Low probability, large fluctuations of the noise in detectors of gravitational waves

Transcription

1 European Research Council Low probability, large fluctuations of the noise in detectors of gravitational waves Nickname oftheproject: RareNoise Project Number: Principal Investigator: Livia Conti INFN Team Members: Michele Bonaldi CNR Lamberto Rondoni Politecnico di Torino infn it

2 The team Livia Conti, PI experimentalist INFN Padova 1FTE Stefano Longo technologist (DAQ & computing) INFN Padova 1FTE Mario Saraceni Matteo Pegoraro technologist (mechanics) technologist (electronics) Rosella Battistella INFN Padova INFN Padova financial officer 1FTE 0.1FTE INFN LNL Michele Bonaldi experimentalist CNR IFN Trento 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 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 1e-15 LIGO They are macroscopic instruments but with displacement sensitivity approaching the quantum limit. Theirnoise budget iscalculated very accurately; any subtle noise contribution must be taken into account: as both rms and statistics Dis placement [m m/ Hz] 1e-20 1e1 Frequency [Hz] 1e3 With their high h sensitivityand long acquisition iiti times GW dt detectorst might ihtprove the natural application of NonEquilibrium Theories to macroscopic systems

5 Non equilibrium in GW interferometers Thermal gradient due to laser power dissipated in the mirror How to compute the spontaneous vibration fluctuations ( thermalnoise ) 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 hthappens 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) similar NonEquilibrium issue

6 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?

7 This project: 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 Measurements at 300K and 77K Specialization of rod model to experim materials Molecular dynamics tests of Fluctuation Theorems Refinement of the theory Application of theory of Fluctuations to GW detectors Experimental work : Phase 1 Experimental work: Phase 2 Experimental work : Phase 3 Theoretical work

8 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 tl(aluminum) and a semiconductor (Silicon) repeated measurements at different temperatures: 300K, 77K, 4K, ie at different materialparameters material equilibrium T [K] Expected losses Phase 1 Al5056, Si 300, Phase 2 Al5056, Si Phase 3 Si 300,

9 Theoretical work Modelof of rods used in the experiments and subject to steady state state thermalgradients: 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 ti potentials ti 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 m application to interferometric L. Conti - RareNoise - Amaldi 09 GW detectors

10 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

11 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. ~900Hz resonance diameter 600mm thermodynamic temperature 4.2K readout: capacitive transucer (bias 8MV/m) low loss matching transformer (5H/4μH) double stage SQUID amplifier (500hbar) the displacement sensitivity is of order several m/ Hz over a ~100Hz bandwidth overall, a system of 3 coupled ldresonators: 2 mechanical + 1 electrical

12 Cooling of AURIGA 2 types of cooling employed in AURIGA, with different effects: Thermodynamic cooling to 4.2K Feedback cooling to T eff ~ 0.01K of bar+transducer+electronics, of only the 3 electromechanical modes via thermal contact with LHe bath. via electronic feedback It reduces the thermal noise of mechanics and electronics by lowering both the temperature and (for the bar in Al5056) the losses. 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 losses of the electromechanical The effective losses of the electromechanical oscillators drop to oscillators raise to

13 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 )

14 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)

15 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. τ = integration ti 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 τ time averaged heat absorbed by oscillator positive mean, independent of τ net heat transfer from the bath to the oscillator: the reverse (ie Q τ <0) is very rare PRL in press, arxiv: v1 RareNoise & Auriga collaborations

16 Power injected by the thermal bath (ε τ : 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 singularity in the 2 nd derivative of the (large deviation function of the) injected power = predictions for τ/τ/ 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 PRL in press, arxiv: v1 RareNoise & Auriga collaborations