M1L5p.txt

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We want to now talk about realization
of quantum logic and quantum gates with single photons.
But I also said that we are actually
using the language of quantum communications, a kind
of information processing, to describe general physics
in a very nice way.
So first, when we talk about photons,
we should talk about our qubits.
And right now, you may think that having a single photon
and having no photon in a mode are two possibilities
and you could use them as qubits.
However, I will tell you today that it is better, actually,
to use always one photon, but in two different waveguides,
in two different modes.
But we'll get there in a moment.
So the first task at hand is we want to manipulate photons.
And for that, I want to introduce phase shifters
and beam splitters.
And just to give you the punchline right away, what
I want to show you is that those two simple devices, beam
splitter-- a half-silvered mirror-- a phase shifter, which
is just a piece of glass which you can put into one
of the laser beams-- that those two elements and those two
basic operations, if they are now put together, if they are
now-- you do a beam splitter, a phase shifter, another beam
splitter, and such-- you can realize
any single-qubit operation.
So therefore, if we have our one qubit state
with single photons, every-- any possible state of those qubit
can be realized using these optical elements.
So therefore, when I say we start--
we're going to realize how we can manipulate photons
with optical elements and such-- I'm
not going through a zoo of optical elements.
Those two will do it all.
With the phase shifter-- that's what we discussed
at the end of last class-- if you have two modes
and we shift the phase in one of the modes-- just
simply put a glass, a piece of glass into it-- then
there is a phase shift.
And why do we need two modes?
Well, phases are usually, at least in experiments,
not absolutely defined.
You need a phase reference.
And here, the mode a acts as a phase reference.
Let me address one question which a student asked me
after class, and this was related to-- with-- phases
appear in more than one place.
The student's question was motivated
that if you have one photon, it's a Fock state.
A Fock state is a circle in the course of probability,
and therefore, the electric field has no phase.
Well, this is the phase of the electric field.
But here, we are talking about the phase of the wave function.
And a Fock state within photons is an eigenstate
of the harmonic oscillator.
It has a time dependence e to the i omega t.
And we can change its phase.
So this is the kind of phase shift I've introduced here.