1. In Search of the “Absolute” Optical Phase
Pete Roos (JILA, NIST, CU)
JILA, NIST, CU (Boulder)
U of T (Toronto)
Xiaoqin (Elaine) Li
Ryan Smith
Jessica Pipis
Steve Cundiff
Rich Mirin
Tara Fortier
David Jones
Ravi Bhat John Sipe

2. Outline Important concepts and motivation How fast is ultrafast?
The “Absolute” optical phase.
Why do we care?
Creation and control of ultrashort pulses
Modelocking.
“Absolute” phase evolution – time vs. frequency.
Detection methods.
Quantum interference control (QIC) in semiconductors
Background.
Concepts and theory.
Experimental studies and stabilization using QIC.

3. How Fast is Ultrafast?
Within an order of magnitude or two of 10 fs (1 fs = s).
Scaling example:
1 s
1 fs

4. “Absolute” Optical Phase
Ultrafast optics approaching interesting regime:
Optical carrier cycle (~ 3fs)
Carrier-envelope
(CE) phase
Envelope
Pulse Duration
(~10 fs)
Carrier
Pulse envelope provides “absolute” phase reference.

5. Why do we care? 1. Can affect light-matter interactions.
Extreme nonlinear optics.
Photoionization and x-ray generation.
Photoelectron emission from metal surfaces.
Coherent control experiments.
2. Ultimate control of light.
Not only control of intensity envelope … field.
Optical waveform synthesis.
AWG at optical frequencies.
3. Precision measurements.
Optical frequency metrology.
Linear / nonlinear spectroscopy.

6. Outline Important concepts and motivation How fast is ultrafast?
The “Absolute” optical phase.
Why do we care?
Creation and control of ultrashort pulses
Modelocking.
“Absolute” phase evolution – time vs. frequency.
Detection methods.
Quantum interference control (QIC) in semiconductors
Background.
Concepts and theory.
Experimental studies and stabilization using QIC.

7. Short Laser Pulses External switch: Gain Mirrors Output beam Switch
Internal switch:
Gain
Mirrors
Switch
Pulses

8. Ultrashort Laser Pulses
Modelocking:
Intensity
Frequency
30 modes
all in phase
30 modes
random phases
Intensity
Time
Coherent interference effect.
Requires phase locked modes.

9. CE Phase Instability In laser cavity: vgroup≠ vphase
CE phase evolves from pulse to pulse outside cavity.
Laser
Cavity
Free Space
High
Reflector
Output
Coupler

10. Random Evolution Uncontrolled CE phase evolution:
Limits meaningful physics and applications.

11. No Evolution Fixed CE phase:
Enables meaningful physics and applications.

12. Controlled Evolution Df Df Df Df Df Controlled CE phase evolution:
Also enables meaningful physics and applications.

13. Time vs. Frequency Domain
E(t)
fce
Time Domain tp t
F.T. t
fce
I(n) n
Frequency Domain
frep=1/t
~1/tp
fce x2
n, fce
2n, 2fce
2n, fce
fce

14. Time vs. Frequency Domain
E(t) Df
2Df
Time Domain t
Frequency Domain
I(n) n
F.T.
f0=frepDf/2p x2
n+f0
2n+2f0
2n+f0 f0

15. Some Detection Methods
Second harmonic generation (n-to-2n)
Telle et al., Appl. Phys. B (1999);
Jones et al., Science 288, 635 (2000);
Apolonski et al., PRL 85, 740 (2000) n 2n 2
Photoionization of gases
Durfee et al., PRL (1999);
Paulus et al., Science 414, 182 (2002)
vapor
Photoelectron emission from metals
Lemell et al., PRL 90, (2003);
Apolonski et al., PRL 92, (2004)
metal
Rabi sideband interference
Vu et al., PRL 92, (2004);
Mücke et al., Opt. Lett (2004)
semiconductor
3, Rabi

16. Outline Important concepts and motivation How fast is ultrafast?
The “Absolute” optical phase.
Why do we care?
Creation and control of ultrashort pulses
Modelocking.
“Absolute” phase evolution – time vs. frequency.
Detection methods.
Quantum interference control (QIC) in semiconductors
Background.
Concepts and theory.
Experimental studies and stabilization using QIC.

17. ~sin[(fa+fb)-(fc+fd)]
Quantum Interference
Two distinct quantum mechanical pathways.
Connect same initial and final states.
~sin[(fa+fb)-(fc+fd)]
~sin(2fn-f2n) fa fb fc fd
f2n fn
State population
Shapiro et al, J Chem Phys 84, 4103 (1986)
Atomic photoionization
Yin et al, PRL 69, 2353 (1992)
Molecular photodissociation
Sheehy et al, PRL 74, 4799 (1995)
Semiconductor spin currents
Bhat et al, PRL 85, 5432 (2000)
Semiconductor charge currents
Haché et al, PRL 78, 306 (1997)
Relative optical phase can coherently control:

18.  sin(2fce-fce) = sin(fce)
QIC in Semiconductors
fce
Quantum interference between 1 and 2 photon absorption.
Asymmetry in momentum space  directional current.
Sensitive to relative phase between n and 2n.
sin(2fn-f2n)
 sin(2fce-fce) = sin(fce)
Photocurrent direction and magnitude sensitive to CE phase.

19. From Fermi’s Golden Rule:
QIC in Semiconductors
Velocity
Charge
Transition
Amplitudes
From Fermi’s Golden Rule: { }
One-photon
Two-photon
Atanasov et al., PRL 76, 1703 (1996); Haché et al., PRL 78, 306 (1997)

20. { } QIC in Semiconductors Velocity Charge Transition Amplitudes
Atanasov et al., PRL 76, 1703 (1996); Haché et al., PRL 78, 306 (1997)
Velocity
Charge
Transition
Amplitudes { }
One-photon
absorption
Two-photon
Quantum
Interference

21. { } QIC in Semiconductors Even in k One-photon absorption Two-photon
Quantum
Interference
Even in k

22. { } QIC in Semiconductors Even in k Odd in k One-photon absorption
Two-photon
Quantum
Interference
Even in k
Odd in k

23. { } QIC in Semiconductors Even in k Odd in k Odd in k One-photon
absorption
Two-photon
Quantum
Interference
Even in k
Odd in k
Odd in k

24. Stabilized Ti:sapphire modelocked laser
Simplified Setup
Stabilized Ti:sapphire modelocked laser
~15 fs, 93 MHz rep. rate,
up to 400 mW avg. power
Fiber
broadening
Time delay adjust
Prism n
Split
mirror
LT-GaAs
Lens
Prism 2n
Sample
Lock-in
amplifier
I/V
RF spectrum
analyzer

25. Signal Amplitude
Current ≈ 100 pA
Now have >500 pA.

26. Incident Power < J > ~ In (I2n)1/2
Roos et al., JOSA B (to be published)

27. CE Phase Sensitivity
Verification that phase of QIC signal varies with shifts in carrier-envelope phase.
Fortier et al., PRL 92, (2004)

28. Detection Bandwidth With transimpedance amplifier: 830 kHz.
Roos et al., JOSA B (to be published)

29. Simplified Stabilization Setup
Ti:sapphire laser
Prism
High reflector
Output coupler
Pump
Ti:sapphire
crystal
Prism
Fiber
broadening
Time delay adjust
To phase noise
analysis n
Split
mirror 2n
Lens
Sample
Mixer
Stabilization
electronics
I/V ~
Synthesizer

30. Stabilization via QIC CE phase evolution stabilized.
Roos et al., Opt. Lett. (to be published)

31. Summary
“Absolute” (carrier-envelope) phase: phase difference between carrier peak and envelope peak.
Important for light-matter interactions, optical waveform synthesis, precision measurements.
Modelocked lasers enable access to “absolute” phase.
To detect: compare phase of spectral components in frequency domain through nonlinear process.
Quantum interference control (QIC) in semiconductors gives phase-sensitive photocurrent.
“Absolute” phase stabilization using QIC.