonic and subsequent sum-frequency generation, the resulting
light near $355\text{\,}\mathrm{nm}$ wavelength is used to pump an optical
parametric oscillator (OPO; GWU, model primoScan ULD400). For the excitation
spectroscopy measurements, its tunable emission in the visible spectral range
is frequency doubled and guided into the vacuum chamber through a viewport
[Fig. 2(a)]. To monitor the excitation beam wavelength, radiation scattered
off the viewport is guided to a fiber-coupled spectrometer (Thorlabs, model
CCS200). Inside the vacuum chamber, the excitation beam is focused into the
center of the high-pressure cell by a lens with $25\text{\,}\mathrm{cm}$ focal
length to a beam diameter near $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$. For
the detection of atoms transferred to the $5p^{5}6p$ and $5p^{5}6p^{\prime}$
excited states by two-photon transitions [see Fig. 1(b)], part of the ensuing
secondary emission near $172\text{\,}\mathrm{nm}$ wavelength leaving the high-
pressure cell through a window in a direction orthogonal to the excitation
beam is collected with a concave mirror and guided onto the entrance slit of a
commercial VUV spectrometer (McPherson, model 234/302). This consists of a
concave grating and an open-nose CCD camera (Andor, model iDus 420), whose
sensor chip can be cooled down to $-70\text{\,}\mathrm{\SIUnitSymbolCelsius}$.
For the chosen width of the entrance slit of
$10\text{\,}\mathrm{\SIUnitSymbolMicro m}$, the spectral resolution of the
spectrometer is about $0.1\text{\,}\mathrm{nm}$.

Figure 2(b) shows the setup used for the absorption spectroscopy measurements.
Here, a laser-induced plasma (LIP [35, 36, 37]) is used as a broadband light
source in the wavelength range near the second excimer continuum, implemented
by focusing a part of the emission of the pump laser and its second harmonic
(at 1064 and $532\text{\,}\mathrm{nm}$ wavelength, respectively) into a
stainless-steel cell filled with argon gas at a pressure of about
$1\text{\,}\mathrm{bar}$. After the radiation generated in the LIP is
collected and collimated, it is guided through a high-pressure spectroscopy
cell of the same type as used in the above-described excitation spectroscopy
setup via two dichroic mirrors (each exhibiting a reflectivity maximum
centered around $165\text{\,}\mathrm{nm}$ wavelength with a
$20\text{\,}\mathrm{nm}$ spectral width). The transmitted VUV radiation then
passes a VUV bandpass filter (maximum transmissivity at
$150\text{\,}\mathrm{nm}$, spectral width about $50\text{\,}\mathrm{nm}$) and
is focused onto the entrance slit of a commercial VUV spectrometer (H+P
spectroscopy, model easyLight). The latter comprises a concave grating and an
intensified CCD camera (Andor, model iStar 320T), allowing for gated detection
with gate widths as short as $2\text{\,}\mathrm{ns}$, much shorter than the
length of the plasma pulse, which is in the order of a few-hundred
nanoseconds. To allow for a driving of the $5p^{6}\rightarrow 5p^{5}6p$ two-
photon transitions via VUV radiation near $172\text{\,}\mathrm{nm}$ on its
passage through the xenon-filled spectroscopy cell [see Fig. 1(c)], the VUV
beam is spatially overlapped with an additional counterpropagating beam,
exploiting the dichroic mirrors’ transmissivity for visible light. This beam
is tuned to near $500\text{\,}\mathrm{nm}$ wavelength, well within the tuning
range of our OPO source. A spectrum of the VUV beam generated in the LIP, as
recorded with the intensified CCD camera, is shown in the inset of Fig. 2(b).
The observed spectrum is significantly affected by the reflection and
transmission profiles of the dichroic mirrors and the VUV filter, both of
which contribute to the required high suppression of the residual visible and
infrared scattered radiation. The width of the obtained spectrum is sufficient
to cover the wavelength range in which VUV absorption is expected.

##  III Two-Photon Excitation Spectroscopy Measurements

We have studied degenerate two-photon excitation of the xenon
$5p^{6}\rightarrow 5p^{5}6p$ transition, driven by two photons of the same
wavelength [see Fig. 1(b)]. Subsequent deexcitation to the intermediate
$5p^{5}6s$ configuration, or the associated strongly bound molecular dimer
levels of this excimer system, is possible either radiatively by emission of
an infrared photon or by collisional deactivation, via the indicated crossings
of the quasimolecular levels in Fig. 1(a). Reported collisional deactivation
rates are
$6120\text{\,}\times\mathrm{1}\mathrm{0}^{-12}\mathrm{{}^{3}}\mathrm{c}\mathrm{m}\mathrm{/}\mathrm{s}$
[38], depending on the particular level of the $5p^{5}6p$ configuration, which
at room temperature corresponds to a rate of
$0.142.8\text{\,}{\mathrm{bar}}^{-1}\text{\,}{\mathrm{ns}}^{-1}$. In the xenon
pressure range of 10 to $80\text{\,}\mathrm{bar}$ covered by the present work,
this causes the quench rate to clearly exceed that of spontaneous emission
(around $30\text{\,}\mathrm{ns}$ natural lifetime) and hence we expect the
transfer to the $5p^{5}6s$ configuration to be dominated by collisional
deexcitation. From this state, deexcitation to the $5p^{6}$ ground state
occurs radiatively, by emission of photons on the second excimer continuum
around $172\text{\,}\mathrm{nm}$ wavelength [39, 40, 24]. Figure 3(a) shows
experimental spectra of the laser-induced fluorescence for the three different
excitation wavelengths $249.8\text{\,}$, $252.8\text{\,}$, and
$256.4\text{\,}\mathrm{nm}$, corresponding to a tuning near the
$5p^{6}\rightarrow 5p^{5}6p[1/2]_{0}$, $5p^{5}6p[3/2]_{2}$, and
$5p^{5}6p[5/2]_{2}$ transitions, respectively, recorded at a xenon pressure of
$20\text{\,}\mathrm{bar}$. Within the experimental accuracy, the observed
emission spectra well agree in all three cases and do not or only weakly
depend on the excitation mechanism, as expected from Kasha’s rule, and can be
identified as the familiar emission spectra of the second excimer continuum.
Next, Fig. 3(b) shows the variation of the spectrally integrated fluorescence
yield on the square of the used pulse energy for an excitation wavelength of
$256.5\text{\,}\mathrm{nm}$. The data on this scale can be well fitted with a
linear function, as expected for a two-photon excitation [41, 42].

Figure 3: (a) Xenon emission spectra recorded at a pressure of
$20\text{\,}\mathrm{bar}$ for different excitation wavelengths driving the
$5p^{6}\rightarrow 5p^{5}6p$ two-photon transitions. (b) Relation between the
fluorescence yield (data points) and the square of the pulse energy of the
excitation laser beam, along with a linear fit (line), for a fixed excitation
wavelength of $256.5\text{\,}\mathrm{nm}$.

In the following, excitation spectroscopy measurements are presented, aimed at
determining the fluorescence yield. The measurements have been conducted at a
fixed pulse energy of $2\text{\,}\mathrm{mJ}$, corresponding to a
$2.5\text{\,}\mathrm{kJ}\text{\,}{\mathrm{cm}}^{-2}$ energy density in the
focus. Figure 4 shows the relation between the spectrally integrated
fluorescence yield and the wavelength of the exciting laser beam for different
xenon pressures. The main plot shows data for pressures in the range from 10
to $40\text{\,}\mathrm{bar}$, i.e., with the sample in the gaseous phase, and
the vertical dashed lines illustrate the expected positions for the
undisturbed $5p^{6}\rightarrow 5p^{5}6p[1/2]_{0}$, $5p^{5}6p[3/2]_{2}$, and
$5p^{5}6p[5/2]_{2}$ atomic transitions at $80\,119.0\text{\,}$,
$79\,212.5\text{\,}$, and $78\,119.8\text{\,}{\mathrm{cm}}^{-1}$
($249.6\text{\,}\mathrm{,}$ 252.5, and $256.0\text{\,}\mathrm{nm}$),
respectively; see the wave-number scale at the top of the figure [31]. In the
data set recorded at the lowest pressure of $10\text{\,}\mathrm{bar}$, the
corresponding transitions are clearly resolved experimentally, with three
distinct peaks at around $249.6\text{\,}$, $252.5\text{\,}$, and
$256.0\text{\,}\mathrm{nm}$ wavelength. In this regime, one observes a very
pronounced asymmetry of the three resonances. The blue edges are very steep
and their spectral positions coincide with those of the undisturbed atomic
transitions to within our $0.1\text{\,}\mathrm{nm}$ experimental wavelength
accuracy. In contrast, on their red edges, the observed features exhibit a
broadened shape. Strongly asymmetric line shapes have also been observed in
earlier work investigating the $5p^{6}\rightarrow 5p^{5}6p$ transition
manifold at lower gas pressures and can be ascribed to downward-bending
potential-energy curves of the $5p^{5}6p\,(J=0,2)$ states [24].

Figure 4: Excitation spectra of the $5p^{6}\rightarrow 5p^{5}6p$ two-photon
transitions in xenon. The main plot shows the relation between the spectrally
integrated fluorescence yield and the wavelength of the exciting laser beam
for different xenon pressures in the gaseous phase. The vertical dashed lines
indicate the expected spectral positions of the $5p^{6}\rightarrow
5p^{5}6p[1/2]_{0}$, $5p^{5}6p[3/2]_{2}$, and $5p^{5}6p[5/2]_{2}$ transitions
(from left to right) of the atomic xenon system [31]. The inset shows a data
set recorded at $80\text{\,}\mathrm{bar}$ pressure, well within the
supercritical regime. Note the extended wavelength range and different
vertical scale of the inset as compared to the main plot.

Around $251.2\text{\,}\mathrm{nm}$, an additional feature can be observed, its
spectral position coinciding quite well with the $5p^{6}\rightarrow
5p^{5}5d[1/2]_{0}$ transition expected at
$79\,771.3\text{\,}{\mathrm{cm}}^{-1}$ ($250.7\text{\,}\mathrm{nm}$), which
for atoms is dipole forbidden, but has been observed earlier and attributed to
a pressure-induced transition [43].

With increasing pressure, we observe both a broadening and a shift of the
resonances. The observed pressure shift of the $5p^{6}\rightarrow
5p^{5}6p[1/2]_{0}$, $5p^{5}6p[3/2]_{2}$, and $5p^{5}6p[5/2]_{2}$ resonances is
$9.3\pm 1.4\text{\,}$, $8.3\pm 1.2\text{\,}$, and $8.5\pm
1.1\text{\,}{cm^{-1}}\mathrm{/}\mathrm{bar}$ toward lower wave numbers,
respectively. At the highest pressure in the gaseous phase investigated here
of $40\text{\,}\mathrm{bar}$, the peaks partly overlap.

The inset in Fig. 4 shows a two-photon excitation spectrum recorded at a
pressure of $80\text{\,}\mathrm{bar}$ (note the different wavelength scale),
well within the supercritical phase, the transition to which occurs at a
pressure of $58.4\text{\,}\mathrm{bar}$ at room temperature [44]. At this
point, the extent of the pressure broadening renders resolving the individual
spectral components of the two-photon transitions to the $5p^{5}6p$
configuration unfeasible. The distinct change of spectral features upon
crossing into the supercritical regime has been observed earlier [20].

Figure 5 illustrates experimental spectra of two-photon transitions to the
higher-lying $5p^{5}6p^{\prime}$ configuration for different xenon pressures,
covering the wavelength range from 221 to $231\text{\,}\mathrm{nm}$. The
vertical dashed lines show the expected $5p^{6}\rightarrow
5p^{5}6p^{\prime}[1/2]_{0}$ and $5p^{5}6p^{\prime}[3/2]_{2}$ transitions at
wave numbers $89\,860.0\text{\,}$ and $89\,162.4\text{\,}{\mathrm{cm}}^{-1}$
($222.6\text{\,}$ and $224.3\text{\,}\mathrm{nm}$) [31]. The two resonances
are clearly observed experimentally, and again a pressure shift as well as a
broadening are visible, becoming much more pronounced in the supercritical
regime. In general, the pressure broadening of the resonances is less
pronounced here than in the case of the $5p^{6}\rightarrow 5p^{5}6p$
transitions, enabling the visualization of the data for all recorded pressures
in the same plot.

Figure 5: Excitation spectra of the higher-lying xenon $5p^{6}\rightarrow
5p^{5}6p^{\prime}$ two-photon transitions for different pressures. The
vertical dashed lines indicate the expected spectral positions of the
undisturbed $5p^{6}\rightarrow 5p^{5}6p^{\prime}[1/2]_{0}$ and
$5p^{5}6p^{\prime}[3/2]_{2}$ transitions.

##  IV Probing Stokes shift compensation with an auxiliary light field

In this section, we report results of a scheme devised to compensate for the
small reabsorption probability due to the Stokes shift of the emission
following one-photon excitation on the one-photon $5p^{6}\rightarrow 5p^{5}6s$
transition of xenon near $147\text{\,}\mathrm{nm}$. The strong binding of the
excited dimer state in dense ensembles leads to the formation of a Xe2 excimer
molecule, followed by the spontaneous emission of a highly Stokes-shifted
photon. As mentioned above, our aim here is to obtain a large spectral overlap
between absorption and emission in this excimer system at room temperature,
facilitating the efficient thermalization of vacuum-ultraviolet photons by
repeated absorption and emission processes in future microcavity-based
experiments.

Here we investigate whether reabsorption of photons around
$172\text{\,}\mathrm{nm}$ can be enhanced by irradiation with an auxiliary
light field around $500\text{\,}\mathrm{nm}$ wavelength, such that excitation
into higher levels becomes possible, here specifically in a nondegenerate two-
photon transition to the $5p^{5}6p$ manifold [see Fig. 1(c)]. For these
investigations, the absorption setup shown in Fig. 2(b) is used.

Figure 6(a) shows experimental data for the increase of the absorption of VUV
radiation around $172\text{\,}\mathrm{nm}$ wavelength at a xenon pressure of
$35\text{\,}\mathrm{bar}$, as induced by irradiation of the auxiliary light
field. For this measurement, the gate width of the ICCD camera was set to
$8\text{\,}\mathrm{ns}$, equaling the pulse length of the OPO source. The used
pulse energy was $15\text{\,}\mathrm{mJ}$, which in conjunction with a beam
diameter of $5\text{\,}\mathrm{mm}$ (matching that of the overlapping VUV
beam) and the pulse length corresponds to an intensity of
$96\text{\,}\mathrm{W}\text{\,}{\mathrm{m}}^{-2}$ (average over one pulse).
The three visible peaks at around $167\text{\,}$, $170\text{\,}$, and
$173\text{\,}\mathrm{nm}$ wavelength, for which an absorption signal of the
VUV radiation is observed upon irradiation with the auxiliary light field
tuned to a wavelength of $500\text{\,}\mathrm{nm}$, are attributed to the two-
photon transitions $5p^{6}\rightarrow 5p^{5}6p[1/2]_{0}$, $5p^{5}6p[3/2]_{2}$,
and $5p^{5}6p[5/2]_{2}$, respectively (see, also, our earlier data of Fig. 4
for degenerate two-photon spectroscopy with the same upper-state
configuration) [31]. The maximum value of the absorption coefficient of
$0.05\text{\,}{\mathrm{cm}}^{-1}$ corresponds to an observed reduction of
$10\text{\,}\mathrm{\char 37\relax}$ of the VUV signal at the corresponding
wavelength after passing through the $2\text{\,}\mathrm{cm}$-long cell.

Figure 6: Absorption spectra of the $5p^{6}\rightarrow 5p^{5}6p$ two-photon
transitions in xenon for a gas pressure of $35\text{\,}\mathrm{bar}$, driven
nondegenerately with VUV light in the spectral range near the second excimer
continuum and an auxiliary light field. (a) Experimental data, recorded with
the auxiliary light field tuned to a wavelength of $500\text{\,}\mathrm{nm}$.
The plot illustrates the observed variation of the VUV absorption in the gas
cell vs wavelength, showing an absorption spectrum of the $5p^{6}\rightarrow
5p^{5}6p[1/2]_{0}$, $5p^{5}6p[3/2]_{2}$, and $5p^{5}6p[5/2]_{2}$ two-photon
transitions (from left to right). (b) Corresponding data for different
wavelengths of the auxiliary light field, resulting in spectrally shifted
spectra. (c) The same absorption data as in (b), visualized as a function of
the wave-number sum of the two driving light fields, causing the absorption
spectra to lie on top of each other. For comparison, the dashed line
represents a (degenerate) two-photon excitation spectrum, recorded at the
comparable pressure of $40\text{\,}\mathrm{bar}$ (see, also, Fig. 4).

To obtain further evidence that the observed VUV absorption spectra are indeed
the consequence of a two-photon process, we have conducted measurements at
different wavelengths of the auxiliary light field, resulting in spectrally
shifted but otherwise unaltered absorption spectra [Fig. 6(b)]. Figure 6(c)
shows the same spectra visualized as a function of the wave-number sum of the
two light fields driving the two-photon transition. As expected, in this
visualization, the four signals well lie on top of each other. For comparison,
the dashed line represents the corresponding degenerate two-photon excitation
spectrum for the comparable gas pressure of $40\text{\,}\mathrm{bar}$ (as
shown in Fig. 4), with the data sets being in good agreement regarding their
general shape. It is visible that the relative heights of the three maxima are
roughly comparable, while in the case of degenerate two-photon excitation, the
$5p^{6}\rightarrow 5p^{5}6p[1/2]_{0}$ transition is more dominant than the
other lines. We ascribe this to the different excitation schemes used to drive
the respective transitions. The observed slightly larger linewidth in the
absorption data is attributed to the inferior wavelength resolution of the
gated VUV spectrometer used for these measurements. Our results suggest that
the reabsorption probability for VUV photons in the wavelength range around
the second excimer continuum can indeed be increased by involving higher-
energetic states of the xenon system.

##  V Conclusions

To conclude, we have reported work investigating two-photon spectroscopy of
xenon in the gaseous and supercritical regimes. Both excitation and absorption
spectroscopic measurements of the short-wavelength $5p^{6}\rightarrow
5p^{5}6p$ and $5p^{5}6p^{\prime}$ two-photon transitions at pressures of up to
$95\text{\,}\mathrm{bar}$ have been conducted.

Two-photon excitation appears to be a promising avenue to pump future
microcavity-based Bose-Einstein condensates of vacuum-ultraviolet photons, as
such a scheme allows the pump radiation to be at longer wavelengths than the
emission. Typically, for the wavelength range above $200\text{\,}\mathrm{nm}$,
powerful frequency-converted continuous-wave laser sources are widely
available and, e.g., the emission of a frequency-quadrupled Nd laser near
$266\text{\,}\mathrm{nm}$ wavelength may be utilized for pumping via two-
photon transitions to the $5p^{5}6p$ excited-state configuration of
supercritical xenon.

The key challenge to realize a photon condensate in the vacuum-ultraviolet
spectral regime is to identify a suitable thermalization medium. The
nondegenerate two-photon absorption measurements performed in this work have
illustrated that the large Stokes shift present in the xenon excimer system
can be compensated by irradiation of an auxiliary light field. To enhance the
magnitude of the reabsorption to a level suitable for the thermalization of
photons in a microcavity, an increase of the laser pulse intensity by three to
four orders of magnitude would be required, as should be feasible with a
stronger focusing of the auxiliary light field to around
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ beam diameter, which corresponds
to the typical size of the thermal photon cloud in present microcavity-based
photon BEC experiments.

A further attractive candidate system for the thermalization of vacuum-
ultraviolet photons is constituted by noble gas mixtures [45, 46], e.g., xenon
along with a lighter noble gas in the gaseous or supercritical phase, which,
in principle, is not restricted to pulsed operation. In such heteronuclear
systems, the excited quasimolecular states are much less strongly bound,
resulting in reduced Stokes shifts between absorption and emission spectral
profiles. Other candidate systems are mixtures of small heteronuclear
molecules, such as the carbon monoxide system, with a noble buffer gas.

###### Acknowledgements.

We acknowledge support of the Deutsche Forschungsgemeinschaft within project
WE 1748-25 (Grant No. 684913) and SFB/TR 185 (Grant No. 277625399).

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