Quantum spin chains with fractional revival

A systematic study of fractional revival at two sites in $XX$ quantum spin chains is presented and analytic models with this phenomenon are exhibited. The generic models have two essential parameters and a revival time that does not depend on the length of the chain. They are obtained by combining two basic ways of realizing fractional revival in a spin chain each bringing one parameter. The first proceeds through isospectral deformations of spin chains with perfect state transfer. The second arises from the recurrence coefficients of the para-Krawtchouk polynomials with a bi-lattice orthogonality grid. It corresponds to an analytic model previously identified that can possess perfect state transfer in addition to fractional revival.

[1]  I. Jex,et al.  Quantum State Transfer and Network Engineering , 2013 .

[2]  M. Rosenblum,et al.  Generalized Hermite Polynomials and the Bose-Like Oscillator Calculus , 1993, math/9307224.

[3]  L. Vinet,et al.  Exact Fractional Revival in Spin Chains , 2015, 1506.08434.

[4]  Simone Severini,et al.  Number-theoretic nature of communication in quantum spin systems. , 2012, Physical review letters.

[5]  Leonardo Banchi,et al.  Perfect wave-packet splitting and reconstruction in a one-dimensional lattice , 2015, 1502.03061.

[6]  L. Vinet,et al.  Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer , 2011, 1110.6475.

[7]  R. W. Robinett Quantum wave packet revivals , 2004 .

[8]  Leon M. Hall,et al.  Special Functions , 1998 .

[9]  R. Chakrabarti,et al.  Quantum communication through a spin chain with interaction determined by a Jacobi matrix , 2009, 0912.0837.

[10]  Irene Marzoli,et al.  Quantum carpets, carpets of light , 2001 .

[11]  David S. Watkins,et al.  Some Perspectives on the Eigenvalue Problem , 1993, SIAM Rev..

[12]  Quantum state transfer in spin chains with q-deformed interaction terms , 2010, 1005.2912.

[13]  L. Vinet,et al.  Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials , 2016, 1605.00708.

[14]  An Exactly Solvable Spin Chain Related to Hahn Polynomials , 2011, 1101.4469.

[15]  Li Dai,et al.  Engineering quantum cloning through maximal entanglement between boundary qubits in an open spin chain , 2010 .

[16]  C. P. Sun,et al.  Fractional revivals of the quantum state in a tight-binding chain , 2007 .

[17]  T. Chihara,et al.  An Introduction to Orthogonal Polynomials , 1979 .

[18]  Alastair Kay,et al.  Perfect, Efficent, State Transfer and its Application as a Constructive Tool , 2009, 0903.4274.

[19]  C. P. Sun,et al.  Quantum-state transfer via the ferromagnetic chain in a spatially modulated field , 2005 .

[20]  Leandro Moral,et al.  Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle , 2002 .

[21]  Luc Vinet,et al.  How to construct spin chains with perfect state transfer , 2011, 1110.6474.

[22]  David L. Aronstein,et al.  FRACTIONAL WAVE-FUNCTION REVIVALS IN THE INFINITE SQUARE WELL , 1997 .

[23]  Rene F. Swarttouw,et al.  Hypergeometric Orthogonal Polynomials , 2010 .

[24]  Luc Vinet,et al.  Almost perfect state transfer in quantum spin chains , 2012, 1205.4680.

[25]  Sougato Bose,et al.  Quantum communication through spin chain dynamics: an introductory overview , 2007, 0802.1224.

[26]  G. M. L. Gladwell,et al.  Inverse Problems in Vibration , 1986 .

[27]  Matthias Christandl,et al.  Mirror inversion of quantum states in linear registers. , 2004, Physical review letters.

[28]  T. S. Mahesh,et al.  Efficient simulation of unitary operators by combining two numerical algorithms: An NMR simulation of the mirror-inversion propagator of an XY spin chain , 2014 .