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arXiv:2205.10465 · Physical Review A

Thermal conductivity of an ultracold paramagnetic Bose gas

Reuben R. W. Wang, John L. Bohn

Published Aug 25, 2022• 8 citations
arXivHTMLPDF

Abstract

We analytically derive the transport tensor of thermal conductivity in an ultracold, but not yet quantum degenerate, gas of Bosonic lanthanide atoms using the Chapman-Enskog procedure. The tensor coefficients inherit an anisotropy from the anisotropic collision cross section for these dipolar species, manifest in their dependence on the dipole moment, dipole orientation, and $s$-wave scattering length. These functional dependences open up a pathway for control of macroscopic gas phenomena via tuning of the microscopic atomic interactions. As an illustrative example, we analyze the time evolution of a temperature hot spot which shows preferential heat diffusion orthogonal to the dipole orientation, a direct consequence of anisotropic thermal conduction.

DOI
10.1103/physreva.106.023319

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We analytically derive the transport tensor of thermal conductivity in an ultracold, but not yet quantum degenerate, gas of Bosonic lanthanide atoms using the Chapman-Enskog procedure. The tensor coefficients inherit an anisotropy from the anisotropic collision cross section for these dipolar species, manifest in their dependence on the dipole moment, dipole orientation, and sss-wave scattering length. These functional dependences open up a pathway for control of macroscopic gas phenomena via tuning of the microscopic atomic interactions. As an illustrative example, we analyze the time evolution of a temperature hot spot which shows preferential heat diffusion orthogonal to the dipole orientation, a direct consequence of anisotropic thermal conduction.
We present a hydrodynamic model of ultracold, but not yet quantum condensed, dipolar bosonic gases. Such systems present both sss-wave and dipolar scattering, the latter of which results in anisotropic transport tensors of thermal conductivity and viscosity. This paper presents an analytic derivation of the viscosity tensor coefficients, utilizing the methods established by Wang and Bohn [R. R. W. Wang and J. L. Bohn, Phys. Rev. A 106, 023319 (2022)], where the thermal conductivities were derived. Taken together, these transport tensors then permit a comprehensive description of hydrodynamics that is now embellished with dipolar anisotropy. An analysis of attenuation in linear waves illustrates the effect of this anisotropy in dipolar fluids, where we find a clear dependence on the dipole orientation relative to the direction of wave propagation.
We derive the Boltzmann equation for relaxation rate, viscosity and thermal conductivity in ultra cold normal dipolar bose gas. We use anisotropic dipole- dipole interaction. We obtain the temperature dependence of the relaxation rate and give formal expressions for the shear viscosity and thermal conductivity coefficients. These coefficients are proportional to . The different form of potentials in calculations show themselves in the coefficients of the viscosity and thermal conductivity. The ratio of the viscosity coefficient for dipole-dipole interaction to contact potential is three order and this ratio for thermal conductivity is two order.
Analytic expressions for the differential cross sections of ultracold atoms and molecules that scatter primarily due to dipolar interactions are derived within the first-order Born approximation and are shown to agree with the partial wave expansion. These cross sections are applied to the problem of cross-dimensional rethermalization. Strikingly, the rate of rethermalization can vary by as much as a factor of 2, depending on the orientation of the dipoles. Thus the anisotropic dipole-dipole interaction can have a significant effect even on the behavior of a nondegenerate ultracold gas.
We study spin-dependent heat transport in quantum gases, focusing on transport phenomena related to pure spin currents and spin-dependent temperatures. Using the Boltzmann equation, we compute the coupled spin-heat transport coefficients as a function of temperature and interaction strength for energy-dependent sss-wave scattering. We address the issue of whether spin-dependent temperatures can be sustained on a time and length scale relevant for experiments by computing the spin-heat relaxation time and diffusion length. We find that the time scale for spin-heat relaxation time diverges at low temperatures for both bosons and fermions, indicating that the concept of spin-heat accumulation is well defined for degenerate gases. For bosons, we find power-law behavior on approach to Bose condensation above the critical temperature, as expected from the theory of dynamical critical phenomena.
Interactions between particles play an important role in quantum degenerate gases.\nIn fact, the system’s behavior is usually largely determined by the strength, range, and\nsymmetry of the interactions, even if very weak. For more than two decades after the\nfirst experimental realization of a Bose-Einstein condensate (BEC) in 1995, investigations of ultracold atomic gases have mainly considered contact-type interactions, which\nmodel the short-range van der Waals interactions between the atoms in terms of a single\nparameter, the s-wave scattering length. However, some atomic or molecules species\npossess a magnetic or electric dipole moment and additionally interact among each\nother via the dipole-dipole interaction (DDI), which is long-ranged and anisotropic.\nSignatures of the DDI have been first observed in a BEC of chromium atoms in 2005.\nIn the last several years, a new class of atoms from the lanthanide series, e.g., dysprosium and erbium, with stronger dipolar properties, have come into play. This permits\na more full-fledged study of dipolar effects in BECs. Furthermore, ultracold molecules\nand highly excited Rydberg atoms are other promising examples for futures studies of\nsystems where dipolar interaction will be even more dominant, but they still need experimental efforts to achieve the desired quantum regime. Whereas the weak DDI in a\nchromium BEC is well described with the Gross-Pitaevskii equation, stronger dipolar\ninteractions certainly necessitate a beyond-mean-field description within a Bogoliubov\ntheory.\nIn parallel to research on bosons, cold fermions also trigger great interest because\nthey are actually often found in nature, e.g., within the electron gas of metals, as\nneutrons of heavy stars, or as quarks in plasmas as constituent elements of composite particles. Contrary to Bose systems, quantum degeneracy in experiments is much\nmore difficult to achieve in Fermi systems, since s-wave scattering is absent between\nidentical fermions, due to the Pauli exclusion principle. It was first achieved in 1999\nfor alkali atoms using a technique based on the sympathetic cooling with a second spin\nstate, another species, or a different isotope. For highly magnetic atoms, quantum degeneracy was achieved for dysprosium in 2012 using the standard sympathetic cooling\ntechnique, while in 2014 erbium was cooled deep into the degenerate regime using a\ndirect evaporative cooling mediated by dipolar collisions. This direct cooling scheme\nivallows producing very dense Fermi gas down to 10% of the Fermi temperature.\nFurthermore, a novel kind of strongly dipolar quantum gases became available in\nthe last several years. These are weakly bound polar molecules produced from atoms\nwith large magnetic dipole moments, such as erbium. Only very recently a quantum\ndegenerate dipolar Fermi gas of potassium-rubidium molecules has been experimentally realized. Unlike previously considered magnetic systems, heteronuclear molecules\nsuch as potassium-rubidium possess large electric dipole moments. The next natural\nstep is to polarize this system in a preferential direction by an external electric field,\nsuch that the DDI dominates the behavior of the system, which would open up the\nrealm for experimental investigation of strong dipolar Fermi gases...
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.