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When measuring quantum spins at two or more different times, the later measurements are affected by measurement backaction occurring due to the earlier measurements. This makes the measurement of temporal quantum correlation functions challenging. In this paper, I propose a measurement protocol that mitigates the effect of measurement backaction by exploiting spin selection rules. I show that, under suitable conditions, the effect of measurement backaction on two-time quantum correlations becomes negligible when probing a system consisting of spins with large spin quantum numbers $lgg s$ by coupling it to a spin-$s$ ancilla degree of freedom. A potential application of such a measurement protocol is the probing of an array of Bose-Einstein condensates by light.
We propose a method to probe time dependent correlations of non trivial observables in many-body ultracold lattice gases. The scheme uses a quantum non-demolition matter-light interface, first, to map the observable of interest on the many body system into the light and, then, to store coherently such information into an external system acting as a quantum memory. Correlations of the observable at two (or more) instances of time are retrieved with a single final measurement that includes the readout of the quantum memory. Such method brings at reach the study of dynamics of many-body systems in and out of equilibrium by means of quantum memories in the field of quantum simulators.
We review the use of an external auxiliary detector for measuring the full distribution of the work performed on or extracted from a quantum system during a unitary thermodynamic process. We first illustrate two paradigmatic schemes that allow one to measure the work distribution: a Ramsey technique to measure the characteristic function and a positive operator valued measure (POVM) scheme to directly measure the work probability distribution. Then, we show that these two ideas can be understood in a unified framework for assessing work fluctuations through a generic quantum detector and describe two protocols that are able to yield complementary information. This allows us also to highlight how quantum work is affected by the presence of coherences in the systems initial state. Finally, we describe physical implementations and experimental realisations of the first two schemes.
Measuring unitarily-evolved quantum mechanical two-time correlations is challenging in general. In a recent paper [P.~Uhrich {em et al.}, Phys. Rev.~A {bf 96}, 022127 (2017)], a considerable simplification of this task has been pointed out to occur in spin-$1/2$ lattice models, bringing such measurements into reach of state-of-the-art or near-future quantum simulators of such models. Here we discuss the challenges of an experimental implementation of measurement schemes of two-time correlations in quantum gas microscopes or microtrap arrays. We propose a modified measurement protocol that mitigates these challenges, and we rigorously estimate the accuracy of the protocols by means of Lieb-Robinson bounds. On the basis of these bounds we identify a parameter regime in which the proposed protocols allow for accurate measurements of the desired two-time correlations.
The Floquet Hamiltonian has often been used to describe a time-periodic system. Nevertheless, because the Floquet Hamiltonian depends on a micro-motion parameter, the Floquet Hamiltonian with a fixed micro-motion parameter cannot faithfully represent a driven system, which manifests as the anomalous edge states. Here we show that an accurate description of a Floquet system requires a set of Hamiltonian exhausting all values of the micro-motion parameter, and this micro-motion parameter can be viewed as an extra synthetic dimension of the system. Therefore, we show that a $d$-dimensional Floquet system can be described by a $d+1$-dimensional static Hamiltonian, and the advantage of this representation is that the periodic boundary condition is automatically imposed along the extra-dimension, which enables a straightforward definition of topological invariants. The topological invariant in the $d+1$-dimensional system can ensure a $d-1$-dimensional edge state of the $d$-dimensional Floquet system. Here we show two examples where the topological invariant is a three-dimensional Hopf invariant. We highlight that our scheme of classifying Floquet topology on the micro-motion space is different from the previous classification of Floquet topology on the time space.
We present a major update to QuSpin, SciPostPhys.2.1.003 -- an open-source Python package for exact diagonalization and quantum dynamics of arbitrary boson, fermion and spin many-body systems, supporting the use of various (user-defined) symmetries in one and higher dimension and (imaginary) time evolution following a user-specified driving protocol. We explain how to use the new features of QuSpin using seven detailed examples of various complexity: (i) the transverse-field Ising chain and the Jordan-Wigner transformation, (ii) free particle systems: the Su-Schrieffer-Heeger (SSH) model, (iii) the many-body localized 1D Fermi-Hubbard model, (iv) the Bose-Hubbard model in a ladder geometry, (v) nonlinear (imaginary) time evolution and the Gross-Pitaevskii equation on a 1D lattice, (vi) integrability breaking and thermalizing dynamics in the translationally-invariant 2D transverse-field Ising model, and (vii) out-of-equilibrium Bose-Fermi mixtures. This easily accessible and user-friendly package can serve various purposes, including educational and cutting-edge experimental and theoretical research. The complete package documentation is available under http://weinbe58.github.io/QuSpin/index.html.