2,452 research outputs found
Verifying continuous variable entanglement of intense light pulses
Three different methods have been discussed to verify continuous variable
entanglement of intense light beams. We demonstrate all three methods using the
same set--up to facilitate the comparison. The non--linearity used to generate
entanglement is the Kerr--effect in optical fibres. Due to the brightness of
the entangled pulses, standard homodyne detection is not an appropriate tool
for the verification. However, we show that by using large asymmetric
interferometers on each beam individually, two non-commuting variables can be
accessed and the presence of entanglement verified via joint measurements on
the two beams. Alternatively, we witness entanglement by combining the two
beams on a beam splitter that yields certain linear combinations of quadrature
amplitudes which suffice to prove the presence of entanglement.Comment: 11 pages, 7 figures, to appear in Phys. Rev.
Operator Approach to the Master Equation for the One-Step Process
Presentation of the probability as an intrinsic property of the nature leads
researchers to switch from deterministic to stochastic description of the
phenomena. The procedure of stochastization of one-step process was formulated.
It allows to write down the master equation based on the type of of the kinetic
equations and assumptions about the nature of the process. The kinetics of the
interaction has recently attracted attention because it often occurs in the
physical, chemical, technical, biological, environmental, economic, and
sociological systems. However, there are no general methods for the direct
study of this equation. Leaving in the expansion terms up to the second order
we can get the Fokker-Planck equation, and thus the Langevin equation. It
should be clearly understood that these equations are approximate recording of
the master equation. However, this does not eliminate the need for the study of
the master equation. Moreover, the power series produced during the master
equation decomposition may be divergent (for example, in spatial models). This
makes it impossible to apply the classical perturbation theory. It is proposed
to use quantum field perturbation theory for the statistical systems (the
so-called Doi method). This work is a methodological material that describes
the principles of master equation solution based on quantum field perturbation
theory methods. The characteristic property of the work is that it is
intelligible for non-specialists in quantum field theory. As an example the
Verhulst model is used because of its simplicity and clarity (the first order
equation is independent of the spatial variables, however, contains
non-linearity). We show the full equivalence of the operator and combinatorial
methods of obtaining and study of the one-step process master equation.Comment: in Russian; in Englis
Measurement-induced disturbances and nonclassical correlations of Gaussian states
We study quantum correlations beyond entanglement in two-mode Gaussian states
of continuous variable systems, by means of the measurement-induced disturbance
(MID) and its ameliorated version (AMID). In analogy with the recent studies of
the Gaussian quantum discord, we define a Gaussian AMID by constraining the
optimization to all bi-local Gaussian positive operator valued measurements. We
solve the optimization explicitly for relevant families of states, including
squeezed thermal states. Remarkably, we find that there is a finite subset of
two-mode Gaussian states, comprising pure states, where non-Gaussian
measurements such as photon counting are globally optimal for the AMID and
realize a strictly smaller state disturbance compared to the best Gaussian
measurements. However, for the majority of two--mode Gaussian states the
unoptimized MID provides a loose overestimation of the actual content of
quantum correlations, as evidenced by its comparison with Gaussian discord.
This feature displays strong similarity with the case of two qubits. Upper and
lower bounds for the Gaussian AMID at fixed Gaussian discord are identified. We
further present a comparison between Gaussian AMID and Gaussian entanglement of
formation, and classify families of two-mode states in terms of their Gaussian
AMID, Gaussian discord, and Gaussian entanglement of formation. Our findings
provide a further confirmation of the genuinely quantum nature of general
Gaussian states, yet they reveal that non-Gaussian measurements can play a
crucial role for the optimized extraction and potential exploitation of
classical and nonclassical correlations in Gaussian states.Comment: 16 pages, 5 figures; new results added; to appear in Phys. Rev.
Polarization squeezing with cold atoms
We study the interaction of a nearly resonant linearly polarized laser beam
with a cloud of cold cesium atoms in a high finesse optical cavity. We show
theoretically and experimentally that the cross-Kerr effect due to the
saturation of the optical transition produces quadrature squeezing on both the
mean field and the orthogonally polarized vacuum mode. An interpretation of
this vacuum squeezing as polarization squeezing is given and a method for
measuring quantum Stokes parameters for weak beams via a local oscillator is
developed
Quantum state of two trapped Bose-Einstein condensates with a Josephson coupling
We consider the precise quantum state of two trapped, coupled Bose Einstein
condensates in the two-mode approximation. We seek a representation of the
state in terms of a Wigner-like distribution on the two-mode Bloch sphere. The
problem is solved using a self-consistent rotation of the unknown state to the
south pole of the sphere. The two-mode Hamiltonian is projected onto the
harmonic oscillator phase plane, where it can be solved by standard techniques.
Our results show how the number of atoms in each trap and the squeezing in the
number difference depend on the physical parameters. Considering negative
scattering lengths, we show that there is a regime of squeezing in the relative
phase of the condensates which occurs for weaker interactions than the
superposition states found by Cirac et al% (quant-ph/9706034, 13 June 1997).
The phase squeezing is also apparent in mildly asymmetric trap configurations.Comment: 26 pages, 11 figure
Mode structure and photon number correlations in squeezed quantum pulses
The question of efficient multimode description of optical pulses is studied.
We show that a relatively very small number of nonmonochromatic modes can be
sufficient for a complete quantum description of pulses with Gaussian
quadrature statistics. For example, a three-mode description was enough to
reproduce the experimental data of photon number correlations in optical
solitons [S. Spalter et al., Phys. Rev. Lett. 81, 786 (1998)]. This approach is
very useful for a detailed understanding of squeezing properties of soliton
pulses with the main potential for quantum communication with continuous
variables. We show how homodyne detection and/or measurements of photon number
correlations can be used to determine the quantum state of the multi-mode
field. We also discuss a possible way of physical separation of the
nonmonochromatic modes.Comment: 14 pages, 4 figures; minor revisions of the text, new references; to
appear in the Phys. Rev.
Entanglement and squeezing in a two-mode system: theory and experiment
We report on the generation of non separable beams produced via the
interaction of a linearly polarized beam with a cloud of cold cesium atoms
placed in an optical cavity. We convert the squeezing of the two linear
polarization modes into quadrature entanglement and show how to find out the
best entanglement generated in a two-mode system using the inseparability
criterion for continuous variable [Duan et al., Phys. Rev. Lett. 84, 2722
(2000)]. We verify this method experimentally with a direct measurement of the
inseparability using two homodyne detections. We then map this entanglement
into a polarization basis and achieve polarization entanglement.Comment: submitted to J. Opt. B for a Special Issue on Foundations of Quantum
Optic
Highly non-Gaussian states created via cross-Kerr nonlinearity
We propose a feasible scheme for generation of strongly non-Gaussian states
using the cross-Kerr nonlinearity. The resultant states are highly
non-classical states of electromagnetic field and exhibit negativity of their
Wigner function, sub-Poissonian photon statistics, and amplitude squeezing.
Furthermore, the Wigner function has a distinctly pronounced ``banana'' or
``crescent'' shape specific for the Kerr-type interactions, which so far was
not demonstrated experimentally. We show that creating and detecting such
states should be possible with the present technology using electromagnetically
induced transparency in a four-level atomic system in N-configuration.Comment: 12 pages, 7 figure
Multi-photon, multi-mode polarization entanglement in parametric down-conversion
We study the quantum properties of the polarization of the light produced in
type II spontaneous parametric down-conversion in the framework of a multi-mode
model valid in any gain regime. We show that the the microscopic polarization
entanglement of photon pairs survives in the high gain regime (multi-photon
regime), in the form of nonclassical correlation of all the Stokes operators
describing polarization degrees of freedom
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