Frequency
combs lasers and Ramsey-comb spectroscopy
On this page the background of
frequency comb lasers and the Ramsey-comb spectroscopy method is
given. To learn more about our three main spectroscopy targets for
fundamental tests, click on the following links: the 1S-2S
helium-ion experiment, the X-EF
molecular hydrogen experiment, and the Meta-stable helium experiment.
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Above:
frequency comb principle, below: our
Ti:Sapphire frequency comb (it looks
different now). We have two more
commercial frequency combs (linked to a Cs
clock and a sub-Hz ultra-stable laser)
based on Er-fiber with wavelength
extension fibers and frequency doubling to
cover approximately 500-2000 nm.
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Frequency
comb lasers - the starting point
All
the work in our lab is in one way or the other
based on frequency comb lasers. Frequency combs
are typically modelocked lasers, emitting
phase-coherent pulses at a regular interval. This
is the result of interference of many equidistant
modes (with spacing frequency f_rep, so that the
spectrum looks like a 'comb') that lase at the
same time. A Ti:Sapphire based comb laser can
easily emit 100 000 or more individual modes.
Using a nonlinear "f:2f" interferometer, and other
devices and electronics, it is possible to fix the
mode spacing f_rep, and the starting point of the
'comb' f_0 (also known as f_ceo), to an atomic
clock reference (a commercial Cs clock in our
case). All the modes of the comb are then known
with the same accuracy as the atomic clock.
In our lab we have 2 Er-fiber based comb lasers:
one as a facility for the group, and one ultra-low
noise version for the He+ experiment (both from
Menlo Systems). We also have a home-built
Ti:Sapphire frequency comb which we use for the H2
experiments and have used too for the Xe
experiment (see below).
The traditional way of using a frequency comb is
to use it as an optical 'tape measure'. One mixes
a bit of light from a laser you want to know the
frequency of with light from the frequency comb,
and count the resulting beat note. If you know the
mode of the frequency comb you are making a beat
with, then you can determine its frequency. In
this manner we perform precision spectroscopy, and
a few recent papers we have been involved in based
on such measurements are listed below.
S. Patra, M. Germann,
J.-Ph. Karr, M. Haidar, L. Hilico, V.I. Korobov,
F.M.J. Cozijn, K.S.E. Eikema, W. Ubachs, J.C.J.
Koelemeij
Proton-electron mass ratio from laser spectroscopy
of HD+ at the part-per-trillion level
Science 10.1126/science.aba0453 (2020)
N.
Holsch, M. Beyer, E.J. Salumbides, K.S.E.
Eikema, W. Ubachs, C. Jungen, F. Merkt
Benchmarking Theory
with an Improved Measurement of the Ionization
and Dissociation Energies of H2
Phys. Rev. Lett. 122, 103002 (2019)
R.J.
Rengelink, Y. van der Werf, R.P.M.J.W.
Notermans, R. Jannin, K.S.E. Eikema, M.D.
Hoogerland, W. Vassen,
Precision
spectroscopy of helium in a magnetic
wavelength optical dipole trap
Nature Physics
14, 1132 (2018)
C-F Cheng, J. Hussels,
M. Niu, H.L. Bethlem, K.S.E. Eikema, E.J.
Salumbides, W. Ubachs, M. Beyer, N. Holsch, J.A.
Agner, F. Merkt, T.G. Tao, S.M. Hu, C. Jungen,
Dissociation Energy of
the Hydrogen Molecule at 10(-9) Accuracy
Phys. Rev. Lett. 121, 013001 (2018)
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Ramsey-comb
spectroscopy principle
The
Ramsey-comb method has been invented in our lab
and uses only two pulses from a frequency comb,
which are amplified to an energy of typically a
few mJ. By taking only two pulses, the
repetition of the comb laser is compromised, and
therefore, initially, also the accuracy. This
has to do with phase shifts induced by the
amplification process, or any upconversion done
afterwards. The phase shifts are difficult to
control and measure, but there is a way around
it.
The
beginning: Ramsey spectroscopy with two
amplified frequency comb pulses
Even
so, with just two pulses we performed one of the
most accurate measurements (6 MHz at an optical
frequency of 6 PHz) in the extreme ultraviolet
at 51 nm using this method, published in Phys.
Rev. Lett. 105, 063001 (2010).
The principle is based on Ramsey-spectroscopy:
when a single pulse is resonant with a
transition in an atom or molecule, it can bring
the atom/molecule in a superposition state of
the ground and excited state. A second (phase
coherent, and carefully timed) pulse does the
same, and both can interfere (a more complete
picture is to use the Bloch-sphere
representation for the excitation process, but
the interference model works quite intuitive and
is valid for low excitation amplitudes). If one
then changes the delay between the pulses (by
delta t) then both contributions can be thought
to interfere, leading to a cosine-like
dependence of the excited state population,
depending on the transition frequency and the
pulse delay (and phase). Because the pulse delay
and phase are known from the frequency comb
laser, one can infer the transition frequency
from this signal (the cosine line in the picture
to the right).
If you can only have one 'macro' delay of time T
(typically 8 ns), then you need to know the
phase of the pulses very precisely, and this is
difficult in practice. However, we found a way
around the phase problem such that the original
accuracy of the comb laser is effectively
restored.
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Top:
Ramsey-comb laser principle and first
demonstration with Rb and Cs two-photon
spectroscopy (Nature Physics
10, 30-33 (2014)), bottom: The
Ramsey-comb excitation principle based on
a series of excitations with two-pulses at
different macro-delays nT.
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The solution: Ramsey-comb spectroscopy
Instead of using a single pulse pair, a new
laser setup enables us to repeat the Ramsey experiment
with many different multiples of the initial delay time
T (see the picture above). We call such a series as
'Ramsey-comb' measurement. The laser is constructed in a
way that the phase shift induced between the two pulses
remains constant to a high degree (a few mrad) while
jumping integer multiples of the repetition time T. If
we evaluate only the difference (phase) of the
Ramsey-signals, then the technical phase shift from
amplification actually drops out (it is common-mode). In
this manner we have shown kHz level accuracy, and better
is certainly possible! (while before, with only one
pulse pair, we could only reach MHz-level accuracy).
This means we have mJ level pulses available combined
with frequency comb accuracy, and we can use these
powerful pulses to drive multi-photon transitions or
convert the light through nonlinear optics to much
shorter wavelengths.
For an extensive description of the principles, see:
J. Morgenweg and K.S.E. Eikema
Ramsey-comb spectroscopy:
Theory and signal analysis
Phys. Rev. A 89,
052510 (2014)
http://dx.doi.org/10.1103/PhysRevA.89.052510
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Ramsey-comb
spectroscopy demonstrations
Our first experiments with Ramsey-comb excitation
where performed in the near-infrared (around 800
nm) with excitation of Rb and Cs atoms in a cell.
We then extended the wavelength range to the deep
UV (212 nm) by sequential frequency doubling for
excitation of Kr in an atomic beam, and to even
shorter wavelength (202 nm) for measuring the X-EF
transition in H2 (improving it by 100x).
In the most recent experiment we have used
high-harmonic generation, and demonstrated
Ramsey-comb spectroscopy at 110 nm from the 7th
harmonic of 770 nm (see references below). The
next (huge) step would be to excite the 1S-2S
transition in He+ at ~30 nm!
You can find more information about the H2,
He+,
and metastable-helium
experiments via the "Research" page.
Below are a few of our publications based on
Ramsey-comb spectroscopy:
L.S.
Dreissen, C. Roth, E.L. Grundeman, J.J. Krauth,
M.G.J. Favier, and K.S.E. Eikema,
Ramsey-comb precision spectroscopy in xenon at
vacuum ultraviolet wavelengths produced with
high-order harmonic generation,
Phys.
Rev. A 101, 143001 (2020)
L.S. Dreissen, C. Roth, E.L. Grundeman,
J.J. Krauth, M.G.J. Favier, and K.S.E. Eikema,
High-precision Ramsey-Comb Spectroscopy Based on
High-Harmonic Generation,
Phys.
Rev. Lett. 123, 143001 (2019)
R.K.
Altman, L.S. Dreissen, E.J. Salumbides, W.
Ubachs and K.S.E. Eikema,
Deep-Ultraviolet
Frequency Metrology of H2 for Tests of Molecular
quantum Theory
Phys.
Rev. Lett. 120, 043204 (2018)
R.K.
Altmann, S. Galtier, L.S. Dreissen, and K.S.E.
Eikema,
High-Precision
Ramsey-Comb spectroscopy at Deep-Ultraviolet
Wavelengths
Phys. Rev. Lett.
117, 173201 (2016)
J. Morgenweg, I. Barmes and K.S.E. Eikema,
Ramsey-comb
spectroscopy with intense ultrashort laser pulses
Nature Physics 10,
30-33 (2014)
Also see the News and
Views by Scott A. Diddams on page 8-9 of the same
issue:
http://www.nature.com/nphys/journal/v10/n1/full/nphys2852.html
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We gratefully acknowledge financial
support from the following organizations:
Questions? Contact: k.s.e.eikema@vu.nl
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