Erlangen 2018 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 6: Quantum Information (Concepts and Methods) I
Q 6.4: Talk
Monday, March 5, 2018, 11:30–11:45, K 1.019
Exclusion principles for hard-core bosons — •Macauley Davy1, Felix Tennie1, Vlatko Vedral1,2, and Christian Schilling1 — 1Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom — 2Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
The particle exchange symmetry strongly shapes the behavior of quantum systems even in the one-particle picture: While fermionic occupation numbers obey Pauli’s exclusion principle, bosons can multiply occupy any one-particle quantum state |ϕ⟩ and even form a Bose-Einstein condensate. One may therefore wonder how the situation looks like for hard-core bosons, fulfilling mixed commutation relations. We first observe that for arbitrary systems of N hard-core bosons on d lattice sites the maximal possible occupation number is given by Nmax=(N/d)(d−N+1) which is smaller than N but larger than 1. Nmax can only be achieved for states |ϕ⟩ which are maximally unbiased w.r.t. the lattice site basis {|j⟩}j=1d (“momentum states”) and when the total system is maximally delocalized. We generalize this result by relating the maximal occupation number Nmax(ϕ) of a fixed one-particle state |ϕ⟩ =∑j=1d cj |j⟩ to the unbiasedness of |ϕ⟩ w.r.t. to the basis of lattice site states.