1,450 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
Field-induced barrier transparency of Bloch waves in tight-binding lattices
A rectangular potential barrier for a Bloch particle in a tight-binding
lattice is shown to become fully transparent by the application of a strong ac
field with appropriate amplitude and frequency. Such a curious phenomenon bears
some connection with the field-induced barrier transparency effect known for
freely-moving particles scattered by an ac-driven rectangular barrier; however,
for a Bloch particle transparency is not related to a resonant tunnneling
process across the cycle-averaged oscillating potential barrier, as for the
freely-moving quantum particle. The phenomenon of field-induced transparency is
specifically discussed here for photonic transport in waveguide arrays and
demonstrated by full numerical simulations of the paraxial (Schr\"{o}dinger)
wave equation beyond the tight-binding approximation
Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation
It is well known that pulse-like solutions of the cubic complex
Ginzburg-Landau equation are unstable but can be stabilised by the addition of
quintic terms. In this paper we explore an alternative mechanism where the role
of the stabilising agent is played by the parametric driver. Our analysis is
based on the numerical continuation of solutions in one of the parameters of
the Ginzburg-Landau equation (the diffusion coefficient ), starting from the
nonlinear Schr\"odinger limit (for which ). The continuation generates,
recursively, a sequence of coexisting stable solutions with increasing number
of humps. The sequence "converges" to a long pulse which can be interpreted as
a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR
Autoprotolysis constants in nonaqueous solvents and aqueous organic solvent mixtures
The recent IUPAC document on standardization of pH measurements in nonaqueous solvents and aqueous-organic solvent mixtures (P.A.C. 57 865 (1985)) underlines the importance of the autoprotolysis constant, K, which defines the normal range of pH in the relevant solvent. The recommended e.m.f. method of determination and the standard states implied by different K definitions are duly focused. This compilation is articulated in two Tables the first of which reports K data for 100% pure solvents mostly at 298.15 K and the other concerns binary aqueous-organic mixtures of different compositions and at various temperatures
Loschmidt echo and fidelity decay near an exceptional point
Non-Hermitian classical and open quantum systems near an exceptional point
(EP) are known to undergo strong deviations in their dynamical behavior under
small perturbations or slow cycling of parameters as compared to Hermitian
systems. Such a strong sensitivity is at the heart of many interesting
phenomena and applications, such as the asymmetric breakdown of the adiabatic
theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions
and photonic catastrophe. Like for Hermitian systems, the sensitivity to
perturbations on the dynamical evolution can be captured by Loschmidt echo and
fidelity after imperfect time reversal or quench dynamics. Here we disclose a
rather counterintuitive phenomenon in certain non-Hermitian systems near an EP,
namely the deceleration (rather than acceleration) of the fidelity decay and
improved Loschmidt echo as compared to their Hermitian counterparts, despite
large (non-perturbative) deformation of the energy spectrum introduced by the
perturbations. This behavior is illustrated by considering the fidelity decay
and Loschmidt echo for the single-particle hopping dynamics on a tight-binding
lattice under an imaginary gauge field.Comment: 11 pages, 6 figures, to appear in Annalen der Physi
Non-Markovian Decay and Lasing Condition in an Optical Microcavity Coupled to a Structured Reservoir
The decay dynamics of the classical electromagnetic field in a leaky optical
resonator supporting a single mode coupled to a structured continuum of modes
(reservoir) is theoretically investigated, and the issue of threshold condition
for lasing in presence of an inverted medium is comprehensively addressed.
Specific analytical results are given for a single-mode microcavity resonantly
coupled to a coupled resonator optical waveguide (CROW), which supports a band
of continuous modes acting as decay channels. For weak coupling, the usual
exponential Weisskopf-Wigner (Markovian) decay of the field in the bare
resonator is found, and the threshold for lasing increases linearly with the
coupling strength. As the coupling between the microcavity and the structured
reservoir increases, the field decay in the passive cavity shows non
exponential features, and correspondingly the threshold for lasing ceases to
increase, reaching a maximum and then starting to decrease as the coupling
strength is further increased. A singular behavior for the "laser phase
transition", which is a clear signature of strong non-Markovian dynamics, is
found at critical values of the coupling between the microcavity and the
reservoir.Comment: to appear in Phys. Rev. A (December 2006 issue
Coherent tunneling by adiabatic passage in an optical waveguide system
We report on the first experimental demonstration of light transfer in an
engineered triple-well optical waveguide structure which provides a classic
analogue of Coherent Tunnelling by Adiabatic Passage (CTAP) recently proposed
for coherent transport in space of neutral atoms or electrons among
tunneling-coupled optical traps or quantum wells [A.D. Greentree et al., Phys.
Rev. B 70, 235317 (2004); K. Eckert et al., Phys. Rev. A 70, 023606 (2004)].
The direct visualization of CTAP wavepacket dynamics enabled by our simple
optical system clearly shows that in the counterintuitive passage scheme light
waves tunnel between the two outer wells without appreciable excitation of the
middle well.Comment: submitted for publicatio
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