Deliverable 64
Report on WP3/T2: Tecnical report
O. Arcizet1, T. Briant1, P.-F. Cohadon1, M. De Rosa2,3, A. Heidmann1,
F. Marin2,4, C. Molinelli1, F. Marino2, M. Pinard1, P. Verlot1
1
CNRS - LKB, Paris, France
INFN, Sezione di Firenze, Italy
3
INOA, Sezione di Napoli, Italy
4
Dip. di Fisica, Università di Firenze, Italy
2
Coordinators: Antoine Heidmann (CNRS LKB), Francesco Marin (INFN – FI)
Measurements of photo-thermal effect at low temperature
Introduction
The displacement sensitivity of optical interferometers is limited by several dissipative phenomena.
One of such effects is the dynamic photothermal effect due to the fluctuations of the laser power
absorbed by the mirrors and converted into surface displacements through thermal expansion. The
purpose of Task T2 is to carry out a deep experimental investigation of this photothermal noise by
using the effect induced by an intensity modulation of the light entering a Fabry-Perot cavity. This
measurement can be performed over a wide frequency range, with the temperature ranging between
tenths of Kelvin up to room temperature, and with low-losses optical coatings.
During the last years, we have investigated the photo-elastic effect over a wide frequency range and
different spot sizes, including finite mirror size effects at low frequency and coating effects at high
frequency. We have developed a theoretical model to describe the observed finite size and coating
effects. We have also performed a theoretical investigation of possible instabilities and dynamics in a
high-finesse cavity where both radiation pressure and photothermal effects are considered. We have
finally built a very high-finesse cavity suitable for cryogenic application and started an experiment to
study photo-elastic effects at low temperature.
In this fourth-year report, we present the current modifications of the experimental setup in order to
measure the photothermal effect at low temperature, the results obtained with the updated setup
demonstrating a back-action noise cancellation which may be of interest for dual-resonators
gravitational-wave detectors, and the first results obtained at low temperature.
Experimental setup for photothermal measurements at low temperature
We have modified the setup used at the Laboratoire Kastler Brossel for the measurement of mirror
thermal noise at room temperature, in order to be able to study photothermal effects at low temperature.
During the first years, we have developed a new cavity with a very high finesse (230 000), which can
support a more intense incident beam (a few milliwatts) and suitable for cryogenic applications. During
the last year, we have successfully built and tested a dual laser injection in the high-finesse cavity.
We send in the cavity an intensity-modulated incident laser beam, frequency-stabilized on a very stable
reference cavity at room temperature. This intensity modulation will provide a modulated photothermal
effect observable on the light reflected by the cavity. To separate the observation of the photothermal
effect from the incident intensity modulation, we send another probe beam in the cavity to detect the
resulting mirror deformations. The new setup is shown in Figure 1.
Figure 1:
Experimental setup for the observation of thermo-elastic effects at low temperature. The
incident laser beam is divided in two parts before entering the high-finesse cavity in the cryostat: an
intensity-modulated beam (in red) induces thermo-elastic effects in the cavity, whereas the phase of a
meter beam (in blue) is detected by a homodyne detection to monitor the resulting mirror deformations
We have also improved the laser stability by using a more stable reference cavity and changing parts of
the electronics used for the frequency locking of the laser. Due to the larger cavity finesse, we have
observed a thermal bistability for incident intensity larger than 300 mW, which prevents to reach a
stable working point at the cavity resonance. We have thus improved the frequency locking in order to
reach a good stability at the cavity resonance for sufficiently high incident powers, by using a PoundDrever-Hall technique to lock the intense laser beam at the resonance. We have then obtained a stable
operation up to a few mW incident power. We have now two acousto-optic modulators in order to
change the optical frequencies of both signal and probe beams, so that we can compensate the
birefringence effects in the high-finesse cavity.
The experiment requires a perfect isolation of the phase of the probe beam with respect to the intensity
of the modulated beam. We have carefully eliminated unwanted optical reflections by inserting halfand quarter-wave plates to compensate birefringence effects. To prevent electrical interference, a
specific electronic circuit drives the electro-optic modulator at its minimum transmission with a halffrequency modulation, the system then delivering a modulation at the desired frequency. We have
finally reached a quantum-limited sensitivity at the 10-20 m/Hz level.
Observation of back-action cancellation
We have used our new setup with the dual laser injection to demonstrate the first effects of radiation
pressure in our high-finesse cavity, namely a cancellation of back-action noise in cavity-length
measurements, due to a destructive interference between radiation-pressure effects on both mirrors[1].
The cancellation has been observed thanks to a noisy intensity modulation of the intense beam entering
the cavity in order to mimic the quantum incident intensity fluctuations. We have also proven the
sensitivity improvement both in length and weak-force measurements, by applying respectively a
frequency modulation to the laser and an external force to the mirrors (see Figure 2).
This back-action cancellation effect may be useful to improve the sensitivity of wideband gravitationalwave detectors based on dual resonators. In dual spheres with optical readout, for example, the
fundamental modes of both spheres have different resonant frequencies and their responses to a
gravitational wave are out-of-phase in between the two resonances. The response is then enhanced by
the out-of-phase behaviour of the two modes in the intermediate frequency domain, resulting in a flat
response between the two resonances. In contrast, the radiation-pressure forces exerted on the two
resonators are equal and opposite, so that one gets a destructive interference between back-action
effects on both resonators: the global back-action noise is then cancelled and one gets an important
noise reduction on the whole frequency band between the two resonances, leading to a drastic
sensitivity improvement as observed in our experiment.
Figure 2:
Back-action cancellation and sensitivity improvement in response to a cavity length
variation. The signal (discrete peaks a), applied at different frequencies by a modulation of the laser
frequency, is only visible in presence of radiation-pressure noise (curve b) around the dips where backaction is cancelled by a destructive interference between the two mirrors' motion.
Cryogenic operation
We have developed a cryostat specifically designed for our high-finesse cavity, where the cavity is
thermally coupled by copper wires to the liquid helium tank, but mechanically connected to the input
windows in order to minimize the vibrations. Although we have been able to observe the optical
resonance of the cavity at low temperature, we did not obtain a sufficiently stable operation of the
cavity at resonance. We have thus tried a lot of improvements, including the change of optical access
and thermal shields, a servo control of the thermal drifts, the modification of the copper wires to
minimize the vibration transmission without degrading the thermal characteristics. Despite these
improvements, the thermal noise at low temperature (4 K) appears to be contaminated by an excess
noise due to an unstable working point of the cavity around the optical resonance. We have thus
decided to use a new commercial cryostat (Janis model ST500) which appears to have very small
mechanical vibrations and low thermal drifts. We have then been able to observe the thermal noise
spectrum of the mirrors at low temperature over a wide bandwidth, and the result is in very good
agreement with the observation at room temperature (see Figure 3).
Error!
Figure 3:
New cryostat used for the high-finesse cavity (left) and preliminary observation
of thermal noise spectra at room temperature (black) and at low temperature in the cryostat (red).
References
[1] “Observation of back-action cancellation in interferometric and weak force measurements”,
T. Caniard, P. Verlot, T. Briant, P.F. Cohadon, A. Heidmann, Phys. Rev. Lett. 99, 110801 (2007)