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arXiv:1208.1861 · Physical Review A

Quantum control of spin correlations in ultracold lattice gases

Philipp Hauke, R. J. Sewell, Morgan W. Mitchell, Maciej Lewenstein

Published Feb 8, 2013• 31 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.021601

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arXiv:cond-mat/0608306•Physical Review Letters•Mar 9, 2007•46 citations
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.
A forthcoming challenge in ultracold lattice gases is the simulation of quantum magnetism. That involves both the preparation of the lattice atomic gas in the desired spin state and the probing of the state. Here we demonstrate how a probing scheme based on atom-light interfaces gives access to the order parameters of nontrivial quantum magnetic phases, allowing us to characterize univocally strongly correlated magnetic systems produced in ultracold gases. This method, which is also nondemolishing, yields spatially resolved spin correlations and can be applied to bosons or fermions. As a proof of principle, we apply this method to detect the complete phase diagram displayed by a chain of (rotationally invariant) spin-1 bosons.
Quantum optics and ultracold gases are established fields, but they almost do not overlap: the quantum nature of light is typically neglected in works on ultracold atoms. In our work the quantumness of both light and ultracold matter plays a key role. First, we show that light is a quantum nondemolition (QND) probe of many-body phases: they can be distinguished by correlations and full distribution functions (we consider bosons, fermions, and dipolar molecules). Light is not only sensitive to densities, but also to the matter-field interference. Second, we prove that the measurement backaction constitutes a novel source of competitions in many-body systems, especially, for non-QND cases. This leads to a plethora of new phenomena: oscillations of multipartite entangled modes, protection and break-up of fermion pairs, antiferromagnetic orders, long-range pair tunnelling and entanglement beyond Hubbard models. We prove that feedback control induces phase transitions and tunes their universality class. Third, the quantization of trapping potential (quantum optical lattices) leads to novel phases, including both density orders (supersolids, density waves) and bond orders of matter fields (superfluid and supersolid dimers, trimers). Results beyond ultracold atoms include: We extend the paradigm of feedback control from the state control to control of phase transitions. We present the measurement backaction as a novel source of competitions in many-body physics. We merge quantum Zeno dynamics and non-Hermitian physics and show a novel type of Zeno phenomena with Raman transitions beyond Zeno dynamics. We propose quantum simulators based on collective light-matter interaction. Our models can be applied to arrays of other systems (qubits). In general, quantum measurements and feedback produce new phenomena untypical to both closed unitary systems and open dissipative ones in many-body physics.
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].