Mohammad Mehboudi

Individual quantum probes for optimal thermometry

The unknown temperature of a sample can be estimated with minimal disturbance by putting it in thermal contact with an individual quantum probe. If the interaction time is sufficiently long so that the probe thermalizes, the temperature can be read-out directly from its steady state. Here we prove that the optimal quantum probe, acting as a thermometer with maximal thermal sensitivity, is an effective two-level atom with a maximally degenerate excited state. When the total interaction time is insufficient to produce full thermalization, we optimize the estimation protocol by breaking it down into sequential stages of probe preparation, thermal contact, and measurement. We observe that frequently interrogated probes initialized in the ground state achieve the best performance. For both fully and partly thermalized thermometers, the sensitivity grows significantly with the number of levels, though optimization over their energy spectrum remains always crucial.

Thermometry precision in strongly correlated ultracold lattice gases

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.

Achieving sub-shot-noise sensing at finite temperatures

We investigate sensing of magnetic fields using quantum spin chains at finite temperature and exploit quantum phase crossovers to improve metrological bounds on the estimation of the chain parameters. In particular, we analyze the XX spin chain and show that the magnetic sensitivity of this system is dictated by its adiabatic magnetic susceptibility, which scales extensively (linearly) in the number of spins N. Next, we introduce an iterative feedforward protocol that actively exploits features of quantum phase crossovers to enable super-extensive scaling of the magnetic sensitivity. Moreover, we provide experimentally realistic observables to saturate the quantum metrological bounds. Finally, we also address magnetic sensing in the Heisenberg XY spin chain.

Enhancement of low-temperature thermometry by strong coupling

Luis A. Correa,1, 2 Martı́ Perarnau-Llobet,3, 4 Karen V. Hovhannisyan,5, 4 Senaida Hernández-Santana,4 Mohammad Mehboudi,2 and Anna Sanpera2, 6 1School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom∗ 2Departament de Fı́sica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain 3Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany 4Institut de Ciències Fotòniques (ICFO), The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain 5Department of Physics and Astronomy, Ny Munkegade 120, 8000 Aarhus, Denmark 6Institució Catalana de Recerca i Estudis Avançats (ICREA), Psg. Lluı́s Companys 23, 08010 Barcelona, Spain (Dated: August 8, 2017)

Global and local thermometry schemes in coupled quantum systems

We study the ultimate bounds on the estimation of temperature for an interacting quantum system. We consider two coupled bosonic modes that are assumed to be thermal and using quantum estimation theory establish the role the Hamiltonian parameters play in thermometry. We show that in the case of a conserved particle number the interaction between the modes leads to a decrease in the overall sensitivity to temperature, while interestingly, if particle exchange is allowed with the thermal bath the converse is true. We explain this dichotomy by examining the energy spectra. Finally, we devise experimentally implementable thermometry schemes that rely only on locally accessible information from the total system, showing that almost Heisenberg limited precision can still be achieved, and we address the (im)possibility for multiparameter estimation in the system.

Testing a Quantum Heat Pump with a Two-Level Spin

Once in its non-equilibrium steady state, a nanoscale system coupled to several heat baths may be thought-of as a quantum heat pump. Depending on the direction of its stationary heat flows it may function as e.g. a refrigerator or a heat transformer. These continuous heat devices can be arbitrarily complex multipartite systems, and yet their working principle is always the same: They are made up of several elementary three-level stages operating in parallel. As a result, it is possible to devise external black-box testing strategies to learn about their functionality and performance regardless of any internal details. In particular, one such heat pump can be tested by coupling a two-level spin to one of its contact transitions. The steady state of this external probe contains information about the presence of heat leaks and internal dissipation in the device, and also, about the direction of its steady-state heat currents. Provided that the irreversibility of the heat pump is low, one can further estimate its coefficient of performance. These techniques may find applications in the emerging field of quantum thermal engineering, as they facilitate the diagnosis and design optimization of complex thermodynamic cycles.

Fluctuation-dissipation theorem for non-equilibrium quantum systems

The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolutions, as given by quantum maps. Third, it brings out the full connection between the FDT and the Quantum Fisher information, the figure of merit in quantum metrology.