Light Scattering for Thermometry of Fermionic Atoms in an Optical Lattice

Abstract

We propose a method for measuring the temperature of fermionic atoms in an optical lattice potential from the intensity of the scattered light in the far-field diffraction pattern. We consider a single-component gas in a tightly-confined two-dimensional lattice, illuminated by far off-resonant light driving a cycling transition. Our calculations show that thermal correlations of the fermionic atoms generate fluctuations in the intensity of the diffraction pattern of light scattered from the atomic lattice array and that this signal can be accurately detected above the shot noise using a lens to collect photons scattered in a forward direction (with the diffraction maxima blocked). The sensitivity of the thermometer is enhanced by an additional harmonic trapping potential. Ultra-cold atomic gases in optical lattices can constitute almost ideal realizations of Hubbard models [1,2] that are fundamental to strongly-correlated physics. Recent experiments on fermionic atoms in lattices have demonstrated both a superfluid pairing [3] and a Mott insulator [4,5], opening up possibilities for experimental simulation of even more complex strongly-correlated systems, such as antiferromagnetic phases and high-T c superconductivity. Thermal energy is a major control parameter in fermionic lattice systems and characterizing phase diagrams is fundamentally related to the ability to perform accurate temperature measurements.Here we show that the temperature of fermionic atoms in a 2D optical lattice can be accurately determined by measurement of the light scattering from the atoms. The diffraction pattern is insensitive to thermal atomic correlations but blocking the diffraction maxima and collecting light scattered outside the diffraction orders using a lens provides a measurable optical signal that reflects thermal and quantum fluctuations of lattice atoms.The temperature of fermionic atoms in optical-lattice experiments has been deduced indirectly from the temperature of the trapped cloud of atoms before turning up the lattice [4,5], and by detecting double-occupancy in a two-species gas by converting atom pairs into molecules [4,6]. Other temperature measurements detected atomic shot-noise [7] or the sharpness of interference peaks [3] in absorption images after a ballistic expansion. This existing technology provided vital information about temperature but it has limitations, and there is a clear need for new methods; e.g., detecting atomic shot noise proved inconclusive in some superfluid/thermal lattice systems [8] and it was argued that detecting superfluidity from the sharpness of interference peaks can be ambigious as even a thermal gas may show misleadingly sharp peaks [9]. Moreover, a range of phenomena occur below the Néel temperatures [10] of these systems, e.g., antiferromagnetic ordering and superfluid pair hopping, but this requires significantly more cooling than current experLens

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“…For example, the thermometry of fermions in optical lattices based on light scattering was suggested in Refs. [36,37], where the idea of the light detection outside the diffraction maxima was shown useful as well.…”

Engineering many-body dynamics with quantum light potentials and measurements

“…Thus, the possibility to use measurement for such a selective suppression of dynamics is well verified. Furthermore, it may be possible to implement the dynamical effects discussed here using other types of systems that are also based on off-resonant scattering, such as molecules [57], fermions [58], spins [59], ions [60], and semiconductor [61] and superconducting qubits [62], as their dynamics are based on similar mathematical structures.…”

Optical Bragg, atomic Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices

“…The Optical Bragg scattering (Fig.1a) has been used previously to study periodic lattice structures of cold atoms loaded on optical lattices 6 . It was also proposed as an effective method for the thermometry of fermions in an optical lattice 7 . Recently, it was argued that it can be used to detect the putative anti-ferromagnetic ground state of fermions in OL 8 .…”