RareNoise. Livia Conti INFN Padova RareNoisePrincipal Investigator.

Transcription

1 RareNoise Livia Conti INFN Padova RareNoisePrincipal Investigator RareNoise is funded by a Starting Independent Researcher Grant of ERC (IDEAS/FP7). Start in: July 2008 Duration: 5 years The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/ )/ ERC grant agreement n The EC is not liable for any use that can be made on the information contained herein.

2 RareNoise: the team Livia Conti, PI experimentalist INFN Padova 1FTE Stefano Longo technologist INFN Padova 1FTE A.Basheed Gounda experimentalist INFN Padova 1FTE Mario Saraceni technologist INFN Padova 1FTE Matteo Pegoraro technologist INFN Padova 0.1FTE Michele Bonaldi experimentalist CNR-IFN Trento 0.5FTE Antonio Borrielli experimentalist CNR-IFN Trento 1FTE Lamberto Rondoni theoretician Politecnico di Torino 0.7FTE Paolo De Gregorio theoretician Politecnico di Torino 1FTE

3 Driving question: What are the spontaneous vibration fluctuations of an elastic body non at the thermodynamic equilibrium? eg subject to a steady-state thermal gradient Answer: small fluctuations: similar to those at the equilibrium large fluctuations: we don t know. Indications suggest they are more frequent than at the equilibrium. Moreover there is not a general rule to predict departure point from gaussian distribution At the thermodynamic equilibrium: the spontaneous vibration fluctuations have normal distribution and are quantified by the Fluctuation-Dissipation Theorem

4 Displacement [m/ Hz] Why this question? Non equilibrium systems are ubiquitous in nature: eg Universe, Earth, atmosphere, oceans. Interest in NonEquilibrium fluctuations so far limited to experimental investigations of behaviour of nanodevices and theoretical studies for motivating the 2 law of thermodynamics. So far only a few, ad-hoc applications of theoretical results to macroscopic systems Novel application: Gravitational Wave detectors They are macroscopic instruments but with displacement sensitivity approaching the quantum limit. 1e-15 LIGO Their noise budget is calculated very accurately; any subtle noise contribution must be taken into account: as both rms and statistics 1e-20 1e1 Frequency [Hz] 1e3 With their high sensitivity and long acquisition times GW detectors might prove the natural application of NonEquilibrium Theories to macroscopic systems

5 AURIGA: stationary gaussian GW detector 13.6 days, Epoch vetoes not needed apart from cryogenic maintenance Duty time 98% Very stationary Gaussian noise Outliers 9 events/day with SNR > 6 Event rate 3700 /day with SNR > 4 L. Conti - CdS Padova, 4 Feb 08 5

6 Non equilibrium in GW interferometers Thermal gradient due to laser power dissipated in the mirror How to compute the spontaneous vibration fluctuations ( thermal noise ) in non-equilibrium instruments? Future Japanese cryogenic interferometer For small fluctuations one could apply the Fluctuation- Dissipation theorem using position-dependent temperature: T=T(x) (local equilibrium). But: what is the probability of the large fluctuations? Indications suggest that they are more frequent than if gaussian Moreover: what happens to the acoustic modes? The modes cannot be defined locally! The concept of local equilibrium does not apply to the acoustic modes. So far the problem is addressed as if thermal equilibrium and normal mode expansion hold. Nota Bene: Cryogenics is being considered for 3 rd generation EU Interferometer (design study supported by FP7: ET) similar NonEquilibrium issue

7 Intricating the thermal budget: thermal compensation Absorbed light power causes mirror thermal deformation need of compensation for recovering optimal mirror geometry Surface towards heater Mirror surface Operating detector GEO600 What is the distribution of the spontaneous vibration fluctuations of such a non-equilibrium body?

8 Application of Fluctuation Theorem Let us monitor the spontaneous length fluctuations of a rod of length L at temperature T 1 T 1 Now apply a steady-state thermal gradient DT between the ends by flowing power W=dQ/dt. The rod expands by DL via thermal expansion: T 1 +DT T 1 pdf L pdf L DL DL?? L Whatever the pdf is (and we don t know!), the Fluctuation Theorem states that in an integration time t this probability ratio is: p( L DL) p( L DL) W exp t k 1 T1 T B 1 1 DT 19 exp 10 Eg, for W=1W, t=1sec, T 1 =300K, DT=10K L

9 What do we foresee? Spontaneous fluctuations distribute differently from the equilibrium normal distribution: findings indicate that : large amplitude fluctuations become more frequent Gaussian component plus long non-gaussian tails Example: Gaussian distribution contaminated by Laplace distribution (with weight a L ) Such a mix of Gaussian and non-gaussian behavior has been seen in the power fluctuations in resistors, the relaxation of glassy systems, turbulent flows, and energy fluctuations in granular media. Population of the large fluctuation tails is a problem for GW detectors: L. Conti - RareNoise - commii increase - dic/08 of the false alarm rate

10 July 2008 RareNoise: mutually reinforcing experimental + theoretical work YEAR 1 YEAR 2 YEAR 3 YEAR 4 YEAR 5 Exp. Setup & calibrations Model of rod vibrating under thermal gradient Measurements at 300K Measurements at 77K Measurements at 4.2K Production of Si oscillators Exp. Setup & calibrations Measur. at 300K Specialization of rod model to experim materials Molecular dynamics tests of Fluctuation Theorems Refinement of the theory of Fluctuations Measur. at 77K Application of theory to GW detectors Experimental work : chamber1, 300K Experimental work: chamber2, in cryostat Experimental work Theoretical work

11 Experimental work Goal: Observe spontaneous vibration fluctuations of elastic bodies, ie mechanical resonators, subject to steady-state thermal gradient Nota Bene: At the equilibrium thermal fluctuations are due to dissipations (Fluctuation Dissipation Theorem). Control of dissipations is mandatory if fluctuations are to be studied. focus on material low intrinsic dissipations, as in high precision experiments investigation of 2 kinds of low mechanical loss materials: a metal (Aluminum) and a semiconductor (Silicon) repeated measurements at different temperatures: 300K, 77K, 4K, ie at different material parameters material equilibrium T [K] Expected losses Phase 1 Al5056, Si 300, Phase 2 Al5056, Si Phase 3 Si 300,

12 Theoretical work Model of rods used in the experiments and subject to steady-state thermal gradients: numerical studies of the NonEquilibrium fluctuations. mathematical and numerical investigations of 1-dimensional chains of oscillators subject to thermal gradient Specialization of the particle interaction potentials to the experimental materials Coupling of several 1dim chains to go beyond 1dim: nonequilibrium molecular dynamics simulations Computation of observables not sensed experimentally: characterization of the nonequilibrium state of the system and of its noise. refinements of the nonequilibrium theory assessment of validity of the normal mode expansion formalism application to interferometric GW detectors

13 Potential impact Impact on GW detectors: if NonEquilibrium effects are important need to reconsider design of future detector and/or adapt data analyses Also impact on experiments with low signal-to-noise ratios Impact on NonEquilibrium theories: new theoretical results availability of large amount of data with different material conditions and regimes, with focus on very low losses and intrinsic loss mechanisms from toy models to realistic models simulations NonEquilibrium theories have impact on micro-nano motors. Assessment of validity of the normal mode expansion in non-equilibrium systems Impact also in many fields

14 The phase 1 oscillator Completed dynamical and structural analysis of the part by FEM Material: Al5056 Pendulum modes: 30Hz, 40 Hz Torsional mode : 80 Hz Flexural modes: 300Hz, 500Hz Longitudinal mode: 1500Hz Flexural modes: 2600Hz, 3600Hz..

15 The Al5056 oscillator prototype with capacitive readout amplifier housing gap = 44mm The prototype oscillator with its readout electronics mounted on top of the prototype suspension: Class. Quant. Grav., in press

16 Mechanical suspension prototype We decided to start experiencing with an already available vacuum chamber, to better design the final (and larger) chamber and suspension for the room T measurements 3 stage, 3-axis mechanical filter to suppress low frequency mechanical noise Expected gain at 1500Hz : -140dB Dynamical and structural analysis by FEM Eg a low frequency mode of 1 stage FEM model Materials: Al7075-T6, Steel

17 oscillator + suspension assembly

18 Prototype: mechanical suspensions Vacuum chamber housing 1 oscillator, for testing The mechanical suspension: 3 stages Performance of the single stage: Estimated attenuation of -180dB along all spatial directions, as planned. This is enough to observe thermal noise of prototype oscillator. Thanks to this successful test, we can design the suspension for the final chamber with more confidence. submitted to Rev. Sci. Instrum.

19 Test of the low noise amplifier coupled to the oscillator home-made amplifier gain: output noise: voltage noise at the amplifier input: 6nV/sqrt(Hz) at 1.5kHz After 1 month since biasing the capacitive sensor, we observed no charge leakage.

20 Equilibrium thermal noise measurements Vbias = 500V gap = 44mm C sens = 370pF C para = 211pF electric field =7, V/m submitted to Rev. Sci. Instrum. 7 ore di dati: ampiezza 2 del picco di risonanza T=(285±6) K T=(320±6) K

21 Thermal control in the prototype chamber Peltier cells with heat sink We control the temperature of the base of the oscillator rod by acting on Peltier cells on top of the vacuum chamber, with a PID loop: the cells are in thermal contact with the rod via radiative and conductive heat transfer. ±50mK prototype vacuum chamber passive thermal insulator With a second PID loop, we control the temperature of the oscillating mass by acting on a IR heater facing the mass.

22 Prototype silicon oscillator We designed a prototype silicon oscillator on the basis of the design of the aluminum oscillator prototype: thanks to the tests on the aluminum oscillator, we have made a few significative improvements to the design. silicon rod, to be glued onto the aluminum body 1 st longitudinal resonance at 1.5kHz capacitor for displacement readout assembly in february 2010; tests in spring 2010

23 Setup for room T campaign Peltier cells for controlling oscillator base temperature copper strips for conductive heat path 4 stages mechanical suspension vacuum chamber 3 oscillators (Al5056, Si) with active control of the temperature of the oscillating mass isolated platform where the experiment will be mounted passive, thermal insulator LNL

24 A case study: AURIGA AURIGA is gravitational wave bar detector located at INFN Legnaro (Padova, Italy) bar: material Al5056 mass 2300kg length 3m 1 st longitud. resonance diameter 600mm thermodynamic temperature ~900Hz 4.2K readout: capacitive transucer (bias 8MV/m) low loss matching transformer (5H/4mH) double stage SQUID amplifier (500hbar) the displacement sensitivity is of order several m/ Hz over a ~100Hz bandwidth overall, a system of 3 coupled resonators: 2 mechanical + 1 electrical

25 Cooling of AURIGA 2 types of cooling employed in AURIGA, with different effects: Thermodynamic cooling to 4.2K of bar+transducer+electronics, via thermal contact with LHe bath. It reduces the thermal noise of mechanics and electronics by lowering both the temperature and (for the bar in Al5056) the losses. The losses of the electromechanical oscillators drop to Feedback cooling to T eff ~ 0.01K of only the 3 electromechanical modes via electronic feedback It improves the electronic stability and eases the data analysis; it does not improve the sensitivity to an external force such as an impinging gravitational wave. The effective losses of the electromechanical oscillators raise to

26 Feedback cooling - cold damping AURIGA modeled as the system of 3 coupled resonators (2 mechanical, 1 electrical): 3 normal modes Model each mode as RLC series electrical mode: T 0 = 4.6K We measure the noisy position of the 3 oscillators and feed back a force proportional to their velocity, equivalent to an additional damping. For each oscillator the resulting Langevin equation does not satisfy the Einstein relation: the additional damping R d calms down the oscillator (cooling to T eff ) BUT the thermal driving force remains the same (due to bath at T 0 >T eff )

27 In AURIGA, to stabilize the readout electronics, we measure the noisy position of an oscillator and feed back a force proportional to its velocity, equivalent to an additional damping. Standard scheme, does not improve sensitivity to GWs (Fsignal). Now considered to reduce the thermal vibration noise and allow the observation of quantum effects.

28 Active cooling: spectrum AURIGA runs continuously with fixed feedback settings. However, we investigated the effect of changing feedback settings. these numbers indicate the equivalent temperature of the mode, in mk units non-equilibrium steady states caused by stochastic driving PRL 101, (2008)

29 Application of 1 st law of Thermodynamics With feedback off, the thermal driving forces the motion of the oscillator. This energy is given back to the bath by the intrinsic damping R. With feedback on, part the energy is extracted as work done on the feedback (additional damping R d ): this results in cooling. t integration time time averaged oscillator s energy difference symmetric as for an equilibrium oscillator time averaged work done by oscillator positive by definition positive mean, independent of t time averaged heat absorbed by oscillator positive mean, independent of t net heat transfer from the bath to the oscillator: the reverse (ie Q t <0) is very rare PRL 103, (2009) RareNoise & Auriga collaborations

30 Power injected by the thermal bath (e t : normalized power) it maintains the dissipative system in a nonequilibrium steady state 3 years Auriga data compared with theoretical model for stochastically driven Langevin system: a transition is expected in the PDF of ε t the Fluctuation Relation for ε t is nonlinear. singularity in the 2 nd derivative of the (large deviation function of the) injected power = predictions for t/t eff testing Fluctuation Relations is a standard tool to characterize nonequilibrium systems: here we test the FR for the power injected by the thermal bath. This feature was never observed before in an harmonic oscillator. PRL 103, (2009) RareNoise & Auriga collaborations

31 Further investigation on oscillators with feedback digital protocol: the feedback feeds back the current I s scaled by a factor G (<1) and time delayed by t d analog protocol: the feedback acts as a low pass filter with cut frequency W and gain A. Auriga implements the analog protocol but is studied as digital protocol: the two descriptions are equivalent in the case of high quality factors and t d =p/2w 0, W<<w 0 (and AW=Gw 0 ).

32 We have computed the power spectral density of the output current in the presence of themal noise and feedback for the 2 protocols and at different Q and feedback parameters Digital protocol, high Q case (Q=10 5 ) predicted a shift of the resonant frequency with increasing feedback gain De Gregorio et al., J. Stat. Mech. (2009) P10016

33 Digital protocol, low Q case (Q=1) equilibrium G=0.75 predicted a discontinuity in the dominant frequency De Gregorio et al., J. Stat. Mech. (2009) P10016

34 Molecular dynamics Development of 1, 2 and 3dimensional models to simulate the behaviour of a solid rod subject to thermal gradient: study of fluctuations in non-equilibrium states in collaboration with dr. Yi Ding - ETH Zürich 1dim models already interesting at equilibrium n. of particles: evaporation problem solvedrisolto il problema della evaporazione several kinds of thermostats successful in reproducing thermal expansion now standard potentials are being considered: late we will specialize to Al5056 and silicon work in progress

35 The ERC funding and the project management Reports to funding agency (ERC): financial reports any 18 months (ie 4 reports); scientific reports any 30 month (ie 2 reports). Personell: only L.Conti is charged to INFN. Others are either hired by the project or permanent staff of partner institutions In February 2010 the presence of the project in INFN will likey be formalized by the opening of a new experiment ( sigla ) in CSNII. This will solve a number of difficulties we encountered with INFN and will ease expansion of the project to interested researchers.