28 research outputs found
Quantum Control of a Single Qubit
Measurements in quantum mechanics cannot perfectly distinguish all states and
necessarily disturb the measured system. We present and analyse a proposal to
demonstrate fundamental limits on quantum control of a single qubit arising
from these properties of quantum measurements. We consider a qubit prepared in
one of two non-orthogonal states and subsequently subjected to dephasing noise.
The task is to use measurement and feedback control to attempt to correct the
state of the qubit. We demonstrate that projective measurements are not optimal
for this task, and that there exists a non-projective measurement with an
optimum measurement strength which achieves the best trade-off between gaining
information about the system and disturbing it through measurement back-action.
We study the performance of a quantum control scheme that makes use of this
weak measurement followed by feedback control, and demonstrate that it realises
the optimal recovery from noise for this system. We contrast this approach with
various classically inspired control schemes.Comment: 12 pages, 7 figures, v2 includes new references and minor change
N-Photon wave packets interacting with an arbitrary quantum system
We present a theoretical framework that describes a wave packet of light
prepared in a state of definite photon number interacting with an arbitrary
quantum system (e.g. a quantum harmonic oscillator or a multi-level atom).
Within this framework we derive master equations for the system as well as for
output field quantities such as quadratures and photon flux. These results are
then generalized to wave packets with arbitrary spectral distribution
functions. Finally, we obtain master equations and output field quantities for
systems interacting with wave packets in multiple spatial and/or polarization
modes.Comment: 20 pages, 8 figures. Published versio
Self-calibrating Quantum State Tomography
We introduce and experimentally demonstrate a technique for performing
quantum state tomography on multiple-qubit states despite incomplete knowledge
about the unitary operations used to change the measurement basis. Given
unitary operations with unknown rotation angles, our method can be used to
reconstruct the density matrix of the state up to local sigma-z rotations as
well as recover the magnitude of the unknown rotation angle. We demonstrate
high-fidelity self-calibrating tomography on polarization-encoded one- and
two-photon states. The unknown unitary operations are realized in two ways:
using a birefringent polymer sheet---an inexpensive smartphone screen
protector---or alternatively a liquid crystal wave plate with a tuneable
retardance. We explore how our technique may be adapted for quantum state
tomography of systems such as biological molecules where the magnitude and
orientation of the transition dipole moment is not known with high accuracy.Comment: 13 pages, 4 figure
Optimised generation of heralded Fock states using parametric down conversion
The generation of heralded pure Fock states via spontaneous parametric down
conversion (PDC) relies on perfect photon-number correlations in the output
modes. Correlations in any other degree of freedom, however, degrade the purity
of the heralded state. In this paper, we investigate spectral entanglement
between the two output modes of a periodically poled waveguide. With the intent
of generating heralded 1- and 2-photon Fock states, we expand the output state
of the PDC to second order in photon number. We explore the effects of spectral
filtering and inefficient detection, of the heralding mode, on the count rate,
g(2) and purity of the heralded state, as well as the fidelity between the
resulting state and an ideal Fock state. We find that filtering can decrease
spectral correlations, however, at the expense of the count rate and increased
photon-number mixedness in the heralded output state. As a physical example, we
model a type II PP-KTP waveguide pumped by lasers at wavelengths of 400 nm, 788
nm and 1930 nm. The latter two allow the fulfillment of extended phase matching
conditions in an attempt to eliminate spectral correlations in the PDC output
state without the use of filtering, however, we find that even in these cases,
some filtering is needed to achieve states of very high purity.Comment: 28 pages, 25 figures, revised expressions for two-photon fidelit