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Ultrafast Pulse Shaping Approaches to Coherent Control. Debabrata Goswami Tata Institute of Fundamental Research Mumbai, India Funding: TIFR & Min. Info. Tech. An Ultrafast Laser Pulse.

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ultrafast pulse shaping approaches to coherent control

Ultrafast Pulse Shaping Approaches to Coherent Control

Debabrata Goswami

Tata Institute of Fundamental Research

Mumbai, India

Funding: TIFR & Min. Info. Tech.

an ultrafast laser pulse
An Ultrafast Laser Pulse
  • Coherent superposition of many monochromatic light waves within a range of frequencies that is inversely proportional to the duration of the pulse

Short temporal duration of the ultrafast pulses results in a very broad spectrum quite unlike the notion of monochromatic wavelength property of CW lasers.

e.g.

Commercially

available

Ti:Sapphire

Laser at 800nm

10 fs (FWHM)

94 nm

wavelength

time

CW

Laser

Delta function

~0.1 nm

wavelength

time

pulse shaping
Pulse Shaping
  • Control over the amplitude, phase, frequency and/or inter-pulse separation
  • Complex pulse shaping aims to control one or more of the above-mentioned parameters in a programmable manner, according to user specification.

Can be represented by Linear Filtering Scheme:

Time Domain:

    • Eout(t) = Ein(t)g (t)  => convolution
    • Hard Job—Timescales not quite accessible with conventional electronics (typically ns)!

Frequency Domain

    • Eout() = Ein ()G ()
possibilities
Possibilities…

Typical Lasers

Our Work

  • Terabit/sec data transmission capabilities for optical communication.
  • Coherent Control of atoms and molecules.
  • Exploring capabilities of experimentally realizing quantum computation.
  • Control of biomolecules in both center-of-mass and internal degrees of freedom motion.
  • Bring about analogs of pulsed NMR…
pulse shaping wdm why it s better

Time

Pulse Shaping WDM: Why it’s better
  • Switching Window T (Switch Speed), DTR=1/ T
  • Pulse Width T0 (Bandwidth Available), DTR~1/ T0

Time

ultrahigh ratio data compression
Ultrahigh Ratio Data Compression

4 ms

20 ps

  • Ultra-high Ratio (~105) Data Compression
  • High fidelity, good SNR
  • All-one Case Return to Zero format Amplitude Shift Keying
slide8

Transform limited

laser pulse

Frequency sweep generated

by an optical fiber

~15 ps

20 ps

Frequency sweep generated

by an grating or prism pair

slide9

Effect of Simple Shaped Pulses: Frequency Chirped Pulses

(a) Theoretical

(b) Experimental

(a) Comparison of the probability of excitation as a function of applied Rabi frequency, for 2 ps transform-limited (Gaussian) pulses. indicated by crosses (+), and bandwidth equivalent 20 ps frequency-swept (Gaussian) pulses, indicated by circles (0).

(b)Fluorescence excitation curves for the pentacene/p-terphenyl mixed crystal system excited by 3 ps near transform-limited laser pulses, indicated by circles (0), and by bandwidth equivalent 20 ps laser pulses chirped by the diffraction grating method, indicated by crosses (+). Each point is the average of ten laser shots.

JCP, 101,6439 (1994)

two level feynmann s pseudo polarization vector

z

y

x

=(2+2)1/2

Two Level Feynmann’s pseudo-Polarization Vector

D = w~w0

E=e.ei(wt+f)

hw0

m. e

W=

h

interferometer pulse shaping
Interferometer Pulse Shaping

Femtosecond Reaction Dynamics, p. 291

(D.A. Wiersma, editor, North-Holland,

Amsterdam, 1994); Ultrafast Phenomena, IX.

acousto optic modulated pulse shaping technology
Acousto-Optic Modulated Pulse Shaping Technology

Acousto-optic laser pulse shaping

Femtosecond Reaction Dynamics, p. 291

(D.A. Wiersma, editor, North-Holland, Amsterdam, 1994);

Opt. Lett., 19, 737 (1994).

ultrashort pulse version
Ultrashort Pulse Version

Grating 1

Concave Mirror 1

Mask

Concave Mirror 2

Grating 2

the pulse shaper

1

experiment

theory

0.8

0.6

Intensity (arb)

0.4

0.2

0

-5

-4

-3

-2

-1

0

1

2

Time (ps)

The Pulse-Shaper

Examples of Phase & Amplitude Modulation

Intensity (arb)

wavelength (nm)

slide20

Calibration

Application:

schematic of the feedback loop
Schematic of the Feedback Loop

Initialize the system

RF Pulse Shaper

Computer

Take spectrum from OSA; normalize it.

Update the RF waveform

Compare with normalized target; Within set limit?

Optical Spectrum Analyzer

(OSA)

Ultrafast Laser Pulse Shaper

END

examples amplitude modulation
Examples: Amplitude Modulation
  • Real time programmable
  • Well confined temporal shape for TDM switching
slide25

Phase Modulation: Tunable Delay Line

  • M(tRF)=ewRF*tRF
  • M(wlaser)=ewRF* a /vac (wlaser-w0,laser)
  • Eout(wlaser)=Ein(wlaser)* ewRF* a/vac (wlaser-w0,laser)
  • Eout(tlaser)=FT {Ein(wlaser)* ewRF* a/vac (wlaser-w0,laser)}

=Ein(t+t)

  • t=a/vac DwRF
slide26

Rapid Tunable Delay Line

110 MHz

115 MHz

120 MHz

125 MHz

130 MHz

7

135 MHz

140 MHz

145 MHz

6

150 MHz (Start)

150 MHz (End)

155 MHz

160 MHz

5

165 MHz

170 MHz

175 MHz

Crosscorrelation sig. (arb. units)

4

180 MHz

185 MHz

190 MHz

3

195 MHz

2

1

0

10

12

14

16

18

20

22

24

26

28

2

4

0

6

8

Time (ps)

examples of strut trace

2500

Retrieved

Phase

40

Linear Sweep

2000

Retrieved

Spectrum

20

E() = ei2

1500

Measured

Spectrum

Intensity (arb)

0

Delay (ps)

1000

-20

500

-40

0

780

790

800

810

820

830

392

396

400

404

408

1

experiment

theory

6

0.8

Cubic Phase

4

E() = ei3

0.6

2

Delay (ps)

Intensity (arb)

0

0.4

-2

0.2

-4

-6

0

-5

-4

-3

-2

-1

0

1

2

397

398

399

400

402

403

401

Time (ps)

STRUT-Wavelength (nm)

Examples of STRUT-trace

Direct measurement of phase and amplitude-profile of shaped pulses

1

Phase (rad)

0.5

0

Wavelength (nm)

STRUT-Wavelength (nm)

slide29

6

4

2

Delay (ps)

0

-2

-4

-6

397

398

399

400

402

403

401

Wavelength (nm)

Linear Sweep: eiw2t

Cubic Phase: eiw3t

Cubic Phase: e-iw3t

slide30

5

4

3

2

1

0

\' (ps), intensity (arb)

-1

-2

-3

Intensity

-4

’

-5

788

793

798

803

wavelength (nm)

1.0

Population

0.5

0

15

15

10

5

10

0

-5

5

Detuning (cm-1)

Rabi Frequency (cm-1)

-10

-15

0

Hyperbolic Secant Pulse

Time-Domain

Spectrum

1.0

Real

Imaginary

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Time (ps)

  • Population inversion through adiabatic rapid passage.
  • Robust because of rectangular inversion-profile.
  • Little Reshaping when propagating through dense media

Inversion Profile

slide31

A: Femtosecond Gaussian pulse (plotted as a function of time in the box below A)

B: Grating that spectrally spreads the pulse.

C: Acousto-optic modulatoris in the center of the system

D: The RF-wave propagates through the AOM, creates a spatial mask inside the crystal and shapes the optical pulse.

E: The undiffracted beam passes out of the system

F: Grating that recombines the spectrum

G: Pulse picker picks the shaped output pulse

In this schematic, the input optical pulse is modeled as consisting of four different wavelengths, blue, yellow, orange, and red, which would represent a 4-bit system. In principle, the AOM is capable of shaping 1000 bits. The white parts of the diffracted spectrum are left undiffracted by the AOM. The output (G and the box below the G) shows the shaped output pulse as a function of wavelength. As the rf wave propagates, different shapes are created. The pulse picker G picks the pulse at the correct time out of the pulse train. Here the pulse picker is shown separately selecting a particular pulse H, but in the experiment, the pulse picker is located inside the regenerative amplifier I.

slide34

Quantum Example: Effect of Ultrashort Pulses on Rubidium Atoms

-6

-4

-2

0

2

4

Rubidium atoms when excited with femtosecond pulses show hitherto unknown strong stimulated emission that lasts only a few picoseconds as seen from the STRUTs’ below. We believe pulse propagating effects are manifested in terms of chirp generation of the pump pulse that is showing adiabatic sweeping effects. Rubidium atoms in particular spin-polarized state are used for Magnetic Imaging Studies and are useful in medical diagnostic applications.

Delay (ps)

-8

405

-4

385

400

405

380

395

Time (ps)

400

Wavelength (nm)

4

Wavelength

385

8

380

slide35

Transform-Limited Pulse vs. Sech Pulse

-8

-4

405

4

Time (ps)

400

8

385

380

Wavelength (nm)

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5

-4

-3

-2

-1

0

1

2

3

4

5

Delay (ps)

396 397 398 399 400

396 397 398 399 400

396 397 398 399 400

STRUT Wavelength (nm)

Rubidium atoms when excited with femtosecond pulses show hitherto unknown strong stimulated emission that lasts only a few picoseconds as seen from the STRUTs’ below. Pulse propagating effects are manifested in terms of chirp generation of the pump pulse that is showing adiabatic sweeping effects. Rubidium atoms in particular spin-polarized state are used for Magnetic Imaging Studies and are useful in medical diagnostic applications.

ensemble cnot gate

Shaped Pulse

A

B

AB

“Inverting” Pulse

1

1

0

1

0

1

“Dark” Pulse

0

1

1

0

0

0

Ensemble CNOT Gate

A quantum mechanical ensemble B that can either be in the ground (state 0) or excited (state 1) interacts with the control pulse A, which provides robust chirped pulse inversion (condition 1) and the self-induced transparency or dark pulse (condition 0)

what is coherent control
What is Coherent Control?
  • Study of possible control on the future of any coherent light-matter interaction is Coherent Control.
  • Since the original inception of control over quantum phenomenon as a goal, the potential applications have broadened out beyond chemical reactivity
  • Coherent control could lead to logic gates for Quantum Computer
slide39

Laser Selective Chemistry: the "Holy Grail"

Example: excite a high overtone of the C-H stretch in toluene

H

H

H

H

H

H

Chemical

Laser

H

OH

H

OH

OH

Reaction

H

H

H

H

H

H

In practice, this almost never works. The overtones of the

normal modes carry the oscillator strength, but they are not

eigenstates. Usually many different modes end up excited; this

is called "intramolecular vibrational redistribution" (IVR).

slide40

Bond Selective Chemistry: Choice of Molecules

H

D

O

O

Laser

Laser

D

H

HOD + H  H2 + OD

HOD + H  HD + OH

Chemical reactions break bonds between atoms in a molecule. Before the bond breaks, it must be elongated first. If the molecule begins to vibrate along the "reaction coordinate" before the reaction starts, the bond will be weakened and hence facilitate the reaction. In 1995, Prof. F. Fleming Crim took the partially deuterated water molecule, HOD, as an example to show the first ever example of bond-selected chemistry. HOD can react with H atoms in two ways. They demonstrated that it is possible to control the path the reaction takes by judiciously choosing the initial vibrational state of the HOD with laser excitation. States that are predominantly OH-stretching produce H2 + OD, while OD-stretching states react to produce HD + OH. In essence, the initially excited bond is the one that breaks in the reaction.

slide41

Fe+ FeCO+ Fe(CO)2+ Fe(CO)3+ Fe(CO)4+ Fe(CO)6+

(b)

(a)

(a) Schematic experimental setup. Femtosecond laser pulses are modified in a computer controlled pulse shaper. Ionic fragments from molecular photodissociation are recorded with a reflecton TOF mass spectrometer. This signal is used directly as feedback in the controlling evolutionary computer algorithm to optimize the branching ratios of photochemical reactions.

(b) Relative Fe(CO)5 photodissociation product yields. The yields are derived from the relative peak heights of the mass spectra. The ratio of Fe(CO)5+/Fe+ is maximized (solid blocks) as well as minimized (open blocks) by the optimization algorithm, yielding significantly different abundances of Fe+ and Fe(CO)5+ in the two cases. The peak heights of all other masses [Fe(CO)+ up to Fe(CO)4+] have not been included in the optimization procedure.

Gerber et.al. SCIENCE 282, 1919 OCTOBER 1998

molecular decoherence ivr
Molecular Decoherence: IVR

Ever since the early days of quantum mechanics, there has been an implicit dream of controlling atomic and molecular dynamics. It was pursued with even greater vigor with the discovery of the first laser. However, such quantum mechanical "control" has remained as an evading issuea dream. The major reason for its elusive nature is the energy and coherence randomization due to the typically strong coupling amongst the molecular degrees of freedom, such as intramolecular vibrational relaxation (IVR).

Normal Mode Picture

Eigenstate Picture

Couplings

• • •

Normal Mode

Doorway

Overtone:

states

"Bright State"

Other rovibrational

Oscillator strength

levels: "Dark States"

from normal mode

is distributed among

many eigenstates

Ground state

Ground state

manifestation of ivr in anthracene

|5>

|2>

|4>

|3>

1420cm-1

excitation

|1>

Manifestation of IVR in Anthracene

Effect of Gaussian Pulse

Experimental Results: Felkar & Zewail, 82, 2961-3010 (1985)

model calculations with shaped pulses
Model Calculations with Shaped Pulses

Anthracene

|5>

|2>

|4>

|3>

1420cm-1

excitation

|1>

Adiabatic Passage With Intense Pulses

Adiabatic Half Passage

Resonance

QC Theory:

Goswami,

(PRL, 88, 177901-1,2002)

Goswami & Warren, JCP(92), PRA(94))

slide45

Generating complex waveforms: Applications

Amplification

Applications (e.g. Quantum Control)

conclusions
Conclusions
  • Programmable Ultrafast Pulse Shaping approaches involve linear filtering either in the time-domain or Fourier domain modulation techniques.
  • Choosing a combination of two specific shaped pulses: one that always generates inversion and the other that always generates self-induced transparency allows us to construct a scalable CNOT gate.
  • Single or multi-photon intramolecular dephasing can be kept to a minimum for the duration of “locking” period under adiabatic conditions. The effect occurs under adiabatic condition & is insensitive to inhomogeneities in Rabi frequency.
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