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arXiv:1501.03095 · New Journal of Physics

Thermometry precision in strongly correlated ultracold lattice gases

Mohammad Mehboudi, Maria Moreno-Cardoner, Gabriele De Chiara, Anna Sanpera

Published May 18, 2015• 67 citations
arXivHTMLPDF

Abstract

The precise knowledge of the temperature of an ultracold lattice gas simulating a strongly correlated system is a question of both fundamental and technological importance. Here, we address such question by combining tools from quantum metrology together with the study of the quantum correlations embedded in the system at finite temperatures. Within this frame we examine the spin- XY chain, first estimating, by means of the quantum Fisher information, the lowest attainable bound on the temperature precision. We then address the estimation of the temperature of the sample from the analysis of correlations using a quantum non demolishing Faraday spectroscopy method. Remarkably, our results show that the collective quantum correlations can become optimal observables to accurately estimate the temperature of our model in a given range of temperatures.

DOI
10.1088/1367-2630/17/5/055020

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The precise knowledge of the temperature of an ultracold lattice gas simulating a strongly correlated system is a question of both fundamental and technological importance. Here, we address such question by combining tools from quantum metrology together with the study of the quantum correlations embedded in the system at finite temperatures. Within this frame we examine the spin- XY chain, first estimating, by means of the quantum Fisher information, the lowest attainable bound on the temperature precision. We then address the estimation of the temperature of the sample from the analysis of correlations using a quantum non demolishing Faraday spectroscopy method. Remarkably, our results show that the collective quantum correlations can become optimal observables to accurately estimate the temperature of our model in a given range of temperatures.
Temperature estimation of interacting quantum many-body systems is both a challenging task and topic of interest in quantum metrology, given that critical behavior at phase transitions can boost the metrological sensitivity. Here we study noninvasive quantum thermometry of a finite, two-dimensional Ising spin lattice based on measuring the dephasing dynamics of a spin probe coupled to the lattice. We demonstrate a strong critical enhancement of the achievable precision in terms of the quantum Fisher information, which depends on the coupling range and the interrogation time. Our numerical simulations are compared to instructive analytic results for the critical scaling of the sensitivity in the Curie-Weiss model of a fully connected lattice and to the mean-field description in the thermodynamic limit, both of which fail to describe the critical spin fluctuations on the lattice the spin probe is sensitive to. Phase metrology could thus help to investigate the critical behavior of finite many-body systems beyond the validity of mean-field models. Published by the American Physical Society 2024
While the ability to measure low temperatures accurately in quantum systems is important in a wide range of experiments, the possibilities and the fundamental limits of quantum thermometry are not yet fully understood theoretically. Here we develop a general approach to low-temperature quantum thermometry, taking into account restrictions arising not only from the sample but also from the measurement process. {We derive a fundamental bound on the minimal uncertainty for any temperature measurement that has a finite resolution. A similar bound can be obtained from the third law of thermodynamics. Moreover, we identify a mechanism enabling sub-exponential scaling, even in the regime of finite resolution. We illustrate this effect in the case of thermometry on a fermionic tight-binding chain with access to only two lattice sites, where we find a quadratic divergence of the uncertainty}. We also give illustrative examples of ideal quantum gases and a square-lattice Ising model, highlighting the role of phase transitions.
Abstract Controlling and measuring the temperature in different devices and platforms that operate in the quantum regime is, without any doubt, essential for any potential application. In this review, we report the most recent theoretical developments dealing with accurate estimation of very low temperatures in quantum systems. Together with the emerging experimental techniques and developments of measurement protocols, the theory of quantum thermometry will decisively impinge and shape the forthcoming quantum technologies. While current quantum thermometric methods differ greatly depending on the experimental platform, the achievable precision, and the temperature range of interest, the theory of quantum thermometry is built under a unifying framework at the crossroads of quantum metrology, open quantum systems, and quantum many-body physics. At a fundamental level, theoretical quantum thermometry is concerned with finding the ultimate bounds and scaling laws that limit the precision of temperature estimation for systems in and out of thermal equilibrium. At a more practical level, it provides tools to formulate precise, yet feasible, thermometric protocols for relevant experimental architectures. Last but not least, the theory of quantum thermometry examines genuine quantum features, like entanglement and coherence, for their exploitation in enhanced-resolution thermometry.
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.
This thesis is devoted to quantum information processing using strongly correlated many-body systems, and we have focused our interest on systems realized with ultracold atoms in optical lattices. We have proposed different protocols based either on the free dynamics followed by a particular initial state -out of the ground-state manifold-, or on the non-trivial quantum dynamics generated by the optimal modulation of optical lattices. Our protocols demonstrate the potential of strongly correlated systems to perform short-distance quantum communication. Protocols based on dynamical manipulations of the optical lattices have also been extended to two-dimensional lattices to prepare decoherence-free cluster states. We have also proposed a novel scheme combining free dynamics and continuous measurements, which lead to the Quantum Zeno effect, for quantum information processing in spin chains. Despite of the recent progress in using atoms trapped in optical lattices to prepare and manipulate strongly correlated systems, the precise detection and experimental characterization of such states is a major challenge in modem physics. We have exploited some of the proposed protocols to analyze strongly correlated systems from the quality of their performance when implementing a quantum information task. Our approach provides a new insight into the study of these complex and fascinating systems. Regarding the detection, we have also addressed the fundamental problem of inferring the state of a given quantum system. First, we have studied the optimal state estimation of the most fundamental quantum system, a two-level system or qubit. Second, we have also considered and proposed new methods to tackle the experimental challenge of detecting the many-body systems prepared with ultracold atoms in optical lattices. We have extended the applicability of the noise-correlation method to detect a mesoscopic Schrodinger cat many-body state. Despite the success of this method, it has the drawback that it demolishes the physical system. To overcome such limitation, we have proposed an . extension of the well-known Faraday effect at the quantum level, which yields a quantum non-demolition method to detect strongly correlated systems.
We will present recent experimental work on the thermodynamics of strongly interacting Fermi gases. We have developed a general method to probe with high precision the Equation of State (EoS) of locally homogeneous ultracold gases. This allows stringent tests of recent many-body theories. First, we focus on the finite-temperature EoS of the unpolarized unitary gas. Precise thermometry is provided by adding to the Fermi gas of 6Li a trace of bosonic 7Li. We show that the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid transition. Second, we address the zero-temperature EoS of the spin-polarized system in the BEC-BCS crossover. Surprisingly, despite strong interactions, the polarized phase behaves as a mixture of two ideal gases: a Fermi gas of majority atoms and a non-interacting gas of dressed quasi-particles, the Fermi polarons. We also obtain the equation of state of the superfluid state as a function of interaction strength, that we compare to Monte Carlo simulations and to the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids.