141 research outputs found
Multi-mode density matrices of light via amplitude and phase control
A new method is described for determining the quantum state of correlated
multimode radiation by interfering the modes and measuring the statistics of
the superimposed fields in four-port balanced homodyne detection. The full
information on the -mode quantum state is obtained by controlling both the
relative amplitudes and the phases of the modes, which simplifies the
reconstruction of density matrices to only Fourier transforms. In
particular, this method yields time-correlated multimode density matrices of
optical pulses by superimposing the signal by a sequence of short
local-oscillator pulses.Comment: 6 pages, late
Diluted maximum-likelihood algorithm for quantum tomography
We propose a refined iterative likelihood-maximization algorithm for
reconstructing a quantum state from a set of tomographic measurements. The
algorithm is characterized by a very high convergence rate and features a
simple adaptive procedure that ensures likelihood increase in every iteration
and convergence to the maximum-likelihood state.
We apply the algorithm to homodyne tomography of optical states and quantum
tomography of entangled spin states of trapped ions and investigate its
convergence properties.Comment: v2: Convergence proof adde
Number phase uncertainty relations: verification by homodyning
It is shown that fundamental uncertainty relations between photon number and
canonical phase of a single-mode optical field can be verified by means of
balanced homodyne measurement. All the relevant quantities can be sampled
directly from the measured phase-dependent quadrature distribution.Comment: 1 Ps figure (divided in 3 subfigures) using REVTE
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
Broadband detection of squeezed vacuum: A spectrum of quantum states
We demonstrate the simultaneous quantum state reconstruction of the spectral
modes of the light field emitted by a continuous wave degenerate optical
parametric amplifier. The scheme is based on broadband measurement of the
quantum fluctuations of the electric field quadratures and subsequent Fourier
decomposition into spectral intervals. Applying the standard reconstruction
algorithms to each bandwidth-limited quantum trajectory, a "spectrum" of
density matrices and Wigner functions is obtained. The recorded states show a
smooth transition from the squeezed vacuum to a vacuum state. In the time
domain we evaluated the first order correlation function of the squeezed output
field, showing good agreement with the theory.Comment: 11 pages, 5 figure
Bounds on Integrals of the Wigner Function
The integral of the Wigner function over a subregion of the phase-space of a
quantum system may be less than zero or greater than one. It is shown that for
systems with one degree of freedom, the problem of determining the best
possible upper and lower bounds on such an integral, over all possible states,
reduces to the problem of finding the greatest and least eigenvalues of an
hermitian operator corresponding to the subregion. The problem is solved
exactly in the case of an arbitrary elliptical region. These bounds provide
checks on experimentally measured quasiprobability distributions.Comment: 10 pages, 1 PostScript figure, Latex file; revised following
referees' comments; to appear in Physical Review Letter
Operational Theory of Homodyne Detection
We discuss a balanced homodyne detection scheme with imperfect detectors in
the framework of the operational approach to quantum measurement. We show that
a realistic homodyne measurement is described by a family of operational
observables that depends on the experimental setup, rather than a single field
quadrature operator. We find an explicit form of this family, which fully
characterizes the experimental device and is independent of a specific state of
the measured system. We also derive operational homodyne observables for the
setup with a random phase, which has been recently applied in an ultrafast
measurement of the photon statistics of a pulsed diode laser. The operational
formulation directly gives the relation between the detected noise and the
intrinsic quantum fluctuations of the measured field. We demonstrate this on
two examples: the operational uncertainty relation for the field quadratures,
and the homodyne detection of suppressed fluctuations in photon statistics.Comment: 7 pages, REVTe
Measuring quantum optical Hamiltonians
We show how recent state-reconstruction techniques can be used to determine
the Hamiltonian of an optical device that evolves the quantum state of
radiation. A simple experimental setup is proposed for measuring the
Liouvillian of phase-insensitive devices. The feasibility of the method with
current technology is demonstrated on the basis of Monte Carlo simulated
experiments.Comment: Accepted for publication on Phys. Rev. Lett. 8 eps figures, 4
two-column pages in REVTE
Reply on the ``Comment on `Loss-error compensation in quantum- state measurements' ''
The authors of the Comment [G. M. D'Ariano and C. Macchiavello to be
published in Phys. Rev. A, quant-ph/9701009] tried to reestablish a 0.5
efficiency bound for loss compensation in optical homodyne tomography. In our
reply we demonstrate that neither does such a rigorous bound exist nor is the
bound required for ruling out the state reconstruction of an individual system
[G. M. D'Ariano and H. P. Yuen, Phys. Rev. Lett. 76, 2832 (1996)].Comment: LaTex, 2 pages, 1 Figure; to be published in Physical Review
How to determine a quantum state by measurements: The Pauli problem for a particle with arbitrary potential
The problem of reconstructing a pure quantum state ¿¿> from measurable quantities is considered for a particle moving in a one-dimensional potential V(x). Suppose that the position probability distribution ¿¿(x,t)¿2 has been measured at time t, and let it have M nodes. It is shown that after measuring the time evolved distribution at a short-time interval ¿t later, ¿¿(x,t+¿t)¿2, the set of wave functions compatible with these distributions is given by a smooth manifold M in Hilbert space. The manifold M is isomorphic to an M-dimensional torus, TM. Finally, M additional expectation values of appropriately chosen nonlocal operators fix the quantum state uniquely. The method used here is the analog of an approach that has been applied successfully to the corresponding problem for a spin system
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