Quantum correlations in periodically driven spin chains: Revivals and steady-state properties

Abstract

We study the dynamics of microscopic quantum correlations, viz., bipartite entanglement and quantum discord between nearest neighbor sites, in Ising spin chain with a periodically varying external magnetic field along the transverse direction. Quantum correlations exhibit periodic revivals with the driving cycles in the finite-size chain. The time of first revival is proportional to the system size and is inversely proportional to the maximum group velocity of Floquet quasi-particles. On the other hand, the local quantum correlations in the infinite chain may get saturated to non-zero values after a sufficiently large number of driving cycles. Moreover, we investigate the convergence of local density matrices, from which the quantum correlations under study originate, towards the final steady-state density matrices as a function of driving cycles. We find that the geometric distance, d, between the reduced density matrices of nonequilibrium state and steady-state obeys a power-law scaling of the form d ∼ n −B , where n is the number of driving cycles and B is the scaling exponent. The steady-state quantum correlations are studied as a function of time period of the driving field and are marked by the presence of prominent peaks in frequency domain. The steady-state features can be further understood by probing band structures of Floquet Hamiltonian and purity of the bipartite state between nearest neighbor sites. Finally, we compare the steady-state values of the local quantum correlations with that of the canonical Gibbs ensemble and infer about their canonical ergodic properties. Moreover, we identify generic features in the ergodic properties depending upon the quantum phases of the initial state and the pathway of repeated driving that may be within the same quantum phase or across two different equilibrium phases.

Integrable quantum many-body sensors for AC field sensing

“…Therefore, a non-integrable quantum sensor may not be useful for many-body steady state AC field quantum sensing. On the other hand, integrable systems are known to reach a steady state where certain physical quantities depart from their infinite temperature value, and therefore, one may conclude that the heating effect might be absent in the integrable systems [80,85].…”

“…The two-site density matrix of the system, therefore, is given by The other non-zero elements are given as u 32 = u * 23 , and u 41 = u * 14 . The non-zero correlators σs i ⊗ σs i+1 can be obtained using the formalism presented in [85]. Once the two-site density matrix is obtained, the symmetric logarithmic derivative for the two-qubit state can be calculated.…”

Nonclassical atomic system dynamics time-dependently interacts with finite entangled pair coherent parametric converter cavity fields

“…More quantum information resources were realized form qubit-cavity interaction (which is described by the popular Jaynes-Cummings model [35]) as: quantum coherence quantum correlation [19,20,21,22,23], squeezing [24], and producing quntum states [25]. Atomic squeezing phenomena of the atomic variance and the entropy squeezing [24] have more potential applications in the quantum optical measurements [26], quantum teleportation [27], and restrain the decoherence in quantum systems [28].…”

Driving enhanced quantum sensing in partially accessible many-body systems

“…In addition, if the scaling becomes sub-Heisenberg, due to the mixedness of the density matrix, then is there any way to retrieve the Heisenberg scaling? Non-equilibrium dynamics of periodically driven many-body systems has been exploited for investigating the emergence of steady state [33], Floquet timecrystals [34], topological systems [35,36], entanglement generation [37][38][39][40][41], Floquet spectroscopy [42,43], dynamically controlled quantum thermometry [44], and Floquet dynamical phase transitions [45][46][47]. The useful features of periodically driven many-body systems are: (i) any local subsystem reaches a steady state; and (ii) the Floquet mechanism is applicable which simplifies the study of the dynamics.…”

“…In non-integrable systems, a periodic field drives any small subsystem to a featureless infinite temperature thermal steady state with no memory of the Hamiltonian parameters [48]. On the other hand, for integrable models, a non-trivial steady state can be obtained which carries a wealth of information about the Hamiltonian parameters [33,[37][38][39][40][41][49][50][51]. An important, yet unexplored, open question is whether the local steady states in periodically driven integrable systems can be used for enhancing the sensing precision with partial accessibility in many-body sensors.…”