Decoherence from chaotic environment

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Decoherence from chaotic environment
Hwa-Kyun Park (KIAS)
Collaborator Sang-Wook Kim (SNU)
(H-K Park, S. W. Kim, PRA 67,060102)
(S. W. Kim, H.-K. Park, quant-ph/0311115)
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• Overview
• Introduction fidelity, chaotic env
• Two Coupled delta kicked rotors
• Weak localization of composed particle
• Summary

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• Overview
• Introduction fidelity, chaotic env
• Two Coupled delta kicked rotors
• Weak localization of composed particle
• Summary

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Quantum mechanics
Classical world
No superposition
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Quantum mechanics
Linearity -gt Superposition
Classical world
classical
No superposition
quantum
(Pointer state Zurek, PRD vol 24,1516)
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Quantum mechanics
Linearity ---gt Superposition
Superposition ---------------------------gt
interference
Coherence of quantum phase
Decoherence (dephasing)
Classical world
No interference
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Decoherence (dephasing)
The phase of systemenv well definded
System
Environment
The phase of only the system usually not well
defined
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Decoherence (dephasing)
System
The phase of only the system well defined in
this case
Environment
The phase of only the system is not well defined.
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Decoherence (dephasing)
Entanglement of system and environment -gt
decoherence
-gt How entanglement occurs?
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Initial state
Imry, PRA 41, 3436 (1990)
U
After interaction with environment
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Initial state
U
After interaction with environment
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Zurek et.al, PRL 89, 170405 (2002)
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Decay of Fidelity of environment decoherence
rate
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Jalabert Pastawski PRL 86, 2490 (2002)
Fidelity
For the chaotic system, fidelity decays
exponentially. The decay rate is given by the
mean Lyapunov exponent.
Even for a few degrees of freedom, if the
dynamics of the environment is chaotic,
decoherence can occur.
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Zurek, NATURE 412,712 (2001)
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Fidelity
Decay of Fidelity of environment decoherence
rate
For the chaotic system, fidelity decays
exponentially.
Thus chaotic environment is efficient to generate
decoherence.
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Evolution of two Gaussians in phase space
Chaotic evolution under slightly different
Hamiltonians,
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• Overview
• Introduction fidelity, chaotic env
• Two coupled delta kicked rotors
• Weak localization of composed particle
• Summary

(H-K Park, S. W. Kim, PRA 67,060102)
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Decoherence from internal degree of freedom of
composed system (a macroscopic object which
consists of many particles)
Kolovsky, EPL 27, 79 (1994)
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To get a decoherence from internal dynamics,
- Large degrees of freedom
- A few degrees of freedom, chaotic ?
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Decoherence from internal degree of freedom of
composed system
Chaotic internal dynamics (with a few degrees of
freedom) can cause decoherence on the dynamics
of the composed particle?
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Model two coupled delta-kicked rotors
Canonical transform to the CM relative
coordinates
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Delta-kicked rotor
classical
quantum
evolution per each kick
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Delta-kicked rotor
Localization due to quantum interference (cf.
Anderson localization)
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Model two coupled delta-kicked rotors
w
Canonical transform to the CM relative
coordinates
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Model two coupled delta-kicked rotors
Breakdown of localization
Correspondence of quantum and classical entropy
Canonical transform to the CM relative
coordinates
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From top to bottom, w0.0 (single delta kicked
rotor), 0.1,0.2,,0.7
(w confinement width)
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Breakdown of localization
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Correspondence of quantum and classical entropy
From top to bottom, w0.2,0.4,0.6, 0.8, and 1.0
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Model two coupled delta-kicked rotors
Breakdown of localization
Correspondence of quantum and classical entropy

Internal dynamics single degree of freedom,
chaotic -gt noisy amplitude of kick -gt decoherence
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Noise
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• Overview
• Introduction fidelity, chaotic env
• Two Coupled delta kicked rotors
• Weak localization of composed particle
• Summary

(S. W. Kim, H.-K. Park, quant-ph/0311115)
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Weak localization of composed particle
but
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but

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Summary

• Decay of the fidelity of environment
• decoherence rate

2. Two coupled delta-kicked rotors Even with a
few degrees of freedom, chaotic internal dynamics
can yield decoherence to the CM motion.
3. Weak localization of composed system can be
suppressed by coupling to the internal dynamics
which gives decoherence.
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Acknowledgement

• Sang-Wook Kim (SNU)
• Heung-Sun Sim (KIAS)
• H. Schomerus (MPIPKS)