Optimal control of effective Hamiltonians.

We present a systematic scheme for the optimization of quantum simulations. Specifically, we show how polychromatic driving can be used to significantly improve the driving of Raman transitions in the Lambda system, which opens new possibilities for controlled driving-induced effective dynamics.

[1]  P. Gaspard,et al.  Non-Abelian optical lattices: anomalous quantum Hall effect and Dirac fermions. , 2009, Physical review letters.

[2]  Christiane P Koch,et al.  Optimal strategies for estimating the average fidelity of quantum gates. , 2013, Physical review letters.

[3]  W. Ketterle,et al.  Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices. , 2013, Physical review letters.

[4]  V. Krotov,et al.  Global methods in optimal control theory , 1993 .

[5]  T. Seligman,et al.  First experimental realization of the Dirac oscillator. , 2013, Physical review letters.

[6]  Remo Guidieri Res , 1995, RES: Anthropology and Aesthetics.

[7]  F. Mintert,et al.  Accurate effective Hamiltonians via unitary flow in Floquet space. , 2013, Physical review letters.

[8]  M. Lewenstein,et al.  Tunable gauge potential for neutral and spinless particles in driven optical lattices. , 2012, Physical review letters.

[9]  Xiaolong Deng,et al.  Ultracold lattice gases with periodically modulated interactions. , 2012, Physical review letters.

[10]  André Eckardt,et al.  Superfluid-insulator transition in a periodically driven optical lattice. , 2005, Physical review letters.

[11]  Tarik Yefsah,et al.  Spin-injection spectroscopy of a spin-orbit coupled Fermi gas. , 2012, Physical review letters.

[12]  G. Floquet,et al.  Sur les équations différentielles linéaires à coefficients périodiques , 1883 .

[13]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[14]  Hui Zhai,et al.  Spin-orbit coupled degenerate Fermi gases. , 2012, Physical review letters.

[15]  F. Mintert,et al.  Smooth optimal control with Floquet theory , 2012, 1205.5142.

[16]  Xiao-Gang Wen,et al.  High-temperature fractional quantum Hall states. , 2010, Physical review letters.

[17]  Philipp Hauke,et al.  Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields , 2013, Nature Physics.

[18]  Timo O. Reiss,et al.  Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. , 2005, Journal of magnetic resonance.

[19]  S. S. Hodgman,et al.  Negative Absolute Temperature for Motional Degrees of Freedom , 2012, Science.

[20]  W. Magnus On the exponential solution of differential equations for a linear operator , 1954 .

[21]  S. Blanes,et al.  The Magnus expansion and some of its applications , 2008, 0810.5488.

[22]  M. Paternostro,et al.  Entanglement control in hybrid optomechanical systems , 2012, 1204.0780.

[23]  J. Barreiro,et al.  Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. , 2013, Physical review letters.

[24]  M. Lewenstein,et al.  Non-abelian gauge fields and topological insulators in shaken optical lattices. , 2012, Physical review letters.

[25]  E. Rico,et al.  Atomic quantum simulation of U(N) and SU(N) non-Abelian lattice gauge theories. , 2012, Physical review letters.

[26]  D. D’Alessandro Introduction to Quantum Control and Dynamics , 2007 .

[27]  C Sias,et al.  Dynamical control of matter-wave tunneling in periodic potentials. , 2007, Physical review letters.