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Ideal Dynamical Decoherence Control Goren Gordon , Gershon Kurizki Weizmann Establishment of Science, Israel Daniel Lidar College of Southern California, USA QEC07 USC Los Angeles, USA Dec. 17-21, 2007 Framework General dynamical decoherence control formalism Brief review of

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Ideal Dynamical Decoherence Control Goren Gordon , Gershon Kurizki Weizmann Institute of Science, Israel Daniel Lidar University of Southern California, USA QEC07 USC Los Angeles, USA Dec. 17-21, 2007

Outline Universal dynamical decoherence control formalism Brief review of Calculus of Variations Analytical determination of mathematical statement for ideal regulation Numerical results Conclusions

Decoherence Scenarios Ion trap Cold particle in (flawed) optical grid Keller et al. Nature 431 , 1075 (2004) Hã¤ffner et al. Nature 438 643 (2005) Jaksch et al. PRL 82, 1975 (1999) Mandel et al. Nature 425, 937 (2003) Ion in pit Kreuter et al. PRL 92 203002 (2004)

Universal dynamical decoherence control formalism Kofman & Kurizki, Nature 405 , 546(2000); PRL 87 , 270405 (2001); PRL 93 , 130406(2004) Gordon, Erez and Kurizki, J. Phys. B, 40 , S75 (2007) [review] framework + tweak shower coupling Fidelity of an introductory energized state: Average altered decoherence rate Reservoir reaction (memory) capacity Phase regulation

Universal dynamical decoherence control formalism Kofman & Kurizki, Nature 405 , 546(2000); PRL 87 , 270405 (2001); PRL 93 , 130406(2004) Gordon, Erez and Kurizki, J. Phys. B, 40 , S75 (2007) [review] Time-area Frequency-space F t ( ï· ) System-shower coupling range G( ï· ) Spectral balance force No regulation (Golden Rule)

2 1 2 G( ï· ) B A Universal dynamical decoherence control formalism Single-qubit decoherence control Decay because of limited temperature shower coupling Proper dephasing Multi-qudit trap safeguarding Imposing DFS by dynamical balance Entanglement passing and revival Dephasing control amid quantum calculation ( Gordon et al. J. Phys. B, 40 , S75 (2007)) (Gordon & Kurizki, PRL 97 , 110503 (2006)) (Gordon, unpublished) (Gordon & Kurizki, PRA 76 , 042310 (2007))

Brief outline of Calculus of Variations Want to minimize the useful: With the requirement: The methodology: 1. Explain Euler-Lagrange mathematical statement Get arrangement: 2. Embed the answer for the requirement: Get 3. Get arrangement as a limitation\'s component:

Analytical inference of ideal balance Resonant field adequacy AC-Stark move Want to minimize the normal altered decoherence rate : With the vitality imperative (a given tweak vitality): ( Gordon et al. J. Phys. B, 40 , S75 (2007))

Analytical induction of ideal balance Want to minimize the normal altered decoherence rate : With the vitality limitation (a given regulation vitality): Use documentation: Euler-Lagrange mathematical statement for ideal adjustment

Analytical determination of ideal balance Euler-Lagrange comparison for ideal balance Using the vitality requirement, one can acquire: Equation for Optimal Modulation

Numerical results Viola & Lloyd PRA 58 2733 (1998) Shiokawa & Lidar PRA 69 030302(R) (2004) Vitali & Tombesi PRA 65 012305 (2001) Agarwal, Scully, Walther PRA 63 , 044101 (2001) Compare ideal balance to Bang-Bang (BB) control:

Numerical results Viola & Lloyd PRA 58 2733 (1998) Shiokawa & Lidar PRA 69 030302(R) (2004) Vitali & Tombesi PRA 65 012305 (2001) Agarwal, Scully, Walther PRA 63 , 044101 (2001) Compare ideal tweak to Bang-Bang (BB) control:

Numerical results Viola & Lloyd PRA 58 2733 (1998) Shiokawa & Lidar PRA 69 030302(R) (2004) Vitali & Tombesi PRA 65 012305 (2001) Agarwal, Scully, Walther PRA 63 , 044101 (2001) Compare ideal balance to Bang-Bang (BB) control: DD condition

Numerical results Optimal heartbeat shape X F. T.

Numerical results Optimal heartbeat shape

Conclusions Dynamical decoupling and Bang-Bang regulations are environment-uncaring, i.e. disregard coupling range Optimal adjustment âreshapesâ (peeps) the beat to minimize spectral cover of the framework shower coupling and regulation spectra Current results utilizing widespread dynamical decoherence control are also pertinent to rot and fitting dephasing , at limited temperatures Extensions to multi-partite deocherence and trap optimal control underwayâ¦ Thank you !!! âKnow thy enemyâ .