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arXiv:1306.3365 · Physical Review A

Efficient demagnetization cooling of atoms and its limits

Valentin Volchkov, Jahn Rührig, Tilman Pfau, Axel Griesmaier

Published Apr 17, 2014• 13 citations
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Abstract

Demagnetization cooling relies on spin-orbit coupling that brings motional and spin degrees of freedom into thermal equilibrium. In the case of a gas, one has the advantage that the spin degree of freedom can be cooled very efficiently using optical pumping. We investigate demagnetization cooling of a chromium gas in a deep optical dipole trap over a large temperature range and reach high densities up to $5\ifmmode\times\else\texttimes\fi{}{10}^{19}$ m${}^{\ensuremath{-}3}$. We study the loss mechanism under such extreme conditions and identify excited-state collisions as the main limiting process. We discuss that in some systems demagnetization cooling has a realistic potential of reaching degeneracy by optical cooling only.

DOI
10.1103/physreva.89.043417

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Demagnetization cooling relies on spin-orbit coupling that brings motional and spin degrees of freedom into thermal equilibrium. In the case of a gas, one has the advantage that the spin degree of freedom can be cooled very efficiently using optical pumping. We investigate demagnetization cooling of a chromium gas in a deep optical dipole trap over a large temperature range and reach high densities up to 5\ifmmode×\else\texttimes\fi10195\ifmmode\times\else\texttimes\fi{}{10}^{19}5\ifmmode×\else\texttimes\fi1019 m\ensuremath−3{}^{\ensuremath{-}3}\ensuremath−3. We study the loss mechanism under such extreme conditions and identify excited-state collisions as the main limiting process. We discuss that in some systems demagnetization cooling has a realistic potential of reaching degeneracy by optical cooling only.
In this thesis, I study optical pumping as a powerful cooling tool for trapped ultra-cold atoms in a highly collisional regime. First application of optical pumping is a continuous loading scheme used to transfer atoms from a guided beam into a hybrid trap. Further, I introduce a Sisyphus cooling scheme based on radio-frequency transitions and optical pumping, operating simultaneously to the accumulation of atoms in the trap. The combined scheme of continuous loading and Sisyphus cooling is demonstrated for a large range of initial conditions of the guided atoms. Thereby, I show that collisional thermalization occurs in a steady-state for almost arbitrary initial conditions, provided that the first dissipative step is able to prevent the atom from leaving the trap during its first passage. On the one hand, this scheme could be applied to a wide range of atomic or molecular beams. On the other hand, phase-space density of 4*10^-4 is reached in a continuous operation mode with chromium atoms. In the second part, I investigate demagnetization cooling based on dipolar relaxation collisions driving the thermalization of the internal (spin) and the external (motional) degrees of freedom. In the case of a gas, one has the advantage that the spin degree of freedom can be cooled very efficiently using optical pumping. It is shown, that demagnetization cooling of a gas is more efficient than evaporation cooling in terms of phase-space density gain versus loss of atoms. This allows reaching a temperature of 6uK at a phase-space density of 0.03. It is observed, that both, continuous Sisyphus cooling and demagnetization cooling are limited by a density dependent loss mechanism. I present circumstantial evidence for excited-state collisions as the dominant limiting process. Finally, I discuss possible extensions to the current experimental procedures, possibly allowing reaching quantum degeneracy by optical means only.
Demagnetization cooling utilizes dipolar relaxations that couple the internal degree of freedom (spin) to the external (angular momentum) in order to cool an atomic cloud efficiently. Optical pumping into a dark state constantly recycles the atoms that were thermally excited to higher spin states. The net energy taken away by a single photon is very favorable since the lost energy per atom is the Zeeman energy rather than the recoil energy. As the density of the atomic sample rises the presence of the photons leads to limiting processes. In our previous publication [Volchkov et al. (2014)] we have shown that light-assisted collisions are such an important limiting process. In this paper we suppress light-assisted collisions by detuning the optical pumping light such that the Condon point coincides with the first node of the ground state wave function of two colliding atoms. This leads to an increased cooling efficiency χ ≥ 17 as well as to increased maximum densities of n ≈ 1 · 10(20) m(-3). However, due to the high number of involved molecular states the net suppression is not strong enough to reach quantum degeneracy.
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.
We propose a cooling scheme based on depolarisation of a polarised cloud of trapped atoms. Similar to adiabatic demagnetisation, we suggest to use the coupling between the internal spin reservoir of the cloud and the external kinetic reservoir via dipolar relaxation to reduce the temperature of the cloud. By optical pumping one can cool the spin reservoir and force the cooling process. In case of a trapped gas of dipolar chromium atoms, we show that this cooling technique can be performed continuously and used to approach the critical phase space density for BEC
We propose a cooling scheme based on depolarisation of a polarised cloud of trapped atoms. Similar to adiabatic demagnetisation, we suggest to use the coupling between the internal spin reservoir of the cloud and the external kinetic reservoir via dipolar relaxation to reduce the temperature of the cloud. By optical pumping one can cool the spin reservoir and force the cooling process. In case of a trapped gas of dipolar chromium atoms, we show that this cooling technique can be performed continuously and used to approach the critical phase space density for BEC.
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.