Measure of
Time-frequency bandwidth relation: Experimental demonstration of Heisenberg
Uncertainty Principle
OBJECTIVE:
There is relationship between time width and frequency bandwidth in every
spectroscopic experiments. This time width and frequency bandwidth relationship
comes from uncertainty principle, which comes from Fourier Transformation. In
daily experimental life, it is used in techniques like FTIR, FTNMR etc.
THEORY: The
Heisenberg Uncertainty principle states that it is impossible to measure the
two conjugate quantities (whose operators do not commute) simultaneously with
arbitrary accuracy. As the laser pulse goes onto the shorter and shorter in
time domain, it spectral bandwidth goes on increasing. The uncertainty in time and spectrum are
related by
Where, ∆t is the time width
and ∆ɷ is the spectral width. For the Gaussian shaped pulse, this
relation becomes
Now, we cannot measure ∆ɷ
directly from our spectrum, as there we have intensity vs. wavelength plot.
Here,
where, c
is the velocity of light in vacuum, λ is the central wavelength.
INSTRUMENTS UTILIZED:
1.
Laser
switchable between CW and pulsed mode: Ti:Sapphire
laser provides this unique facility.
2.
HR
2000 spectrometer.
3.
Multimode
optical fiber.
SOFTWARE USED:
1.
Ocean
optics OOIBase32 for spectrum collection
2.
Origin
pro for data plotting and analysis
Note: For user operation and usage no
specific software needed.
EXPERIMENT PROCEDURE:
1.
Turn
on the laser.
2.
Measure
the spectra of the CW laser using HR 2000 spectrometer. It has delta bandwidth.
3.
Turn
on the ML switch to turn the laser in pulsed mode.
4.
Measure
the spectrum of pulsed laser.
5.
Measure
the pulse width of the laser (for femtosecond pulse, use autocorrelation
technique, described in the other experiment).
6.
For
measuring ∆t and ∆λ, get the FWHM (Full Width at Half Maximum) of the respective plots, which we take as the said
parameters.
7.
Check
for the validity of eqn. (1) or (2) (whichever is applicable).
Laser spectrum (left one: femto
second pulsed, right one: CW laser)