Quantum Memory Assisted Probing of Dynamical Spin Correlations

We propose a method to probe time-dependent correlations of nontrivial observables in many-body ultracold lattice gases. The scheme uses a quantum nondemolition 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 a method brings to 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.

Figure 1

Schematic representation as a quantum circuit of the protocol to measure dynamical correlations. $S$ ($M$) is the many-body system (the quantum memory), and $L_i$ is the $i$th light beam used in the protocol. The definition of the quantum gates is provided in the text. (a) Scheme for measuring $\widehat{\mathcal{J}}$ at two different instances of times, which after repetition give $F_S(t)$. (b) Scheme to measure $F_M(t)$ by using a quantum memory.

Figure 2

Fourier transforms of $F_M$ and $F_S$ for the Hamiltonian [Eq. (7)]. The results are obtained with exact diagonalization for a chain of 12 spins, with a standing wave configuration such that $k=\pi /(2a)$ and $\alpha =0$. $C_M$ (filled red circles and dashed line) and $C_S$ (empty blue squares and solid line) are plotted as a function of $\omega$. Vertical dashed green lines show the spectrum of the Hamiltonian. The inset shows the strongly varying $F_M$ (red), Eq. (6), and the almost flat $F_S$ (blue), Eq. (3), as a function of time. The uncertainty in the QMAP signal due to experimental limitations is plotted as error bars (losses in the quantum memory lead to a $5\%$ reduction of the signal); see the Supplemental Materials for details [28].