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Is |45> = |H> + |V> an entangled state?
Is (|1>a + |1>b >)/sqrt 2?
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Entangled state
send in 2nd atom:
send in 1st atom:
measure in arbitrary basis: apply π/2-pulse to 2nd atom, shifted by φ w.r.t. pulse on 1st atom
Correlations insufficient to violate Bell inequality (V = 45%)- imperfect Ramsey interference- residual blackbody photons- 2-atom events
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Ramsey fringes
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QND measurement
time (s)
Quantum jumps of light recording the birth and death of a photon in a cavity, Gleyes et al., Nat. 446, 297 (2007)
Noise probabilities:p(g|1) = 13%p(e|0) = 9%
use majority vote for 8 consecutive atomsP(“0”|1) < 0.0014P(“1”|0) < 0.00025)
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This QND distinguished between 0 and 1 photon.
Question: Can we use it to distinguish between 0, 1 and 2 photons?
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QND measurement
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Quantum Phase Gate
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GHZ Three-atom entanglement
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• Quantum Integrated CircuitsQuantum currents & voltagesMicrofabricated “atoms”
• Digital to Analog ConverterClassical: V = a[0] 1 + a[1] 2 + a[2] 4 + …a[9] 512
Quantum: Ψ = α0 |0〉 + α1 |1〉 + α2 |2〉 + … α9 |9
John MartinisUC Santa Barbara
Generating Arbitrary Photon States
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Qubit
CC
qubit resonator(H.O.)
Resonator
( /2 total)
|0>
|1>
|2>
|3>
|4>
|5>
|g>
|e>
Qubit control
resonator control
Qubit Coupled to Photons (Harmonic Oscillator)Qubit-resonator first demonstrated in Saclay (1987),
GHz coupling easy in phase qubitsDesign follows cQED (Yale)Readout through qubit (Saclay87, NIST), high fidelity
Similar to ion traps (NIST), Rydberg (ENS)
stim
ulat
ed
emiss
ion
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Generating Fock States: Pumping Photons One by One
|0>
|1>
|2>
|3>
|4>
|0>
|1>
|2>
|3>
|4>
|g> |e>
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Fock States: Swap oscillations depend on |n〉
Stim
ulat
ed E
miss
ion
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Fock States: Photon number distribution for |1〉
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Fock States: Photon number distribution for |2〉
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Fock States: Photon number distribution for |3〉
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Fock States: Photon number distribution for |4〉
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Fock States: Photon number distribution for |5〉
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State preparation:
swaptime τ
Coherent states
Qubit
Res.
|g〉
|0〉 Gaussian pulse, vary
ampl.
Gau
ssia
n pu
lse a
mp.
meas.
coherent state
|α〉
vary swap time to probe resonator state
swap time τ (ns)
Poissondistribution
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υχσβυχσβ πηασε θυβιτ γρουπ
Energy level representation of desired state
Reverse-engineer final state by building pulse sequence backwards
arrow indicates complex amplitudeof corresponding basis state
zero amplitude
Generating Arbitrary States
Law and Eberly, PRL (1996)
Desired final state
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iMeasure using qubit and watching evolution (usual method):
Fourier transform yields number
composition:
Now try:
Cannot distinguish
based on this measure!
1photon
3photons
Generating Arbitrary States:Quantum Digital to Analog Converter
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Off-Diagonal Decay of Density Matrix
(far-element decay)
(decay cascade)