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Register a new userOptimal parent Hamiltonians for time-dependent states
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Given a generic time-dependent many-body quantum state, we determine the associated parent Hamiltonian. This procedure may require, in general, interactions of any sort. Enforcing the requirement of a fixed set of engineerable Hamiltonians, we find the optimal Hamiltonian once a set of realistic elementary interactions is defined. We provide three examples of this approach. We first apply the optimization protocol to the ground states of the one-dimensional Ising model and a ferromagnetic $p$-spin model but with time-dependent coefficients. We also consider a time-dependent state that interpolates between a product state and the ground state of a $p$-spin model. We determine the time-dependent optimal parent Hamiltonian for these states and analyze the capability of this Hamiltonian of generating the state evolution. Finally, we discuss the connections of our approach to shortcuts to adiabaticity.
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We investigate simultaneous estimation of multi-parameter quantum estimation with time-dependent Hamiltonians. We analytically obtain the maximal quantum Fisher information matrix for two-parameter in time-dependent three-level systems. The optimal coherent control scheme is proposed to increase the estimation precisions. In a example of a spin-1 particle in a uniformly rotating magnetic field, the optimal coherent Hamiltonians for different parameters can be chosen to be completely same. However, in general, the optimal coherent Hamiltonians for different parameters are incompatibility. In this situation, we suggest a variance method to obtain the optimal coherent Hamiltonian for estimating multiple parameters simultaneously, and obtain the optimal simultaneous estimation precision of two-parameter in a three-level Landau-Zener Hamiltonian.
The validity of optimized dynamical decoupling (DD) is extended to analytically time dependent Hamiltonians. As long as an expansion in time is possible the time dependence of the initial Hamiltonian does not affect the efficiency of optimized dynamical decoupling (UDD, Uhrig DD). This extension provides the analytic basis for (i) applying UDD to effective Hamiltonians in time dependent reference frames, for instance in the interaction picture of fast modes and for (ii) its application in hierarchical DD schemes with $pi$ pulses about two perpendicular axes in spin space. to suppress general decoherence, i.e., longitudinal relaxation and dephasing.
We introduce a method for the search of parent Hamiltonians of input wave-functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between reduced density matrix and parent Hamiltonian that is exact at the field theory level, and a minimization procedure on the space of relative entropies, which is particularly convenient due to its convexity. As examples, we show how our method correctly reconstructs the parent Hamiltonian correspondent to several non-trivial ground state wave functions, including conformal and symmetry-protected-topological phases, and quantum critical points of two-dimensional antiferromagnets described by strongly coupled field theories. Our results show the entanglement structure of ground state wave-functions considerably simplifies the search for parent Hamiltonians.
We formulate a set of conditions under which dynamics of a time-dependent quantum Hamiltonian are integrable. The main requirement is the existence of a nonabelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time-dependence into various quantum integrable models, so that the resulting non-stationary Schrodinger equation is exactly solvable. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.
In this work we address systems described by time-dependent non-Hermitian Hamiltonians under time-dependent Dyson maps. We shown that when starting from a given time-dependent non-Hermitian Hamiltonian which is not itself an observable, an infinite chain of gauge linked time-dependent non-observable non-Hermitian Hamiltonians can be derived from it. The matrix elements of the observables associated with all these non observable Hamiltonians are, however, all linked to each other, and in the particular case where global gauges exist, these matrix elements becomes all identical to each other. In this case, therefore, by approaching whatever the Hamiltonian in the chain we can get information about any other Hamiltonian. We then show that the whole chain of time-dependent non-Hermitian Hamiltonians collapses to a single time-dependent non-Hermitian Hamiltonian when, under particular choices for the time-dependent Dyson maps, the observability of the Hamiltonians is assured. This collapse thus shows that the observability character of a non-Hermitian Hamiltonian prevents the construction of the gauge-linked Hamiltonian chain and, consequently, the possibility of approaching one Hamiltonian from another.
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