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Optical frequency standard
Brief description of the research
The objective of this work is the realization of an all-optical ultra-stable microwave oscillator based
on the transfer of ultra-low noise signals between the optical range (ultra-stable laser) and the
microwave domain using an optical frequency comb.
Detailed description
Introduction
Quite generally, frequency standards with a high oscillation frequency profit from a better stability
than those with lower oscillation frequencies. Although optical sources are used for some
functionalities (optical pumping, laser cooling of atoms), all present primary and secondary
frequency standards are "microwave-based” as they probe an atomic transition whose frequency
belongs to the microwave part of the electromagnetic spectrum (1-10 GHz or 109-1010 Hz). Moving
from a microwave standard to an optical standard, in which the frequency belongs to the optical
spectrum (frequency in the range of 100 THz or 1014 Hz), will enable us to bridge a gap of ~5 orders of
magnitude on oscillation frequency; this offers a strong potential of improvement in terms of the
stability of the standard.
Optical frequency comb
Since optical frequencies are extremely high, they cannot be directly measured by frequency
counting. No optical detector is able to measure 1014 Hz, which is in sharp contrast to microwave
frequencies, where detectors for multi-GHz operation are commercially available. Until recently, it
was thus nearly impossible to precisely measure optical frequencies, as required for instance for the
definition of the second. There were only a handful of institutions worldwide being capable of
performing such experiments. They used an extremely complicated infrastructure involving about
ten stages of non-linear optical and microwave elements. These elements were necessary to bridge
the large frequency ratio between a microwave cesium transition and optical frequencies. Such a
“harmonic frequency chain” occupied an area of the size of several large rooms and was run by a
considerable number of specialized personnel.
The discovery of optical frequency combs in 1999 by T. Hänsch and J. Hall (Nobel prize in Physics in
2005) has revolutionized optical frequency metrology. An optical frequency comb can be regarded
like a ruler containing 105 – 106 equidistant
optical frequencies. This ruler can directly
and very precisely relate optical frequencies
(THz-PHz or 1012-1015 Hz) to microwave
frequencies (GHz or 109-1010 Hz). It allows us
therefore to establish a direct and highly
exact relation between microwave atomic
clocks and optical frequencies.
An optical frequency comb consists of an ultra-short pulse (<100 fs) laser source with a fixed
repetition frequency (0.1-1 GHz). The shorter the pulses used, the larger becomes the spectral
coverage of the optical comb. With 100 fs pulses, one typically gets to 200 nm spectral width around
1550 nm.
Applications of optical frequency combs
The optical frequency comb allows us the find an exact relation between optical frequencies and
microwave frequencies or vice-versa. This technique has various interesting applications:
Ultra-stable microwave oscillator
An important activity of the LTF in the domain of optical frequency standards concerns the
generation of an ultra-stable microwave signal using an all-optical approach. The basic idea is to
transfer the relative stability of an extremely stable laser (∆ν/ν = 10-15 in a second) from the optical
into the microwave domain. This will be done using an optical comb by “division” of the optical
frequency with a large cardinal number, approximately N = 100’000. The goal of this approach is the
replacement of the currently used hydrogen maser; an operation which would be advantageous
regarding cost as well as short and mid-term (t < 1’000 seconds) stability performance. The relative
stability goal is 10-15 in one second.
In order to achieve such a high performance level, an ultra-stable laser is required. Stabilization of
the laser will be done by locking it to a narrow cavity resonance of a high-finesse Fabry-Perot cavity
(F > 100’000) using the Pound-Drever-Hall method. While this locking would be excellent for short
term stability, locking to a molecular transition will minimize long term drifts. This stabilization
scheme will result in a laser linewidth reduction down to several Hz and a considerable decrease of
the frequency noise.
Since the short term stability of the laser is directly linked to the mirror distance of the Fabry-Perot
cavity, the latter itself should be as stable as possible. This requirement imposes severe constraints
on the design of the cavity mounting. More specifically, we will use a mirror spacer made from ultralow expansion (ULETM) glass which will be supported at only four carefully chosen points; this
measure will minimize mechanical deformations due to gravitational effects. In addition, the cavity
will be placed in a thermal shield thereby minimizing radiative and convective heat exchange with
the walls of the surrounding vacuum chamber. The vacuum chamber, finally, is at a pressure on the
order of 10-8 mbar and placed on an anti-vibration table.
A first, more traditional approach for the realization of such an ultra-stable microwave generator
consists in locking one tooth of the optical comb directly on the ultra-stable laser at 1.55 µm:
ν N = N ⋅ f rep + f 0 = ν laser ⇒ f rep = (ν laser − f 0 )/ N . This technique necessitates a self-referenced
frequency comb, in which the offset frequency f0 is measured and stabilized. In order to stabilize f0
using the so-called 1f:2f interferometry method, the optical comb must cover more than one octave
of the electromagnetic spectrum, which in turn requires a relatively complicated experimental setup
using non-linear fiber amplifiers.
In order to avoid this complication, a different approach will be studied in parallel. It consists of
difference frequency generation (DFG). This is a non-linear three wave process, where the output
frequency, called idler (I), corresponds exactly to the frequency difference (νI = νP-νS) between the
incoming pump (P) and signal (S) beam frequencies. Employing difference frequency generation in a
periodically poled Lithiumniobate (PPLN) crystal between two distant subsets of teeth at 1.16 µm (νP)
and 1.55 µm (νS), a third optical comb in the mid-infrared wavelength range at 4.6 µm (νI) will be
produced. One tooth of this new optical comb will then be locked to an ultra-stable mid-infrared
quantum cascade (QC) laser. This stabilization will again be achieved by locking the QC laser on a
resonance of a high finesse Fabry-Perot cavity (short-term stability) and on a molecular absorption
line (mid- and longer-term stability). The advantage of using a QC laser lies in its small physical
dimensions and its excellent intrinsic linewidth properties. Due to its symmetric gain curve and a
resulting nearly zero linewidth enhancement factor, its linewidth is expected to be a factor of 10-100
smaller than in a traditional diode laser.
A further important advantage of the DFG process is that the offset frequency must no longer be
known and stabilized: when the difference frequency is generated, the offset frequency f0 cancels in
any case:
ν I = ν P −ν S = ( N P ⋅ f rep + f 0 ) − ( N S ⋅ f rep + f 0 ) = ( N P − N S ) f rep = ν laser ⇒ f rep = ν laser /( N P − N S )
.
This avoids the costly and sophisticated requirement of using an octave-spanning frequency comb. A
spectrally narrower comb, which is much easier to handle and cheaper to fabricate, can be used. This
comb is then free to shift in frequency as only the constant difference between two of its teeth is
relevant for the locking to the QC laser and the stabilization.