ОПТИКА И СПЕКТРОСКОПИЯ, 2007, том 103, № 2, с. 235-239
КВАНТОВАЯ ОПТИКА И ПРЕЦИЗИОННЫЕ = ИЗМЕРЕНИЯ, ПРИЛОЖЕНИЯ К ГРАВИТАЦИОННЫМ
ЭКСПЕРИМЕНТАМ
УДК 535.14
ULTRA-SENSITIVE OPTICAL MEASUREMENT OF THERMAL AND QUANTUM NOISES
© 2007 r. T. Caniard, T. Briant, P.-F. Cohadon, M. Pinard, and A. Heidmann
Laboratoire Kastler Brossel, Case 74, F75252 Paris Cedex 05, France Received October 12, 2006
Abstract—We have developed an experiment of ultrasensitive interferometric measurement of small displacements based on a high-finesse Fabry-Perot cavity. We have observed the internal thermal noise of mirrors and fully characterized their acoustics modes with a sensitivity of 3 x 10-20 m/Hz1/2. This unique sensitivity is a step towards the first observation of the radiation pressure effects and the resulting standard quantum limit in interferometric measurements. Our experiment may become a powerful facility to test quantum noise reduction schemes such as the use of squeezed light or quantum locking of mirrors. As a first result, we present the observation of a cancellation of radiation pressure effects in our cavity. This back-action noise cancellation was first proposed within the framework of gravitational-wave detection with dual resonators, and may drastically improve the sensitivity of such measurements.
PACS: 42.50.Lc
1. INTRODUCTION
The sensitivity in interferometric measurements such as gravitational-wave interferometers is ultimately limited by quantum noise of light. A gravitational wave is detected as a phase difference between the two optical arms of a Michelson interferometer [1, 2]. Phase fluctuations of the incident laser beam introduce noise in the measurement whereas radiation pressure of light induces unwanted mirrors displacements. Both noises are conjugate and lead to a quantum limit for the sensitivity of the measurement [3-6]. Number of quantum noise reduction schemes have been proposed which rely on the use of squeezed light sent into the interferometer [7-9] or on the use of the quantum correlations induced by radiation pressure between phase and intensity fluctuations [10]. The possibility to implement these techniques in real interferometers gave rise to new methods such as the quantum locking of mirrors [11] or the detuning of the signal recycling cavity [12].
Similar quantum limits exist in position measurements with a single optical cavity, and several schemes involving a cavity with a movable mirror have been proposed either to create non-classical states of both the radiation field [13, 14] and of the motion of the mirror [15], or to perform QND measurements [16]. Very sensitive optical transducers have also been proposed for gravitational-wave detection with resonant detectors such as Weber bars [17] or dual spheres [18]. In the context of dual resonators, recent results [19] have theoretically shown that the sensitivity can be strongly improved by a back-action noise cancellation effect. This cancellation results from a destructive interference between quantum radiation-pressure effects on both resonators.
We present in this paper an experiment developed to study radiation-pressure effects in interferometric measurements. It is based on the ultrasensitive measurement of small displacements of mirrors in a high-finesse Fabry-Perot cavity. We have studied the internal thermal noise of mirrors at room temperature [20, 21], and improvements of our setup are in progress to reach the necessary sensitivity to observe quantum effects of radiation pressure. We have in particular designed a dual injection system in the high-finesse cavity in order to study the quantum correlations between the fluctuations of radiation pressure and the resulting mirror displacement. We have also started stable operation of the cavity at low temperature in a cryogenic environment, in order to reduce the thermal noise.
We first present in Sec. 2 the fundamental limitations enforced by light to interferometric displacement measurements. Our experimental setup and results on thermal noise are described in Sec. 3. We finally report in Sec. 4 the first experimental demonstration of back-action cancellation of radiation pressure observed in our cavity. The effect is equivalent to the one predicted in dual resonant gravitational-wave detectors.
2. POSITION MEASUREMENT AND QUANTUM LIMITS
The displacements of a mirror can be measured with a light beam reflected upon it. A displacement of the mirror induces a linear phase-shift of the reflected beam providing a way to read out the mirror motion. The mechanical response of the mirror to the radiation pressure of the incident beam disturbs the mirror motion and corresponds to the back-action of the measurement. When the mirror is part of a high-finesse optical
Frequency stabilization
Laser
Frequency lock-in
AOM
Spectrum analyzer
Mode cleaner
Int. stab.
1
Homodyne detection
Fl EOM
Probe beam
KT1 LN
Intensity detection
Signal beam
s-
Local oscillator
B
High-finesse cavity
Fig. 1. Experimental setup. The high-finesse cavity is composed of two high-quality cylindrical mirrors. The laser is frequency and intensity stabilized and is locked on the cavity resonance via an acousto-optic modulator (AOM). Two beams are sent into the cavity: an intense signal beam which can be intensity-modulated by an electro-optic modulator (EOM) in order to apply a radiation pressure force on the mirrors, and a weaker probe beam to monitor the mirror displacements. The phase of the reflected probe beam is measured by an homodyne detecting. For simplicity, polarizing selective elements are not shown.
cavity, the optical resonance enhances the optomechanical coupling between the mirror and the light, since the phase of the field reflected by the cavity becomes very sensitive to the mirror displacements. At resonance, the phase-shift 89™' of the reflected field is given by
e out e il
Ô9 = Ô9
+ 8 &(8 xSig + 8 xrad )/X
(1)
where X is the optical wavelength, ^ the cavity finesse, and 8q>in the phase fluctuations of the incident beam. The signal 8xslg can either be a physical displacement of the mirror, such as the response to an external force or the thermal noise, or an apparent variation of the cavity length due for example to a gravitational wave. The mirror displacement 8xrad is induced by the quantum fluctuations of the radiation pressure exerted by the in-tracavity field. In the framework of linear response theory, the mirror response 8xrad at frequency Q to the radiation pressure fluctuations 8Frad is proportional to the mechanical susceptibility x of the mirror:
8Xrad(Q) = X(Q)8Frad(Q) = 2hkx(Q)81(Q), (2)
where k is the field wavevector, and 8I are the intracav-ity intensity fluctuations.
The sensitivity of the measurement is actually limited by the phase noise of the light beam and by the radiation pressure noise. The phase noise 8^in is inversely
proportional to the square root VI of the mean incident intensity whereas the radiation pressure noise Sxrad
/-in
is proportional to VI . A compromise between phase and intensity noises then leads to the well-known Standard Quantum Limit [1-3], which corresponds to a minimum measurable displacement equal to
M x(Q)|.
3. EXPERIMENTAL SETUP
The experimental setup of our experiment is shown in Fig. 1. It is based on a very high-finesse cavity built with two high-quality cylindrical mirrors with very low losses and high damage threshold. We have obtained a finesse of230 000. The cavity is very short and compact (0.25 mm long) in order to reach a large cavity bandwidth and to reduce the influence of laser frequency noise.
The light beam entering the cavity is provided by a Titane-Sapphire laser working at 810 nm and frequency stabilized on an external reference cavity. The light beam is also intensity stabilized and spatially filtered by a mode cleaner. Due to the outstanding finesse of the cavity, we have observed a thermal bistability for incident powers greater than 300 ^W. To overcome this difficulty we lock the laser frequency onto the optical resonance of the cavity via a dual feedback loop which drives both the reference cavity at low frequency and an acousto-optic modulator (AOM) at higher frequency. This modulator is inserted in front of the mode cleaner and used as a frequency shifter via a double pass of the light through the modulator. This technique allows us to apply large variations to the light frequency without disturbing the other servo loops of the laser source. Moreover, the acousto-optic modulator is inserted before the mode cleaner and the intensity stabilization in order to preserve the other characteristics of the laser source.
We have also developed a dual-beam injection system in order to apply a radiation pressure force onto the mirrors via an intense incident beam (signal beam) and to detect the resulting motion by monitoring the phase of a weaker beam (probe beam) with an homodyne detection. This system is essential to characterize the displacements induced by the quantum fluctuations of radiation pressure, by observing the quantum correlations between the intensity of the reflected intense beam (which reproduces the fluctuations of radiation pres-
sure) and the phase of the weaker beam (which reflects the mirror displacements).
To avoid any spurious effects arising from a bad optical isolation between both beams or from electrical interferences when we apply a classical modulation onto the electro-optic modulator (EOM in Fig. 1) to produce a classical radiation pressure, the setup requires a perfect isolation of the phase of the probe beam with respect to the intensity of the signal beam. We have carefully eliminated unwanted optical reflections by inserting half- and quarter-wave plates in front of the highfinesse cavity to precisely compensate its birefringence effects. To eliminate the electrical interferences, we have built a specific electronic to drive the EOM at its minimu
Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.