Detecting atoms in a lattice with two Detecting atoms in a lattice with two photon raman transitionsphoton raman transitions
Inés de Vega, Diego Porras, Ignacio CiracMax Planck Institute of Quantum Optics
Garching (Germany)
Summary
3) Conclusions
1) Motivation: what is an atom lattice?
why measuring atoms in a lattice?
2) Measuring atoms in a lattice: Time of flight experiments
Our method
“I am not afraid to consider the final question as to whether, ultimately---in the great future---we can arrange the atoms the way we want; the very atoms, all the way down! “
Richard Feynman, December 29th 1959 at the annual meeting of the American Physical Society at the California Institute of Technology (Caltech)
Richard Feynman, December 29th 1959 at the annual meeting of the American Physical Society at the California Institute of Technology (Caltech)
What would the properties of materials be if we could really arrange the atoms the way we want them? […] I can't see exactly what would happen, but I can hardly doubt that when we have some control of the arrangement of things on a small scale we will get an enormously greater range of possible properties that substances can have, and of different things that we can do.
What is an optical lattice
A standing wave in the space gives rise to a conservative force over the atoms
Optical potential
V0
What is an optical lattice
A standing wave in the space gives rise to a conservative force over the atoms
Optical potential
V0
Space dependent Stark shift: when
Laser blue detuned >0 atoms go to the
Potential minima
>0
What is an optical lattice
Due to the periodic potential, the discrete levels in each well form Bloch bands
We consider the atoms placed in the lowest Bloch band
Described with creation fuction of a particle of spin α:
Wannier functions localiced in each lattice site.
Creation operator with bosonic (fermionic) conmutation (anticonmutation) relations
Atom Hamiltonian in second quantization
Gives rise to a kinetic term, with magnitude “t”
Gives rise to a repulsive term, with magnitude ~ U.
Atom Hamiltonian in second quantization
Gives rise to a kinetic term, with magnitude “t”
Gives rise to a repulsive term, with magnitude ~U.
Spin-spin interactions (example, for atoms with J=1)
Atom Hamiltonian in second quantization
Gives rise to a kinetic term, with magnitude “t”
Gives rise to a repulsive term, with magnitude ~U.
Variating parameters t and U, this hamiltonian undergoes Quantum Phase Transitions
An optical lattice is controllable
V0
We can change the standing wave parameters: V0 and λ
We can apply an external magnetic field to increase scattering length
We can use state dependent potentials
λ B
Mott state very important:
1) To simulate magnetic Hamiltonians (spin-spin interactions)
2) As a quantum register (where highly entangled states, cluster states, can be created)
t>>U :Shallow lattice (large kinetic energy), gives rise to a superfluid state
T<<U :Deep lattice, strong interactions, gives rise to a Mott state. Atoms are localized in each site.
Why measuring atoms in a latticeA lattice is a nice quantum simulator, and may be a nice implementation of a quantum computer but...
...how can we read out the information from it?
Time of flight experiments Off-resonant Ramman scattering of light
and more...
Interaction between atoms and light
Adiabatically eliminating the e> level
Duan, Cirac, Zoller (2002)
Laser ge
z
x
y
Emited photon
se
Lkkk
Photon counting type of measure
z
x
y
k
Detected correlations of photons
Correlations of atom variables in momentum
space
And if we consider T<<1/Γ we detect atom correlations in the
ground states(1)
(2)
This is our main assumption.
We check the relative error between (1) and (2) with respect to the number of photons that are emitted.
0.3 0.2 0.1 0.1 0.2 0.3q
20
20
40
60
80
q1L
Checking the assumption T<<1/Γ
Even if there were some lattice sites without an atom, this function for large is approximately a delta.
3 NL
Through the Quantum Regression Theorem this is the evolution that
correlations have
Checking the assumption T<<1/Γ
0.5 1 1.5 2
13
14
15
Number of y-polarized photons in θ for T=0.0025 This is the type of
things we measure
Nyy () number of photons detectedNyy () number photons comming from ground state
Conclusions
-Not destructive: one can perform measures of the state in the middle of an experiment and then continue
-More freedom to compute different correlations and hence to detect more complex phases-More precission with respect to time of flight:
Signal to noise ration in Time of flight ~
in Raman scattering~
N/1
N
-3D information
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