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arXiv:0809.0312 · Physical Review Letters

Probing Spatial Spin Correlations of Ultracold Gases by Quantum Noise Spectroscopy

Georg M. Bruun, Brian M. Andersen, Eugene Demler, Anders Søndberg Sørensen

Published Jan 20, 2009• 37 citations
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Abstract

Spin noise spectroscopy with a single laser beam is demonstrated theoretically to provide a direct probe of the spatial correlations of cold fermionic gases. We show how the generic many-body phenomena of antibunching, pairing, antiferromagnetic, and algebraic spin liquid correlations can be revealed by measuring the spin noise as a function of laser width, temperature, and frequency.

DOI
10.1103/physrevlett.102.030401

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Spin noise spectroscopy with a single laser beam is demonstrated theoretically to provide a direct probe of the spatial correlations of cold fermionic gases. We show how the generic many-body phenomena of antibunching, pairing, antiferromagnetic, and algebraic spin liquid correlations can be revealed by measuring the spin noise as a function of laser width, temperature, and frequency.
We theoretically demonstrate that optical measurements of electron spin noise can be a spectroscopic probe of the entangled quantum states of ultracold fermionic atom gases and unambiguously reveal the detailed nature of the underlying interatomic correlations. Different models of the effective interatomic interactions predict entirely new sets of resonances in the spin noise spectrum. Once the correct effective interatomic interaction model is identified, the detailed noise line shapes of the spin noise can be used to constrain this model. We estimate the magnitude of spin noise signals expected in ultracold fermionic atom gases via noise measurements in classical alkali vapors, which demonstrate the feasibility of this approach.
The subtle interplay between quantum statistics and interactions is at the origin of many intriguing quantum phenomena connected to superfluidity and quantum magnetism. The controlled setting of ultracold quantum gases is well suited to study such quantum correlated systems. Current efforts are directed towards the identification of their magnetic properties, as well as the creation and detection of exotic quantum phases. In this context, it has been proposed to map the spin-polarization of the atoms to the state of a single-mode light beam. Here we introduce a quantum-limited interferometer realizing such an atom-light interface with high spatial resolution. We measure the probability distribution of the local spin-polarization in a trapped Fermi gas showing a reduction of spin-fluctuations by up to 4.6(3) dB below shot-noise in weakly interacting Fermi gases and by 9.4(8) dB for strong interactions. We deduce the magnetic susceptibility as a function of temperature and discuss our measurements in terms of an entanglement witness.
This thesis describes experiments which investigate ultracold atom \nensembles in an optical lattice. Such quantum gases are powerful models for solid state physics. Several novel methods are demonstrated that probe the special properties of strongly correlated states in lattice potentials. Of these, quantum noise spectroscopy reveals spatial correlations in such states, which are hidden when using the usual methods of probing atomic gases. Another spectroscopic technique makes it possible to demonstrate the existence of a shell structure of regions with constant densities. Such coexisting phases separated by sharp boundaries had been theoretically predicted for the Mott insulating state.\nThe tunneling processes in the optical lattice in the strongly correlated regime are probed by preparing the ensemble in an optical superlattice potential. This allows the time-resolved observation of the tunneling dynamics, and makes it possible to directly identify correlated tunneling processes.\n
Summary form only given. Ultra-cold atomic gases trapped in optical lattices offer an unprecedented playground for studying the quantum phases of many-body systems. In particular, quantum states of ultra-cold lattice gases with spin degrees of freedom may be used to simulate quantum magnetism and to investigate physics relevant for our understanding of high-Tcsuperconductivity. While enormous progress has been made towards engineering such systems, achieving the regime of high-Tcsuperconductivity remains experimentally extremely challenging because of the low temperatures required [1].Here, we describe a new technique for the preparation of quantum spin-correlations in a lattice gas of ultracold atoms using atom-light interaction of the kind routinely employed in quantum spin polarization spectroscopy (QPS) [2], a promising technique for detecting quantum phases in lattice gases via quantum non-demolition (QND) measurement. Motivated by recent experimental work demonstrating the generation of spin-squeezing and entanglement in atomic ensembles via QND measurement [3], and by the recent extension of these ideas to unpolarized ensembles [5], we propose an alternative approach to preparing quantum spin-correlations, demonstrating that a simple modification of the experimental scheme of Ref. [4] allows for the on-demand preparation of spatial spin-correlations in a quantum lattice gas. Our method is based on entropic cooling via QND measurement and feedback, and allows the creation and detection of quantum spin-correlations, as well as a certain degree of multipartite entanglement, which we verify by deriving a novel generalization of the entanglement witness decribed in Ref. [5]. The proposed technique works with an unpolarized ensemble of non-interacting spins such as may be obtained by loading ultracold atoms into a deep optical lattice. We illustrate the procedure with examples drawn from the bilinear-biquadratic Hamiltonian, which can be modeled by a 1D chain of spin-1 atoms, showing that it is possible to prepare exponentially- and algebraically-decaying correlations, as well as spatial correlation signatures of more exotic quantum phases such as quantum criticalities.
We show how spin–spin correlations, detected in a non-destructive way via spatially resolved quantum polarization spectroscopy, strongly characterize various phases realized in trapped ultracold fermionic atoms. Polarization degrees of freedom of the light couple to spatially resolved components of the atomic spin. In this way, quantum fluctuations of matter are faithfully mapped onto those of light. In particular, we demonstrate that quantum spin polarization spectroscopy provides a direct method to detect the Fulde–Ferrell–Larkin–Ovchinnikov phase realized in a one-dimensional imbalanced Fermi system.