A. A. Clerk, S. M. Girvin, and A. D. Stone Departments of Applied Physics and Physics, Yale...
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Transcript of A. A. Clerk, S. M. Girvin, and A. D. Stone Departments of Applied Physics and Physics, Yale...
A. A. Clerk, S. M. Girvin, and A. D. StoneDepartments of Applied Physics and Physics,
Yale University
Q:What characterizes an “ideal” quantum detector?
(cond-mat/0211001)
(and many discussions with M. Devoret & R. Schoelkopf)
Mesoscopic Detectors and Mesoscopic Detectors and the Quantum Limitthe Quantum Limit
Generic Weakly-Coupled Detector
QI
“gain”
1. Measurement Rate: How quickly can we distinguish the two qubit states?
0
m
P(m
,t)
SQQ ´ 2 s dt h Q(t) Q(0) i
2. Dephasing Rate: How quickly does the measurement decohere the qubit?
The Quantum Limit of Detection
Quantum limit: the best you can do is measure as fast as you dephase:
QI
•Dephasing? Need orthogonal to
•Measurement? Need distinguishable from
• What symmetries/properties must an arbitrary detector possess to reach the quantum limit?
Why care about the quantum limit?• Minimum Noise Energy in Amplifiers:
(Caves; Clarke; Devoret & Schoelkopf)
• Minimum power associated with Vnoise?
SI
Q Iz
• Detecting coherent qubit oscillations (Averin & Korotkov)
How to get to the Quantum Limit
•Now, we have:
• λ’ is the “reverse gain”: IQ
• λ’ vanishes (monitoring output does not further dephase)
QI
A.C., Girvin & Stone, cond-mat/0211001Averin, cond-mat/0301524
•Quantum limit requires:
• (i.e. no extra degrees of freedom)
What does it mean?• To reach the quantum limit, there should be no unused
information in the detector…
Mesoscopic Scattering Detector: (Pilgram & Buttiker; AC, Girvin & Stone)
QI
L R
L
R
What does it mean?• To reach the quantum limit, there should be no unused
information in the detector…
Mesoscopic Scattering Detector: (Pilgram & Buttiker; AC, Girvin & Stone)
QI
L R
L
R
Transmission probability depends on qubit:
The Proportionality Condition• Need:
Phase condition?•Qubit cannot alter relative phase between reflection and transmission•No “lost” information that could have been gained in an interference experiment….
L R
Q I
Not usual symmetries!
Transmission Amplitude Condition
Ensures that no information is lost when averaging over energy
versus
Q IL R
L
R
L
R
1)
2)
The Ideal Transmission Amplitude
Necessary energy dependence to be at the quantum limit
Corresponds to a real system-- the adiabatic quantum point contact! (Glazman, Lesovik, Khmelnitskii & Shekhter, 1988)
4 2 2 4
0.2
0.4
0.6
0.8
1 T
- 0
Information and Fluctuations
• No information lost when energy averaging:
Look at charge fluctuations:
• No information lost in phase changes:
meas for current experiment meas for phase experiment
Q IL R
Reaching quantum limit = no wasted information
Measurement Rate for Phase Experiment
meas for current experiment meas for phase experiment
t
r
Information and Fluctuations (2)
Can connect charge fluctuations to information in more complex cases:
Q IL R
Reaching quantum limit = no wasted information
meas for current experiment meas for phase experiment
2. Normal-Superconducting Detector
1. Multiple Channels
Extra terms due to channel structure
Partially Coherent Detectors• What is the effect of adding dephasing to the mesoscopic
scattering detector? Look at a resonant-level model…
L
R
• Symmetric coupling to leads no information in relative phase
L R
I = 0
• Assume dephasing due to an additional voltage probe (Buttiker)
Partially Coherent Detectors• Reducing the coherence of the detector enhances charge
fluctuations… total accessible information is increased
• A resulting departure from the quantum limit…
0.2 0.4 0.6 0.8 1
1.2
1.4
1.6
1.8
2
0.2 0.4 0.6 0.8 1
0.2
0.4
0.6
0.8
1Charge Noise (SQ)
Conclusions
QI
• Reaching the quantum limit requires that there be no wasted information in the detector; can make this condition precise.
• Looking at information provides a new way to look at mesoscopic systems:
• New symmetry conditions• New way to view fluctuations
• Reducing detector coherence enhances charge fluctuations, leads to a departure from the quantum limit