The experimental plan of displacement- and frequency-noise free laser interferometer

Transcription

1 7th Edoardo Amaldi Conferene on Gravitational Waves (Amaldi7) Journal of Physis: Conferene Series 122 (2008) The experimental plan of displaement- and frequeny-noise free laser interferometer K Kokeyama 1, S Sato 2, A Nishizawa 3, S Kawamura 2, Y Chen 4, RL Ward 5,APai 4, K Somiya 4, and A Sugamoto 6 1 Graduate Shool of Humanities and Sienes, Ohanomizu University, 2-1-1, Otsuka, Bunkyo-ku, Tokyo, Japan 2 TAMA Projet, National Astronomial Observatory of Japan, , Osawa, Mitaka, Tokyo Japan 3 Graduate Shool of Human and Environmental Studies, Kyoto University, Kyoto , Japan 4 Max-Plank-Institut für Gravitationsphysik, Am Mühlenberg 1, Potsdam, Germany 5 LIGO Projet 18-34, California Institute of Tehnology, Pasadena, California 91125, USA 6 Ohanomizu University, 2-1-1, Otsuka, Bunkyo-ku, Tokyo, Japan keiko.kokeyama@nao.a.jp Abstrat. We present the partial demonstration of displaement- and laser-noise free interferometer (DFI) and the next experimental plan to examine the omplete onfiguration. A part of the full implementation of DFI has been demonstrated to onfirm the anellation of beamsplitter displaements. The displaements were suppressed by about two orders of magnitude. The aim of the next experiment is to operate the system and to onfirm the anellation of all displaement noises, while the gravitational wave (GW) signals survive. The optial displaements will be simulated by eletro-opti modulators (EOM). To simulate the GW ontribution to laser lights, we will use multiple EOMs. 1. Introdution Gravitational waves (GW) have been searhed for years by ground-based GW detetors [1-6]. However, they have not been deteted yet sine their amplitudes are quite tiny and the detetors are disturbed by a great amount of noise. The sensitivities of the detetors are limited by various noises, e.g., seismi- and gravity gradient disturbanes, thermal noises in mirrors and suspensions, and shot noises. Reently, theoretial investigation of the GW detetors whih are free from both the displaement noises of the optis and the laser frequeny noises have been proposed [7, 8]. In these two papers, it was shown that when an N-test-mass array (N >d+2,d is the spatial dimension of the array of test masses) onsists of multiple interferometers, a signal ombination whih does not sense displaement- and frequeny-noises but sense the GW ontribution an be onstruted. It is arried out by the fat that the GW ontribution to phase shifts of laser light takes a form different from that of optial displaements. In the next setion, the DFI onfiguration suggested in [9] will be introdued. In setion 3, the result of a proof-of-priniple experiment will be presented. The experimental plan of the next experiment will be explained in setion Ltd 1

2 7th Edoardo Amaldi Conferene on Gravitational Waves (Amaldi7) Journal of Physis: Conferene Series 122 (2008) MZI3 MZI1 A beamsplitter L D z 2 y C 2 x D 1 mirror L B MZI4 MZI2 C 1 Figure 1. The 3-D DFI onfiguration. It onsists of 4 Mah-Zehnder interferometers, MZI1, MZI2, MZI3 and MZI4. A and B are beamsplitters, and C 1,2 and D 1,2 are steering mirrors. Path lengths between mirrors and beamsplitters are L. The light path of MZI1 is A t D 2 B r - A r C 2 B t ; MZI2 is B t D 2 A r -B r C 2 A t ; MZI3 is A t C 1 B r -A r D 1 B t ; MZI4 is B t C 1 A r -B r D 1 A t ;. The subsripts r and t denote refletion and transmission at the beamsplitters. 2. DFI onfiguration Referene [9] proposed 2D and 3D optial designs of DFI implemented by four Mah-Zehnder interferometers (MZI). Figure 1 shows the 3D design that will be based. In this otahedron onfiguration, two MZIs are ombined to onstrut one bidiretional MZI where the two MZIs are ounterpropagating on the same optial path. The path length of AC 2, C 2 B, AD 2, and D 2 B are the same so that the MZI1 and MZI2 responses to the folding mirrors are idential. The displaements of the two folding mirrors are deteted redundantly by the two MZIs and an be eliminated learly by ombining the two signals. To eliminate the beamsplitter displaements, an additional pair of idential bidiretional MZIs is employed. Thus the two pairs of bidiretional MZIs sense the two beamsplitters redundantly and the displaement noises an be removed. The frequeny noises are aneled by eah MZI itself beause of the same arm lengths (AC 2 B and AD 2 B for MZI1 and MZI2, AC 1 B and AD 1 B for MZI3 and MZI4). The GW signals will remain in the ombined signal beause the GW and displaement noises ontribute to light propagation in different manners. As disussed in [9], the DFI signal has the GW response whih is proportional to (Ω GW L/) 2 for 3D onfiguration in the low frequeny range, where Ω GW is the GW frequeny. 3. Partial demonstration So far, the displaement noises of the folding mirrors were simulated by EOMs and a suppression of about 45 db was attained by using one bidiretional MZI [10]. The beamsplitter motion has also been simulated by an EOM and the suppression of the displaement noises was onfirmed [11]. For the next step, we atually atuated the beamsplitter, and onfirmed the anellation of the displaement-noise signals. In this experiment, the GW effets were not simulated Experiment Depited in Fig. 2 is the optial layout of this experiment. Four mirrors and two beamsplitters ompose two MZIs whih share the beamsplitters. These interferometers expressed in 2D orrespond to the ombination of MZI1 and MZI3 in Fig. 1. In this 2D onfiguration, the two input beams enter the interferometer. The inident beam of MZI1 is parallel to the x axis. The inident beam of MZI3 is in the angle θ 3 (π/4 <θ 3 < 3π/4) in respet to the x axis. The two beams are separated by beamsplitter A, then propagate the inline arms (AD 2 B and AC 1 B, for MZI1 and MZI3, respetively) and the perpendiular arms (AC 2 B and AD 1 B, for MZI1 2

3 7th Edoardo Amaldi Conferene on Gravitational Waves (Amaldi7) Journal of Physis: Conferene Series 122 (2008) ontrol C 1 MZI1 C 2 A y MZI3 PD3 B D 2 D 1 PD1 ontrol out x z Figure 2. The setup for the proof-ofpriniple experiment. The two MZIs are symmetri aross the AB axis. l and l denote the length between a beamsplitter and a mirror of MZI1 and MZI3, respetively. The path AD 2 of MZI1 is parallel to the x axis. The path AC 1 of MZI3 is in the angle θ 3 (π/4 < θ 3 < 3π/4) in respet to the x axis. The beamsplitter B are atuated by an attahed PZT. This displaement is sensed by the two MZIs redundantly. The two outputs (out1 and out3 for MZI1 and MZI3) are eletrially subtrated so that the beamsplitter displaement signals are suppressed. and MZI3, respetively). Here, we defined that the inline arm is the path transmitting A and the perpendiular arm is the path refleted by A. The two beams interfere after the seond beamsplitter, B. There are two output ports after the seond beamsplitter. The laser fields are deteted by the photo detetors, PD1 and PD3, for MZI1 and MZI3, respetively. One of the output signals is used to ontrol via mid-fringe loking. The other signal is to monitor the beamsplitter displaements. The PZT (piezoeletri transduer) is attahed to the beamsplitterholder to simulate displaement noises. The output signals of MZI1 (out1) and MZI3 (out3) are sent to the eletri subtrater to anel the displaement noises. When beamsplitter B is exited by the attahed PZT at an angular frequeny and an amplitude dl 0, the paths length are hanged. The output voltages of PD1 and PD3 an be respetively written as, V PD1 (ω) ω 0dl 1 V PD3 (ω) ω 0dl 3 (1) (2) where ω 0 is the angular frequeny of the laser light. dl 1 = 2dl 0 and dl 3 = 1 os(2θ 3) os(3π/4 θ 3 ) dl 0 are aused by the angles of the beamsplitter. Subtrating these two signals, we an remove the displaement-noise signals. In order to the maximal subtration, the photo intensities at the two detetors were adjusted in suh a way that the two output voltages agree at the outside the ontrol band. In addition, the ontrol gains were adjusted so that the ontrol ranges agree among the two MZIs Result Figure 3 shows the result of the displaement-noise suppression. The plots are the magnitude and phase of the transfer funtions from the atuated beamsplitter to out1, out3, and the subtrated signal, inluding the response funtions of the PZT and the photo detetors. The magnitude of out1 and out3 were tuned appropriately so that the displaement-noise signals are maximally aneled. About two orders of suppression was ahieved in a frequeny region in 3

4 7th Edoardo Amaldi Conferene on Gravitational Waves (Amaldi7) Journal of Physis: Conferene Series 122 (2008) Magnitude Phase magnitude 1 magnitude 2 subtrated magnitude frequeny [Hz] phase 1 phase 2 subtrated phase frequeny [Hz] Figure 3. Magnitude and phases of the transfer funtion from beamsplitter displaements to output signals. Solid-red and dashed-blue plots are magnitudes of the transfer funtion from the beamsplitter to PD1 and PD3, respetively, giving almost same response below about 1 khz. Dotted-blak lines are magnitude and phase of the DFI signal. Approximately two orders of magnitude of suppression an be seen from DC to 1 khz. The suppression depends on subtle adjustments of the balane between the two outputs. whih the PZT an be exited onsistently. Many mehanial resonants due to the PZT, and ones aused by oupling of the PZT and the beamsplitter were seen above 1 khz. In this region, the displaement-noise were not aneled. 4. Experimental Plan for 3D Full Configuration In our next experiment, the DFI will be onstruted in 3D spae and operated in the full onfiguration just as shown in Fig. 1. We will onfirm that all test-mass displaements are aneled while GW signals are retained in the DFI signals. The mirror displaements, beamsplitter displaements, and the GW effets should be simulated. The signals of the four MZIs will be extrated and ombined so that displaement noises disappear. The output voltage of eah interferometer an be written in frequeny domain V 1 (Ω) ω ] 0 [dx C2 e iωl/ + dx D2 e iωl/ + dx A e 2iΩL/ + dx B (3) V 2 (Ω) ω [ 0 dx C2 e iωl/ + dx D2 e iωl/ + dx A + dx B e 2iΩL/] (4) V 3 (Ω) ω 0 V 4 (Ω) ω 0 [dx C1 e iωl/ + dx D1 e iωl/ + dx A e 2iΩL/ + dx B ] (5) [ dx C1 e iωl/ + dx D1 e iωl/ + dx A + dx B e 2iΩL/] (6) where dx C1,dx C2 are the amplitudes of the displaement of C 1,C 2 and so on. Using eletri subtraters, we will obtain the DFI signal V DFI (ω), by ombining the signals; V DFI (Ω) = (V 1 (Ω) V 2 (Ω)) (V 3 (Ω) V 4 (Ω)). (7) As was given by Eq. (16) in [9], when the η ξ polarized GWs ome along the z diretion, the DFI signal will respond to the GWs in suh a way that H GW = iω 0he i2ωl/ [ (2 2)[1 e (4+2 2)iΩL/ ]+(2+ ] 2)[e 4iΩL/ e 2 2iΩL/ ]. (8) 4Ω 4

5 7th Edoardo Amaldi Conferene on Gravitational Waves (Amaldi7) Journal of Physis: Conferene Series 122 (2008) Magnitude frequeny [Hz] Figure 4. Transfer funtion from the GW signal to the DFI signal when L = 0.4 m. The peak frequeny depends on the length L. In our experiment, GW signals are expeted around 200 MHz. The GW effets will be simulated by using multiple EOMs. where we have denoted with h the amplitude of the GW. Figure 4 shows the plot of the response when the arm length L=0.4m. The GW signals retain around approximately 200 MHz for this sale. The frequeny of the sensitivity peak depends on L. Below the peak frequeny, the response is attenuated in proportional to f 2. It is noted that the DFI tehnique is not yet known to offer a pratial advantages in strain sensitivity at low frequenies for the GW detetors of urrent sensitivity beause there are merely little displaement noises at high frequenies where the GW signals are retained. The observation range an be lower for the DFI with longer arms Optial-displaement simulator The mirror noises are injeted by EOMs in the same way as the previous proof-of-priniple experiment shown in [10]. For example, when the displaements of mirror D 2 is simulated, we put an EOM near D 2. The beamsplitter noises will be simulated by two EOMs for one beamsplitter. Although there must be four idential EOMs to mimi the beamsplitter displaements naively, the two EOMs will be applied on the two optial paths beause of the fat that atuating two lengths differentially and atuating one length of the two are similar effets. For example, when the displaements of beamsplitter A is simulated, one EOM will be put near A on the AC 2 side, and the other EOM will be put near A on the AD 1 side GW simulator The GWs affets not only one point on the laser path but the whole path. Therefore putting an EOM on a laser path an not simulate suh effets beause it yields phase hanges at only one point where it is putting on. A straight forward way to simulate the real GW effets is to fill EOMs the whole laser paths. However, suh many EOMs overing laser paths will ause the serious redution of interferometer ontrast. Therefore we adopt a triky proedure. First, we will put an EOM at one point and take data then put the EOM at the next point and take data. Repeating this proedure and summing them, we will be able to dupliate the GW effet on the laser path. 5. Conlusions In this paper we have presented the demonstration of the partially implemented DFI. The noise suppression of about two orders of magnitude was ahieved. The displaement noise of a beamsplitter was injeted by the attahed PZT. In addition, the next experimental plan has been presented. The DFI in the 3D onfiguration will be built and operated. The GW-signal survival will be onfirmed around 200 MHz while all the optial displaements are aneled in the DFI signals. The optial displaements will be simulated by EOMs. 5

6 7th Edoardo Amaldi Conferene on Gravitational Waves (Amaldi7) Journal of Physis: Conferene Series 122 (2008) Aknowledgments The authors gratefully aknowledge the support of the researh Japan Soiety for the Promotion of Siene and Grant-in-Aid for Sientifi Researh. This researh is also supported in part by the United States National Siene Foundation grant PHY for the onstrution and operation of the LIGO Laboratory and the Siene. This paper has LIGO Doument Number LIGO-P Z. Referenes [1] A. Abramovii et al., Siene 256, 325 (1992) [2] D. Sigg et al., Class. Quantum Grav. 23, S51 (2006) [3] F. Aernese et al., Class. Quantum Grav. 23, S635 (2006) [4] H. Lük et al., Class. Quantum Grav. 23, S71 (2006) [5] M. Ando et al., Class. Quantum Grav. 22, S881 (2006) [6] D. E. MClelland et al., Class. Quantum Grav. 23, S41 (2006) [7] S. Kawamura and Y. Chen, 2004 Phys. Rev. Lett [8] Y. Chen and S. Kawamura, 2006 Phys. Rev. Lett [9] Y. Chen et al, 2006 Phys. Rev. Lett [10] S. Sato et al, 2007 Phys. Rev. Lett [11] S. Sato et al, in this volume 6