30 research outputs found
Non-Hermitian shortcut to stimulated Raman adiabatic passage
We propose a non-Hermitian generalization of stimulated Raman adiabatic
passage (STIRAP), which allows one to increase speed and fidelity of the
adiabatic passage. This is done by adding balanced imaginary (gain/loss) terms
in the diagonal (bare energy) terms of the Hamiltonian and choosing them such
that they cancel exactly the nonadiabatic couplings, providing in this way an
effective shortcut to adiabaticity. Remarkably, for a STIRAP using delayed
Gaussian-shaped pulses in the counter-intuitive scheme the imaginary terms of
the Hamiltonian turn out to be time independent. A possible physical
realization of non-Hermitian STIRAP, based on light transfer in three
evanescently-coupled optical waveguides, is proposed.Comment: 7 pages, 4 figure
Quantum simulation of the Riemann-Hurwitz zeta function
We propose a simple realization of a quantum simulator of the Riemann-Hurwitz
(RH) \zeta\ function based on a truncation of its Dirichlet representation. We
synthesize a nearest-neighbour-interaction Hamiltonian, satisfying the property
that the temporal evolution of the autocorrelation function of an initial bare
state of the Hamiltonian reproduces the RH function along the line \sigma+i
\omega t of the complex plane, with \sigma>1. The tight-binding Hamiltonian
with engineered hopping rates and site energies can be implemented in a variety
of physical systems, including trapped ion systems and optical waveguide
arrays. The proposed method is scalable, which means that the simulation can be
in principle arbitrarily accurate. Practical limitations of the suggested
scheme, arising from a finite number of lattice sites N and from decoherence,
are briefly discussed.Comment: 6 pages, 3 figure