Abstract
A quantum phase transition between the symmetric (polar) phase and the phase with broken symmetry can be induced in a ferromagnetic spin-1 Bose–Einstein condensate in space (rather than in time). We consider such a phase transition and show that the transition region in the vicinity of the critical point exhibits scalings that reflect a compromise between the rate at which the transition is imposed (i.e. the gradient of the control parameter) and the scaling of the divergent healing length in the critical region. Our results suggest a method for the direct measurement of the scaling exponent ν.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. A quantum phase transition (QPT) is a dramatic change of the nature of the ground state of a quantum system due to a small change of an external parameter, e.g. magnetic field. Thus, the ground state may be ferromagnetic (paramagnetic) when a system is exposed to a magnetic field B < Bc (B > Bc). A critical point Bc separates the phases. Various physical quantities near it, such as magnetization, follow typically power law scaling characterized by critical exponents. When the system is forced to make a transition from one phase to another through either time-dependent or position-dependent variation of the parameter inducing a transition, its response reflects its critical exponents.
Main results. We study one of the most experimentally accessible systems undergoing a QPT: a ferromagnetic spin-1 Bose–Einstein condensate. We show that by using an inhomogeneous magnetic field increasing from B < Bc to B > Bc within the sample, one can induce a QPT in space. The properties of the transition region (where the system's order changes) can be used to extract the critical exponent ν characterizing divergence of the coherence length of the condensate.
Wider implications. The results of this work are universal and can be applied to numerous systems undergoing a QPT. Our research exhibits parallels between QPT dynamics (when driving is time-dependent) and statics (when driving is position-dependent). It also suggests a novel way for experimental measurement of the critical exponent ν.