170 research outputs found
Bound entanglement in the Jaynes-Cummings model
We study in detail entanglement properties of the Jaynes-Cummings model
assuming a two-level atom (qubit) interacting with the first levels of an
electromagnetic field mode (qudit) in a cavity. In the Jaynes-Cummings model,
the number operator is the conserved quantity that allows for the exact
diagonalization of the Hamiltonian and thus we study states that commute with
this conserved quantity and whose structure is preserved under the
Jaynes-Cummings dynamics. Contrary to the common belief, we show that there are
bound entangled states that satisfy the symmetries imposed by the conservation
of the number of excitations when . Furthermore we show that \emph{the
Jaynes-Cummings interaction can be used to generate bound-entanglement} between
the atom and the mode.Comment: Improved abstract, references and new section on the generation of
bound entanglement using the JC interactio
Why you should not use the electric field to quantize in nonlinear optics
We show that using the electric field as a quantization variable in nonlinear
optics leads to incorrect expressions for the squeezing parameters in
spontaneous parametric down-conversion and conversion rates in frequency
conversion. This observation is related to the fact that if the electric field
is written as a linear combination of bosonic creation and annihilation
operators one cannot satisfy Maxwell's equations in a nonlinear dielectric.Comment: This version corrects a minor typo from the published version in
Optics Letters. Eq. 22 should have an \epsilon_0 that is lacking in the OL
versio
Fast optimization of parametrized quantum optical circuits
Parametrized quantum optical circuits are a class of quantum circuits in
which the carriers of quantum information are photons and the gates are optical
transformations. Classically optimizing these circuits is challenging due to
the infinite dimensionality of the photon number vector space that is
associated to each optical mode. Truncating the space dimension is unavoidable,
and it can lead to incorrect results if the gates populate photon number states
beyond the cutoff. To tackle this issue, we present an algorithm that is orders
of magnitude faster than the current state of the art, to recursively compute
the exact matrix elements of Gaussian operators and their gradient with respect
to a parametrization. These operators, when augmented with a non-Gaussian
transformation such as the Kerr gate, achieve universal quantum computation.
Our approach brings two advantages: first, by computing the matrix elements of
Gaussian operators directly, we don't need to construct them by combining
several other operators; second, we can use any variant of the gradient descent
algorithm by plugging our gradients into an automatic differentiation framework
such as TensorFlow or PyTorch. Our results will find applications in quantum
optical hardware research, quantum machine learning, optical data processing,
device discovery and device design.Comment: 21 pages, 10 figure
Melting of Lennard-Jones rare gas clusters doped with a single impurity atom
Single impurity effect on the melting process of magic number Lennard-Jones,
rare gas, clusters of up to 309 atoms is studied on the basis of Parallel
Tempering Monte Carlo simulations in the canonical ensemble. A decrease on the
melting temperature range is prevalent, although such effect is dependent on
the size of the impurity atom relative to the cluster size. Additionally, the
difference between the atomic sizes of the impurity and the main component of
the cluster should be considered. We demonstrate that solid-solid transitions
due to migrations of the impurity become apparent and are clearly
differentiated from the melting up to cluster sizes of 147 atoms
High efficiency in mode selective frequency conversion
Frequency conversion (FC) is an enabling process in many quantum information
protocols. Recently, it has been observed that upconversion efficiencies in
single-photon, mode-selective FC are limited to around 80%.In this letter we
argue that these limits can be understood as time-ordering corrections (TOCs)
that modify the joint conversion amplitude of the process. Furthermore we show,
using a simple scaling argument, that recently proposed cascaded FC protocols
that overcome the aforementioned limitations act as "attenuators" of the TOCs.
This observation allows us to argue that very similar cascaded architectures
can be used to attenuate TOCs in photon generation via spontaneous parametric
down-conversion. Finally, by using the Magnus expansion, we argue that the
TOCs, which are usually considered detrimental for FC efficiency, can also be
used to increase the efficiency of conversion in partially mode selective FC
Broadband pseudothermal states with tunable spectral coherence generated via nonlinear optics
It is well known that the reduced state of a two-mode squeezed vacuum state
is a thermal state---i.e. a state whose photon-number statistics obey a
geometric distribution. More exotic \emph{broadband} states can be realized as
the reduced state of two spectrally-entangled beams generated using nonlinear
optics. We show that these broadband "pseudothermal" states are tensor products
of states in spectral Schmidt modes, whose photon-number statistics obey a
geometric distribution. We study the spectral and temporal coherence properties
of these states and show that their spectral coherence can be tuned---from
perfect coherence to complete incoherence---by adjusting the pump spectral
width. In the limit of a cw pump, these states are tensor products of true
thermal states, but with different temperatures at each frequency. This could
be an interesting state of light for investigating the interplay between
spectral, temporal, and photon-number coherences.Comment: 6 pages main text, 1 full-page figure (12 pages total including
reference and appendices
Strong coupling of two quantum emitters to a single light mode: the dissipative Tavis-Cummings ladder
A criterion for strong coupling between two quantum emitters and a single
resonant light mode in a cavity is presented. The criterion takes into account
the escape of cavity photons and the spontaneous emission of the emitters,
which are modeled as two level systems. By using such criterion, the
dissipative Tavis-Cummings ladder of states is constructed, and it is shown
that the inclusion of one more emitter with respect to the Jaynes-Cummings
(single emitter) case increases the effective parameter region in which
order Rabi splitting is observed.Comment: 3 figure
Franck-Condon factors by counting perfect matchings of graphs with loops
We show that the Franck-Condon Factor (FCF) associated to a transition
between initial and final vibrational states in two different potential energy
surfaces, having and vibrational quanta, respectively, is equivalent to
calculating the number of perfect matchings of a weighted graph with loops that
has vertices. This last quantity is the loop hafnian of the
(symmetric) adjacency matrix of the graph which can be calculated in steps. In the limit of small numbers of vibrational quanta per normal
mode our loop hafnian formula significantly improves the speed at which FCFs
can be calculated. Our results more generally apply to the calculation of the
matrix elements of a bosonic Gaussian unitary between two multimode Fock states
having and photons in total and provide a useful link between certain
calculations of quantum chemistry, quantum optics and graph theory.Comment: 13+3 pages, 4 figures. Source code available at
https://github.com/XanaduAI/fockgaussia
Gaussian Boson Sampling using threshold detectors
We study what is arguably the most experimentally appealing Boson Sampling
architecture: Gaussian states sampled with threshold detectors. We show that in
this setting, the probability of observing a given outcome is related to a
matrix function that we name the Torontonian, which plays an analogous role to
the permanent or the Hafnian in other models. We also prove that, provided that
the probability of observing two or more photons in a single output mode is
sufficiently small, our model remains intractable to simulate classically under
standard complexity-theoretic conjectures. Finally, we leverage the
mathematical simplicity of the model to introduce a physically motivated, exact
sampling algorithm for all Boson Sampling models that employ Gaussian states
and threshold detectors.Comment: 5+5 pages, 2 figures. Closer to published versio
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