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arXiv:1312.3520 · Europhysics Letters (EPL)

Coleman-Weinberg mechanism in spinor Bose-Einstein condensates

Shun Uchino

Published Aug 1, 2014• 0 citations
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Abstract

It is argued that a continuous quantum phase transition between different ordered phases in spinor Bose-Einstein condensates predicted by the mean-field theory is vulnerable to quantum fluctuations. By analyzing Lee-Huang-Yang corrections in the condensate, we demonstrate that the so-called Coleman-Weinberg mechanism takes place in such a transition, that is, the transition becomes of the first order by quantum fluctuations. A jump to be expected in this first-order transition is induced by a correction from density fluctuations despite a transition between different magnetic properties with keeping condensation. We exemplify this with an experimentally relevant case and show that a measurement of a condensate depletion can be utilized to confirm the first-order transition.

DOI
10.1209/0295-5075/107/30004

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It is argued that a continuous quantum phase transition between different ordered phases in spinor Bose-Einstein condensates predicted by the mean-field theory is vulnerable to quantum fluctuations. By analyzing Lee-Huang-Yang corrections in the condensate, we demonstrate that the so-called Coleman-Weinberg mechanism takes place in such a transition, that is, the transition becomes of the first order by quantum fluctuations. A jump to be expected in this first-order transition is induced by a correction from density fluctuations despite a transition between different magnetic properties with keeping condensation. We exemplify this with an experimentally relevant case and show that a measurement of a condensate depletion can be utilized to confirm the first-order transition.
It is argued that a continuous quantum phase transition between different ordered phases in spinor Bose-Einstein condensates predicted by the mean-field theory is vulnerable to quantum fluctuations. By analyzing Lee-Huang-Yang corrections in the condensate, we demonstrate that the so-called Coleman-Weinberg mechanism takes place in such a transition, that is, the transition becomes of the first order by quantum fluctuations. A jump to be expected in this first-order transition is induced by a correction from density fluctuations despite a transition between different magnetic properties with keeping condensation. We exemplify this with an experimentally relevant case and show that a measurement of a condensate depletion can be utilized to confirm the first-order transition.
Spinor Bose-Einstein condensates provide a unique example in which the Bogoliubov theory fails to describe the metastability associated with first-order quantum phase transitions. This problem is resolved by developing the spinor Beliaev theory which takes account of quantum fluctuations of the condensate. It is these fluctuations that generate terms of higher than the fourth order in the order-parameter field which are needed for the first-order phase transitions. Besides the conventional first-order phase transitions which are accompanied by metastable states, we find a class of first-order phase transitions which are not accompanied by metastable states. The absence of metastability in these phase transitions holds to all orders of approximation since the metastability is prohibited by the symmetry of the Hamiltonian at the phase boundary. Finally, the possibility of macroscopic quantum tunneling from a metastable state to the ground state is discussed.
Quantum fluctuations play a pivotal role in determining the ground state properties and phase transitions of ultra-cold bosonic systems. This study presents a comprehensive theoretical investigation of fluctuation effects beyond mean-field theory in dilute Bose gases, examining their impact on the superfluid–Mott insulator transition, quantum droplet formation, and critical phenomena. Beginning with the Gross–Pitaevskii mean-field framework , we systematically incorporate quantum corrections through Bogoliubov theory, yielding the Lee–Huang–Yang (LHY) energy correction scaling as . The quantum depletion quantifies the fraction of atoms driven from the condensate by zero-point fluctuations. For the Bose–Hubbard model , quantum Monte Carlo simulations establish the superfluid–Mott insulator critical point at , shifted 15% from the mean-field prediction. Critical exponents and confirm 3D XY universality. Quantum droplets in binary mixtures are stabilized by the repulsive LHY correction against mean-field collapse, with equilibrium densities matching experimental observations in K mixtures. Finite-size scaling analysis and the Ginzburg criterion delineate regimes where fluctuation effects dominate. All theoretical predictions are validated against precision measurements in ultracold atomic gases.
Ultra-cold spinor Bose gases present rich physics due to the special combination of superfluidity and magnetism in a quantum system. This system was first realized in 1998 by confining a Bose-Einstein condensate in an all-optical trap.\nIn this thesis, we consider the fluctuations of observable quantities in a spin-1 Bose gas. Understanding how fluctuations arise due to the spin excitations of the condensate is important because it offers an insight into how measurement noise reveals the many-body physics of the system.\nTo begin, we present the mean-field and Bogoliubov theory of a uniform spin-1 Bose gas subject to a constant magnetic field, describing the condensate and its low-energy collective excitations.\nWe then develop a formalism to describe the fluctuations in a general density-like observable. We start from the two-point correlation function and cast it in the form of a generalised static structure factor determined by the three Bogoliubov quasiparticle excitation branches. We derive analytic results for the fluctuation amplitudes and the temperature-dependent static structure factors for observables of total density and the three spin densities.\nFor all four magnetic phases, we analyse the spinor order parameter and quasiparticle spectra while numerically mapping out the fluctuation amplitudes and static structure factors for the total and spin density operators.\nWe describe the fluctuations in experimental measurements made within finite cells, which is an important step to making meaningful predictions for experiments. We consider cylindrical cells and gaussian cells as two limiting cases. We apply this analysis to an experimentally realisable system of a quasi-2D spinor gas in a harmonic trap, comparing extensive numeric results with analytic limits.
Abstract Symmetry-breaking quantum phase transitions lead to the production of topological defects or domain walls in a wide range of physical systems. In second-order transitions, these exhibit universal scaling laws described by the Kibble–Zurek mechanism, but for first-order transitions a similarly universal approach is still lacking. Here, we propose a spinor Bose–Einstein condensate as a testbed system where critical scaling behaviour in a first-order quantum phase transition can be understood from generic properties. We demonstrate the applicability of the Kibble–Zurek mechanism for this transition to determine the critical exponents for: (1) the onset of the decay of the metastable state on short times scales, and (2) the number of resulting phase-separated ferromagnetic domains at longer times, as a one-dimensional spin-1 condensate is ramped across a first-order quantum phase transition. The predictions are in excellent agreement with mean-field numerical simulations and provide a paradigm for studying the decay of metastable states in experimentally accessible systems.