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arXiv:1603.03701 · Physical Review A

Hysteresis of noninteracting and spin-orbit-coupled atomic Fermi gases with relaxation

Mekena Metcalf, Chen-Yen Lai, Chih-Chun Chien

Published May 23, 2016• 5 citations
arXivHTMLPDF

Abstract

Hysteresis can be found in driven many-body systems such as magnets and superfluids. Rate-dependent hysteresis arises when a system is driven periodically while relaxing towards equilibrium. A two-state paramagnet driven by an oscillating magnetic field in the relaxation approximation clearly demonstrates rate-dependent hysteresis. A noninteracting atomic Fermi gas in an optical ring potential, when driven by a periodic artificial gauge field and subjected to dissipation, is shown to exhibit hysteresis loops of atomic current due to a competition of the driving time and the relaxation time. This is in contrast to electronic systems exhibiting equilibrium persistent current driven by magnetic flux due to rapid relaxation. Universal behavior of the dissipated energy in one hysteresis loop is observed in both magnetic and atomic systems, showing linear and inverse-linear dependence on the relaxation time in the strong and weak dissipation regimes. While interactions in general invalidate the framework for rate-dependent hysteresis, an atomic Fermi gas with artificial spin-orbit coupling can exhibit hysteresis loops of atomic currents. Cold atoms in ring-shape potentials are thus promising for demonstrating rate-dependent hysteresis and its associated phenomena.

DOI
10.1103/physreva.93.053617

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Hysteresis can be found in driven many-body systems such as magnets and superfluids. Rate-dependent hysteresis arises when a system is driven periodically while relaxing towards equilibrium. A two-state paramagnet driven by an oscillating magnetic field in the relaxation approximation clearly demonstrates rate-dependent hysteresis. A noninteracting atomic Fermi gas in an optical ring potential, when driven by a periodic artificial gauge field and subjected to dissipation, is shown to exhibit hysteresis loops of atomic current due to a competition of the driving time and the relaxation time. This is in contrast to electronic systems exhibiting equilibrium persistent current driven by magnetic flux due to rapid relaxation. Universal behavior of the dissipated energy in one hysteresis loop is observed in both magnetic and atomic systems, showing linear and inverse-linear dependence on the relaxation time in the strong and weak dissipation regimes. While interactions in general invalidate the framework for rate-dependent hysteresis, an atomic Fermi gas with artificial spin-orbit coupling can exhibit hysteresis loops of atomic currents. Cold atoms in ring-shape potentials are thus promising for demonstrating rate-dependent hysteresis and its associated phenomena.
We explore the hysteretic dynamics of spinor Bose-Einstein condensates of ultracold atoms loaded in static 2D ring geometries and subjected to varying synthetic magnetic fields. Electrically neutral, pseudo-spin-1/2 condensates are probed by one-component weak-link potentials that make available paths for the transit of vortices into and out of the ring in both components, and thus can control the number of flux quanta threading the ring hole. For perpendicular fields, domain walls that are dynamically generated in the relative phase of the spin components are shown to play a key role in driving the hysteretic behavior of the whole system through changes in the net magnetic flux. In the presence of spin-orbit coupling, hysteresis is exhibited around the phase transitions found by the metastable current states for varying fields.
We explore the hysteretic dynamics of spinor Bose-Einstein condensates of ultracold atoms loaded in static 2D ring geometries and subjected to varying synthetic magnetic fields. Electrically neutral, pseudo-spin-1/21/21/2 condensates are probed by one-component weak-link potentials that make available paths for the transit of vortices into and out of the ring in both components, and thus can control the number of flux quanta threading the ring hole. For perpendicular fields, domain walls that are dynamically generated in the relative phase of the spin components are shown to play a key role in driving the hysteretic behaviour of the whole system through changes in the net magnetic flux. In the presence of spin-orbit-coupling, hysteresis is exhibited around the phase transitions found by the metastable current states for varying fields.
A new millennia ushered in novel experimental capabilities to investigate engineered quantum systems. Gases consisting of charge neutral atoms are cooled to the ground state and by exploiting the dipole interaction can be trapped by laser light. In ultracold atomic systems the tunneling and interactions are controllable, and the system is absent of disorder. Disorder and interactions in solid-state systems inhibits a complete understanding of transport phenomena. Theoretical investigations into non-equilibrium and equilibrium dynamics of fermions in discretized potentials and in continuum are presented. The affect of controllable, external system parameters is evaluated and exploited to reveal new properties of fermion dynamics. My thesis will begin with an overview of the physics associated with many-body fermion and the models used to obtain results, followed by my thesis research on how matter-waves can be manipulated by lattice geometry and tunneling strengths. Next, I present how dissipation affects current in a continuous ring, demonstrating rate-dependent hysteresis as the particles are driven by an artificial gauge field. After presenting the continuous ring, I will then focus on persistent current and corresponding quantum current fluctuations in a discretized ring. Lissajous curves are found in the system whose area strongly depends on the presence and absence of interactions. Lastly, I will discuss dynamical detection methods for one-dimensional topological insulators using ultracold fermions. All of the results are supported with discussion on how they can be realized using current experimental technology.
In this thesis, we study the coherence and the dynamics of ultracold atomic quantum gases, with a particular regard on Fermi gases. For what concerns the coherence, we study a Fermi gas confined on a ring threaded by an artificial gauge field. First, we show that the persistent current flowing in the ring can be used as probe for the different regimes of the BCS-BEC crossover. We propose a readout protocol for our results, based on the co-expansion of the gas trapped on the ring and a reference gas placed in the center of the ring itself. Next, we show that using the same expansion protocol we can extract information about the phase of the quantum gas. At intermediate times, the expanding cloud provides information about the first order coherence of the Fermi gas. In few-body systems, we can also access the number of particles in the system. At long times, we extract information about the many-body coherence coherence of the gas. Subsequently we focus on the dynamics of a strongly interacting two-component Fermi gas trapped in a harmonic potential. We consider a spin-separated state and then we follow the dynamics until long times. At short times, the dynamics is superdiffusive with dynamical exponents of the Kardar-Parisi-Zhang universality class. At intermediate times, the dynamics is dominated by damped spin oscillations unveleing a spin-drag effect. At long times, we observe thermalization. Ultimately, we study a multicomponent Bose gas in the strongly interacting regime. We first provide the exact solution for the wavefunction and we discuss its symmetry. Afterwards, we study the response of the gas to an artificial gauge field, with particular regard to the period of the persistent current as a function of the gauge flux.
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We present a theory of hysteretic phenomena in Bose gases, using superfluidity in one-dimensional rings and in optical lattices as primary examples. Through this study we are able to give a physical interpretation of swallow-tail loops recently found by many authors in the mean-field energy structure of trapped atomic gases. These loops are a generic sign of hysteresis, and in the present context are an indication of superfluidity. We have also calculated the rate of decay of metastable current-carrying states due to quantum fluctuations.