In Search of the “Absolute” Optical Phase

Xiaoqin (Elaine) Li

Ryan Smith

Jessica Pipis

Steve Cundiff

Rich Mirin

Tara Fortier

David Jones

Ravi Bhat John Sipe

JILA, NIST, CU (Boulder) U of T (Toronto)

Pete Roos (JILA, NIST, CU)

OutlineImportant 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.

How Fast is Ultrafast?

• Within an order of magnitude or two of 10 fs (1 fs = 10-15 s).

1 s

1 fs

• Scaling example:

“Absolute” Optical Phase

Carrier

Envelope

• Pulse envelope provides “absolute” phase reference.

Carrier-envelope

(CE) phase

• Ultrafast optics approaching interesting regime:

Optical carrier cycle (~ 3fs)

Pulse Duration

(~10 fs)

Why do we care?

• Not only control of intensity envelope … field.• Optical waveform synthesis. • AWG at optical frequencies.

2. Ultimate control of light.

• Extreme nonlinear optics.• Photoionization and x-ray generation.• Photoelectron emission from metal surfaces.• Coherent control experiments.

1. Can affect light-matter interactions.

3. Precision measurements.• Optical frequency metrology.

• Linear / nonlinear spectroscopy.

OutlineImportant 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.

Short Laser Pulses

External switch:

Gain

Mirrors

Output

beam

Switch

Pulses

Internal switch:

Gain

Mirrors

Switch

Pulses

Ultrashort Laser Pulses

• Requires phase locked modes.

Modelocking:

Frequency

Intensity

Time

Intensity 30 modes

random phases

30 modes

all in phase

• Coherent interference effect.

OutputCoupler

HighReflector

LaserCavity Free Space

CE Phase Instability

• In laser cavity: vgroup≠ vphase• CE phase evolves from pulse to pulse outside cavity.

Random Evolution

• Uncontrolled CE phase evolution:

• Limits meaningful physics and applications.

No Evolution

• Fixed CE phase:

• Enables meaningful physics and applications.

Controlled Evolution

• Controlled CE phase evolution:

• Also enables meaningful physics and applications.

cece

Time vs. Frequency Domain

I()

0

Frequency Domain

Time Domain

t

E(t)

F.T. ce

ce

ce

ce

ce

ce

ce

ce

x2ce c

e

ce

ce

frep

p

p

Time vs. Frequency Domain

Time Domain

t

E(t)

0

Frequency Domain

I()

F.T.

x2+f0 +f0

+f0

f0

f0=frep

Some Detection Methods

Second harmonic generation (-to-2)Telle et al., Appl. Phys. B (1999);Jones et al., Science 288, 635 (2000);Apolonski et al., PRL 85, 740 (2000)

Rabi sideband interferenceVu et al., PRL 92, 217403 (2004);Mücke et al., Opt. Lett. 29 2160 (2004)

Photoionization of gasesDurfee et al., PRL 83 2187 (1999);Paulus et al., Science 414, 182 (2002)

Photoelectron emission from metalsLemell et al., PRL 90, 076403 (2003);Apolonski et al., PRL 92, 073902 (2004)

semiconductor

Rabi

metal

vapor

OutlineImportant 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.

Quantum Interference

~sinabcd

a

b

c

d

~sin

• Two distinct quantum mechanical pathways.

• Connect same initial and final states.

State populationShapiro et al, J Chem Phys 84, 4103 (1986)

Atomic photoionizationYin et al, PRL 69, 2353 (1992)

Molecular photodissociationSheehy et al, PRL 74, 4799 (1995)

Semiconductor spin currentsBhat et al, PRL 85, 5432 (2000)

Semiconductor charge currentsHaché et al, PRL 78, 306 (1997)

Relative optical phase can coherently control:

E

ConductionBand

ValenceBand

k

QIC in Semiconductors

• Quantum interference between 1 and 2 photon absorption.

Phase-CoherentOctave-Spanning

Pulse

• Sensitive to relative phase between and 2

• Asymmetry in momentum space directional current.

sin

• Photocurrent direction and magnitude sensitive to CE phase.

sincecesin(ce)

ce

ce

QIC in Semiconductors

k

)k(veJ

{ 22 )k(a)k(a

}

Atanasov et al., PRL 76, 1703 (1996); Haché et al., PRL 78, 306 (1997)

Velocity

Charge TransitionAmplitudes

One-photon Two-photon

From Fermi’s Golden Rule:

QIC in Semiconductors

k

)k(veJ

{ ][ c.c.)k(a)k(a2

}2

2 )k(a

2

)k(a

One-photonabsorption

Two-photonabsorption

Atanasov et al., PRL 76, 1703 (1996); Haché et al., PRL 78, 306 (1997)

Velocity

Charge TransitionAmplitudes

QuantumInterference

E

ConductionBand

ValenceBand

k

QIC in Semiconductors

k

)k(veJ

{ ][ c.c.)k(a)k(a2

}2

2 )k(a

2

)k(a

][ cv222

v2c2

pe)exp(iE

pA)k(a

ˆ

One-photonabsorption

Two-photonabsorption

QuantumInterference

E

ConductionBand

ValenceBand

k

Even in k

QIC in Semiconductors

k

)k(veJ

{ ][ c.c.)k(a)k(a2

}2

2 )k(a

2

)k(a

]][[ mvcm

2

vmmc

pepe)exp(i2E

pApA)k(a

ˆˆ

][ cv222

v2c2

pe)exp(iE

pA)k(a

ˆ

One-photonabsorption

Two-photonabsorption

QuantumInterference

E

ConductionBand

ValenceBand

k

Even in k

Odd in k

QIC in Semiconductors

]][[][

][

mvcmcv2

2

2

22

pepepe

)-i(2expEE)k(a)k(a

ˆˆˆ

k

)k(veJ

{ ][ c.c.)k(a)k(a2

}2

2 )k(a

2

)k(a

]][[ mvcm

2

vmmc

pepe)exp(i2E

pApA)k(a

ˆˆ

][ cv222

v2c2

pe)exp(iE

pA)k(a

ˆ

One-photonabsorption

Two-photonabsorption

QuantumInterference

E

ConductionBand

ValenceBand

k

Even in k

Odd in k

Odd in k

Simplified Setup

Stabilized Ti:sapphire modelocked laser

Splitmirror

Time delay adjustFiberbroadening

Lock-in amplifier

I/V

Lens

Sample

RF spectrumanalyzer

Prism

Prism

~15 fs, 93 MHz rep. rate, up to 400 mW avg. power

LT-GaAs

Signal Amplitude

2.2k 2.4k 2.6k

-40

-20

0

10 Hz Res. BW

Signal Background

(b)

RF

Po

we

r (d

B)

Signal Frequency (Hz)

Current ≈ 100 pA

• Now have >500 pA.

Incident Power

• < J > ~ I(I2)1/2

0.0 2.0 4.0 6.0 8.00.0

0.1

0.2

0.3

0.4

0.0 0.2 0.4 0.6 0.8

QIC

Sig

na

l (m

Vrm

s)

Infrared Power (mW)

Theory

2 data

data

Visible Power (mW)

Roos et al., JOSA B (to be published)

CE Phase Sensitivity

25 50 75 100

0.0

0.5

1.0

1.5

Signal Theory

(a) o

o

o

o

40

35

3025

o20o15

Ph

ase

(-

rad

)

Time (s)

• Verification that phase of QIC signal varies with shifts in carrier-envelope phase.

Fortier et al., PRL 92, 147403 (2004)

Detection Bandwidth

• With transimpedance amplifier: 830 kHz.

103 104 105 106 107-20

-10

0

10

CST

=0.2 pf

CST

=0 pf

VoltageAmplification

TransimpedanceAmplification

Rel

ativ

e S

igna

l Pow

er (

dB)

Stabilization Frequency (Hz)

Roos et al., JOSA B (to be published)

Simplified Stabilization Setup

Output coupler

High reflectorPump

Ti:sapphire crystal

Prism

Prism

Splitmirror

Time delay adjustFiberbroadening

Stabilizationelectronics

I/V

LensSample

To phase noiseanalysis

Ti:sapphire laser

~

Mixer

Synthesizer

Stabilization via QIC

• CE phase evolution stabilized.

10-1 100 101 102 103 10410-10

10-5

100

105

1010

Locked

UnlockedP

ha

se N

ois

e P

SD

(ra

d2 /Hz)

Frequency (Hz)

Roos et al., Opt. Lett. (to be published)

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.