NMR studies of quantum chaos in a two-qubit kicked top

Abstract

Quantum chaotic kicked top model is implemented experimentally in a two qubit system comprising of a pair of spin-1/2 nuclei using Nuclear Magnetic Resonance techniques. The essential nonlinear interaction was realized using indirect spin-spin coupling, while the linear kicks were realized using RF pulses. After a variable number of kicks, quantum state tomography was employed to reconstruct the single-qubit density matrices using which we could extract various measures such as von Neumann entropies, Husimi distributions, and Lyapunov exponents. These measures enabled the study of correspondence with classical phase space as well as to probe distinct features of quantum chaos, such as symmetries and temporal periodicity in the two-qubit kicked top. The x and y components of J can be recast in the form of raising and lowering operators as J x = (J + + J − )/2 and J y = (J + − J − )/2i which can then be studied in J z eigenbasis {|m } following the ladder equations J + |m = c m |m + 1 and J − |m = d m |m − 1 .First let us consider the evolution of J + component since J − will simply be its Hermitian conjugate (H.c):Computing the action of U NL on the operator in |m ba-sis,

Efficient Characterization of Quantum Evolutions via a Recommender System

“…This further reinforces the idea that the chaotic regimes of dynamical systems are hard to predict in general. The sensitivity of QKT to experimental imperfections in such chaotic regimes has been reported earlier by Krithika et al [37]. Hence, it is natural that RS finds it challenging to recognize the underlying patterns in the database, based on which it can predict the missing entries.…”

Observation of quantum phase-synchronization in a nuclear spin-system

“…Experimentally, the standard way to extract Husimi distribution is by using Eq. ( 1) after carrying out QST to estimate the steady state density matrix ρ [32]. However, there are two unrelated issues that plague tomographic measurements in quantum systems.…”

“…Our experiment involves a pair of interacting spin-1/2 nuclei and a weak transition-selective RF field applied on one of the spins. The resulting phaselocalization is characterized using Husimi distribution, which typically needs quantum state tomography (QST) [32]. However, QST after a long external drive proved to be highly inefficient because, as the steady state is approached, the irradiated levels saturate and relevant transitions become too faint.…”

Improving the dynamics of quantum sensors with reinforcement learning

“…In contrast to classical chaos, quantum chaos does not exhibit exponential sensitivity to changes of initial conditions due to the properties of unitary quantum evolution, but can be very sensitive to parameters of the evolution [39]. The KT has been realized with atomic spins in a cold gas [40] and with a pair of spin-1 2 nuclei using NMR techniques [41]. Here, we generalize the standard KT to kicks of strength k ℓ at arbitrary times t ℓ as given in equation (6), see also figure 1.…”