Igor Neri with Miquel LopezSuarez and Luca Gammaitoni GRAvitational waves Scienceamptechnology Symposium GRASS 2019 1718 October 2019 Equilibrium vs Outofequilibrium Most of ID: 791460
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Slide1
Operating high sensitivity measurement apparata out of equilibrium
Igor Neri
with
Miquel Lopez-Suarez
and Luca Gammaitoni
GRAvitational
-waves
Science&technology
Symposium (GRASS 2019) 17-18 October 2019
Slide2Equilibrium vs Out-of-equilibrium
Most of the noise studies, as well as the operational condition of high sensitivity measurements
apparatus (e.g. the G.W. interferometers), are considered under the assumption that the entire system is time quasi-stationary and at thermal equilibrium.
This is true even if some of the estimations for some fundamental noises, like thermal noise, have been derived by assuming the validity of fluctuation-dissipation relations that represent the base for non-equilibrium statistical mechanics.
A question arises about the possibility to operate such measurement apparata far from equilibrium or in markedly non stationary conditions.
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Slide3Equilibrium vs Out-of-equilibrium
Previous attempts have been carried out through the application of some clever
external feedback that could modify the apparatus dynamics in order to reduce the system response to noise, in desired frequency ranges.
See e.g.
The reduction in the
brownian motion of electrometers, Milatz J M W and van Zolingen J J 1953
Physica 19 181
Regulation of a microcantilever response by force feedback, Mertz J
et al.
1993 Appl. Phys. Lett. 62 2344
Full mechanical characterization of a cold damped mirror, M.
Pinard
,
et al.
Phys. Rev. A 63, 013808, 2000
Optomechanical scheme for the detection of weak impulsive forces, David Vitali, Stefano Mancini, and Paolo Tombesi, Phys. Rev. A 64, 051401(R) 2001; Erratum Phys. Rev. A 69, 049904 (2004)Feedback Cooling of the Normal Modes of a Massive Electromechanical System to Submillikelvin Temperature, Vinante A et al 2008 Phys. Rev. Lett. 101 033601Observation of a kilogram-scale oscillator near its quantum ground state, LIGO Collab. 2009 New J. Phys. 11 073032.Measurement-based control of a mechanical oscillator at its thermal decoherence rate, Wilson D J et al 2015 Nature 524 325Nonequilibrium Steady-State Fluctuations in Actively Cooled Resonators M. Bonaldi, et al, PRL. 103, 010601 2009RareNoise: non-equilibrium effects in detectors of gravitational waves L Conti, M Bonaldi, and L Rondoni; 2010 Class. Quantum Grav. 27 084032
GRAvitational
-waves
Science&technology
Symposium (GRASS 2019) 17-18 October 2019
Slide4Equilibrium vs Out-of-equilibrium
An interesting contribution from
Minimum Requirements for Feedback Enhanced Force Sensing
, Glen I. Harris, David L.
McAuslan, Thomas M. Stace, Andrew C. Doherty, and Warwick P. Bowen, Phys. Rev. Lett. 111, 103603 –2013
However, two important conditions have to be met:
The system is linear
The transfer characteristic is precisely known
That showed that if the measurement apparatus is linearly coupled to the noise and to the signal, then there exists a
real-time estimation strategy
that reproduces the same measurement record as any arbitrary feedback protocol. In this case any active cooling, stationary or not,
does not improve sensitivity over properly chosen data analysis
.
In all other cases there might be an advantage
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Slide5Cooling via electrostatic feedback in a simple interferometer
Neri, Igor, Miquel López-Suárez, and Luca Gammaitoni. "Operating gravitational wave detectors far from equilibrium."
Classical and Quantum Gravity
35.15 (2018): 155018.
Si
3
N
4
membrane (30 nm, 5x5 mm)
5
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Slide6Cooling via electrostatic feedback in a simple interferometer
Neri, Igor, Miquel López-Suárez, and Luca Gammaitoni. "Operating gravitational wave detectors far from equilibrium."
Classical and Quantum Gravity
35.15 (2018): 155018.
Si
3
N
4
membrane (30 nm, 5x5 mm)
6
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Slide7Cooling via electrostatic feedback in a simple interferometer
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Neri, Igor, Miquel López-Suárez, and Luca Gammaitoni. "Operating gravitational wave detectors far from equilibrium."
Classical and Quantum Gravity
35.15 (2018): 155018.
Slide8Cooling via electrostatic feedback in a simple interferometer
Q = 1.7 10
5
τ
f
= 0.045 s and τ
r
= 0.707 s
Cooling phase
Recovery phase
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Neri, Igor, Miquel López-Suárez, and Luca Gammaitoni. "Operating gravitational wave detectors far from equilibrium."
Classical and Quantum Gravity
35.15 (2018): 155018.
Slide9Cooling via electrostatic feedback in a simple interferometer
Signal injected
With signal injected
Without
signal injected
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Neri, Igor, Miquel López-Suárez, and Luca Gammaitoni. "Operating gravitational wave detectors far from equilibrium."
Classical and Quantum Gravity
35.15 (2018): 155018.
Slide10Cooling via electrostatic feedback in a simple interferometer
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Neri, Igor, Miquel López-Suárez, and Luca Gammaitoni. "Operating gravitational wave detectors far from equilibrium."
Classical and Quantum Gravity
35.15 (2018): 155018.
T
C
= cycle duration,
t
f
= feedback duration, Duty cycle = 1 –
t
f
/T
C
Time
Cooling
(blind)
Recovering
(measuring)
Noise
Slide11Cooling via electrostatic feedback in a simple interferometer
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Neri, Igor, Miquel López-Suárez, and Luca Gammaitoni. "Operating gravitational wave detectors far from equilibrium."
Classical and Quantum Gravity
35.15 (2018): 155018.
T
C
= cycle duration,
t
f
= feedback duration, Duty cycle = 1 –
t
f
/T
C
Time
Cooling
(blind)
Recovering
(measuring)
D 75%
Noise
Slide12Cooling via electrostatic feedback in a simple interferometer
GRAvitational
-waves Science&technology
Symposium (GRASS 2019) 17-18 October 2019
Neri, Igor, Miquel López-Suárez, and Luca Gammaitoni. "Operating gravitational wave detectors far from equilibrium."
Classical and Quantum Gravity 35.15 (2018): 155018.
T
C
= cycle duration,
t
f
= feedback duration, Duty cycle = 1 –
t
f
/T
C
Time
Noise
Cooling
(blind)
Recovering
(measuring)
Steady state
D
75%
Slide13Cooling via electrostatic feedback in a simple interferometer
GRAvitational
-waves Science&technology
Symposium (GRASS 2019) 17-18 October 2019
Neri, Igor, Miquel López-Suárez, and Luca Gammaitoni. "Operating gravitational wave detectors far from equilibrium."
Classical and Quantum Gravity 35.15 (2018): 155018.
T
C
= cycle duration,
t
f
= feedback duration, Duty cycle = 1 –
t
f
/T
C
Time
Noise
Cooling
(blind)
Recovering
(measuring)
D
5
0%
Steady state
Slide14Cooling via electrostatic feedback in a simple interferometer
T
C
= cycle duration, t
f = feedback duration, Duty cycle = 1 – tf/TC
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Neri, Igor, Miquel López-Suárez, and Luca Gammaitoni. "Operating gravitational wave detectors far from equilibrium."
Classical and Quantum Gravity
35.15 (2018): 155018.
Slide15Conclusions
1
Periodic cooling via feedback control is possible and under certain circumstances is capable of improving the signal to noise ratio for transient signals.
2
It is of no special use if the system is
linear and
the transfer characteristic is well known. In any other case there might be an advantage, depending on the relaxation time of the system and on the time scale of the signals to be detected.
3 (further work)
In the case of marked non-linearity there might be an advantage due to energy transfer between different frequency regions.
GRAvitational-waves Science&technology Symposium (GRASS 2019) 17-18 October 2019
Slide16Thank you for your attention!
igor.neri@nipslab.org