Experimental realization of squeezing Lecture 5 Quadrature and squeezed states V Quadrature and squeezed states degree of squeezing direction of squeezing 1 Squeezing basic idea ID: 654795
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Slide1
SqeezingSqueezing operatorExperimental realization of squeezing
Lecture 5: Quadrature and squeezed statesSlide2
V- Quadrature and squeezed statesSlide3
( degree of squeezing, direction of squeezing)
1)
Squeezing: basic idea
position
momentum
Heisenberg uncertainty principle
Coherent state
Noise distribution
symmetric
in phase space
Squeezed state or
Noise distribution not
symmetric
in phase space
Circle
Ellipse
complex amplitude (position in phase space)
complex squeezing parameter Slide4
2)
The squeezing operator
Displacement operator
2 photons processes
Ideal squeezed state
Squeezed vacuum
?
Some properties of the squeezing operator
Hermitian conjugate operation
Transformation of annihilation
and creation operators
?Slide5
Is a minimum uncertainty state ?
State is displaced
in the complex plane
ifSlide6
Average number of photon in the squeezed state
# of photons in
the coherent state
Challenge problem: Find the number state expansion of the squeezed vacuum state
??
What is the photon statistics of a squeezed coherent state?
Another definition of the squeezed state
Bogoliubov transformation
Bosons
is an eigenstate of
Squeezed state is a coherent state for the operator and can thus be obtained by a
coherent displacement of the squeezed vacuum
and
# of photons in the squeezed vacuumSlide7
A different squeezed state
First squeeze then displace
First displace then squeeze
these states are
different
!
Both are minimum uncertainty states
If you first displace by
then squeeze with Slide8
3)
Generation of squeezed states
Squeezed light can be generated in nonlinear optical crystals.
Parametric
amplification
Non linear interaction with the medium
non linearity
(LiNbO3 or lithium triborate (LBO))
non linearity
(optical fiber)
interaction between three distinct light waves
(with different
frequencies
)
Pump
Pump photons are converted
into signal and idler photons
2) Signal
3) Idler
Degenerate parametric
amplification
Photon in the pump
Nonlinear interaction
one c-photon two a-photons
If the pump intensity is large: classical field
vacuum input can generate
a squeezed vacuum
PRL 100 (3),
033602 (2008)
four-wave-mixing (2 pumps now)
nonlinear optical
Kerr
effect
The Kerr effect transforms a coherent state
from a pump laser into a squeezed state
In phase space, higher amplitude regions
induce an increased phase shift
Significant pump powers required
Phonon-photon coupling
Arxiv 1511.03250
30 years of squeezed
light generation