One- and Two-Axis Squeezing via Laser Coupling in an Atomic Fermi-Hubbard Model

Quantum-enhanced multiparameter estimation and compressed sensing of a field

“…We have proposed a multiparameter estimation method that uses two-level atoms trapped in an optical lattice, which share internal-state quantum correlations generated by a one-axis twisting collective interaction Hamiltonian. Such a system can be obtained, for example, by adiabatically raising an optical lattice in an interacting two-component condensate (spin-squeezed Mott state) [4,5] or with fermionic atoms in a Mott-configuration in a lattice in the presence of an external laser which imprints a position-dependent phase to the atoms [6][7][8]. The atoms are used to measure the set of values that takes a field at the location of the different sites.…”

“…To this end, besides the regular arrangement of the atoms, which offers advantages for atomic clocks [1,2] and can be realized by means of optical tweezers or as a result of a Mott transition in a Bose-Einstein condensate [3], one should create spin correlations among the atoms. Two possible schemes, that directly yield the spin-squeezed state with one atom per site, consist in (i) adiabatically raising a lattice in a two-component Bose-Enstein condensate [4,5] or (ii) entangling fermionic atoms located at the lattice sites via virtual tunneling processes plus an external laser which imprints a site-dependent phase [6][7][8]. Similar configurations but with more than one spin on each site can be obtained by splitting a spin-squeezed Bose-Einstein condensate into addressable modes [9,10], or with atoms in a cavity where cavity-mediated interactions [11] or non-local quantum non demolition measurements [12] are used to entangle the modes.…”

Simultaneous minimal-noise estimation of noncommuting rotations of a spin

“…Therein, the authors have demonstrated that the variance of a spin in a selected direction orthogonal to the main axis of the squeezed state for large spins approaches a constant. Later the two-axis squeezing has been studied theoretically [55] and only recently an experimental realization has been proposed [56].…”

Probing quantum correlations in many-body systems: a review of scalable methods

“…It is therefore an important problem to characterize the buildup of quantum entanglement in such systems, beyond the paradigm of biparatite entanglement entropies as typically considered in most works in the field. In the context of quantum spin systems and Hubbard models, several theoretical works have shown that spin-squeezing [251][252][253][254][255][256][257] and other classes of entangled [257] and Bell-correlated states [253] are produced at short time by the out-of-equilibrium dynamics. At the same time, in more general situations the structure of entanglement as well as the suitable entanglement criteria are not known beforehand, and the problem offers a challenge where data-driven methods applied either to numerical simulations (as illustrated in [130]) or to experimental quantum simulation data could find a natural avenue of applications.…”