39 research outputs found
Squeezed state evolution and entanglement in lossy coupled resonator optical waveguides
We investigate theoretically the temporal evolution of a squeezed state in
lossy coupled-cavity systems. We present a general formalism based upon the
tight binding approximation and apply this to a two-cavity system as well as to
a coupled resonator optical waveguide in a photonic crystal. We derive
analytical expressions for the number of photons and the quadrature noise in
each cavity as a function of time when the initial excited state is a squeezed
state in one of the cavities. We also analytically evaluate the time dependant
cross correlation between the photons in different cavities to evaluate the
degree of quantum entanglement. We demonstrate the effects of loss on the
properties of the coupled-cavity systems and derive approximate analytic
expressions for the maximum photon number, maximum squeezing and maximum
entanglement for cavities far from the initially excited cavity in a lossless
coupled resonator optical waveguide.Comment: 10 pages, 6 figure
Third Harmonic THz Generation from Graphene in a Parallel-Plate Waveguide
Graphene as a zero-bandgap two-dimensional semiconductor with a linear
electron band dispersion near the Dirac points has the potential to exhibit
very interesting nonlinear optical properties. In particular, third harmonic
generation of terahertz radiation should occur due to the nonlinear
relationship between the crystal momentum and the current density. In this
work, we investigate the terahertz nonlinear response of graphene inside a
parallel-plate waveguide. We optimize the plate separation and Fermi energy of
the graphene to maximize third harmonic generation, by maximizing the nonlinear
interaction while minimizing the loss and phase mismatch. The results obtained
show an increase by more than a factor of 100 in the power efficiency relative
to a normal-incidence configuration for a 2 terahertz incident field
High harmonic generation in undoped graphene: Interplay of inter- and intraband dynamics
We develop a density matrix formalism in the length gauge to calculate the
nonlinear response of intrinsic monolayer graphene at terahertz frequencies.
Employing a tight-binding model, we find that the interplay of the interband
and intraband dynamics leads to strong harmonic generation at moderate field
amplitudes. In particular, we find that at low temperature, the reflected field
of undoped suspended graphene exhibits a third harmonic amplitude that is 32%
of the fundamental for an incident field of 100 V/cm. Moreover, we find that up
to the seventh harmonic and beyond are generated
Valley-polarization in biased bilayer graphene using circularly polarized light
Achieving a population imbalance between the two inequivalent valleys is a
critical first step for any valleytronic device. A valley-polarization can be
induced in biased bilayer graphene using circularly polarized light. In this
paper, we present a detailed theoretical study of valley-polarization in biased
bilayer graphene. We show that a nearly perfect valley-polarization can be
achieved with the proper choices of external bias and pulse frequency. We find
that the optimal pulse frequency is given by where
is the potential energy difference between the graphene layers. We also
find that the valley-polarization originates not from the Dirac points
themselves, but rather from a ring of states surrounding each. Intervalley
scattering is found to greatly reduce the valley-polarization for high
frequency pulses. Thermal populations are found to significantly reduce the
valley-polarization for small biases. This work provides insight into the
origin of valley-polarization in bilayer graphene and will aid experimentalists
seeking to study valley-polarization in the lab.Comment: 18 pages, 9 figures, v2: elaboration and readability improvement
Optimized nonlinear terahertz response of graphene in a parallel-plate waveguide
Third harmonic generation of terahertz radiation is expected to occur in
monolayer graphene due to the nonlinear relationship between the crystal
momentum and the current density. In this work, we calculate the terahertz
nonlinear response of graphene inside a parallel-plate waveguide including pump
depletion, self-phase, and cross-phase modulation. To overcome the phase
mismatching between the pump field and third-harmonic field at high input
fields due to self-phase and cross-phase modulation, we design a waveguide with
two dielectric layers with different indices of refraction. We find that, by
tuning the relative thicknesses of the two layers, we are able to improve phase
matching, and thereby increase the power efficiency of the system by more than
a factor of two at high powers. With this approach, we find that dispite the
loss in this system, for an incident frequency of THz, we are able to
achieve power efficiencies of for graphene with low Fermi energies of
meV and up to when the Fermi energy is meV
The effects of microscopic scattering on terahertz third harmonic generation in monolayer graphene
Due to its linear dispersion, monolayer graphene is expected to generate a
third harmonic response at terahertz frequencies. There have been a variety of
different models of this effect and recently it has been experimentally
observed. However, there is still considerable uncertainty as to the role of
scattering on harmonic generation in graphene. In this work, we model
third-harmonic generation in doped monolayer graphene at THz frequencies by
employing a nearest-neighbour tight-binding model in the length gauge. We
include optical phonon and neutral impurity scattering at the microscopic
level, and examine the effects of scattering on the third harmonic response. We
also compare the results of a phenomenological semiclassical theory, using a
field-dependent scattering time extracted from the simulation, and find a
significantly lower third harmonic field than that found from the microscopic
model. This demonstrates that third-harmonic generation is much more sensitive
to the nature of the scattering than is the linear response. We also compare
the results of our full simulation to recent experimental results and find
qualitative agreement
Optimization of a Lossy Microring Resonator System for the Generation of Quadrature-Squeezed States
The intensity buildup of light inside a lossy microring resonator can be used
to enhance the generation of squeezed states via spontaneous parametric
downconversion (SPDC). In this work, we model the generation of squeezed light
in a microring resonator that is pumped with a Gaussian pulse via a
side-coupled channel waveguide. We theoretically determine the optimum pump
pulse duration and ring-to-channel coupling constant to minimize the quadrature
noise (maximize the squeezing) in the ring for a fixed input pump energy. We
derive approximate analytic expressions for the optimal coupling and pump pulse
duration as a function of scattering loss in the ring. These results will
enable researchers to easily determine the optimal design of microring
resonator systems for the generation of quadrature-squeezed states.Comment: 16 pages, 11 figure
Continuous-variable entanglement in a two-mode lossy cavity: an exact solution
Continuous-variable (CV) entanglement is a valuable resource in the field of
quantum information. One source of CV entanglement is the correlations between
the position and momentum of photons in a two-mode squeezed state of light. In
this paper, we theoretically study the generation of squeezed states, via
spontaneous parametric downconversion (SPDC), inside a two-mode lossy cavity
that is pumped with a classical optical pulse. The dynamics of the density
operator in the cavity is modelled using the Lindblad master equation, and we
show that the exact solution to this model is the density operator for a
two-mode squeezed thermal state, with a time-dependent squeezing amplitude and
average thermal photon number for each mode. We derive an expression for the
maximum entanglement inside the cavity that depends crucially on the difference
in the losses between the two modes. We apply our exact solution to the
important example of a microring resonator that is pumped with a Gaussian
pulse. The expressions that we derive will help researchers optimize CV
entanglement in lossy cavities.Comment: 12 pages, 6 figure
Counterpropagating continuous variable entangled states in lossy coupled-cavity optical waveguides
We present an integrated source of counterpropagating entangled states based
on a coupled resonator optical waveguide that is pumped by a classical pulsed
source incident from above the waveguide. We investigate theoretically the
generation and propagation of continuous variable entangled states in this
coupled-cavity system in the presence of intrinsic loss. Using a tight-binding
approximation, we derive analytic time-dependent expressions for the number of
photons in each cavity, as well as for the correlation variance between the
photons in different pairs of cavities, to evaluate the degree of quantum
entanglement. We also derive simple approximate expressions for these
quantities that can be used to guide the design of such systems, and discuss
how pumping configurations and physical properties of the system affect the
photon statistics and the degree of quantum correlation.Comment: 14 pages, 9 figure
The impact of nitrogen doping on the linear and nonlinear terahertz response of graphene
It is well known that impurities play a central role in the linear and
nonlinear response of graphene at optical and terahertz frequencies. In this
work, we calculate the bands and intraband dipole connection elements for
nitrogen-doped monolayer graphene using a density functional tight binding
approach. Employing these results, we calculate the linear and nonlinear
response of the doped graphene to terahertz pulses using a density-matrix
approach in the length gauge. We present the results for the linear and
nonlinear mobility as well as third harmonic generation in graphene for
adsorbed and substitutional nitrogen doping for a variety of doping densities.
We show that the conduction bands are more parabolic in graphene structures
with substitutional nitrogen doping than for those with adsorbed nitrogen. As a
result, substitutional doping has a greater impact on the terahertz mobility
and nonlinear response of graphene than adsorbed nitrogen does.Comment: 16 pages, 9 figure