View
216
Download
0
Category
Preview:
Citation preview
Opacity of electromagnetically induced transparency for quantum fluctuations
Pablo Barberis Blostein y Marc Bienert
Instituto Nacional de Astrofisica Optica y electronica. Tonantzintla,
Mexico.
Plan Introduction
Electromagnetically induced transparency (EIT)
Storing a light pulse in an atomic medium Quantum memories
Propagation of quantum states (squeezed states) in EIT. Resonance case Two photon detuning case.
Two level atom illuminated with a laser
Laser
When =0, the electron realizes Rabi oscillations between levels |0 y |1 with frequency:
Laser frequency = Atomic transition frequency.
|| g
|0
|1
Laser
Probability of finding the atom in the excited state:
|0
|1
{
Laser
Light Absorption by the atoms
Medium composed of Three level
atoms.
Laser
The linear response of the absorption is proportional to the imaginary part of electric dipole
operator.
Electromagnetically induced transparency (EIT)
|2
|0
|1 1
2 1
2
Laser 2Laser 1
{
Dark States
Perpendicular states to the dark state.
Dark state
|1 |2
|0
12
iii g
If the system is initially in state |0
|1 |2
|0
12
Dark states and EIT
Dark state:
0- 1
Laser 1 (pump)2{
Laser 2 (probe)
probe
|0
|1 |2
|2
|0
|1 1
2 1
2
Laser 2Laser 1
2 {1 {
Group velocity of a light pulse inside a medium showing EIT
If the pump Rabi frequency is much bigger than the probe Rabi frequency, the light pulse velocity is given
by
Capturing the light
What happens if the field is treated quantum mechanically? Probe field treated quantum
mechanically Classical pump field with Rabi frequency
much bigger than probe field. Adiabatic approximation.
If both fields are treated quantum mechanically:
First quantum EIT experiment:
What I want to answer:
Pump: Coherent state (Ideal Laser)
Three level atomspump
probe
Probe: Quantum state (Squeezed state)
Both fields are treated quantum mechanically, and the Rabi frequencies associated with each field are comparable.
pump
probe
|0
|1 |2
What are the squeezed and coherent states?In the quantum harmonic oscillator:
In a coherent state:
Squeezed state in x
Field quadratures:Annihilation and creation operators of one field
mode.
Analog to position operator
Analog to momentum operator
In the harmonic oscillator:
The quadrature is defined as
Uncertainty relation:
Squeezed state in quadrature =0:
Coherent state:
A mode vacuum is a coherent state with =0
A mode squeezed vacuum is a mode where
Resuming: we want:
Three level atomspump
probe
pump
probe
Initial condition of pump field
Mode in resonance with transition |0-|1 in coherent state |1.
The other modes in state |0.
Initial condition of probe field.
Mode in resonance with transition |0-|2 in a squeezed state such that the field
mean value is 2.
The other modes in a squeezed vacuum.
The mean values after interaction are the same
as before interaction.
What happens with the initial quantum fluctuations?
|0
|1 |2
Equations:
If 2=0 we have:
If 2=1= we have:
Noise spectrum of the probe field quadrature:
Noise spectrum of the pump field quadrature :
|2
|0
|1
2 1
12
P. Barberis-Blostein, M. Bienert, Phys. Rev. Lett. 98, 033602 (2007)
Cavity version: P. Barberis-Blostein, Phys. Rev. A 74, 013803 (2006)
Partial Conclusions When the Rabi frequencies are
comparable, the media is not transparent for the initial quantum fluctuations.
There are two scales: One, that depends on the atomic decayment
rate, and is responsible of the lost of information (absorption) and behaves similar to the usual EIT transparency curve.
Other, that depends on the Rabi frequencies, and is responsible of the oscillation of quantum properties between the pump and probe field.
Resuming: we want:
Three level atomspump
probe
pump
probe
Initial condition of pump field
Mode with detuning with transition |0-|1 in coherent state |1.
The other modes in state |0.
Initial condition of probe field.
Mode with detuning with transition |0-|2 in a squeezed state such that the
field mean value is 2.
The other modes in a squeezed vacuum.
The mean values after interaction are the same
as before interaction.
What happens with the initial quantum fluctuations?
|0
|1 |2
{ {
The probe field is a vacuum squeezed state and the pump field is a coherent detuned state
Small two mode Resonance, equal Rabi frecuencies
implies
The carrier frequencies of the Fields are in a large two mode resonance
Influence of Doppler effect.Vacuum Squeezed state as probe field
Influence of Doppler effect.Squeezed state as probe field
Conclusions
The propagation of a squeezed probe state is very sensitive to two photon detuning. When the detuning is small there are three scales.
A vacuum squeezed state as a probe rotates its squeezed quadrature as it propagates, when the pump field is detuned.
The Doppler effect has a lot of impact in the propagation of squeezed states, preventing the possibility of making EIT experiments with quantum states in thermal clouds.
In EIT media:
Recommended