M5L22h.txt

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When we talk about coherent spectroscopy,
I want to just in 10 minutes or 15 minutes
show you some techniques, spectroscopic techniques, which
exploit the coherence between several quantum states.
And, well, I do it for a number of reasons.
One is coherent spectroscopy actually
allows us to obtain information about the level structure
even if this level structure is much narrower
than the Doppler beats.
So it is a sub-Doppler technique to exploit coherence.
And before people had lasers, before people invented
sub-Doppler laser spectroscopy, often coherent spectroscopy
was the only way how you could obtain a detailed structure
of the atom.
So the reason why I explain coherent spectroscopy
is to just give you a little bit of idea about that you
appreciate how smart people were before lasers were developed.
But also, it illustrates what coherence can do for us.
So it's a nice example for the concept of coherence.
When I was a graduate student, textbooks
had dozens of pages, 50 pages, on coherent spectroscopy.
The Hanle effect, quantum beat measurements,
it's all old-fashioned.
Because with the laser, we have now-- and especially
[INAUDIBLE] atoms and the laser, we
have such wonderful tools to go to
the ultimate fundamental precision of quantum
measurements.
But still, coherence is important.
So let me talk about one method which is called
quantum beat spectroscopy.
The selling point about quantum beat
spectroscopy is that it allows the measurement of narrow level
spacings-- just think about [INAUDIBLE] splitting
in a magnetic field-- without any form
of narrow-band excitation.
So you can also put it like this.
If you don't have any way to selectively excite levels,
but you're interested what is the level spacing but you
cannot sort of have a narrow-band laser,
have atoms which stand still and scan and get peak, peak, peak,
what you can still do is you can just excite all the levels
at once.
In other words, you hit the atom with a broad laser,
like with a sledgehammer, and then using your beat node,
you see some blinking quantum beat between the excitation
of the levels.
So that's the idea.
So we have-- we assume we have a ground state,
and then we have an excited-state manifold.
And in this excited-state manifold,
we have several levels distributed
over an energy interval delta.
And yes, we don't have a narrow-band source.
We may just have a classical light source.
But if you use a short pulse that the pulse duration is
much smaller than the splitting between energy levels,
then we create a coherent superposition of those levels.
So therefore, what we create at time
T equals 0 is a coherent superposition of energy eigen
levels.
And the important thing is that this is a time T equals 0,
but now when time goes on, each amplitude, each part
of the wave function, evolves with its eigenfrequency, omega
i.
And if we would then look at, let's say,
the emissions spectrum as a function of time,
we will find that-- and I will give you a little bit more
detail later-- that yes, there is the decay approximated
with a natural spontaneous emission
time with the inverse of the natural line widths,
but we observe some oscillations, which
is the interference term of the different terms in the wave
function.
So therefore, if you would take this spectrum
and perform a Fourier transform, you
will actually observe different peaks.
This is frequency, and the frequency peaks
are at discrete frequencies corresponding to frequency
differences between the excited state.
And ideally, the widths of this is determined
by the natural line widths.