Why is AFM challenging?

1. Jump to contact:k>max(-VTS/z(static)

kA>max(-FTSoscillating mode)

ideal amplitude is A~]

2. Non-monotonic imaging signal

3. Long-range vs. short range forces [F(z)]

4. Noise in the deflection sensor (particularly 1/f noise)

5. FM AFM helps in all cases except 2!

Thermal limits

Energy in damped driven harmonic oscillator = kBT

This allows one to determine the thermal limit of force gradient sensing in AFM:

{zosc= F’ zo Q/k Is the signal near resonance}

How does one measure a high Q system?

Challenge of measuring high Q system

Albrecht, Grutter, Horne Rugar J. Appl. Phys. 69, 668 (1994)

Better sensitivity with high Q cantilevers

Q=115 slope detection

Q=65,000 FM detection

Q=65,000 slope detection

Albrecht, Grutter, Horne Rugar J. Appl. Phys. 69, 668 (1994)

P. Grutter, McGill University

AC techniques

Change in resonance curve can be detected by:

• Lock-in (A or ) *

• FM detection (f and Adrive)

Albrecht, Grutter, Horne and RugarJ. Appl. Phys. 69, 668 (1991)

(*) used in Tapping™ mode

f

A

f1 f2 f3

P. Grutter, McGill University

Some words on Tapping™

Amount of energy dissipated

into sample and tip strongly depends on operation conditions.

Challenging to

determine magnitude or sign of force.

NOT necessarily less

power dissipation than repulsive contact AFM.

Anczykowski et al., Appl. Phys. A 66, S885 (1998)

P. Grutter, McGill University

Ultimate limits of force sensitivity

1. Brownian motion of cantilever!

thermal limits Martin, Williams, Wickramasinghe JAP 61, 4723 (1987)Albrecht, Grutter, Horne, and Rugar JAP 69, 668 (1991)

D. Sarid ‘Scanning Force Microscopy’

Roseman & Grutter, RSI 71, 3782 (2000)

A2 = kBT/k

A…rms amplitude T=4.5K

2. Other limits:- sensor shot noise- sensor back action- Heisenberg

D.P.E. Smith RSI 66, 3191 (1995)

Bottom line:Under ambient conditions energy resolution ~ 10-24J << 10-21J/molecule

QfkA

TBk

f

f Bo

023

0

2

Other limitations?

- sensor shot noise

- sensor back action

- Heisenberg

D.P.E. Smith, Rev. Sci. Instr. 66, 3191 (1995)

Sensor Shot Noise

Effectively, the fluctuations in laser pressure (due to photon statistics) give rise in a fluctuation in the mean position of the cantilever.

P…laser power, f…bandwidth

…wavelength h…Planck’s constant

c…speed of light …interferometer phase

NB: can be used to ‘cool’ high finesse cavities!

Sensor Back Action

P…laser power, f…bandwidth

…wavelength h…Planck’s constant

c…speed of light

Optical pressure

Off resonance

On resonance

Optimization

Minimize:

and obtain optimized laser power (for off resonance set Q=1):

Heisenberg

Minimal detectable energy

with Minimal bandwidth

Quantum limit

So what?

How about detecting a single spin?Idea: combine MFM and resonant excitation of the cantilever by combining ultimate AFM techniques and NMR.

MRFM

D. Rugar, R. Budakian, H. J. Mamin & B. W. Chui, Nature 430, 329 (2004)

Magnetic Resonance Force Microscopy (MRFM)

Another cool thing: thermodynamic squeezed state

D. Rugar and P. Grutter, Phys. Rev. Lett. 67, 699 (1993)

Course Evaluations!