Perfect state transfer in a spin chain without mirror symmetry

Abstract

We introduce an analytical XX spin chain with asymmetrical transport properties. It has an even number N + 1 of sites labeled by n = 0, · · · N . It does not exhibit perfect state transfer (PST) from end-to-end but rather from the first site to the next to last one. In fact, PST of one-excitation states takes place between the even sites: n ↔ N − n − 1, n = 0, 2, · · · , N − 1; while states localized at a single odd site undergo fractional revival (FR) over odd sites only. Perfect return is witnessed at double the PST/FR time. The couplings and local magnetic fields are related to the recurrence coefficients of the dual -1 Hahn polynomials.

Analytic "Newton's cradles" with perfect transfer and fractional revival

“…Indeed, everything presented in the mass-weighed coordinates in the fixed-fixed section would still apply, but the actual pulse will not be completely transmitted. Perfect state transfer without mirror-symmetry has been shown to be possible in quantum spin chains between sources and targets that are asymmetrically located [9,19]. It would be interesting to investigate such behavior in a fixed-free mass-spring chain, as well as in non-mirror-symmetric free-free and fixed-fixed systems.…”

“…As mentioned, orthogonal polynomials play a central role in the construction of such analytic models [5][6][7][8][9]. In dealing with quantum systems, a condition on the associated polynomials for perfect transfer to occur is that their spectra be given in terms of integer.…”

Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials

“…Those corresponding to the Krawtchouk and dual Hahn polynomials were the first ones found [31]. A model associated to a special case of the -Racah polynomials was exhibited [29] as well as one corresponding to the dual −1 Hahn polynomials [32,33] -a representative family of the interesting sets obtained from → −1 limits of the Askey-Wilson polynomials and their relatives. (A standard reference for information on most of these polynomials is [34].)…”

Coherent ground-state transport of neutral atoms

“…Because of its simplicity, spin-chain system with nearest-neighbor hopping has been extensively used to realize quantum state transmission [1][2][3][4][5][6][7][8][9][10]. In order to achieve high-fidelity transfer of quantum information, various transport protocols have been put forward, such as modulation of the couplings between neighboring spins [11][12][13][14][15][16], exploitation of the chiral topological edge states [17,18], and construction of a stimulated Raman adiabatic passage [19][20][21], especially combined with the topologically protected edge states [22,23]. Among many physical systems, Rydberg atom has been regarded as a good candidate to simulate spin-chain models on account of its remarkable properties [24][25][26][27][28][29][30].…”