38 research outputs found
Quantum State Tomography of Complex Multimode Fields using Array Detectors
We demonstrate that it is possible to use the balanced homodyning with array
detectors to measure the quantum state of correlated two-mode signal field. We
show the applicability of the method to fields with complex mode functions,
thus generalizing the work of Beck (Phys. Rev. Letts. 84, 5748 (2000)) in
several important ways. We further establish that, under suitable conditions,
array detector measurements from one of the two outputs is sufficient to
determine the quantum state of signals. We show the power of the method by
reconstructing a truncated Perelomov state which exhibits complicated structure
in the joint probability density for the quadratures.Comment: 14 pages text and 3 figures. To be submitted to PR
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.
Three-dimensional theory for interaction between atomic ensembles and free-space light
Atomic ensembles have shown to be a promising candidate for implementations
of quantum information processing by many recently-discovered schemes. All
these schemes are based on the interaction between optical beams and atomic
ensembles. For description of these interactions, one assumed either a
cavity-QED model or a one-dimensional light propagation model, which is still
inadequate for a full prediction and understanding of most of the current
experimental efforts which are actually taken in the three-dimensional free
space. Here, we propose a perturbative theory to describe the three-dimensional
effects in interaction between atomic ensembles and free-space light with a
level configuration important for several applications. The calculations reveal
some significant effects which are not known before from the other approaches,
such as the inherent mode-mismatching noise and the optimal mode-matching
conditions. The three-dimensional theory confirms the collective enhancement of
the signal-to-noise ratio which is believed to be one of the main advantage of
the ensemble-based quantum information processing schemes, however, it also
shows that this enhancement need to be understood in a more subtle way with an
appropriate mode matching method.Comment: 16 pages, 9 figure
Direct measurement of optical quasidistribution functions: multimode theory and homodyne tests of Bell's inequalities
We develop a multimode theory of direct homodyne measurements of quantum
optical quasidistribution functions. We demonstrate that unbalanced homodyning
with appropriately shaped auxiliary coherent fields allows one to sample
point-by-point different phase space representations of the electromagnetic
field. Our analysis includes practical factors that are likely to affect the
outcome of a realistic experiment, such as non-unit detection efficiency,
imperfect mode matching, and dark counts. We apply the developed theory to
discuss feasibility of observing a loophole-free violation of Bell's
inequalities by measuring joint two-mode quasidistribution functions under
locality conditions by photon counting. We determine the range of parameters of
the experimental setup that enable violation of Bell's inequalities for two
states exhibiting entanglement in the Fock basis: a one-photon Fock state
divided by a 50:50 beam splitter, and a two-mode squeezed vacuum state produced
in the process of non-degenerate parametric down-conversion.Comment: 18 pages, 7 figure
Direct sampling of the Susskind-Glogower phase distributions
Coarse-grained phase distributions are introduced that approximate to the
Susskind--Glogower cosine and sine phase distributions. The integral relations
between the phase distributions and the phase-parametrized field-strength
distributions observable in balanced homodyning are derived and the integral
kernels are analyzed. It is shown that the phase distributions can be directly
sampled from the field-strength distributions which offers the possibility of
measuring the Susskind--Glogower cosine and sine phase distributions with
sufficiently well accuracy. Numerical simulations are performed to demonstrate
the applicability of the method.Comment: 10 figures using a4.st
Complementarity and the uncertainty relations
We formulate a general complementarity relation starting from any Hermitian
operator with discrete non-degenerate eigenvalues. We then elucidate the
relationship between quantum complementarity and the Heisenberg-Robertson's
uncertainty relation. We show that they are intimately connected. Finally we
exemplify the general theory with some specific suggested experiments.Comment: 9 pages, 4 figures, REVTeX, uses epsf.sty and multicol.st
Homodyne detection for measuring internal quantum correlations of optical pulses
A new method is described for determining the quantum correlations at
different times in optical pulses by using balanced homodyne detection. The
signal pulse and sequences of ultrashort test pulses are superimposed, where
for chosen distances between the test pulses their relative phases and
intensities are varied from measurement to measurement. The correlation
statistics of the signal pulse is obtained from the time-integrated difference
photocurrents measured.Comment: 7 pages, A4.sty include
Quantum inference of states and processes
The maximum-likelihood principle unifies inference of quantum states and
processes from experimental noisy data. Particularly, a generic quantum process
may be estimated simultaneously with unknown quantum probe states provided that
measurements on probe and transformed probe states are available. Drawbacks of
various approximate treatments are considered.Comment: 7 pages, 4 figure
Time-of-arrival distributions from position-momentum and energy-time joint measurements
The position-momentum quasi-distribution obtained from an Arthurs and Kelly
joint measurement model is used to obtain indirectly an ``operational''
time-of-arrival (TOA) distribution following a quantization procedure proposed
by Kocha\'nski and W\'odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA
distribution is not time covariant. The procedure is generalized by using other
phase-space quasi-distributions, and sufficient conditions are provided for
time covariance that limit the possible phase-space quasi-distributions
essentially to the Wigner function, which, however, provides a non-positive TOA
quasi-distribution. These problems are remedied with a different quantization
procedure which, on the other hand, does not guarantee normalization. Finally
an Arthurs and Kelly measurement model for TOA and energy (valid also for
arbitrary conjugate variables when one of the variables is bounded from below)
is worked out. The marginal TOA distribution so obtained, a distorted version
of Kijowski's distribution, is time covariant, positive, and normalized
Spin squeezing and pairwise entanglement for symmetric multiqubit states
We show that spin squeezing implies pairwise entanglement for arbitrary
symmetric multiqubit states. If the squeezing parameter is less than or equal
to 1, we demonstrate a quantitative relation between the squeezing parameter
and the concurrence for the even and odd states. We prove that the even states
generated from the initial state with all qubits being spin down, via the
one-axis twisting Hamiltonian, are spin squeezed if and only if they are
pairwise entangled. For the states generated via the one-axis twisting
Hamiltonian with an external transverse field for any number of qubits greater
than 1 or via the two-axis counter-twisting Hamiltonian for any even number of
qubits, the numerical results suggest that such states are spin squeezed if and
only if they are pairwise entangled.Comment: 6 pages. Version 3: Small corrections were mad