Conditional Measurements in Cavity QED

7/31/2019 Conditional Measurements in Cavity QED

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Conditional Measurements in cavityQED

Luis A. Orozco

Joint Quantum InstituteDepartment of Physics


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University of Maryland, College Park, Maryland:Matthew L. TerracianoRebecca OlsonDavid Norris

Jietai Jing

Miami University, Oxford, Ohio:Perry Rice

James Clemens

University of Auckland, New ZealandHoward J. Carmichael

Work supported by:National Science Foundation, National Institute of Standards andTechnology


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Cavity QED:

Quantum electrodynamics for pedestrians(Haroche). No need to renormalize. Only one mode

of the electromagnetic field:

ATOM(S) + CAVITY MODE

Perturbative: dissipation >> coupling (Purcell)

Non Perturbative: dissipation


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v E d g =Coupling:

eaPr Sed 02 / 32 / 1 96.555 ==

d depends on the radial and angular parts of thewavefunctions of the electrons. For the D 2 lines

in alkali (Rb) it is a few times a 0 (el radio deBohr radius) times the electric charge.


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How large is the electric field of a photon in an

optical cavity as those from Maryland, CalTechor Garching?

Electric field in a wall plug! ~ 100 V/cm

It is possible to measure it!


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( )MHz3 2.6, 2,2

2 / ,

2 ,

2

g

Cavity QED System


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Jaynes-Cummings Model

)(21 aaaa H c za

+++ +++= g

0,g

How does a single atom interact with a single mode of theelectromagnetic field?

1,,0, ge

No interaction term:

ground state

degenerateexcited states

With interaction term:

0,g ground state

( )1,0,2

1ge =

excited states


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Dissipative Processes : Loss of a photon from the cavity due to imperfect mirrors.

: Spontaneous emission from an atom inside the cavity tomodes other than the cavity mode.

Be careful about impedance matching!

Dissipation is not always bad. Cavity loss allows us to look inside of the cavity to study the dynamics of the system.

Can we use spontaneous emission in the same way?


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eqg

g pq

eg

ggss ,12

,22

,02

,1,022

++=

),,( and ),,( , gqqg p pa ===

A photodetection collapses the steady state into thefollowing non-steady state from which the system evolves.

eqg

g pqga collapsess ,02

,1,0 +=

( ) ( ) ( )[ ] 221 ,0,1,0 Oe f g f g +++=

Conditional dynamics from the system wavefunction

Field Atomic Polarization


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Intensity correlation function measurements:

2)2(

)(

)()()(

t I

t I t I g

+=

Gives the probability of detecting a photon attime t + given that one was detected at time t .This is a conditional measurement:

I

I g c

)()()2(

=


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7 663 536 starts 1 838 544 stops


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Exchange of excitation:

Coupled system, maybe entanglement.


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Classically g(2)

(0)> g(2

)() and also |g(2)

(0)-1|> |g(2

)()-1|

antibunched

Non-classical


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Pushed MOT Apparatus

Magneto-optical trap of 85Rb atoms

N ~ 10 8 atoms.

Loading time ~ 50 200 ms. Launched toward the cavity with a resonant

push beam.


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LVIS

Atom beamAPD

A PD

PBS

B

Probe

Drive the cavity with linearly ( ) polarized light.Light emitted in orthogonal direction mustcome from a spontaneous emission.

Separate the output into two polarizationsto distinguish spontaneous emission from

cavity drive.

Experimental Schematic


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Atomic structure of Rb atoms. Quite different from 2 levels.


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Atom transit data,

measured with APD


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If the steady state wave function is separable then we should be ableto write the wave function as a product state:

AC SS =

( ) ( eC gC D D D eg +++= 210 210

ee Ae Ag Ae Ag AgeeegegSS

01201001201

+++++=

If we let A 1G = D 1, A 2g = D 2, and A 0e = C e, then the followingcondition must be satisfied for a product state: A 1e = D 1CE = A OeA1g

If this is not true There is entanglement!


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LVIS ( Low Velocity Intense Source)

Continuous source of cold atoms ~ 1 atom in cavity at all times! Similar to MOT but with a retro optic in the vacuum with a hole for

extracting a beam of atoms. Can be pulsed by plugging hole in retro optic with a MOT beam and

unplugging after a MOT forms.


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Autocorrelation of Fluorescence Mode

Traditional Correlation Measurement

Conditional Average on Oscilloscope

2

)2( )0()()()0()( =+

++

bb

bbbb FFg


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Quantum Trajectory Theory

15 photons in driven mode


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Concurrence Measurements


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Conditional Measurements in Cavity QED

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