Mesoscopic Quantum Coherence Length in a 1D Spin Chain

Interesting experiment reported in Science, “Mesoscopic Phase Coherence in a Quantum Spin Fluid,” Xu et al (available here). The authors discuss a one dimenionsional spin chain where each site has a spin 1 system. This system is coupled antiferromagnetically to its nearest neighbor. Now such systems have a ground state whose two spin correlation, [tex]$langle S_i S_j rangle[/tex] decays exponentially as a function of the distance between site i and site j. However, if you examine the more complicated correlation function [tex]$langle S_i exp [ i pi sum_{i<k<j} S_k]S_j rangle[/tex] this tends to a constant as the distance between the two sites increases. Thus a more complicated order exists in this system, one which is not revealed by a simple two spin correlation function (In this traitorous world, nothing is true or false, all is according to the color of the crystal through which you look.) This order is known as a string order. In particular the ground state of the system is roughly a superposition over Neel states (over [tex]$S_z=pm 1$[/tex]) with [tex]$S_z=0$[/tex] inserted into these states. The amplitude of each of these states in the superposition is exponetially decreasing in the number of inserted $S_z=0$ states.
Okay, cool, so there is this nice model which has a very cool ground state whose order isn't in a two spin correlation but some other, more interesting order. But what is cool about this experiment is that the authors are able to examine the excitations in this system. In particular they examine the creation of a triplet pair excitation at rest and show that these propogate over a fairly large distance before losing their coherence (roughly fifty lattice units.) Indeed, if I am reading the article correctly, it seems that this coherence is limited only by the length of the chains themselves (at low temperature, at higher temperature thermal excitations can shorten this coherence length.) Cool! This, I think, should give hope to those who are interested in using spin chains for quantum computation, although, of course, TIALWFAQC (this is a long way from a quantum computer.)

2 Replies to “Mesoscopic Quantum Coherence Length in a 1D Spin Chain”

    “Coherent Optical Spectroscopy of a Strongly Driven Quantum Dot” (Science)
    “Progressive field-state collapse and quantum non-demolition photon counting” (Nature)
    “Generation of optical ‘Schrödinger cats’ from photon number states” (Nature)

  2. Do you think you can learn something by examining big patterns at the same time? Like the way electrons behave near the virtual cathode region of a cylindrical magnetron?

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