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arXiv:cond-mat/0608306 · Physical Review Letters

Quantum Polarization Spectroscopy of Ultracold Spinor Gases

K. Eckert, Łukasz Zawitkowski, Anna Sanpera, Maciej Lewenstein, Eugene Simon Polzik

Published Mar 9, 2007• 46 citations
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Abstract

We propose a method for the detection of ground state quantum phases of spinor gases through a series of two quantum nondemolition measurements performed by sending off-resonant, polarized light pulses through the gas. Signatures of various mean-field as well as strongly correlated phases of F=1 and F=2 spinor gases obtained by detecting quantum fluctuations and mean values of polarization of transmitted light are identified.

DOI
10.1103/physrevlett.98.100404

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We propose a method for the detection of ground state quantum phases of spinor gases through a series of two quantum nondemolition measurements performed by sending off-resonant, polarized light pulses through the gas. Signatures of various mean-field as well as strongly correlated phases of F=1 and F=2 spinor gases obtained by detecting quantum fluctuations and mean values of polarization of transmitted light are identified.
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.
We describe a technique for the preparation of quantum spin correlations in a lattice gas of ultracold atoms using an atom-light interaction of the kind routinely employed in quantum spin polarization spectroscopy. Our method is based on entropic cooling via quantum nondemolition 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 using a generalization of the entanglement witness described previously M. Cramer et al., Phys. Rev. Lett. 106, 020401 (2011). We illustrate the procedure with examples drawn from the bilinear-biquadratic Hamiltonian, which can be modeled by a one-dimensional chain of spin-1 atoms.
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 study the static and dynamic magnetic properties of ultracold quantum gases, in particular the spinor physics of F = 1 and F = 2 Bose-Einstein condensates of 87Rb atoms. Our data lead to the conclusion, that the F = 2 ground state of 87Rb is polar, while we find the F = 1 ground state to be ferromagnetic. The dynamics of spinor systems is linked to an interplay between coherent mean-field interactions, losses and interactions with atoms in the thermal cloud. Within this rich parameter space we observe indications for coherent spinor dynamics and novel thermalization regimes.
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.
We study the atom-light interaction in the fully quantum regime, with the focus on off-resonant light scattering into a cavity from ultracold atoms trapped in an optical lattice. The detection of photons allows the quantum nondemolition (QND) measurement of quantum correlations of the atomic ensemble, distinguishing between different quantum states. We analyse the entanglement between light and matter and show how it can be exploited for realising multimode macroscopic quantum superpositions, such as Schrödinger cat states, for both bosons and fermions. We provide examples utilising different measurement schemes and study their robustness to decoherence. Finally, we address the regime where the optical lattice potential is a quantum dynamical variable and is modified by the atomic state, leading to novel quantum phases and significantly altering the phase diagram of the atomic system.