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Communications in Theoretical Physics

Multiple-quantum-coherence dynamics of spin-1 Bose–Einstein condensate during quantum phase transitions

Fulin Deng, Peng Xu, Su Yi, Wenxian Zhang

Published Nov 27, 2023• 2 citations
Publisher

Abstract

Abstract Multiple quantum coherences are often employed to describe quantum many-body dynamics in nuclear spin systems and recently, to characterize quantum phase transitions in trapped ions. Here we investigate the multiple-quantum-coherence dynamics of a spin-1 Bose–Einstein condensate. By adjusting the quadratic Zeeman shift, the condensate exhibits three quantum phases. Our numerical results show that the spectrum of multiple quantum coherence does indeed catch the quantum critical points. More importantly, with only a few low-order multiple quantum coherences, the spin-1 condensate exhibits rich signals of the many-body dynamics, beyond conventional observables. The experimental implementation of such multiple quantum coherence protocol is also discussed.

DOI
10.1088/1572-9494/ad0fd9

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Abstract Multiple quantum coherences are often employed to describe quantum many-body dynamics in nuclear spin systems and recently, to characterize quantum phase transitions in trapped ions. Here we investigate the multiple-quantum-coherence dynamics of a spin-1 Bose–Einstein condensate. By adjusting the quadratic Zeeman shift, the condensate exhibits three quantum phases. Our numerical results show that the spectrum of multiple quantum coherence does indeed catch the quantum critical points. More importantly, with only a few low-order multiple quantum coherences, the spin-1 condensate exhibits rich signals of the many-body dynamics, beyond conventional observables. The experimental implementation of such multiple quantum coherence protocol is also discussed.
Abstract Three-dimensional (3D) strongly correlated many-body systems, especially their dynamics across quantum phase transitions, are prohibitively difficult to be numerically simulated. We experimentally demonstrate that such complex many-body dynamics can be efficiently studied in a 3D spinor Bose–Hubbard model quantum simulator, consisting of antiferromagnetic spinor Bose–Einstein condensates confined in cubic optical lattices. We find dynamics and scaling effects beyond the scope of existing theories at superfluid–insulator quantum phase transitions, and highlight spin populations as a good observable to probe the quantum critical dynamics. Our data indicate that the scaling exponents are independent of the nature of the quantum phase transitions. We also conduct numerical simulations in lower dimensions using time-dependent Gutzwiller approximations, which qualitatively describe our observations.
We have experimentally investigated the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition at zero quadratic Zeeman shift qqq. The rate of instability shows good agreement with predictions based upon solutions to the Bogoliubov--de Gennes equations. A key feature of this work was removal of magnetic field inhomogeneities, resulting in a steep change in behavior near the transition point. The quadratic Zeeman shift at the transition point was resolved to 250 mHz uncertainty, equivalent to an energy resolution of ${k}_{B}\phantom{\rule{4pt}{0ex}}\ifmmode\times\else\texttimes\fi{}$ (12 pK). A small (2--3 $\ensuremath{\sigma}$) shift of the transition point was observed, from q=0q=0q=0 to q=+650q=+650q=+650 mHz, whose physical mechanism is currently unknown. In this work, we demonstrate a sub-Hz precision measurement of a phase transition in quantum gases. It paves the way toward observing shifts of the transition point due to finite particle number NNN that scale as 1/N1/N1/N, and also to potential Heisenberg limited spectroscopy with antiferromagnetic spinor gases [L.-N. Wu and L. You, Phys. Rev. A 93, 033608 (2016)].
Quantum phase transitions universally exist in the ground and excited states of quantum many-body systems, and they have a close relationship with the nonequilibrium dynamical phase transitions, which however are challenging to identify. In the system of spin-1 Bose-Einstein condensates, though dynamical phase transitions with correspondence to equilibrium phase transitions in the ground state and uppermost excited state have been probed, those taking place in intermediate excited states remain untouched in experiments thus far. Here we unravel that both the ground- and excited-state quantum phase transitions in spinor condensates can be diagnosed with dynamical phase transitions. A connection between equilibrium phase transitions and nonequilibrium behaviors of the system is disclosed in terms of the quantum Fisher information. We also demonstrate that near the critical points parameter estimation beyond the standard quantum limit can be implemented. This work not only advances the exploration of excited-state quantum phase transitions via a scheme that can immediately be applied to a broad class of few-mode quantum systems, but also provides a new perspective on the relationship between quantum criticality and quantum enhanced sensing.
Spin-orbit-coupled bosons can exhibit rich equilibrium phases at low temperature and in the presence of particle-particle interactions. In the case with a 1D synthetic spin-orbit interaction, it has been observed that the ground state of a Bose gas can be a normal phase, stripe phase, or magnetized phase in different parameter regimes. The magnetized states are doubly degenerate and consist of a many-particle two-state system. In this work, we investigate the nonequilibrium quantum dynamics by switching on a simple one-dimensional optical lattice potential as external perturbation to induce resonant couplings between the magnetized phases, and predict a quantum spin dynamics which cannot be obtained in the single-particle systems. In particular, due to particle-particle interactions, the transition of the Bose condensate from one magnetized phase to the other is forbidden when the external perturbation strength is less than a critical value, and a full transition can occur only when the perturbation exceeds such critical strength. This phenomenon manifests itself a dynamical phase transition, with the order parameter defined by the time-averaged magnetization over an oscillation period, and the critical point behavior being exactly solvable. The thermal fluctuations are also considered in detail. From numerical simulations and exact analytic studies we show that the predicted many-body effects can be well observed with the current experiments.
We unravel the correlation effects of the second-order quantum phase transitions emerging on the ground state of a harmonically trapped spin-1 Bose gas, upon varying the involved Zeeman terms, as well as its breathing dynamics triggered by quenching the trapping frequency. It is found that the boundaries of the associated magnetic phases are altered in the presence of interparticle correlations for both ferromagnetic and antiferromagnetic spin-spin interactions, an effect which becomes more prominent in the few-body scenario. Most importantly, we unveil a correlation-induced shrinking of the antiferromagnetic and broken-axisymmetry phases implying that ground states with bosons polarized in a single spin component are favored. Turning to the dynamical response of the spinor gas it is shown that its breathing frequency is independent of the system parameters while correlations lead to the formation of filamentary patterns in the one-body density of the participating components. The number of filaments is larger for increasing spin-independent interaction strengths or for smaller particle numbers. Each filament maintains its coherence and exhibits an anticorrelated behavior while distinct filaments show significant losses of coherence and are two-body correlated. Interestingly, we demonstrate that for an initial broken-axisymmetry phase an enhanced spin-flip dynamics takes place which can be tuned either via the linear Zeeman term or the quench amplitude.