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

2 INFN, Sezione di Firenze, Italy

3 INOA, Sezione di Napoli, Italy

4 Dip. di Fisica, Università di Firenze, Italy

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 (230000), 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 300mW, 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 Pound-Drever-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 half- and 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 half-frequency modulation, the system then delivering a modulation at the desired frequency. We have finally reached a quantum-limited sensitivity at the 10-20m/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 gravitational-wave 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 back-action 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).

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)