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arXiv:0908.3046 · Physical Review Letters

Spin Gradient Thermometry for Ultracold Atoms in Optical Lattices

David Weld, Patrick Medley, Hirokazu Miyake, David Hucul, David E. Pritchard, Wolfgang Ketterle

Published Dec 7, 2009• 127 citations
arXivHTMLPDF

Abstract

We demonstrate spin gradient thermometry, a new general method of measuring the temperature of ultracold atoms in optical lattices. We realize a mixture of spins separated by a magnetic field gradient. Measurement of the width of the transition layer between the two spin domains serves as a new method of thermometry which is observed to work over a broad range of lattice depths and temperatures, including in the Mott insulator regime. We demonstrate the thermometry using ultracold rubidium atoms, and suggest that interesting spin physics can be realized in this system. The lowest measured temperature is 1 nK, indicating that the system has reached the quantum regime, where insulating shells are separated by superfluid layers.

DOI
10.1103/physrevlett.103.245301

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We demonstrate spin gradient thermometry, a new general method of measuring the temperature of ultracold atoms in optical lattices. We realize a mixture of spins separated by a magnetic field gradient. Measurement of the width of the transition layer between the two spin domains serves as a new method of thermometry which is observed to work over a broad range of lattice depths and temperatures, including in the Mott insulator regime. We demonstrate the thermometry using ultracold rubidium atoms, and suggest that interesting spin physics can be realized in this system. The lowest measured temperature is 1 nK, indicating that the system has reached the quantum regime, where insulating shells are separated by superfluid layers.
We demonstrate a new cooling method in which a time-varying magnetic field gradient is applied to an ultracold spin mixture. This enables preparation of isolated spin distributions at positive and negative effective spin temperatures of ±50 pK. The spin system can also be used to cool other degrees of freedom, and we have used this coupling to cool an apparently equilibrated Mott insulator of rubidium atoms to 350 pK. These are the lowest temperatures ever measured in any system. The entropy of the spin mixture is in the regime where magnetic ordering is expected.
Interesting spin Hamiltonians can be realized with ultracold atoms in a two-component Mott insulator (2CMI) [Adv. Phys. 56, 243 (2007); Rev. Mod. Phys. 80, 885 (2008)]. It was recently demonstrated that the application of a magnetic field gradient to the 2CMI enables new techniques of thermometry [Phys. Rev. Lett. 103, 245301 (2009)] and adiabatic cooling [e-print arXiv:1006.4674]. Here we present a theoretical description which provides quantitative analysis of these two techniques. We show that adiabatic reduction of the field gradient is capable of cooling below the Curie or N\'eel temperature of certain spin-ordered phases.
We propose a method for measuring the temperature of strongly correlated phases of ultracold atom gases confined in spin-dependent optical lattices. In this technique, a small number of 'impurity' atoms—trapped in a state that does not experience the lattice potential—are in thermal contact with atoms bound to the lattice. The impurity serves as a thermometer for the system because its temperature can be straightforwardly measured using time-of-flight expansion velocity. This technique may be useful for resolving many open questions regarding thermalization in these isolated systems. We discuss the theory behind this method and demonstrate proof-of-principle experiments, including the first realization of a three-dimensional (3D) spin-dependent lattice in the strongly correlated regime.
At ICAP we presented the efforts and progress at MIT towards using ultracold atoms for the realization of various forms of quantum magnetism. These efforts include a study of fermions with strong repulsive interactions in which we obtained evidence for a phase transition to itinerant ferromagnetism, the characterization of cold atom systems by noise measurements, and a new adiabatic gradient demagnetization cooling scheme which has enabled us to realize temperatures of less than 350 picokelvin and spin temperatures of less than 50 picokelvin in optical lattices. These are the lowest temperatures ever measured in any physical system.
A method is proposed to directly measure the temperature of a gas of weakly interacting fermionic atoms loaded into an optical lattice. This technique relies on Raman spectroscopy and is applicable to experimentally relevant temperature regimes. Additionally, a similar spectroscopy scheme can be used to obtain information on the quasiparticle properties and Hubbard bands of the metallic and Mott-insulating states of interacting fermionic spin mixtures. These two methods provide experimentalists with probes to accurately characterize fermionic quantum gases confined to optical lattices.
We model the dynamics of two species of bosonic atoms trapped in an optical lattice within the Mott regime by mapping the system onto a spin model. A field gradient breaks the cloud into two domains. We study how the domain wall evolves under adiabatic and diabatic changes of this gradient. We determine the time scales for adiabaticity and study how temperature evolves for slow ramps. We show that after large, sudden changes of the field gradient, the system does not equilibrate on typical experimental time scales. We find interesting spin dynamics even when the initial temperature is large compared to the superexchange energy. We discuss the implication of our results for researchers wishing to use such a two-component system for thermometry or as part of a cooling scheme.