71 research outputs found
Filtering of the absolute value of photon-number difference for two-mode macroscopic quantum superpositions
We discuss a device capable of filtering out two-mode states of light with
mode populations differing by more than a certain threshold, while not
revealing which mode is more populated. It would allow engineering of
macroscopic quantum states of light in a way which is preserving specific
superpositions. As a result, it would enhance optical phase estimation with
these states as well as distinguishability of "macroscopic" qubits. We propose
an optical scheme, which is a relatively simple, albeit non-ideal, operational
implementation of such a filter. It uses tapping of the original polarization
two-mode field, with a polarization neutral beam splitter of low reflectivity.
Next, the reflected beams are suitably interfered on a polarizing beam
splitter. It is oriented such that it selects unbiased polarization modes with
respect to the original ones. The more an incoming two-mode Fock state is
unequally populated, the more the polarizing beam splitter output modes are
equally populated. This effect is especially pronounced for highly populated
states. Additionally, for such states we expect strong population correlations
between the original fields and the tapped one. Thus, after a photon-number
measurement of the polarizing beam splitter outputs, a feed-forward loop can be
used to let through a shutter the field, which was transmitted by the tapping
beam splitter. This happens only if the counts at the outputs are roughly
equal. In such a case, the transmitted field differs strongly in occupation
number of the two modes, while information on which mode is more populated is
non-existent (a necessary condition for preserving superpositions).Comment: 11 pages, 12 figure
Orthogonality of Biphoton Polarization States
Orthogonality of two-photon polarization states belonging to a single
frequency and spatial mode is demonstrated experimentally, in a generalization
of the well-known anti-correlation 'dip' experiment.Comment: Submitted to Phys.Rev.Let
Conditioned Unitary Transformation on biphotons
A conditioned unitary transformation ( polarization rotation) is
performed at single-photon level. The transformation is realized by rotating
polarization for one of the photons of a polarization-entangled biphoton state
(signal photon) by means of a Pockel's cell triggered by the detection of the
other (idler) photon after polarization selection. As a result, polarization
degree for the signal beam changes from zero to the value given by the idler
detector quantum efficiency. This result is relevant to practical realization
of various quantum information schemes and can be used for developing a new
method of absolute quantum efficiency calibration
Biphoton compression in standard optical fiber: exact numerical calculation
Generation of two-photon wavepackets, produced by spontaneous parametric down
conversion in crystals with linearly chirped quasi-phase matching grating, is
analyzed. Although being spectrally broad, two-photon wavepackets produced this
way are not Fourier transform limited. In the paper we discuss the temporal
compression of the wavepackets, exploiting the insertion of a standard optical
fiber in the path of one of the two photons. The effect is analyzed by means of
full numerical calculation and the exact dispersion dependencies in both the
crystal and the fiber are considered. The study opens the way to the practical
realization of this idea.Comment: 10 pages, 16 figure
Generation of different Bell states within the SPDC phase-matching bandwidth
We study the frequency-angular lineshape for a phase-matched nonlinear
process producing entangled states and show that there is a continuous variety
of maximally-entangled states generated for different mismatch values within
the natural bandwidth. Detailed considerations are made for two specific
methods of polarization entanglement preparation, based on type-II spontaneous
parametric down-conversion (SPDC) and on SPDC in two subsequent type-I crystals
producing orthogonally polarized photon pairs. It turns out that different Bell
states are produced at the center of the SPDC line and on its slopes,
corresponding to about half-maximum intensity level. These Bell states can be
filtered out by either frequency selection or angular selection, or both. Our
theoretical calculations are confirmed by a series of experiments, performed
for the two above-mentioned schemes of producing polarization-entangled photon
pairs and with two kinds of measurements: frequency-selective and
angular-selective.Comment: submitted for publicatio
Statistical Reconstruction of Qutrits
We discuss a procedure of measurement followed by the reproduction of the
quantum state of a three-level optical system - a frequency- and spatially
degenerate two-photon field. The method of statistical estimation of the
quantum state based on solving the likelihood equation and analyzing the
statistical properties of the obtained estimates is developed. Using the root
approach of estimating quantum states, the initial two-photon state vector is
reproduced from the measured fourth moments in the field . The developed
approach applied to quantum states reconstruction is based on the amplitudes of
mutually complementary processes. Classical algorithm of statistical estimation
based on the Fisher information matrix is generalized to the case of quantum
systems obeying Bohr's complementarity principle. It has been experimentally
proved that biphoton-qutrit states can be reconstructed with the fidelity of
0.995-0.999 and higher.Comment: Submitted to Physical Review
Symbolic approach and induction in the Heisenberg group
We associate a homomorphism in the Heisenberg group to each hyperbolic
unimodular automorphism of the free group on two generators. We show that the
first return-time of some flows in "good" sections, are conjugate to
niltranslations, which have the property of being self-induced.Comment: 18 page
Polarization state of a biphoton: quantum ternary logic
Polarization state of biphoton light generated via collinear
frequency-degenerate spontaneous parametric down-conversion is considered. A
biphoton is described by a three-component polarization vector, its arbitrary
transformations relating to the SU(3) group. A subset of such transformations,
available with retardation plates, is realized experimentally. In particular,
two independent orthogonally polarized beams of type-I biphotons are
transformed into a beam of type-II biphotons. Polarized biphotons are suggested
as ternary analogs of two-state quantum systems (qubits)
Measurement of qutrits
We proposed the procedure of measuring the unknown state of the three-level
system - the qutrit, which was realized as the arbitrary polarization state of
the single-mode biphoton field. This procedure is accomplished for the set of
the pure states of qutrits; this set is defined by the properties of SU(2)
transformations, that are done by the polarization transformers.Comment: 9 pages, 9 figure
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