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arXiv:1212.2273

Magnetization Cooling of an Electron Gas

Nodar L. Tsintsadze, Levan N. Tsintsadze

Published Dec 11, 2012• 5 citations
arXivHTMLPDF

Abstract

We propose an adiabatic magnetization process for cooling the Fermi electron gas to ultra-low temperatures as an alternative to the known adiabatic demagnetization mechanism. We show via a new adiabatic equation that at the constant density the increase of the magnetic field leads to the temperature decrease as $T\sim 1/H^2$.

DOI
10.48550/arxiv.1212.2273

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We propose an adiabatic magnetization process for cooling the Fermi electron gas to ultra-low temperatures as an alternative to the known adiabatic demagnetization mechanism. We show via a new adiabatic equation that at the constant density the increase of the magnetic field leads to the temperature decrease as T∼1/H2T\sim 1/H^2T∼1/H2.
To study the relativistic thermodynamic properties of a Fermi gas in a strong magnetic field, we construct the relativistic thermodynamic potential by the relativistic Fermi distribution function taking into account that the motion of particles in a plane perpendicular to the magnetic field is quantized. With this general potential at hand, we investigate all the thermodynamic quantities as a function of densities, temperatures and the magnetic field. We obtain a novel set of adiabatic equations. Having the expression of the pressure and adiabatic state equations, we determine the sound velocity for several cases revealing a new type of sound velocity. Finally, we disclose the magnetic cooling in the quantized electron Fermi gas, which is based on an adiabatic magnetization in contrast to the known adiabatic demagnetization.
This work reports on the first experimental realization of demagnetization cooling in a gas. In the presence of an external magnetic field, particles with a permanent magnetic dipole moment try to minimize their energy by aligning their dipole along the field, thus generating a macroscopic magnetization of the material. If the field is reduced enough, the particles are able to change their orientation and to do magnetic work during such a demagnetization process. This is done at the expense of their kinetic energy, with a consequent reduction of the temperature of the system. So far such a process has not been detected in gases because at low density the rate of demagnetization is very low. But Cr atoms have such a large magnetic dipole moment (6 muB) that for experimentally accessible densities of 1013atoms/cm3and sufficiently low fields (around 250 mG), they can demagnetize on a timescale of a few seconds.
The Fermi-Hubbard model describes ultracold fermions in an optical lattice and exhibits antiferromagnetic long-ranged order below the N\'eel temperature. However, reaching this temperature in the laboratory has remained an elusive goal. In other atomic systems, such as trapped ions, low temperatures have been successfully obtained by adiabatic demagnetization, in which a strong effective magnetic field is applied to a spin-polarized system and the magnetic field is adiabatically reduced to zero. Unfortunately, applying this approach to the Fermi-Hubbard model encounters a fundamental obstacle: the SU(2)\text{SU}(2)SU(2) symmetry introduces many level crossings that prevent the system from reaching the ground state, even in principle. However, by breaking the SU(2)\text{SU}(2)SU(2) symmetry with a spin-dependent tunneling, we show that adiabatic demagnetization can achieve low-temperature states. Using density matrix renormalization group (DMRG) calculations in one dimension, we numerically find that demagnetization protocols successfully reach low-temperature states of a spin-anisotropic Hubbard model, and we discuss how to optimize this protocol for experimental viability. By subsequently ramping spin-dependent tunnelings to spin-independent tunnelings, we expect that our protocol can be employed to produce low-temperature states of the Fermi-Hubbard model.
A new method for cooling atomic hydrogen down to 100 µK or below is suggested. The method exploits the unique properties of atomic hydrogen, which are the following: atomic hydrogen does not condense at temperatures as low as 20 µK and cannot be heated by IR radiation in the absence of atom-wall collisions. Therefore, the most efficient and well-known gas cooling technique can be employed, namely, the adiabatic expansion of the volume occupied by the gas (this approach is used in a gas-expansion machine). It is suggested to adiabatically expand the volume of a magnetic trap containing atomic hydrogen.
We propose a method to reach conditions of high degeneracy in a trapped Fermi gas, based on the adiabatic transfer of a small fraction of atoms from a magnetic to a tighter optical trap. The transformation yields a large increase of the Fermi energy, without a significant change of the temperature. The large enhancement of the central density emphasizes the role of the interactions and makes the system much closer to the BCS transition. We show that, despite Pauli blocking, the thermalization processes ensuring equilibrium in the optical trap are not suppressed at low temperature.
In a previous paper, we calculated the equation of state of a Fermi gas at arbitrary temperature in a uniform and constant magnetic field of arbitrary strength. (Such a gas is now referred to as a magnetized Fermi gas.) In the present paper, we have studied the properties of the equation of state and have obtained simplified expressions for the normal stresses and the energy and particle densities. These expressions can be used in astrophysical applications. We have found that under suitable conditions of degeneracy (the temperature approaching 0), a magnetized Fermi gas behaves exactly as a one-dimensional gas, which has been studied extensively as a theoretical problem. We have also obtained expressions for the grand partition function.