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arXiv:2103.01798 · Physical Review A

Few strongly interacting fermions of different mass driven in the vicinity of a critical point

Damian Włodzyński, Tomasz Sowiński

Published Nov 19, 2021• 1 citation
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Abstract

It was recently argued that one-dimensional systems of several strongly interacting fermions of different mass undergo critical transitions between different spatial orderings when the external confinement adiabatically changes its shape. In this work, we explore their dynamical properties when finite-time drivings are considered. By detailed analysis of many-body spectra, we show that the dynamics is typically guided only by the lowest eigenstates and may be well understood in the language of the generalized Landau-Zener mechanism. In this way, we can precisely capture the dynamical response of the system to the external driving. As a consequence, we show that by appropriate tailoring of the parameters of the driving, one can target the desired many-body state in a noninfinite time. Our theoretical predictions can be straightforwardly utilized in upcoming state-of-the-art experiments with ultracold atoms.

DOI
10.1103/physreva.104.053317

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It was recently argued that one-dimensional systems of several strongly interacting fermions of different mass undergo critical transitions between different spatial orderings when the external confinement adiabatically changes its shape. In this work, we explore their dynamical properties when finite-time drivings are considered. By detailed analysis of many-body spectra, we show that the dynamics is typically guided only by the lowest eigenstates and may be well understood in the language of the generalized Landau-Zener mechanism. In this way, we can precisely capture the dynamical response of the system to the external driving. As a consequence, we show that by appropriate tailoring of the parameters of the driving, one can target the desired many-body state in a noninfinite time. Our theoretical predictions can be straightforwardly utilized in upcoming state-of-the-art experiments with ultracold atoms.
It was recently argued that one-dimensional systems of several strongly interacting fermions of different mass undergo critical transitions between different spatial orderings when the external confinement adiabatically changes its shape. In this work, we explore their dynamical properties when finite-time drivings are considered. By detailed analysis of many-body spectra, we show that the dynamics is typically guided only by the lowest eigenstates and may be well-understood in the language of the generalized Landau-Zener mechanism. In this way, we can capture precisely the dynamical response of the system to the external driving. As consequence, we show that by appropriate tailoring parameters of the driving one can target desired many-body state in a finite time.
The ground-state properties of a few spin-1/2 fermions with different masses and interacting via short-range contact forces are studied within an exact diagonalization approach. It is shown that, depending on the shape of the external confinement, different scenarios of the spatial separation between components manifested by specific shapes of the density profiles can be obtained in the strong interaction limit. We find that the ground-state of the system undergoes a specific transition between orderings when the confinement is changed adiabatically from a uniform box to a harmonic oscillator shape. We study the properties of this transition in the framework of the finite-size scaling method adopted to few-body systems.
We investigate the excitation properties of finite ultracold bosonic systems in a one-dimensional harmonic trap with a time-dependent interaction strength. The driving of the interatomic coupling induces excitations of the relative motion exclusively with specific and controllable contributions of momentarily excited many-body states. Mechanisms for selective excitation to few-body analogs of collective modes and acceleration occur in the vicinity of resonances. Via the few-body spectrum and a Floquet analysis, we study the excitation mechanisms and the corresponding impact of the driving frequency and strength as well as the initial correlation of the bosonic state. The fundamental case of two atoms is analyzed in detail and forms a key ingredient for the bottom-up understanding of cases with higher atom numbers, thereby examining finite-size corrections to macroscopic collective modes of oscillation.
The conventional Kibble-Zurek mechanism (KZM) and finite-time scaling (FTS) provide universal descriptions of the driven critical dynamics from gapped initial states based on the adiabatic-impulse scenario. In this paper, by leveraging the large-scale quantum Monte Carlo simulation, we investigate the driven critical dynamics in two-dimensional Dirac systems, which harbor semimetal and Mott insulator phases separated by the quantum critical point (QCP) triggered by the interplay between fluctuations of gapless Dirac fermions and order parameter bosons. A remarkable discovery is that, despite the existence of the gapless initial phase, the driven dynamics can still be captured by the FTS form. This leads us to propose a generalized criterion for the validity of KZM and FTS with a gapless initial state. Accordingly, our results significantly generalize the KZM theory to incorporate composite fluctuations and relax its requirement for a gapped initial state to systems accommodating gapless Dirac fermionic excitations. Through successfully extending the KZM and FTS theory to the strongly interacting Dirac QCP, our work not only brings new fundamental perspective into the nonequilibrium critical dynamics, but also provides a novel theoretical approach to fathom quantum critical properties in fermionic systems.
Many-body systems undergoing quantum phase transitions reveal substantial growth of nonclassical correlations between different parties of the system. This behavior is manifested by characteristic divergences of the von Neumann entropy. Here we show that very similar features may be observed in one-dimensional systems of a few strongly interacting atoms when the structural transitions between different spatial orderings are driven by a varying shape of an external potential. When the appropriate adaptation of the finite-size scaling approach is performed in the vicinity of the transition point, few-fermion systems display a characteristic power-law invariance of divergent quantities.
We study the equilibrium and dynamical properties of a ferromagnetic spinor atomic Bose-Einstein condensate. In the vicinity of the critical point for a continuous quantum phase transition, universal behaviors are observed both in the equilibrium state and in the dynamics when the quadratic Zeeman shift is swept linearly. Three distinct dynamical regions are identified for different sweeping time scales ($\ensuremath{\tau}$) when compared to the time scale ${\ensuremath{\tau}}_{\mathrm{KZ}}\ensuremath{\sim}{N}^{(1+\ensuremath{\nu}z)/\ensuremath{\nu}d}$ decided by external driving in a system with finite size NNN ($\ensuremath{\nu},z$ are critical exponents and ddd the dimensionality). They are manifested by the excitation probability P\mathcal{P}P and the excess heat density Q\mathcal{Q}Q. The adiabatic region of $\mathcal{P}\ensuremath{\sim}\mathcal{Q}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}2}$ follows from the adiabatic perturbation theory when $\ensuremath{\tau}>{\ensuremath{\tau}}_{\mathrm{KZ}}$, while the nonadiabatic universal region of $\mathcal{P}\ensuremath{\sim}\mathcal{Q}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1}$ in the thermodynamic limit is described by the Kibble-Zurek mechanism when ${\ensuremath{\tau}}_{\mathrm{KZ}}>\ensuremath{\tau}>$ the time scale given by initial gap. The Kibble-Zurek scaling hypothesis is augmented with finite-size scaling in the latter region and several experimentally falsifiable features for the finite system we consider are predicted. The region of the fastest sweeping is found to be nonuniversal and far from equilibrium, with P\mathcal{P}P and Q\mathcal{Q}Q essentially being constants independent of $\ensuremath{\tau}$.