# PowerPoint Presentation - Quantum Optics and Spectroscopy

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```					Conditional dynamics and quantum feedback,
an experiment in cavity QED

Luis A. Orozco
UMD College Park
Students:
Matthew Terraciano
Basudev Roy
Michael Scholten
Rebecca Olson

Post Doctoral Associates:
Dan Freimund
Daniela Manoel

Former Students:
Joseph Reiner
Stephan Kuhr (Bonn)

Collaborators:
Howard Wiseman, Griffith University, Brisbane, Australia.
Perry Rice, Miami University, Oxford, Ohio.
Julio Gea-Banacloche, University of Arkansas, Fayetteville, Arkansas
Supported by NSF and NIST
Open Quantum Systems in Quantum Optics

The answer depends on how we probe the system

Quantum Trajectories
Strong coupling:

The fluctuation is larger than the mean. (The smallest
fluctuation is a photon). The signal is going to be noisy.

For noisy signals:

Make measurements in coincidence.

Example:
Handbury Brown and Twiss
Calibration of a high energy detector. (Geiger in 1910 )
Hanbury-Brown and Twiss, (1956)

Measure the size of a star by looking at coincidences of
the intensity fluctuations.

Michelson                         HBT
Detector

Source
Field interference              Intensity Coincidences
Source
A              B

A

B

time

4 coincidences out of 5 A detections; efficiency of B=4/5
It is not necessary to know the efficiency of A!
Hanbury-Brown and Twiss Intensity-Intensity Correlations

I (t ) I (t   )
g ( ) 
( 2)
2
I (t )

The correlation is
largest at equal time

g 2 (0)  g 2 ( )

Schwarz
Intensity correlation function measurements:

ˆ ˆ
I (t ) I (t   )
g ( 2 ) ( )                   2
ˆ
I (t )

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

ˆ
I ( )
g ( 2 ) ( )                 c
ˆ
I
Cavity QED
Quantum Electrodynamics for pedestrians. No renormalization
needed. A single mode of the electromagnetic field of a cavity.

ATOMS + CAVITY MODE
Non perturbative regime: Coupling > dissipation

Dipole coupling between the atom             d  Ev
and the cavity.                           g


The field of one photon in a                     
Ev 
cavity with Volume Veff is:                     2 0Veff
Cavity QED System

 g   
Cavity length  850 m                , ,   5.1, 3.7, 3.0 MHz
 2 2 2 

10-4 photons in the cavity in steady state.

Exchange of Excitation:
Regression of the field to steady state after the
detection of a photon.
Each escape of a photon creates a very large disturbance.

We want to monitor that disturbance or fluctuation.

But we can only get one photon at best every time there is a disturbance.

We have to average the conditional intensity.

How does the data look in the lab?
7 663 536 starts    1 838 544 stops

Non-classical, antibunched
Conditioned measurements in the language of correlation
functions allow the study of the dynamics of the system.

Quantum conditioning, with photodetections, provides the
most ideal times for controlling the evolution of the system.

Feedback on a single photodetection.
Quantum System           Measurement Device

Amplifier

ENVIRONMENT
We have to satisfy three conditions:

Amplitude

Sign of the step (parity)

Time of the step

We only have one bit of information, a click.

We have good knowledge of the dynamics.
Conditional dynamics of the system wavefunction

2g              2 pq               2 g2 q
ss  0, g   1, g            0, e               2, g              1, e
                 2                  

  a , p  p( g , ,  ) and q  q( g , ,  )
ˆ

2 gq
a ss  collapse  0, g  pq 1, g 
ˆ                                                             0, e


    0, g    f1   1, g  f 2   0, e   O 2 

Field         Atomic Polarization
2g
Same coefficients when         f 2 T           f1 T 

Theoretical prediction.
Convergence of the peak with increasing sample size. Error bars are
1 s. The horizontal line passes through thefinal measured value of
the peak.
Questions:

How long can we hold the system and then release it?

How sensitive is it to atomic detuning?

Where is the information stored?

Deterministic source?

Can we feedback the field not the intensity?
Feedback    D = +2 MHz
with
detuning
Atomic
Resonance
D = -2 MHz

Cavity
Resonance
Semiclassical result, the feedback does not work!

How long can we hold the system and then release it?
As long as we want!

How sensitive is it to detunings?
With our protocol we only operate well on resonance.

Where is the information stored?

The detection of the first photon.

Deterministic source?
No, we mostly create the vacuum: |0,g> + |1,g> + …
Future directions:

Cross correlations between field and atomic fluorescence can
track the time evolution of the entanglement.

We want to study this and started looking at a model for a
single atom in the cavity.

Construction is under way for the apparatus to measure it.

We should be able to apply quantum feedback.
Cross correlation between the fluorescence and
the transmitted field. This function tracks the
entanglement.
Quantum trajectory of the atom field entanglement.

The entanglement grows after a spontaneous emission!
Summary:

Knowledge of the conditional state for a
continuously monitored cavity QED system 
Quantum feedback protocols
We trigger on a fluctuation (photon detection)
and change the drive at a particular delay after
detection. Weak driving field manipulation.
The initiation is with a fluctuation, the
feedback is just as for any driven coupled
oscillators.

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