Transcript Document

Experimental Quantum Correlations in
Condensed Phase: Possibilities of
Quantum Information Processing
Debabrata Goswami
CHEMISTRY*CENTER FOR LASERS & PHOTONICS*DESIGN PROGRAM
Indian Institute of Technology Kanpur
Funding:
* Ministry
of Information Technology, Govt. of India
* Swarnajayanti Fellowship Program, DST, Govt. of India
* Wellcome Trust International Senior Research Fellowship, UK
* Quantum & Nano-Computing Virtual Center, MHRD, GoI
* Femtosecond Laser Spectroscopy Virtual Lab, MHRD, GoI
* ISRO STC Research Fund, GoI
Students: A. Nag, S.K.K. Kumar, A.K. De, T. Goswami, I. Bhattacharyya, C. Dutta, A. Bose, S. Maurya, A. Kumar,
D.K. Das, D. Roy, P. Kumar, D.K. Das, D. Mondal, K. Makhal, S. Dhinda, S. Singhal, S. Bandyopaphyay, G. K. Shaw…
Laser sources and pulse characterization
What is an ultra-short light pulse?
τΔν = constant ~ 0.441 (Gaussian envelope)
Laser Time-Bandwidth Relationship
• For a CW Laser
5. 1
) x *2 (ni s
1
5. 0
0
Delta function
~0.1 nm
5 .0 -
1-
0
5-
time
01 -
5 .1 51 -
02 -
wavelength
• 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
10 fs (FWHM)
available
94 nm
Ti:Sapphire
Laser at 800nm
wavelength
time
Pulse Characterization: Intensity Autocorrelation
800
Spectral intensity (a.u.)
Non-collinear Intensity autocorrelation
M1
SPITFIRE PRO
600
400
200
0
600
650
700
750
800
850
900
950
100
150
1000
Wavelength(nm)
M1
BS
M1
L
M1
1.2
M Mirror
L Lens
BS Beam Splitter
PD Photo Diode
Delay
BBO
PD
1.0
SHG Intensituy (a.u.)
M1
M1
0.8
0.6
30 fs
0.4
0.2
0.0
-200 -150 -100
-50
0
50
Delay (fs)
200
Laser Pulse Profile
Laser central wavelength ~730 nm, Pulse width: ~180 fs
Pulse Characterization Under Different Repetition rate
1.4
1 kHz raw dtata
1 kHz fitted data
500 Hz raw data
500 Hz fitted data
333 Hz raw data
333 Hz fitted data
250 Hz raw data
250 Hz fitted data
200 Hz raw data
200 Hz fitted data
100 Hz raw data
100 Hz fitted data
50 Hz raw data
50 Hz final data
25 Hz raw data
25 Hz fitted data
20 Hz raw data
20 Hz fitted data
10 Hz raw data
10 Hz fitted data
5 Hz raw data
5 Hz fitted data
1.2
SHG Intensity (a.u.)
1.0
0.8
0.6
0.4
0.2
0.0
-400
-300
-200
-100
0
100
Pulsewidth (fs)
200
300
400
Laser
repetition
rate (Hz)
1000
500
333
250
200
100
50
25
20
10
5
Pulse
width
(fs)
47
52
58
59
62
67
69
80
81
88
111
Ideal Two-Level System
F∆ + 𝑁∅
Ω

N (t ))
G
2
 GΩ

0
G
H2 2
1
H
FM
ℏ
∗ *
1 1
E(t )   0 (t )ei.t i (t )

I
J
J
0 J
K
1
2
   R  N
1(t)=k(eff.(t))N/
N
N
eff
  n
 R   2  1
n
d (t )
dt

i

2
[  (t ), H
FM
(t )]
Phys. Rep. 374(6), 385-481 (2003)
1
Electric Field
Rabi Frequency
Intensity
Time
Resonance offset (Detuning)
Effect of Transform-limited Guassian Pulse
Excited state population w.r.t Rabi frequency
and detuning
Effect of Transform-limited
Hyperbolic Secant Pulse
Excited state population w.r.t Rabi frequency and detuning
Consider a
& let the
be
For Rotating Wave Approximation (RWA) to hold:
Though this may hold for the central part of the spectrum for a very spread-out spectrum
(e.g., few-cycle pulses), it would fail for the extremities of the spectral range of the pulse.
To prove this point, lets rewrite the above equation as:
At the spectral extremities
FAILS
FAILS
RWA
Failure
When we go to few cycle pulses, we need
to evolve some further issues…
Few cycle limit?
150
150
With RWA
100
Without RWA
Area
Area
100
50
-1.5 -1.0 -0.5
0
0.5 1.0
Detuning
1.5
0
-1.5 -1.0 -0.5
Pulse in Time Domain with FWHM = 1.016576e+02 fs
0
0.5 1.0
Detuning
300
1.5
200
Intensity (arbitrary units)
0
50
100
Secant
Hyperbolic Pulse
6-cycles limit
0
-100
-200
-300
0
50
100
150
200
250
Time (fs)
300
350
400
450
Observations & Problem Statement…
• The constant area theorem for Rabi oscillations, at zero detuning, fail on reaching the
higher areas (and hence, intensity).
• This is dependent on the number of cycles in each pulse. So, let us define a threshold
function for the area, for each type of profile:
where n is the number of cycles, and the minimum is taken over the inversion contours
of the corresponding profile.
Study the DEPENDENCE of ‘χ’ on ‘n’ for DIFFERENT pulse envelop profiles
Effect of Six-Cycle Gaussian Pulse
Effect of
Eleven-Cycle
Gaussian Pulse
Effect of
Thirty-six Cycle
Gaussian Pulse
χ(n)
χ(n)
Typical Example: cosine squared
 χ(n) characterizes the critical limit of area, after which the cycling effect
dominates the envelop profile effect, for few-cycle pulses
 This measure is DEPENDENT on the envelop profile under question.
Present Status
• Many cycle envelop pulses:
• Area under pulse important
• Interestingly,
• Envelop Effect still persists even in the few cycle limit results
• Measure of nonlinearity has to be consistent over both the domains…
The plane wave equations for the two photons and the combined wave
function is given by:
Hamiltonian.
Thus
This two-photon transition probability is independent of δ, the time
delay between the two photons
• Relative Photon delay is immaterial
• Virtual state position is also not extremely significant
• Coherent Control
• Bioimaging
• Multiphoton Imaging
• Optical Tweezers
• 2-D IR Spectroscopy
Femtosecond Pulse Shaper
Measurement
of Nonlinearities