Why is AFM challenging? 1.Jump to contact: k>max(-   V TS /  z  (static) kA>max(-F TS  oscillating 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 = k B T This allows one to determine the thermal limit of force gradient sensing in AFM: {z osc = F’ z o 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 A drive ) Albrecht, Grutter, Horne and Rugar J. Appl. Phys. 69, 668 (1991) (*) used in Tapping™ mode ff AA f 1 f 2 f 3

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) A 2 = k B T/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 ~ J << J/molecule

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  …i nterferometer 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 withMinimal 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)

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