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Optical Spin Transport in Ultracold Quantum Gases.

Yuta Sekino, Hiroyuki Tajima, Shun Uchino

Published Mar 3, 2021• 0 citations
OpenAlex

Abstract

Measurement of frequency-resolved spin transport is a subject of much interest in condensed matter physics. Here we show that the optical spin conductivity being a small AC response of a spin current can be measured with existing methods in ultracold atom experiments. We point out that once interatomic interactions are turned on, the optical spin conductivity becomes nontrivial even in clean ultracold atomic gases and thereby can be a probe of generic quantum states of matter. This is a sharp contrast to the optical mass conductivity which becomes trivial in typical cold-atom systems without disorder and lattice potential. For systems with arbitrary spin degrees of freedom, we construct a general formalism of the optical spin conductivity and derive the $f$-sum rule. To demonstrate the availability of the optical spin conductivity, our formalism is applied to a spin-1/2 Fermi superfluid and a spin-1 Bose-Einstein condensate. It turns out that both superfluids show nontrivial responses that cannot be captured with the Drude conductivity. The application of our proposed method to generic ultracold atomic gases with spin degrees of freedom is feasible.

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•Aug 23, 2010•0 citations
Measurement of frequency-resolved spin transport is a subject of much interest in condensed matter physics. Here we show that the optical spin conductivity being a small AC response of a spin current can be measured with existing methods in ultracold atom experiments. We point out that once interatomic interactions are turned on, the optical spin conductivity becomes nontrivial even in clean ultracold atomic gases and thereby can be a probe of generic quantum states of matter. This is a sharp contrast to the optical mass conductivity which becomes trivial in typical cold-atom systems without disorder and lattice potential. For systems with arbitrary spin degrees of freedom, we construct a general formalism of the optical spin conductivity and derive the fff-sum rule. To demonstrate the availability of the optical spin conductivity, our formalism is applied to a spin-1/2 Fermi superfluid and a spin-1 Bose-Einstein condensate. It turns out that both superfluids show nontrivial responses that cannot be captured with the Drude conductivity. The application of our proposed method to generic ultracold atomic gases with spin degrees of freedom is feasible.
We show that the optical spin conductivity, which is a small ac response of a bulk spin current and elusive in condensed matter systems, can be measured in ultracold atoms. We demonstrate that this conductivity contains rich information on quantum states by analyzing experimentally achievable systems such as a spin-12\frac{1}{2}21​ superfluid Fermi gas, a spin-1 Bose-Einstein condensate, and a Tomonaga-Luttinger liquid. The obtained conductivity spectra, which are absent in the Drude conductivity, reflect quasiparticle excitations and non-Fermi-liquid properties. Accessible physical quantities include the superfluid gap and the contact for the superfluid Fermi gas, gapped and gapless spin excitations as well as quantum depletion for the Bose-Einstein condensate, and the spin part of the Tomonaga-Luttinger liquid parameter elusive in cold-atom experiments. Unlike its mass transport counterpart, the spin conductivity serves as a probe applicable to clean atomic gases without disorder or lattice potentials. Our formalism can be generalized to various systems such as spin-orbit-coupled and nonequilibrium systems.
We theoretically investigate optical (frequency-dependent) bulk spin transport properties in a spin-12\frac{1}{2}21​ topological Fermi superfluid. We specifically consider a one-dimensional system with an interspin ppp-wave interaction, which can be realized in ultracold-atom experiments. Developing the BCS-Leggett theory to describe the BCS to Bose-Einstein condensate (BEC) evolution and the Z2{\mathbb{Z}}_{2}Z2​ topological phase transition in this system, we show how the spin transport reflects these many-body aspects. We find that the optical spin conductivity, which is a small AC response of a spin current, shows the spin-gapped spectrum in the wide parameter region and the gap closes at the Z2{\mathbb{Z}}_{2}Z2​ topological phase transition point. Moreover, the validity of the low-energy effective model of the Majorana zero mode is discussed along the BCS-BEC evolution in connection with the scale invariance at ppp-wave unitarity.
The transport of quantum particles in non ideal material media (eg the conduction of electrons in an imperfect crystal) is strongly affected by scattering from impurities of the medium. Even for a weak disorder, semi-classical theories, such as those based on the Boltzmann equation for matter-waves scattering from the impurities, often fail to describe transport properties and full quantum approaches are necessary. The properties of the quantum systems are of fundamental interest as they show intriguing and non-intuitive phenomena that are not yet fully understood such as Anderson localization, percolation, disorder-driven quantum phase transitions and the corresponding Bose-glass or spin-glass phases. Understanding quantum transport in amorphous solids is one of the main issues in this context, related to electric and thermal conductivities. Ultracold atomic gases can now be considered to revisit the problem of quantum conductivity and quantum transport under unique control possibilities. Dilute atomic Bose-Einstein condensates (BEC) and degenerate Fermi gases (DFG) are produced routinely taking advantage of the recent progress in cooling and trapping of neutral atoms. Transport has been widely investigated in controlled potentials with no defects, for instance periodic potentials (optical lattices). Controlled disordered potentials can also be produced with various techniques such as the use of magnetic traps designed on atomic chips with rough wires, the use of localized impurity atoms, the use of radio-frequency fields or the use of optical potentials. This recently lead to the observation of the Anderson Localisation of a BEC and the measurement of the diffusion coefficient of a 2D gaz in the presence of disorder.
We measure the conductivity of neutral fermions in a cubic lattice. A uniform force is applied at a single frequency by periodic displacement of the trapping potential, and the current response is observed though the global displacement of atoms. In the linear response regime, the steady-state ratio between current and force gives the ac conductivity. The tensor properties of the conductivity reveal temporal and spatial symmetries of the sample. Similarly to optical conductivity commonly measured in materials with reflectivity, exact sum rules relate dynamical measurements to thermodynamic properties. We explore the effect of lattice depth, temperature, interaction strength, and atom number on conductivity. Using a relaxation-time approximation, we extract the transport time of current. Our work enables a direct comparison between cold-atom experiments and conductivity studies of materials.
The transport of quantum particles in non ideal mate- rial media (eg the conduction of electrons in an imperfect crystal) is strongly affected by scattering from impurities of the medium. Even for a weak disorder, semi-classical theories, such as those based on the Boltzmann equation for matter-waves scattering from the impurities, often fail to describe transport properties and full quantum approaches are necessary. The properties of the quan- tum systems are of fundamental interest as they show intriguing and non-intuitive phenomena that are not yet fully understood such as Anderson localization, percola- tion, disorder-driven quantum phase transitions and the corresponding Bose-glass or spin-glass phases. Under- standing quantum transport in amorphous solids is one of the main issues in this context, related to electric and thermal conductivities. Ultracold atomic gases can now be considered to re- visit the problem of quantum conductivity and quan- tum transport under unique control possibilities. Dilute atomic Bose-Einstein condensates (BEC) and degener- ate Fermi gases (DFG) are produced routinely taking advantage of the recent progress in cooling and trap- ping of neutral atoms. Transport has been widely in- vestigated in controlled potentials with no defects, for instance periodic potentials (optical lattices). Controlled disordered potentials can also be produced with various techniques such as the use of magnetic traps designed on atomic chips with rough wires, the use of localized impurity atoms, the use of radio-frequency fields or the use of optical potentials. This recently lead to the ob- servation of the Anderson Localisation of a BEC and the measurement of the diffusion coefficient of a 2D gaz in the presence of disorder.