a. a. clerk, s. m. girvin, and a. d. stone departments of applied physics and physics, yale...
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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