7 research outputs found
Direct probing of the Wigner function by time-multiplexed detection of photon statistics
We investigate the capabilities of loss-tolerant quantum state
characterization using a photon-number resolving, time-multiplexed detector
(TMD). We employ the idea of probing the Wigner function point-by-point in
phase space via photon parity measurements and displacement operations,
replacing the conventional homodyne tomography. Our emphasis lies on
reconstructing the Wigner function of non-Gaussian Fock states with highly
negative values in a scheme that is based on a realistic experimental setup. In
order to establish the concept of loss-tolerance for state characterization we
show how losses can be decoupled from the impact of other experimental
imperfections, i.e. the non-unity transmittance of the displacement
beamsplitter and non-ideal mode overlap. We relate the experimentally
accessible parameters to effective ones that are needed for an optimised state
reconstruction. The feasibility of our approach is tested by Monte Carlo
simulations, which provide bounds resulting from statistical errors that are
due to limited data sets. Our results clearly show that high losses can be
accepted for a defined parameter range, and moreover, that (in contrast to
homodyne detection) mode mismatch results in a distinct signature, which can be
evaluated by analysing the photon number oscillations of the displaced Fock
states.Comment: 22 pages, 13 figures, published versio
Continuous-variable optical quantum state tomography
This review covers latest developments in continuous-variable quantum-state
tomography of optical fields and photons, placing a special accent on its
practical aspects and applications in quantum information technology. Optical
homodyne tomography is reviewed as a method of reconstructing the state of
light in a given optical mode. A range of relevant practical topics are
discussed, such as state-reconstruction algorithms (with emphasis on the
maximum-likelihood technique), the technology of time-domain homodyne
detection, mode matching issues, and engineering of complex quantum states of
light. The paper also surveys quantum-state tomography for the transverse
spatial state (spatial mode) of the field in the special case of fields
containing precisely one photon.Comment: Finally, a revision! Comments to lvov(at)ucalgary.ca and
raymer(at)uoregon.edu are welcom
Measuring Measurement: Theory and Practice
Recent efforts have applied quantum tomography techniques to the calibration
and characterization of complex quantum detectors using minimal assumptions. In
this work we provide detail and insight concerning the formalism, the
experimental and theoretical challenges and the scope of these tomographical
tools. Our focus is on the detection of photons with avalanche photodiodes and
photon number resolving detectors and our approach is to fully characterize the
quantum operators describing these detectors with a minimal set of well
specified assumptions. The formalism is completely general and can be applied
to a wide range of detectorsComment: 22 pages, 27 figure
Photon wave functions, wave-packet quantization of light, and coherence theory
The monochromatic Dirac and polychromatic Titulaer-Glauber quantized field
theories (QFTs) of electromagnetism are derived from a photon-energy wave
function in much the same way that one derives QFT for electrons, that is, by
quantization of a single-particle wave function. The photon wave function and
its equation of motion are established from the Einstein energy-momentum-mass
relation, assuming a local energy density. This yields a theory of photon wave
mechanics (PWM). The proper Lorentz-invariant single-photon scalar product is
found to be non-local in coordinate space, and is shown to correspond to
orthogonalization of the Titulaer-Glauber wave-packet modes. The wave functions
of PWM and mode functions of QFT are shown to be equivalent, evolving via
identical equations of motion, and completely describe photonic states. We
generalize PWM to two or more photons, and show how to switch between the PWM
and QFT viewpoints. The second-order coherence tensors of classical coherence
theory and the two-photon wave functions are shown to propagate equivalently.
We give examples of beam-like states, which can be used as photon wave
functions in PWM, or modes in QFT. We propose a practical mode converter based
on spectral filtering to convert between wave packets and their corresponding
biorthogonal dual wave packets.Comment: 34 pages, 3 figures, minor correction