Stochastic Resonant Damping

1
Stochastic Resonant Damping vs. Stochastic
Resonance
Giovanni Volpe Sandro Perrone J. Miguel
Rubi Dmitri Petrov
The Institute of Photonic Sciences - Barcelona
(Spain)
2
An increased effort to control a noisy
system should lead to a better performance
3
An increased effort to control a noisy
system should lead to a better performance
4
An increased effort to control a noisy
system should lead to a better performance
5
An increased effort to control a noisy
system should lead to a better performance
6
Stochastic Resonant Damping
A general mechanism that explains why an
increased effort can lead to a worse response
Phys Rev E (2008) 77, 051107
7
Stochastic Resonant Damping
A general mechanism that explains why an
increased effort can lead to a worse response

• Brownian motion in an optical trap
• Stochastic Resonant Damping
• SRD vs. SR

Phys Rev E (2008) 77, 051107
8
Stochastic Resonant Damping
A general mechanism that explains why an
increased effort can lead to a worse response

• Brownian motion in an optical trap
• Stochastic Resonant Damping
• SRD vs. SR

Phys Rev E (2008) 77, 051107
9
High-focused laser beams (Optical Tweezers) can
trap microscopic particles
Position Detector
Condenser
Sample
High-NA Objective
Trapping Laser
10
High-focused laser beams (Optical Tweezers) can
trap microscopic particles
Optical Trap Force-field
Trapping Potential
11
High-focused laser beams (Optical Tweezers) can
trap microscopic particles
Optical Trap Force-field
Trapping Potential
12
The more laser power, the more confined the
particle more effort, better result.
Variance nm2
Laser Power
13
The more laser power, the more confined the
particle more effort, better result.
Variance nm2
Laser Power
14
The more laser power, the more confined the
particle more effort, better result.
Variance nm2
Laser Power
15
The more laser power, the more confined the
particle more effort, better result.
Variance nm2
Laser Power
16
The more laser power, the more confined the
particle more effort, better result.
Variance nm2
Laser Power
17
Stochastic Resonant Damping
A general mechanism that explains why an
increased effort can lead to a worse response

• Brownian motion in an optical trap
• Stochastic Resonant Damping
• SRD vs. SR

18
Stochastic Resonant Damping happens when the
confinement effort is noisy
Confining Potential
19
Stochastic Resonant Damping happens when the
confinement effort is noisy
Noise
Confining Potential
Phys Rev E (2008) 77, 051107
20
Stochastic Resonant Damping happens when the
confinement effort is noisy
Variance nm2
Confining Potential Fast Noise
Laser Power /Confinement Effort C
Phys Rev E (2008) 77, 051107
21
Stochastic Resonant Damping happens when the
confinement effort is noisy
Variance nm2
Confining Potential Fast Noise
Laser Power /Confinement Effort C
Phys Rev E (2008) 77, 051107
22
Stochastic Resonant Damping happens when the
confinement effort is noisy
Variance nm2
Confining Potential Slow Noise
Laser Power /Confinement Effort C
Phys Rev E (2008) 77, 051107
23
Stochastic Resonant Damping happens when the
confinement effort is noisy
Variance nm2
Confining Potential Slow Noise
Laser Power /Confinement Effort C
Phys Rev E (2008) 77, 051107
24
Stochastic Resonant Damping happens when the
confinement effort is noisy
Variance nm2
Confining Potential Intermediate Noise
Laser Power /Confinement Effort C
Phys Rev E (2008) 77, 051107
25
Stochastic Resonant Damping happens when the
confinement effort is noisy
Variance nm2
Confining Potential Intermediate Noise
Laser Power /Confinement Effort C
Phys Rev E (2008) 77, 051107
26
Stochastic Resonant Damping happens when the
confinement effort is noisy
Variance nm2
Confining Potential Intermediate Noise
Laser Power /Confinement Effort C
Phys Rev E (2008) 77, 051107
27
Stochastic Resonant Damping happens when the
confinement effort is noisy
Variance nm2
Confining Potential Intermediate Noise
Laser Power /Confinement Effort C
Phys Rev E (2008) 77, 051107
28
Stochastic Resonant Damping Theory
Model
Confining Potential Noise
Phys Rev E (2008) 77, 051107
29
Stochastic Resonant Damping Theory
Model
Variance
Confining Potential Noise
Phys Rev E (2008) 77, 051107
30
Stochastic Resonant Damping Theory
Model
Variance
Confining Potential Noise
Variance (sinusoidal noise)
Phys Rev E (2008) 77, 051107
31
Stochastic Resonant Damping Theory and experiment
15000
Variance nm2
5 Hz
10000
50 Hz
5000
500 Hz
0
0
30
20
10
Laser Power mW
Phys Rev E (2008) 77, 051107
32
Stochastic Resonant Damping Theory and experiment
15000
Variance nm2
5 Hz
10000
50 Hz
5000
500 Hz
0
0
30
20
10
Laser Power mW
Phys Rev E (2008) 77, 051107
33
Stochastic Resonant Damping Theory and experiment
15000
Variance nm2
5 Hz
10000
50 Hz
5000
500 Hz
0
0
30
20
10
Laser Power mW
Phys Rev E (2008) 77, 051107
34
Stochastic Resonant Damping Theory and experiment
15000
Variance nm2
5 Hz
10000
50 Hz
5000
500 Hz
0
0
30
20
10
Laser Power mW
Phys Rev E (2008) 77, 051107
35
Stochastic Resonant Damping
A general mechanism that explains why an
increased effort can lead to a worse response

• Brownian motion in an optical trap
• Stochastic Resonant Damping
• SRD vs. SR

36
Stochastic Resonant Damping is in all systems
because it is a linear effect.
In linear systems there is no stochastic resonance
37
Non-linear systems Both SRD and SR in different
regimes
SRD
SR
Variance nm2
SNR
Laser Power mW
Laser Power mW
38
Stochastic Resonant Damping
A general mechanism that explains why an
increased effort can lead to a worse response

• Brownian motion in an optical trap
• Stochastic Resonant Damping
• SRD vs. SR

Phys Rev E (2008) 77, 051107
39
Stochastic Resonant Damping
A general mechanism that explains why an
increased effort can lead to a worse response
Phys Rev E (2008) 77, 051107