[en] Using the archival data from the Rossi X-ray Timing Explorer, we study the evolution of the Crab pulsar's X-ray profile in a time span of 11 years. The evolutionary trends of the X-ray profile are similar to that observed in radio, but with quantitative differences. Finally, we briefly discuss the constraints of these X-ray properties on the geometry of the emission region of this pulsar.

[en] The uncertainty relations, pioneered by Werner Heisenberg nearly 90 years ago, set a fundamental limitation on the joint measurability of complementary observables. This limitation has long been a subject of debate, which has been reignited recently due to new proposed forms of measurement uncertainty relations. The present work is associated with a new error trade-off relation for compatible observables approximating two incompatible observables, in keeping with the spirit of Heisenberg’s original ideas of 1927. We report the first direct test and confirmation of the tight bounds prescribed by such an error trade-off relation, based on an experimental realisation of optimal joint measurements of complementary observables using a single ultracold ${}^{40}{\mathrm{C}\mathrm{a}}^{+}$ ion trapped in a harmonic potential. Our work provides a prototypical determination of ultimate joint measurement error bounds with potential applications in quantum information science for high-precision measurement and information security. (paper)

[en] We study the X-ray phases of the Crab pulsar utilizing the 11-year observations from the Rossi X-ray Timing Explorer , 6-year radio observations from Nanshan Telescope, and the ephemeris from Jodrell Bank Observatory. It is found that the X-ray phases in different energy bands and the radio phases from the Nanshan Telescope show similar behaviors, including long-time evolution and short-time variations. Such strong correlations between the X-ray and radio phases imply that the radio and X-ray timing noises are both generated from the pulsar spin that cannot be well described by the the monthly ephemeris from the Jodrell Bank observatory. When using the Nanshan phases as references to study the X-ray timing noise, it has a significantly smaller variation amplitude and shows no long-time evolution, with a change rate of (−1.1 ± 1.1) × 10⁻⁷ periods per day. These results show that the distance of the X-ray and radio emission regions on the Crab pulsar has no detectable secular change, and it is unlikely that the timing noises resulted from any unique physical processes in the radio or X-ray emitting regions. The similar behaviors of the X-ray and radio timing noises also imply that the variation of the interstellar medium is not the origin of the Crab pulsar’s timing noises, which is consistent with the results obtained from the multi-frequency radio observations of PSR B1540−06.

[en] With the 12 year long observations by Fermi-LAT, we discover two pairs of spin-down state transitions of PSR J1124–5916, making it the second young pulsar detected to have such behaviors. PSR J1124–5916 shows mainly two states according to its spin-down rate evolution, the normal spin-down state and the low spin-down state. In about 80% of the observation time, the pulsar is in the normal spin-down state, in which the spin-down rate decreases linearly and gives a braking index of 1.98 ± 0.04. The two transitions to the low spin-down state are in MJD 55183–55803 and MJD 56114–56398, respectively, with fractional amplitudes both ∼0.4%. No significant difference between the γ-ray profiles of the two spin-down states is detected, which is similar to PSR B0540–69, the other young pulsar with state transition detected.