# Room-Temperature Continuous-Wave Frequency-Referenced Spectrometer up to 7.5
THz

Michele De Regis  INO, Istituto Nazionale di Ottica-CNR, Largo E. Fermi 6,
Firenze I-50125, Italy  LENS, European Laboratory for Nonlinear Spectroscopy,
Via N. Carrara 1, Sesto Fiorentino (FI) I-50019, Italy  Saverio Bartalini
INO, Istituto Nazionale di Ottica-CNR, Largo E. Fermi 6, Firenze I-50125,
Italy  LENS, European Laboratory for Nonlinear Spectroscopy, Via N. Carrara 1,
Sesto Fiorentino (FI) I-50019, Italy  Marco Ravaro  INO, Istituto Nazionale di
Ottica-CNR, Largo E. Fermi 6, Firenze I-50125, Italy  LENS, European
Laboratory for Nonlinear Spectroscopy, Via N. Carrara 1, Sesto Fiorentino (FI)
I-50019, Italy  Davide Calonico  INRIM, Istituto Nazionale di Ricerca
Metrologica, Strada delle Caccie 6, Torino I-10135, Italy  Paolo De Natale
INO, Istituto Nazionale di Ottica-CNR, Largo E. Fermi 6, Firenze I-50125,
Italy  LENS, European Laboratory for Nonlinear Spectroscopy, Via N. Carrara 1,
Sesto Fiorentino (FI) I-50019, Italy  Luigi Consolino  INO, Istituto Nazionale
di Ottica-CNR, Largo E. Fermi 6, Firenze I-50125, Italy  LENS, European
Laboratory for Nonlinear Spectroscopy, Via N. Carrara 1, Sesto Fiorentino (FI)
I-50019, Italy<EMAIL_ADDRESS>
(August 27, 2024)

###### Abstract

The lack of coherent room-temperature sources in the whole terahertz spectral
window (0.3-10 THz) has significantly hampered the growth of scientific and
technological applications in this range. Among them, high-precision frequency
measurements of molecular transitions play a central role but remain an open
challenge. Here, room-temperature generation and detection of continuous-wave,
broadly tunable, narrow-linewidth THz radiation are presented, and their
application to high-resolution spectroscopy in the broad 1-7.5 THz spectral
range is demonstrated. This result has been achieved by implementing a
Cherenkov phase-matching scheme into a channel waveguide in a nonlinear
crystal. This simple approach, entirely based on robust telecom technology,
unprecedently merges in a single source an ultra-broad continuous wave
spectral coverage and a state-of-the-art accuracy ($\sim 10^{-9}$) in
molecular transition center determination.

August 27, 2024

##  I Introduction

The dream of a metrological-grade, continuous wave (CW) source spanning the
whole THz region is about 30 years old rev_luigi ; lewis , and dates back to
the Tunable Far Infrared (TuFIR) difference-frequency-generation (DFG)
approach evenson ; zink . This kind of source had proven able to perform high
resolution spectroscopy up to 6 THz in a “standard” configuration nolt , with
two examples at frequencies as high as 7.9 odashima1 and 9.1 THz odashima2 ,
thus challenging the most advanced present-day CW THz sources. However, its
low reliability, the low emitted power and the very bulky instrumentation,
have hampered for decades its widespread use. More recently, the simplicity of
its DFG scheme inspired more compact designs hindle ; scheller that, however,
remained far from the former record tunability range combined to metrological
performance. Ultrafast technology has very recently lead to the availability
of commercial THz sources for low resolution applications krok , although even
the most advanced metrological-grade systems could only be used as frequency
reference luigi_natcomm ; barbieri for THz Quantum Cascade Lasers (QCLs)-based
high-accuracy spectrometers saverio_prx . Nonetheless, in the last few
decades, the THz window has fostered a number of scientific and technological
applications, spanning fields as diverse as imaging in biomedicine massi ,
homeland security federici , environmental monitoring luigi_sensors .
In this framework, THz molecular spectroscopy has a key role and high
precision measurements on different molecular transitions have been reported
in the lower part of the THz spectrum, e.g. at 0.29 THz skryl , 0.62 THz hsieh
, 1.1 THz puzzarini , 2.5 THz saverio_prx ; bray ; luigi_sat and 3.3 THz
hagelshuer . Recent technologies, such as Frequency-Comb-based Photo-mixers
hindle ; mouret and Quantum Cascade Lasers (QCLs) saverio_prx ; luigi_sat ;
hagelshuer have demonstrated their capability to perform metrological grade
THz spectroscopic measurements. However, each of these set-ups has its own
potentials and drawbacks: for example, spiral-antenna emitters, used in photo-
mixing synthesizers, show a spectrum limited to 3 THz hindle . Similar
limitations occur for QCL-based spectrometers. Despite having proven a very
narrow emission linewidth miriam ; ravaro , QCLs are intrinsically limited by
the semiconductor material at high frequencies, with a present-day limit set
at about 4.7 THz in CW operation schrottke ; ohtani , while the widest
tunability range is restricted to 330 GHz qin . These limits, added to the
need of cryogenic cooling, have hampered the range of precise spectroscopic
measurements in the THz window. The most recent designs of DFG-based QCLs are
trying to remove these limitations, reaching a single-mode output power as
high as 4 $\mu$W, tuning in the 2-4.35 THz range lu , and, on a different
device, a spectral linewidth of 125 kHz at 20 $\mu$s luigi_io . However, high-
resolution applications have not been attempted on this kind of sources, yet.
In the set-up presented here, we preserve the simplicity of a DFG scheme,
combining it with rugged, reliable, compact and high-power telecom lasers. Our
THz source simultaneously achieves a three octaves spectral coverage (1-7.5
THz), thanks to the wide tunability range of the pump lasers, and $\mu$W-range
power levels, exploiting a waveguided Cherenkov emission scheme. Finally, the
presented source is applied to high-accuracy, because traceable to the primary
frequency standard, molecular spectroscopy, resulting in a state-of-the-art
$10^{-9}$ accuracy in the line centre determination, still preserving a room-
temperature detection scheme.

##  II Waveguided Cherenkov nonlinear generation

Most of the drawbacks of direct lasing devices, photoconductive antennas or
frequency multipliers can be overcome with a nonlinear generation approach.
Thanks to their anharmonic response to optically induced excitations, a wide
range of materials, i.e. semiconductors like GaAs rice ; zheng , GaSe shi and
GaP tanabe ; chang , organic materials (DAST) kawase1 ; kawase2 and
ferroelectric crystals such as LiTaO3 jepsen and Lithium Niobate (LN) hebling
; stepanov , can be exploited for THz generation. In fact, if we consider two
electric fields, $E_{1}$ and $E_{2}$ respectively, at angular frequencies
$\omega_{1}$ and $\omega_{2}=\omega_{1}+\omega_{THz}$, whose difference falls
in the THz range, when they are mixed in such non-linear media, coherent
radiation at other frequencies is produced, including the difference of the
incoming ones $\omega_{THz}$. However, the efficiency of a difference
frequency generation (DFG) process depends on the wavevector mismatch
$\Delta{\mathbf{k}}={\mathbf{k}_{1}}-{\mathbf{k}_{2}}-{\mathbf{k}_{THz}}$
among the three fields, limiting the volume of the nonlinear medium
effectively involved in the frequency down-conversion.
In particular, assuming both the pump fields $E_{1}$ and $E_{2}$ propagating
in the same direction (with velocity $c/n_{pump}$ ), only a finite thickness
of the nonlinear medium is involved in the emission process, namely the
coherence length given by $L_{c}=2\pi/\Delta k=2\pi
c/([\omega_{THz}(n_{pump}-n_{THz}cos\phi))]$.
Here, we have indicated as $n_{THz}$ the THz refractive index in the nonlinear
medium, and with $\phi$ the angle formed by ${\mathbf{k}_{THz}}$ with respect
to ${\mathbf{k}_{1}}$ and ${\mathbf{k}_{2}}$. Different techniques have often
been used to restore the phase matching condition in a collinear emission
geometry (i.e. with $\phi=0$) taking advantage of the material birefringence
shi or, as in the case of periodically-poled Lithium Niobate (PPLN) crystals,
of a spatially periodic modulation of the nonlinear susceptibility sasaki .
A disadvantage of collinear DFG schemes is the strong THz absorption,
typically affecting all the nonlinear materials and motivating the set-up of
non-collinear schemes. For example, M. Koch et al. scheller demonstrated
monochromatic THz surface emission from a PPLN crystal with a generation
efficiency about $10^{-8}$ W-1 and with an optical power in the milliwatt
range. However, the resonant cavity used to increase the pump intensity up to
500 W unavoidably implies a reduction in the tuning range, which is limited to
200 GHz.
In order to overcome such limitations, a different strategy to maintain the
phase matching condition stands in the Cherenkov emission scheme l'huillier ;
huiller:2007a ; deregis:2018 . Indeed, even having a uniformly distributed
nonlinear susceptibility, for a specific direction defined by the so-called
Cherenkov angle

$\displaystyle\phi_{c}=arccos\left(\frac{n_{pump}}{n_{THz}}\right),$ (1)

the perfect phase-matching condition $\Delta k=0$ is exactly fulfilled and the
THz radiation is coherently emitted along the whole crystal length L. Under
these conditions, the generation efficiency $\eta$, increasing $\propto
L^{2}$, is defined by the ratio $P_{THz}/(P_{1}P_{2})$ between the THz power
and the product of the pump beam powers:

$\displaystyle\eta=\frac{L^{2}d_{eff}^{2}\omega_{THz}^{2}}{\varepsilon_{0}c^{3}\pi^{2}n_{THz}n_{pump}^{2}r_{0}^{2}}e^{-(\omega_{THz}/\omega_{0})^{2}}$
(2)

where $d_{eff}$ is the effective nonlinear coefficient, $\varepsilon_{0}$ is
the dielectric constant of vacuum and $r_{0}$ is the waist of the pump laser
beams. In the previous expression, the cut-off frequency $\omega_{0}$ is
determined by the refractive indexes mismatch and by the radius $r_{0}$,
according to the expression
$\omega_{0}=2c/r_{0}(n_{THz}^{2}-n_{pump}^{2})^{-1/2}$. As a consequence,
Cherenkov phase-matching in bulk nonlinear crystals is limited to few THz,
and, in order to achieve a good efficiency in the high frequency part of the
THz spectrum, the pump beam waists have to be in the few-microns range. For
this reason, we propose a novel setup capable of extending the pulsed
operation of K. Suizu et al. Suizu:09 to CW broadband operation, confining the
pump beams radiation in a single-mode linear waveguide.
As a matter of fact, to achieve Cherenkov phase-matching, it is crucial that
the pump fields propagate in the nonlinear medium faster than the THz light,
as in the case of infrared pumps and LN crystals. Because of this latter
feature and of the strong nonlinearities roberts ; harada , combined with the
high photorefractive damage threshold bryan ; furuya and the low absorption
coefficient, in the order of $10^{-4}$ cm-1 in the infrared spectral region
schweig , 5% MgO-doped LN is widely used for THz experiments.

##  III Results and discussion

In our experimental setup, shown in fig.1, two commercial CW laser systems
(Toptica DL Pro and MOT/DL Pro), emitting at telecom wavelengths, provide
narrow linewidth (tens of kHz) radiation, tunable over several THz. A fraction
of the light available from these seeding lasers is sent to a wavelength meter
(Bristol model 721) that provides a measurement of the pump/signal emission
frequencies with an accuracy of about 100 MHz, while their frequency
separation can be continuously adjusted in the range of interest, from 1 to 8
THz. The two monochromatic sources seed two distinct fiber amplifiers: one
amplifier (A1 – IPG Photonics EAR-10K-C-SF, power up to 11 W) operates between
1540 nm and 1565 nm wavelength, providing a tunability range of about 3 THz.
For the other amplifier (A2) two models can be used, operating in two
different narrow bands: 1573-1577 nm (IPG Photonics EAR-7K-1575-SF, with a
power up to 7 W) and 1603-1607 nm (IPG Photonics EAR-3K-1605-SF, with a power
up to 3 W), respectively. The two available combinations allow generation in
the 0.97-4.57 THz and 4.54-8.12 THz spectral ranges, respectively, while the
DFG process transfers the spectral properties of the seed telecom lasers to
the THz beam. As shown in the following, the THz frequency scans, necessary to
perform molecular spectroscopy, are performed in different ways, depending on
how broad and how accurate the scan is needed.
The output beams of the two fiber amplifiers are overlapped by a non-
polarizing beam splitter, while two independent optical systems (not shown in
fig.1), one for each pump laser, allow for a fine adjustment of the beam shape
and polarization, in order to maximize the mode matching for an efficient
coupling to the channel waveguide.

Figure 1: Schematics of the experimental set-up. Black lines represent
electric connections, brown lines represent optical fibers. The shaded grey
panel represents the setup used for frequency referencing to the primary
frequency standard (see section B).

The transverse dimensions of the mode propagating into the waveguide, i.e. the
dimensions of the generating volume, are approximately 5x3 $\mu$m, so that THz
absorption by the nonlinear medium is negligible. Coherent emission occurs
along the whole 1 cm crystal length and, thanks to the high confinement of the
guided modes, the DFG optical process is enhanced inside the waveguide. The
Cherenkov angle is about 65o, with small variations within the tuning range,
and is not large enough to avoid total internal reflection. For this reason, a
silicon prism has been positioned on top of the generating surface, ensuring
(according to the Snell’s law) an efficient extraction of the THz light. A
cylindrical mirror with 1” focal length corrects the wide angular divergence
of the THz beam in the direction orthogonal to the waveguide, leading to a
fairly collimated THz beam, which is sent to the spectroscopic set-up.
The non-zero reflectivity of the crystal surfaces takes to a standing-wave
modulation of the confined radiation intensity during the frequency scans,
inevitably affecting the intensity of the generated THz field. Furthermore,
the total pump intensity, as high as $2.4\cdot 10^{7}$ W/cm2, induces thermal
drifts of the crystal length, whose effects are also present in the THz
signal. These effects were removed from the acquisitions by monitoring the
pump beams powers during the frequency scans, using a 10 Hz mechanical
modulation on one of the pump beams and a fast detector (an InGaAs photodiode
with 150 MHz bandwidth – Thorlabs PDA10CF-EC) placed at the waveguide output.
This setup provides a continuous monitoring of the guided mode intensities
and, therefore, allows retrieval of the generation efficiency $\eta$.

###  III.1 SPECTRAL COVERAGE, MODE-HOP FREE TUNABILITY AND GENERATION
EFFICIENCY

The generated optical power was detected in a non-coherent scheme, using a low
noise Golay-type detector (Tydex GC-1P) with a noise -equivalent power of
about $10^{-10}$ W Hz-1/2 at 10 Hz, and with a calibrated responsivity of 20
kV/W . The THz signal is modulated at 10 Hz by the mechanical chopper placed
along the optical path of one of the IR pump beams, and is then demodulated by
a Lock-in amplifier (Stanford Research Systems SR-830) integrating over
several modulation periods.
In Fig.2, two different broadband scans are shown, in order to demonstrate the
unprecedented CW spectral coverage achieved by this set-up. Wavelength tuning,
here, is determined by the motorized rotatable grating of the external cavity
of the laser seeding the A1 amplifier, Toptica MOT/DL Pro, with an accuracy
better than 1 GHz. The curves reported in Figs.2a and 2b were obtained by
varying the tunable laser wavelength between 1542 nm and 1563 nm with the
other laser emitting at 1575 nm and 1605 nm, respectively.
In order to protect the Golay detector from irreversible damage induced by
residual pump laser radiation, a 1 mm thick polypropylene (PP) filter was
placed before the detector itself. This ensures a 50% transmission of the THz
radiation, and a $10^{-6}$ attenuation factor for the undesired IR residual
radiation. Nevertheless, it introduces broad absorptions around 3.3 THz and
6.8 THz. Both these effects are well visible in the green traces of Fig.2a and
Fig.2b, respectively, showing the THz power detected in the whole generation
bandwidth. A lower but flatter and broader 25% transmission is obtained by
replacing the PP filter with a 1-mm-thick germanium filter (fig. 2 blue
traces). In this condition, the generation curve presents a cut-off at 7.5
THz, that can be probably ascribed to the well-known transverse optical phonon
resonance at 7.5 THz bakker , and to the two-phonon absorption winer arising
in the few mm thick silicon prism.
In the first spectral band, the maximum THz power detected by the Golay cell
is about 0.5 $\mu$W, while the telecom pump powers in the waveguide are 1.8 W
each. This leads to a maximum generation efficiency as high as $\eta=1.5\cdot
10^{-7}$ W-1. A similar efficiency is found in the second band, where a 0.2
$\mu$W power is detected at around 5.2 THz, with pump powers of 1.8 W and 0.8
W, respectively.

Figure 2: Generation curves corresponding to a tunable pump laser wavelength
scan from 1542 to 1563 nm. The fixed wavelength pump lasers operate at 1575 nm
(plot a) ) and 1605nm (plot b)). The blue and green lines were recorded using
a Ge and a polypropylene filter, respectively. The red trace shows the water
absorption profiles simulated using the parameters given in the HITRAN
molecular database.

A box with dry air purging was built along the THz-wave path (not shown in
Fig. 1) in order to reduce the absorption due to water vapor contained in the
laboratory air. Nevertheless, water absorption lines are clearly visible in
fig.2, and can be exploited as frequency calibration marks when comparing with
the absorption spectrum provided by the HITRAN database (red lines in Fig. 2).
The frequency step used in these acquisitions is 0.05 nm, corresponding to
around 6 GHz in frequency, thus comparable with water vapor linewidths at
atmospheric pressure.
In order to achieve a more accurate control on the emitted THz radiation, it
is possible to adjust the wavelength of the laser seeding amplifier A1 using a
piezoelectric tuning of the diode external cavity, driven by a temporized DC
signal. To assess the performance of this tuning mechanism, the generated THz
wave was collimated and sent through a spectroscopy cell, placed before the
detection stage (see fig. 1), and previously filled with low-pressure (in the
range 10-200 Pa) methanol vapors.
Several spectroscopic tests, performed along the whole generation span,
demonstrate that the source provides a 40 GHz mode-hop-free operation along
the whole generation bandwidth, and a tuning coefficient, necessary to
calibrate the frequency scans, could be retrieved (see Appendix B for
details).

Figure 3: Using the piezoelectric actuator on the cavity length of the CW
laser seeding the A1 amplifier, different ranges of THz frequencies can be
investigated: a) 40 GHz mode-hop free continuous spectrum of methanol vapors
at 200 Pa, 0.1 V/step, and simulated spectrum from JPL database. b) 2 GHz scan
at 200 Pa and 25 mV/step, corresponding to 6 MHz/step, Voigt fits of the
recorded transitions and simulated spectrum from JPL database. c) 90 MHz zoom
on the 4.094 transition of Methanol with 0.25 mV/step, corresponding to 60
kHz/step. The experimental data have been fit to a Voigt profile, while the
lower panel shows the fit residuals.

Fig. 3 shows the versatility of such spectrometer, and a comparison with a
simulation based on the Jet Propulsion Laboratory (JPL) molecular database is
shown. Fig. 3a shows the 40 GHz wide mode-hop-free continuous acquisition of
the methanol spectrum, with a gas pressure of 200 Pa and a step of 0.1 V on
the piezoelectric actuator. Fig. 3b shows a 2 GHz zoom around 4.094 THz,
acquired at the same methanol pressure and with a 25 mV step, corresponding to
a frequency resolution of about 6 MHz (see Appendix B for details). In order
to further zoom in the most intense of these transitions, the methanol
pressure was lowered down to 18 Pa, and the acquisition is shown in fig. 3c
over a 90 MHz span. It was recorded with a 0.25 mV step, corresponding to
about 60 kHz resolution in the THz frequency. The acquired profile was fitted
to a Voigt function, which provided an uncertainty on the line center
frequency $\Delta\nu_{C}=33$ kHz and a relative precision of
$(\Delta\nu_{C})/\nu_{C}=8.06\cdot 10^{-9}$.

###  III.2 HIGH-ACCURACY SPECTROSCOPIC MEASUREMENTS

In this section, the performance of our source in terms of high-accuracy
spectroscopy is shown. In order to provide an absolute scale for the THz
radiation, a telecom mode-locked femtosecond laser (Menlo Systems C-fiber HP)
was used as a frequency ruler. The details of the experimental setup are shown
in the grey panel of fig. 1.
The i-th tooth of the comb-like emission of the fs laser has a frequency:

$\displaystyle\nu_{i}=f_{off}+i\cdot f_{rep},$ (3)

where $f_{off}$ is the carrier-envelope offset frequency, and $f_{rep}$ is the
repetition rate frequency, adjustable around 100 MHz for our laser. The two CW
seed lasers are mixed with the closest teeth on a fast detector (Thorlabs
DET10C/M), namely the Nth tooth for the laser seeding the tunable A1
amplifier, and the Mth tooth for the laser seeding one of the two fixed
amplifiers A2. The resulting beat notes are phase locked with standard loop
systems (PLLs) to two synthesized local oscillators (LOs) at a frequency
around 30 MHz, using the seed laser driving current. When the two PLLs are
closed, the two laser frequencies can be written as:

$\nu_{M}=f_{off}+M\cdot f_{rep}+f_{bM}$ (4a) $\nu_{N}=f_{off}+N\cdot
f_{rep}+f_{bN},$ (4b)

where $f_{bN}$ and $f_{bM}$ are the two LOs frequencies, and their signs
depend on whether the beating tooth is at higher or lower frequency with
respect to the seed. The generated THz radiation will be:

$\displaystyle\nu_{THz}=\nu_{M}-\nu_{N}=(M-N)\cdot f_{rep}+f_{bM}-f_{bN}.$ (5)

The two LOs frequencies are generated by two synthesizers, disciplined by a
GPS-Rb-OCXO (Oven Controlled Crystal Oscillator) chain frequency standard,
while a disciplined frequency counter measures the repetition rate. The
uncertainties on the LOs are negligible ($<10^{-11}$), while the frequency
counter returns a 0.05 Hz uncertainty on the instantaneous measurement of
$f_{rep}$. In this configuration, the generated THz frequency can be directly
traced against the primary frequency standard. It is known with an accuracy
depending on the M-N term, and is in the order of few kHz.
When the PLLs on the seed lasers are active, control on the generated THz
frequency is achieved by tuning the mode-locked laser repetition rate. As
shown in the equation providing $\nu_{THz}$, a change of $\Delta f_{rep}$
translates in a $(M-N)\Delta f_{rep}$ change in the THz frequency. Such
acquisitions allow for a very fine tuning over hundreds of MHz scans,
providing an absolute frequency scale for spectroscopic acquisitions. In order
to test the spectrometer accuracy, a set of measurements was performed on
methanol vapor transitions. Such transitions, thoroughly studied for years and
tabulated in catalogues, were used as a benchmark for our set-up.

Figure 4: Measured dependence of the centre frequency on the gas pressure for
the two analysed transitions and corresponding linear fits. The intercept and
slope values from the fits give the absolute frequency and the pressure shift
of the considered line. The insets of the two figures show two acquisitions,
with their respective Voigt fit and fit residuals, for a pressure of 26 Pa.

The insets of figures 4a and 4b show two methanol absorption profiles, the
former reporting the methanol rotational transition
$(J,K,\upsilon_{T})=(14,6,1\rightarrow 15,7,1)$ at 4.094 THz, the latter the
transition $(J,K,\upsilon_{T})=(4,4,2\rightarrow 5,5,2)$ at 5.573 THz,
$\upsilon_{T}$ being the torsional quantum number. These two transitions lie
in two distinct bands covered by the two different fiber laser amplifiers
combinations. An integration time of 3 seconds was chosen as a trade-off
between a good signal-to-noise ratio and an overall measurement time of about
10 minutes. In both cases, the normalized transmitted intensity $I/I_{0}$ is
plotted as a function of frequency. Each recorded transition profile was
fitted to a Voigt profile (see Supplemetary Material). In order to retrieve
the absolute value of the center frequency $\nu_{C}$, a systematic analysis at
different methanol vapor pressures was carried out, and the pressure shift was
measured for both transitions: the linear fits are shown in figs. 4a and 4b.
The resulting transition frequencies are 4,093,879,377(37) kHz for the former,
corresponding to an absolute accuracy of $9.0\cdot 10^{-9}$, while for the
latter the retrieved value of 5,573,381,868(78) kHz results in a $1.4\cdot
10^{-8}$ absolute accuracy.
The obtained results were then compared with previous measurements performed
on the same transitions moruzzi , with the calculations performed by the same
authors, and with the JPL molecular database, based on the simulations by Xu
et al. xu . In particular, the experimental data of moruzzi were taken at a
pressure of 200 Pa, while the pressure shift was not measured. Therefore, we
also added to the comparison the measured frequency values from Ref. 50 but
frequency shifted according to our measured value of self-pressure shift
(-17.1 MHz/mPa for the first transition and 16.2 MHz/mPa for the second).
Regarding the transition at 4.093 THz, the comparisons are reported in fig.
5a. The JPL database value (4,093,878,690(58) kHz) has a discrepancy of about
690 kHz with respect to our data, while the agreement between the previous
measurement in moruzzi and the value from our work significantly improves when
applying the self-pressure shift to the measurements. Fig. 5b shows the
comparison for the transition at higher frequency. The JPL database reports
this transition with an absolute frequency more than 150 MHz away from all the
other values, while our data are much closer to the measurements from moruzzi
. The self-pressure shift coefficient of the two transitions, measured thanks
to the accuracy of our setup, allowed to improve the experimental data from
moruzzi , shifting the measured data closed to the theoretical ones for both
transitions. As a final consideration, when comparing the measurements
presented in this work and the pressure shifted measurements of moruzzi , we
retrieve for both considered transitions a discrepancy very close to 1.9 MHz.
This discrepancy, if confirmed for a larger number of transitions, could be
ascribed to a systematic error on one of the two experimental setups.

Figure 5: The absolute frequency of the two analysed transitions can be found
in the JPL molecular database (green) and both the measured (red) and the
theoretically predicted (blue) values reported in ref moruzzi . These results
are compared with the measurements from the present work (orange). We also
report the measured values from moruzzi , but frequency shifted according to
our measured self-pressure shift coefficient (empty red triangles) (a) A
comparison for the 4.0930 THz transition and (b) for the 5.573 THz one.

##  IV conclusions

In conclusion, we demonstrated high-accuracy spectroscopic operation of a room
temperature CW THz source based on rugged, compact and reliable telecom fiber
laser technology. Our setup uniquely combines, in a single source, an ultra-
broad spectral coverage, spanning from 0.97 to 7.5 THz; a $\mu$W-level
emission power; an absolute frequency reference, enabling measurements of
molecular transition frequencies at an accuracy $\sim 10^{-9}$. The achieved
level of accuracy, if systematically reproduced over a large set of
transitions of selected gases, could help to significantly improve molecular
models. Indeed, significant deviations have been found for the transition
frequencies measured in our work, as compared with previous results, even for
a long studied molecule like methanol. Moreover, the combination of high
resolution and accuracy of our set-up can help to compare previous data with
present ones, by using pressure shift data. Regarding systematic effects that
can affect the actual accuracy, it is worth noting that, besides the
collisional shift, other effects such as Zeeman shift, ac-Stark shift, or
blackbody shift are expected to contribute below the $10^{-10}$ accuracy
scale, and were therefore neglected in our analysis.
The broad spectral coverage of the presented source is enabled by the
simultaneous use of a Cherenkov emission scheme and strong light confinement
in a surface nonlinear waveguide, leading to a significant broadening of the
phase matching bandwidth. Moreover, thanks to the guided-wave approach, our
set-up reaches CW generation efficiencies as high as $1.5\cdot 10^{-7}$ W-1,
and grants power levels high enough for both room temperature detection and
high-accuracy THz spectroscopy. Compared to the metrological performance of
other state-of-the-art spectrometers, our precision is one order of magnitude
better than that achieved with photo-mixing-based synthesizers hsieh , and
comparable to that of the best QCL-based systems saverio_prx , needing however
liquid-He cryogenic temperatures to operate in narrow spectral ranges.
The current limit to the accuracy achievable with our setup is represented by
the Doppler-limited transitions. This limit can be overcome either by directly
performing sub-Doppler measurements in room-temperature samples in a cell
puzzarini ; luigi_sat ; wienold , that could require cryogenic detection due
to the power levels available, or by interrogating a cold gas sample in a
molecular beam insero ; santamaria . Similar approaches, exploiting the
narrower Doppler-free transitions, could get to a further improvement in the
measurement accuracy of at least one order of magnitude, i.e. better than
$\sim 10^{-10}$, thus taking THz measurements even closer to those that can be
performed in other, well developed, spectral regions.

## Acknowledgments

Authors would like to acknowledge support from: European Union FET-Open grant
665158 ‘’Ultrashort Pulse Generation from Terahertz Quantum Cascade
Lasers”-ULTRAQCL Project; European ESFRI Roadmap ‘’Extreme Light
Infrastructure”-ELI Project; European Commission-H2020 Laserlab-Europe, EC
grant agreement number: 654148.

##  Appendix A Crystal plate design

The Y-cut 5%-MgO-doped LiNbO3 (LN) crystal plate (by HC-Photonics corp.) has
8.3x10x0.5 mm3 size. Several channels (two slabs and nine channel waveguides)
are patterned on top of the -Y face with a depth of $\sim$2 $\mu$m. The
single-mode waveguides used in this work are oriented along the 10 mm long
side and were designed for optimal light confinement of near-IR radiation. The
effective mode size is about 5 $\mu$m diameter. In order to take full
advantage of the nonlinear properties of LN, the orientation of the optical
field polarization and the crystal optical axis were chosen parallel both to
the crystal plate surface and to the input facet.

##  Appendix B Mode-hop-free scans and tuning coefficient determination

A number of spectroscopic tests, performed on methanol vapors, were performed
along the whole generation span. These tests are useful to retrieve the
spectrometer performance in terms of mode-hop-free operation, and to retrieve
the frequency/voltage coefficient. Examples of such wide-span scans, with a
methanol vapor pressure of 200 Pa, are shown in Figs. 3a and 3b, and are
reported in the insets of fig. 6, for convenience.
The first and the last absorption dips, visible in the blue trace of Fig. 6a
inset, respectively correspond to the transition $(J,K)=(18,-7\rightarrow
19,-8)$ at 4.085 THz and $(J,K)=(15,-5\rightarrow 15,-4)$ at 4.125 THz with a
variation $(1\rightarrow 2)$ in the torsional state $\upsilon_{T}$. The
transition frequencies were retrieved from the measurements of the pump beam
frequencies provided by the wavelength meter (Bristol model 721), and were
confirmed by a one-to-one comparison between the experimental data and the
methanol spectrum, retrieved from the JPL molecular database (red line in Fig.
6a inset). Fig. 6a inset shows a 40 GHz mode-hop-free operation, that can be
replicated along the whole generation bandwidth. All the line centers have
been assigned and related to the amplitude of the DC signal used to tune the
diode external cavity, as shown in fig. 6a, allowing a precise calibration of
the frequency/voltage curve.
Measurements performed with smaller frequency steps provide an overview on
different line groups, with higher resolution. As an example, the five lines
highlighted by the dashed rectangle in Fig. 6a inset are shown in Fig. 6b
inset. In this 2 GHz wide scan, a linear calibration coefficient of 245 MHz/V
can be retrieved, as shown in Fig. 6b.

Figure 6: a) center frequencies retrieved for the transitions shown in fig. 3a
(replicated in the inset) b) Linear calibration of the piezo scan between
4.0935 and 4.0955 THz, a coefficient of 245 MHz/V is retrieved.

##  Appendix C Spectral lines analysis

The DC voltage signal used to achieve the high-resolution frequency scans was
calibrated comparing the acquired methanol spectrum with the corresponding
line-pattern provided by the JPL molecular database. The spectroscopic cell,
providing a pressure stability with drifts reduced to less than 1% in one
hour, was sealed with a 2 mm thick TPX window and a 1 mm PP window. The PP
filter was removed from the Golay-cell entrance window during the
spectroscopic measurements.
When a laser beam of a given intensity $I_{0}$ passes through an absorbing
material, the optical power density I, measured after a path $L$ within the
sample, is reduced according to the Lambert-Beer law:

$\displaystyle I=I_{0}e^{-\alpha(\nu,p,T)L},$ (6)

where $\alpha(\nu,p,T)$ represents the absorption coefficient and, for a gas
sample, results from the convolution of a temperature-determined Gaussian
profile (the Doppler contribution) with a Lorentzian term that takes into
account the collisional broadening. At room temperature, lowering the vapor
pressure to a few hundred Pa, the collisional width leaves off his dominant
role, and a Voigt profile has to be considered to take into account both the
Gaussian and the Lorentzian contributions.
The central frequencies of each spectral line are retrieved by fitting the
experimental data to the following expression:

$\displaystyle-
ln\left(\frac{I}{I_{0}}\right)=C+A\frac{2lnW_{L}}{\pi^{3/2}W_{D}}\cdot\int^{+\infty}_{-\infty}\frac{e^{-t^{2}}dt}{\left(\sqrt{ln2}\frac{W_{L}}{W_{D}}\right)^{2}+\left(\sqrt{4ln2}\frac{\nu-\nu_{c}}{W_{D}}-t^{2}\right)^{2}}$
(7)

Where $W_{D}$ and $W_{L}$ are the FWHM of the Doppler and Lorentzian
contributions, respectively.

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# Optical spectroscopy and ultrafast pump-probe study of structural phase
transition in 1T'-TaTe2

T. C. Hu  International Center for Quantum Materials, School of Physics,
Peking University, Beijing 100871, China  Q. Wu  International Center for
Quantum Materials, School of Physics, Peking University, Beijing 100871, China
Z. X. Wang  International Center for Quantum Materials, School of Physics,
Peking University, Beijing 100871, China  L. Y. Shi  International Center for
Quantum Materials, School of Physics, Peking University, Beijing 100871, China
Q. M. Liu  International Center for Quantum Materials, School of Physics,
Peking University, Beijing 100871, China  L. Yue  International Center for
Quantum Materials, School of Physics, Peking University, Beijing 100871, China
S. J. Zhang  International Center for Quantum Materials, School of Physics,
Peking University, Beijing 100871, China  R. S. Li  International Center for
Quantum Materials, School of Physics, Peking University, Beijing 100871, China
X. Y. Zhou  International Center for Quantum Materials, School of Physics,
Peking University, Beijing 100871, China  S. X. Xu  International Center for
Quantum Materials, School of Physics, Peking University, Beijing 100871, China
D. Wu  International Center for Quantum Materials, School of Physics, Peking
University, Beijing 100871, China  Songshan Lake Materials Laboratory,
Dongguan, Guangdong 523808, China  T. Dong  International Center for Quantum
Materials, School of Physics, Peking University, Beijing 100871, China  N. L.
Wang<EMAIL_ADDRESS>International Center for Quantum Materials, School of
Physics, Peking University, Beijing 100871, China  Beijing Academy of Quantum
Information Sciences, Beijing 100913, China

###### Abstract

1T'-TaTe2 exhibits an intriguing first-order structural phase transition at
around 170 K. Understanding the electronic structural properties is a crucial
way to comprehend the origin of the structural phase transition. We performed
a combined optical and ultrafast pump-probe study on the compound across the
transition temperature. The phase transition leads to abrupt changes of both
optical spectra and ultrafast electronic relaxation dynamics. The measurements
revealed a sudden reconstruction of band structure. We elaborate that the
phase transition is of the first order and can not be attributed to the
conventional density-wave type instability. Our work is illuminating for
understanding the origin of the structural phase transition.

###### pacs:

Valid PACS appear here

##  I INTRODUCTION

Transition-metal dichalcogenides (TMDS) have attracted tremendous interests
for their intriguing ground states, physical properties and potential
applications Wilson and Yoffe (1969); Ali  _et al._ (2014); Yu  _et al._
(2015). Those low-dimensional compounds of these systems often lead to charge
density wave (CDW) instability Wilson  _et al._ (1975); Morosan  _et al._
(2006); Valla  _et al._ (2004); Hu  _et al._ (2007); Borisenko  _et al._
(2009). Yet, many of those CDW-bearing materials are superconducting Van
Maaren and Schaeffer (1967). The interplay between the two very different
cooperative electronic phenomena is one of the pending issues in condensed-
matter physics. The origin of CDW is most commonly traced to fermi surface
nesting. However, the driving force for higher dimensional CDW formation in
compounds are rather complex so that many mechanisms were constantly proposed
Rice and Scott (1975); Castro Neto (2001); Kiss  _et al._ (2007); Johannes and
Mazin (2008); Shen  _et al._ (2008); Rossnagel (2011). The compounds such as
well-known Ta/NbX2 (X=S, Se, Te) with 1T and 2H sandwich structure provide
fundamental insight into the behavior of correlated electron systems. Among
the TaX2 (X=S, Se, Te) polytypes, the telluride TaTe2 exhibits two intriguing
commensurate CDW states but has not been well studied by spectrocopy yet.
Compare with octahedral polymorphs 1T-TaS2 and 1T-TaSe2, 1T’-TaTe2 presents
stronger electron-phonon interaction and larger lattice distortion. The ground
state of TaTe2 is metallic rather than Mott insulating. The trimerization of
Ta atoms in 1T structure lead to double zigzag chains and an overall
monoclinic distortion of the crystal lattice. So TaTe2 can be regarded as
distorted TaTe6 octahedra 1T’ structure with 3×1 “ribbon-chain” clusters
superstructure at room temperature. Undergoing a structural phase transition
at around 170 K, TaTe2 transforms into 3×3 “butterfly-like” clusters
superstructurevan Landuyt  _et al._ (1974); Sörgel  _et al._ (2006). The
transition leads to anomaly in specific heat, magnetic susceptibility and
electrical resistivity (distinct kink structure with hysteresis)Sörgel  _et
al._ (2006); Liu  _et al._ (2015); Chen  _et al._ (2017a). No different
polytypes with 1T and 2H structures have been found for TaTe2 as so far. The
low temperature (LT) phase could be fully suppressed and a new superconducting
phase emerges at T${}_{c}^{onset}$ $\sim$ 1.7-2.5 K when Tellurium (Te) is
partially replaced by Selenium (Se) Liu  _et al._ (2016); Luo  _et al._
(2015). Additionally, applying external pressure could achieved the bulk
superconductivity of TaTe2 between 4-6 K in the pressure range of 21-50 GPaGuo
_et al._ (2017). As for isostructural CDW compound 1T’-NbTe2 with 3×1
superstructure at 300 KBrown (1966), such a LT phase has not been observed but
exhibits superconductivity at Tc $\sim$ 0.5 KZhang  _et al._ (2019). Another
analogue layered compound IrTe2 with a 5d heavy transition metal element and
strong Te-Te interlayer interaction shows a structural phase transition and
transport properties anomaly as well Yang  _et al._ (2012). Whereas the
absence of gap opening in IrTe2 demonstrated by both optical study and angle
resolved photoemission spectroscopy (ARPES), chemical bonding states and
crystal field splitting theory were considered as origins of the
transitionFang  _et al._ (2013); Ootsuki  _et al._ (2013).

It is essential to know the origin across different CDW states in two-
dimensional CDW systems because of their close connection to superconductors.
Up to now, few theoretical works suggested that the origin of the CDW states
in TaTe2 were driven by fermi surface nestingSharma  _et al._ (2002); Miller
_et al._ (2018). On the other hand, limited experiment works mainly focused on
the measurements of the transport and structure propertiesLiu  _et al._
(2015); Chen  _et al._ (2017a, 2018); Gao  _et al._ (2018); Petkov  _et al._
(2020); El Baggari  _et al._ (2020); Luo  _et al._ (2021). Transport
measurements suggested possible occurrence of fermi surface reconstruction
just below TsLiu  _et al._ (2015); Chen  _et al._ (2017a). However, recently
Kar et al pointed that the fermi surface topology hardly changes across Ts by
their ARPES study on TaTe2Kar  _et al._ (2021). The available experiment
results were still controversial. Other spectroscopy technique detections are
still lacking. It is well-known that optical and ultrafast spectroscopy are
sensitive probes for bulk electronic properties of solids. Therefore, it is
significant to uncover the nature of the structural phase transition by above
techniques.

In this work, we performed combined temperature-dependent optical spectroscopy
and ultrafast pump-probe measurements on single-crystal 1T’-TaTe2 sample . The
optical reflectivity spectra suddenly change just below Ts over a broad energy
range, yielding evidence for reconstruction of fermi surface and an explicit
reduction of conducting carriers in the LT phase. However, no characteristic
feature of energy gap opening related to CDW formation is observed. Ultrafast
pump-probe measurement reveals dramatic change in the electronic relaxation
dynamics near Ts. With the temperature increasing across Ts, the amplitude of
transient reflectivity is enhanced enormously and the decay time becomes much
faster. Furthermore, a number of coherent phonons in LT phase were extracted
by reflectivity oscillations in time domain. Nevertheless, no amplitude mode
of CDW collective excitation could be identified. In combination with above
experiment results we elaborate that the structural phase transition is not of
a density wave type and can not be simply attributed to conventional fermi
surface nesting driven instability. Our work is illuminating for understanding
the transition of the different CDW states.

##  II RESULTS AND DISCUSSION

The single crystals of TaTe2 were synthesized by chemical vapor transport
method with iodine as transport agent. High-purity Ta powders (99.99%) and Te
pellets (99.999%) in a stoichiometric ratio (1:2) with additional iodine
(99.8%, 5 mg/cm3) were loaded into a quartz tube. All processes were operated
in a sealed glove box. Then the quartz tube was sealed under high vacuum and
heated at 560 ∘C - 480 ∘C in a two-zone furnaceGao  _et al._ (2018). After 10
days growth, shiny platelike single crystals (typical size of 4×2.5×0.02 mm3,
inset of Fig.1 (a)) were obtained. The temperature-dependent resistivity was
measured by a standard four-probe method with the cooling/warming rate of
2K/min in the ab plane. The measurement was performed in a Quantum Design
physical property measurement system (PPMS). Resistivity measurements, shown
in Figure 1(a), indicating metallic behavior with a small resistivity value of
about 2.1×10-4 $\Omega\cdot$cm at 300 K. Similar to many two-dimensional CDW
systems, TaTe2 remains metallic state at LT phase and the residual resistance
ratio $\left(RRR=\rho_{300\mathrm{~{}K}}/\rho_{2\mathrm{~{}K}}\right)$ is
about 14. The resistivity curve shows a significant kink hysteresis at around
160 K which suggests the phase transition is of the first order. X-ray
diffraction (XRD) experiment results at room temperature are shown in Fig.1
(b). The strong diffraction peaks of TaTe2 crystals can be indexed as (00L) of
monoclinic phase of TaTe2 (ICDD-PDF21-1201). It can be seen that the full
width at half maximum (FWHM) of the (001) Bragg peak is only about 0.05° in
the inset of Fig.1 (b), indicating the high quality of TaTe2 single crystal.
Detailed chemical compositions investigated by energy dispersive spectroscopy
(EDS) measurements show that the chemical atomic ratios are close to the
standard stoichiometric ratio (Ta:Te $\sim$ 1:1.96). All these sample
fundamental characterizations are in good agreement with reports in
literatureSörgel  _et al._ (2006); Gao  _et al._ (2018); Luo  _et al._ (2021).

Figure 1: Sample characterizations for TaTe2. (a) Temperature-dependent ab-
plane resistivity measurement, a structural phase transition is evident near
160 K. Inset: Single crystal picture of TaTe2. (b) Room temperature powder XRD
patterns of single-crystal and indexing. Inset: The full width at half maximum
(FWHM) of (001) brag peak is about 0.05°, indicating good quality of single
crystal.

The as grown ab-plane (001) optical reflectance measurements were performed on
the Fourier transform infrared spectrometer Bruker 80V in the frequency range
from 100 to 30000 cm-1. An in-situ gold and aluminum evaporation technique was
used to get the reflectance $R(\omega)$. The main panel of Fig.2 (a) shows the
reflectivity up to 12000 cm-1 at five selected temperatures. The inset
displays the experimental reflectance spectrum up to 30000 cm-1 at 300 K. A
good metallic response is observed in the $R(\omega)$ spectrum: At low-
frequency, $R(\omega)$ has high values and approaches unit at zero frequency
limit. Below 4000 cm-1, the frequency-dependent reflectivity decreases almost
linearly in the high temperature (HT) phase. This behavior is similar to the
high-temperature cuprate superconductors. $R(\omega)$ shows minor change as
temperature decreases from 300 K to 180 K. However, when temperature decreases
just below the structural phase transition temperature at 160 K, optical
reflectivity $R(\omega)$ shows an abrupt change. With further decreasing
temperature, the spectral change becomes very small. The very low frequency
$R(\omega)$ increases slightly and forms a small plateau in LT phase,
reflecting enhanced metallic dc conductivity and consisting with the above
resistivity measurements. In the meantime, two weak suppressions in the mid-
infrared region near 800 cm-1 and 2300 cm-1 could be illustrated.

The real part of optical conductivity $\sigma_{1}(\omega)$ was derived from
$R(\omega)$ through Kramers-Kronig transformation in Fig.2 (b). The Hagen-
Rubens relation was used for the low-energy extrapolation of $R(\omega)$. We
have employed the x-ray atomic scattering functions in the high-energy side
extrapolationTanner (2015). The main panel of Fig.2 (b) displays
$\sigma_{1}(\omega)$ below 12000 cm-1 at five selected temperatures, the inset
displays $\sigma_{1}(\omega)$ up to 30000 cm-1 at 300 K. The Drude-type
conductivity was observed in all spectra at low frequency. In HT phase, the
broad width of Drude peak indicates a large scattering rate of the itinerant
carriers. Upon entering the LT phase, the weight of Drude-type conductivity
was suddenly removed. The optical spectra kept almost unchanged at 10 K and 70
K. The overall spectral change reflects a significant band structure
reconstruction associated with the structural phase transition. In other
words, there are two totally different metallic states in HT and LT phase.

Actually, for some structural phase transitions that are relevant to CDW order
formation have some expected optical spectroscopic features: the formation of
an energy gap with related spectral change only at low energy. The so-called
case-I factor of CDW condensate would cause a sharp continuous rise in the
optical conductivity spectral just above the energy gap. With temperature
further decreasing the dip feature in reflectivity becomes more and more
prominent. These features were observed definitely in most of the typical
conventional CDW systems driven by fermi surface nesting such as rare-earth
tri-telluride (RTe3)Hu  _et al._ (2014), LaAgSb2Chen  _et al._ (2017b),
Bi2Rh3Se2Lin  _et al._ (2020) and CuTeLi  _et al._ (2021). On the contrary,
for a purely structural phase transition that is irrelevant to CDW order
formation, the band structure of HT and LT phase is entirely different. So
optical spectra would change suddenly over a broad range energy scale as
observed in BaNi2As2Chen  _et al._ (2009), IrTe2Fang  _et al._ (2013) and
RuPChen  _et al._ (2015). For TaTe2, the spectral change occurs in a wide
frequency range and no continually evident reflectivity suppression is
observed. The overall spectral change is similar to the latter characteristics
which are referred to the purely structural phase transition.

Figure 2: Temperature-dependent optical spectroscopy of TaTe2. (a)
temperature-dependent optical reflectivity measurements below 12000 cm-1,
Inset: Large energy scale range of 100-30000 cm-1 at 300 K. (b) temperature-
dependent optical conductivity below 12000 cm-1,Inset: Optical conductivity
spectrum with large energy scale range of 100-30000 cm-1 at 300 K.

In order to isolate the different components of the electronic excitations and
make quantitative analysis, we employ the Drude-Lorentz model to decompose the
optical conductivity. The Drude component represents the contribution from
conduction electrons while the Lorentz components are used to describe the
excitations across energy gaps and interband transitions. The general formula
for the Drude-Lorentz model is

$\sigma_{1}(\omega)=\sum_{i}\frac{\omega_{pi}^{2}}{4\pi}\frac{\Gamma_{Di}}{\omega^{2}+\Gamma_{Di}^{2}}+\sum_{j}\frac{S_{j}^{2}}{4\pi}\frac{\Gamma_{j}\omega^{2}}{\left(\omega_{j}^{2}-\omega^{2}\right)^{2}+\omega^{2}\Gamma_{j}^{2}}$
(1)

where $\omega_{pi}$ and $\Gamma_{Di}$ are the plasma frequency and the
relaxation rate of each conduction band while $\omega_{j}$, $\Gamma_{j}$, and
$S_{j}$ represents resonance frequency, the damping, and the mode strength of
each Lorentz oscillator, respectively. In general, a single Drude term is used
to extract the itinerant electron contribution but we found that two Drude
components could reproduce the low frequency conductivity much better. This
could be attributed to the multi-band characteristic of the TaTe2 naturallyLiu
_et al._ (2016). Similar two Drude component analysis has been applied to the
optical data of 1T'-MoTe2 and Td -WTe2Kimura  _et al._ (2019), pointing toward
a generic behavior for those multi-band systems. The general formula for the
Drude-Lorentz model is reproduced by two Drude components and one Lorentz
oscillator at 300 K. Below the transition temperature, two additional Lorentz
oscillators (Lorentz 2 and Lorentz 3) are required to fit the curve. Fig.3 (a)
and (b) shows the spectra and fitting curves at two typical temperatures 300 K
and 5 K, respectively. The second Drude term is much broader and has much
larger spectral weight than the first one. In LT phase at 5 K, both Drude
terms shrink substantially and two more Lorentz (L2 and L3) oscillations
centered at around 800 cm-1 and 2300 cm-1 could be resolved.

Figure 3: Drude-Lorentz fitting of optical conductivity for TaTe2. (a) $T$=300
K. (b) $T$=5 K.

The general plasma frequency is obtained as
$\omega_{p}=\left(\omega_{p1}^{2}+\omega_{p2}^{2}\right)^{1/2}$ for overall
perspective, the calculated $\omega_{p}$ decreases from 22800 cm-1 to 15200
cm-1 across phase transition. The overall plasma frequency indicates that a
majority of itinerant charge carriers are suddenly reduced across the
transition. In the meantime, as evidenced by the narrowing of the Drude peak,
both of the scattering rates drops violently, from 720 cm-1 to 32 cm-1 for
Drude 1 term, from 3310 cm-1 to 854 cm-1 for Drude 2 term. The sharply
decrease of scattering rate makes even lower DC resistivity in LT phase
despite the partial free carriers removed. The measurement reveals a sudden
reconstruction of band structure.

Figure 4: Temperature-dependent ultrafast relaxation dynamics for TaTe2. (a)
$\Delta R/R$ in the temperature range of 5-200 K at some selected temperature
points. The dash lines are the single-exponential fitting curves: $\Delta
R/R(t)=A{\cdot}\rm{e}^{-t/\tau_{d}}+{C}.$ The amplitude A (purple cycles) in
(b) and decay time in (c) (blue squares) of the transient reflectivity
extracted from fits to the single-exponential above and below structural phase
transition Ts $\approx$ 160 K. Error bars represent the standard deviation of
the fit.

Our ultrafast pump-probe experiment could further support that the structural
phase transition is not of density wave type. The ultrafast pump-probe
experiment with standard reflection geometry configuration was performed in a
Ti:sapphire amplified laser (Spitfire Ace) of 800-nm pulses with 35-fs
duration at 1-KHz repetition frequency. To minimum sample heating effect as
possible, the fluence of pump beam is set to around 90 $\mu$ J/cm2 while the
probe beam is thirty times weaker than the pump beam. The spot size was
determined to be 110 and 90 $\mu$m in diameter by a 100 $\mu$m diameter
pinhole for the pump and probe spots, respectively. The pump and probe pulses
were set to cross-polarized and an extra grid-polarizer was just mounted
before the silicon detector (Thorlabs, DET36A2) in order to reduce the noise
from stray light. And the probe pulses were splitted for balanced detection in
order to improve signal noise ratio.

Figure 4(a) presents the photo-induced transient reflectivity as a function of
time delay on a freshly-cleaved TaTe2 at a number of selective temperatures.
All data were collected when the sample was warmed up from low temperature. A
sudden change was found precisely at the phase transition temperature (Ts
$\approx$ 160 K). This sudden electron relaxation dynamics change was also
observed just after structural phase transition in YbInCu4 and CsV3Sb5Zhang
_et al._ (2017); Wang  _et al._ (2021). Very prominently, with temperature
increasing across Ts, the amplitude of the photo-induced $\Delta R/R$ is
enhanced dramatically. In LT phase, the pump pulse induces a small rise
followed by a relative slow decay process in transient reflectivity while
there is a fast decay dynamics at HT phase. The measurement reveals that the
compound exhibits two quietly different electronic states just above and below
the Ts.

In order to quantitatively analyze the relaxation of the photo-excited
quasiparticles, we use a single-exponential function to fit the decay process:
$\Delta R/R=A\exp\left(-t/\tau_{d}\right)+C$, Where $A$ in the formula
represents the amplitude of the photo-induced reflectivity change, $\tau_{d}$
stands for the relaxation time and $C$ is constant for long lived thermal
diffusion process. The best fitting curves are shown as dashed lines in Fig.4
(a). The temperature dependence of the extracted fitting parameters $A$ and
$\tau_{d}$ of the single-exponential function are shown in Fig.4 (b) and (c).
It is evident that the compound shows totally different behaviors above and
below Ts. In the HT phase, the decay time of relaxation process gradually
increases from $\sim$ 0.4 ps at 160 K to $\sim$ 1.5 ps at 300 K, but becomes
almost temperature-independent in the LT phase with much slower process at
around 10 ps. As for the amplitude of reflectivity, the value varies a little
until the temperature rises close to Ts. With temperature changes across Ts,
the amplitude suddenly increases from $\sim$ 0.4 at 150 K to $\sim$ 1.6 at 160
K and the whole increasing process is a typical step shape like.

Figure 5:  Temperature-dependent coherent phonon spectroscopy for TaTe2 in
time/frequency domain. (a) Coherent phonon oscillations results in time-domain
after the decay background is subtracted. (b) The fast fourier transformation
(FFT) results of the data in (a). (c) Temperature-dependent intensity map
extracted from (b).

Ultrafast pump-probe spectroscopy could also provide coherent phonon
oscillations’ information after subtracting the electron dynamics background.
We obtained the coherent phonon oscillations in Fig.5 (a) and fast fourier
transform (FFT) results are displayed in Fig.5 (b). A detailed two-dimensional
intensity map as a function of temperature and frequency is presented in Fig.5
(c). The coherent phonon frequencies are in agreement with the previous Raman
experiment results on TaTe2Luo  _et al._ (2021). At HT phase, there are two
distinct peaks at 2.4 THz and 3.3 THz in the frequency domain. At LT phase,
more phonon modes abruptly appear due to the symmetry lowering caused by Ta
atoms further clustering, yielding evidence for the new structural modulation.
Remarkably, phonon at 3.3 THz even splits into one Ag mode phonon peak and one
Bg mode phonon peak which is in good agreement with the density functional
theory (DFT) calculations for the LT phonon spectraGao  _et al._ (2018). The
distinct phonon mode splitting near 3.3 THz further indicates that the phase
transition is a first-order phase transition. On the other hand, conventional
CDW condensate also has collective excitations referred to as amplitude mode
and phase mode. Usually, the energy level of amplitude mode is in the range of
terahertz frequency which could be identified by the ultrafast pump-probe
experimentChen  _et al._ (2017b); Lin  _et al._ (2020); Li  _et al._ (2021);
Demsar  _et al._ (1999, 2002); Yusupov  _et al._ (2008). The amplitude mode
exhibits more pronounced oscillations with temperature decreasing and usually
appears as the strongest oscillations. The mode frequency softens and behaves
like an order parameter when temperature gets close to the TCDWChen  _et al._
(2017b). Nevertheless, no such CDW amplitude mode could be identified from the
above phonon spectra at LT phase. Similarly, we noticed that amplitude mode
was also not observed in recently reported Kagome metal CsV3Sb5 coherent
phonon spectra in LT CDW phase Ratcliff  _et al._ (2021); Wang  _et al._
(2021). It could also suggest that the structural phase transition is not of
conventional density wave type from another aspect.

The above pump-probe experiment results reveal a rather specific situation:
There are two entirely different behaviors above and below structural phase
transition temperature. Both the transient reflectivity amplitude and decay
time change dramatically. A number of coherent phonon modes suddenly appear in
LT phase without clear trace of softening at the structural phase transition
temperature. No observed phonon modes in the LT phase phonon spectra could be
identified as CDW amplitude mode. All those features are well consistent with
the first-order phase transition and entirely different from a usual
conventional second-order CDW condensate behaviors.

Based on our experiment results, we could infer that the origin of structural
phase transition at Ts $\approx$ 160 K could not be attributed to the fermi
surface nesting like many typical two-dimensional CDW systems, i.e., RTe2 and
RTe3 (R=rare earth metal) Garcia  _et al._ (2007); Hu  _et al._ (2014).
Apparently, further theoretical calculations and analyses are still needed to
elucidate the driving force of the structural phase transition in 1T’-TaTe2
precisely.

##  III SUMMARY

In summary, we have performed a combined optical spectroscopy and ultrafast
pump-probe study on single-crystal 1T’-TaTe2 in an effort to understand the
electronic structure in the LT phase. The optical study revealed that the
electronic band structure reconstruction over a broad energy scale. And time-
resolved pump-probe measurements provide further evidence for the phase
transition is of first order that irrelevant to the conventional CDW order
formation. Both studies indicated that the structural phase transition was not
driven by the conventional CDW instability. Our research on 1T’-TaTe2 would
motivate further investigations on the origin or driving force of the phase
transition.

ACKNOWLEDGMENTS

This work was supported by the National Key Research and Development Program
of China (No. 2017YFA0302904), the National Natural Science Foundation of
China (No. 11888101).

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