Sol H. Jacobsen — Page 2

arXiv2010

Exactly solvable three-level quantum dissipative systems via bosonisation of fermion gas-impurity models

We study the relationship between one-dimensional fermion gas-impurity models and quantum dissipative systems, via the method of constructive bosonisation and unitary transformation. Starting from an anisotropic Coqblin-Schrieffer model, a new, exactly solvable, three-level quantum dissipative system is derived as a generalisation of the standard spin-half spin-boson model. The new system has two environmental oscillator baths with ohmic coupling, and admits arbitrary detuning between the three levels. All tunnelling matrix elements are equal, up to one complex phase which is itself a function of the longitudinal and transverse couplings in the integrable limit. Our work underlines the importance of re-examining the detailed structure of fermion-gas impurity models and spin chains, in the light of connections to models for quantum dissipative systems.

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arXiv2008

Regularised Tripartite Continuous Variable EPR-type States with Wigner Functions and CHSH Violations

We consider tripartite entangled states for continuous variable systems of EPR type, which generalise the famous bipartite CV EPR states (eigenvectors of conjugate choices X1 - X2, P1+ P2, of the systems' relative position and total momentum variables). We give the regularised forms of such tripartite EPR states in second-quantised formulation, and derive their Wigner functions. This is directly compared with the established NOPA-like states from quantum optics. Whereas the multipartite entangled states of NOPA type have singular Wigner functions in the limit of large squeezing, r --> infinity, or tanh r --> 1^- (approaching the EPR states in the bipartite case), our regularised tripartite EPR states show singular behaviour not only in the approach to the EPR-type region (s --> 1 in our notation), but also for an additional, auxiliary regime of the regulator (s --> \sqrt{2}). While the s -->1 limit pertains to tripartite CV states with singular eigenstates of the relative coordinates and remaining squeezed in the total momentum, the s --> \sqrt{2} limit yields singular eigenstates of the total momentum, but squeezed in the relative coordinates. Regarded as expectation values of displaced parity measurements, the tripartite Wigner functions provide the ingredients for generalised CHSH inequalities. Violations of the tripartite CHSH bound (B3 \le 2) are established, with B3 ~ 2.09 in the canonical regime (s -->1^+), as well as B3 ~ 2.32 in the auxiliary regime (s --> \sqrt{2^+}).

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