Presentation 1

Report
Quantum trajectories for the
laboratory: modeling engineered
quantum systems
Andrew Doherty
University of Sydney
Goal of this lecture will be to develop a model of the most important
aspects of this experiment using the theory of quantum trajectories
I hope the discussion will be somewhat tutorial and interactive.
Single photon source
Modes of the light approach atom and are scattered off
Every so often a photon is emitted into the light field, spontaneous emission
Single photon source
Modes of the light approach atom and are scattered off
Every so often a photon is emitted into the light field, spontaneous emission
Detector counts photons in scattered field
Single photon source
Modes of the light approach atom and are scattered off
Every so often a photon is emitted into the light field, spontaneous emission
Count rate
Concept of a quantum trajectory
Interact one at a time
undergo projective
measurement
Harmonic oscillators
representing input field
approach system
Single photon source
Evolution for no photon emission
This happens most of the time
Photon emission
Happens some of the time
No photon emission
Probability of no photon emission up to time t
Photon emission at t
Photon emission at time t
Probability of photon emission between t and t+dt
Total probability of photon emission
Distant Detector
Photon emission at time t
Probability of photon emission between t and t+dt
Total probability of photon emission
Detector Efficiency
Photon detection at time t+tp
Probability of photon detection between t+tp and t+tp+dt
Total probability of photon detection
Beam Splitter
Quantum Interference
Two single photon sources
Evolution for no photon emission
Photon detection at c
Photon detection at d
Two single photon sources
Evolution for no photon emission
Photon detection at c
Photon detection at d
Detection at c
Free evolution with no
photon emission
Photon detection at c
Detection at d
Free evolution with no
photon emission
Photon detection at d
Detection at d
Free evolution with no
photon emission
Photon detection at d
Coincidence Probability
Hong-Ou-Mandel Dip
State Preparation
State preparation (shelving)
v
Microwave pi/2-pulses
v
Optical pi-pulses
v
Free evolution
Detection at c
Wait
Wait for any subsequent
photon emission
Microwave pi-pulses
Microwave pi-pulses swap
spin states
Optical pi-pulses
Optical pi-pulses prepare for
second single photon emission
Free evolution
Free evolution up to second
emission
Detection at c
Detection at c and wait
Remote Entanglement
We have a state roughly equal to
With the probability we would have guessed
And output state given by: (could be improved by tightening co-incidence window)
Coincidence Probability
Hong-Ou-Mandel Dip
Notes on this calculation
Fidelity of entangled state has same
dependence on physical parameters
as for HOM experiment. Need
propagation phases to be constant
over interval between photons
Easy to see that other factors like detector
efficiency and path length difference after
the beam splitter factor out also
Timing error hasn’t been included here, could be done easily by modeling the pulse
that prepares the state e. This is another kind of mode-match error and would look
much like the dependence on the decay rates.
Note that difference in the delay time for the two paths factors out. This is because we
have modeled the propagation of the single photon pulse as if the beam were
perfectly monochromatic. This approximation is valid because we are in the Markov
regime but if the delays are too large, this needs to be corrected

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