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arXiv:1609.09604 · Science China Physics Mechanics and Astronomy

Spontaneous decoherence of coupled harmonic oscillators confined in a ring

Zhirui Gong, Zhenwei Zhang, Dazhi Xu, Nan Zhao, Chang-Pu Sun

Published Jan 22, 2018• 6 citations
arXivHTMLPDF
DOI
10.1007/s11433-017-9101-4

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We show that time translation symmetry of a ring system with a macroscopic quantum ground state is broken by decoherence. In particular, we consider a ring-shaped incommensurate charge density wave (ICDW ring) threaded by a fluctuating magnetic flux: the Caldeira-Leggett model is used to model the fluctuating flux as a bath of harmonic oscillators. We show that the charge density expectation value of a quantized ICDW ring coupled to its environment oscillates periodically. The Hamiltonians considered in this model are time independent unlike ``Floquet time crystals'' considered recently. Our model forms a metastable quantum time crystal with a finite length in space and in time.
We consider a two-component linearly coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap acting in both components, we consider Josephson oscillations (JO) initiated by an input in the form of the HO’s ground state (GS) or dipole mode (DM), placed in one component. With the increase of the strength of the self-focusing nonlinearity, spontaneous symmetry breaking (SSB) between the components takes place in the dynamical JO state. Under still stronger nonlinearity, the regular JO initiated by the GS input carries over into a chaotic dynamical state. For the DM input, the chaotization happens at smaller powers than for the GS, which is followed by SSB at a slightly stronger nonlinearity. In the system with the defocusing nonlinearity, SSB does not take place, and dynamical chaos occurs in a small area of the parameter space. In the asymmetric half-trapped system, with the HO potential applied to a single component, we first focus on the spectrum of confined binary modes in the linearized system. The spectrum is found analytically in the limits of weak and strong inter-component coupling, and numerically in the general case. Under the action of the coupling, the existence region of the confined modes shrinks for GSs and expands for DMs. In the full nonlinear system, the existence region for confined modes is identified in the numerical form. They are constructed too by means of the Thomas–Fermi approximation, in the case of the defocusing nonlinearity. Lastly, particular (non-generic) exact analytical solutions for confined modes, including vortices, in one- and two-dimensional asymmetric linearized systems are found. They represent bound states in the continuum.