Quantum phase measurement with multiphoton twin-Fock states has been shown to be optimal for detecting equal numbers of photons at the output ports of a Mach–Zehnder interferometer(i.e., the so-called single-fringe d...Quantum phase measurement with multiphoton twin-Fock states has been shown to be optimal for detecting equal numbers of photons at the output ports of a Mach–Zehnder interferometer(i.e., the so-called single-fringe detection), since the phase sensitivity can saturate the quantum Cramér–Rao lower bound at certain values of phase shift. Here we report a further step to achieve a global phase estimation at the Heisenberg limit by detecting the particle-number difference(i.e., the ?_z measurement). We show the role of experimental imperfections on the ultimate estimation precision with the six-photon twin-Fock state of light. Our results show that both the precision and the sensing region of the ?_z measurement are better than those of the single-fringe detection, due to combined contributions of the measurement outcomes. We numerically simulate the phase estimation protocol using an asymptotically unbiased maximum likelihood estimator.展开更多
Monolayer MnTe_(2)stabilized as 1 T structure has been theoretically predicted to be a two-dimensional(2 D)ferromagnetic metal and can be tuned via strain engineering.There is no naturally van der Waals(vdW)layered Mn...Monolayer MnTe_(2)stabilized as 1 T structure has been theoretically predicted to be a two-dimensional(2 D)ferromagnetic metal and can be tuned via strain engineering.There is no naturally van der Waals(vdW)layered MnTe_(2)bulk,leaving mechanical exfoliation impossible to prepare monolayer MnTe_(2).Herein,by means of molecular beam epitaxy(MBE),we successfully prepared monolayer hexagonal MnTe_(2)on Si(111)under Te rich condition.Sharp reflection high-energy electron diffraction(RHEED)and low-energy electron diffraction(LEED)patterns suggest the monolayer is atomically flat without surface reconstruction.The valence state of Mn^(4+)and the atom ratio of([Te]:[Mn])further confirm the MnTe_(2)compound.Scanning tunneling spectroscopy(STS)shows the hexagonal MnTe_(2)monolayer is a semiconductor with a large bandgap of~2.78 eV.The valence-band maximum(VBM)locates at theΓpoint,as illustrated by angle-resolved photoemission spectroscopy(ARPES),below which three hole-type bands with parabolic dispersion can be identified.The successful synthesis of monolayer MnTe_(2)film provides a new platform to investigate the 2D magnetism.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91636108,11775190,and 11774024)Science Foundation of Zhejiang Sci-Tech University,China(Grant No.18062145-Y)+1 种基金Open Foundation of Key Laboratory of Optical Field Manipulation of Zhejiang Province,China(Grant No.ZJOFM-2019-002)Science Challenge Project,China(Grant No.TZ2018003)
文摘Quantum phase measurement with multiphoton twin-Fock states has been shown to be optimal for detecting equal numbers of photons at the output ports of a Mach–Zehnder interferometer(i.e., the so-called single-fringe detection), since the phase sensitivity can saturate the quantum Cramér–Rao lower bound at certain values of phase shift. Here we report a further step to achieve a global phase estimation at the Heisenberg limit by detecting the particle-number difference(i.e., the ?_z measurement). We show the role of experimental imperfections on the ultimate estimation precision with the six-photon twin-Fock state of light. Our results show that both the precision and the sensing region of the ?_z measurement are better than those of the single-fringe detection, due to combined contributions of the measurement outcomes. We numerically simulate the phase estimation protocol using an asymptotically unbiased maximum likelihood estimator.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11604366,11634007,21872099,and 22072102)the National Natural Science Foundation of Jiangsu Province,China(Grant No.BK 20160397)support from the Youth Innovation Promotion Association of Chinese Academy of Sciences(Grant No.2017370)。
文摘Monolayer MnTe_(2)stabilized as 1 T structure has been theoretically predicted to be a two-dimensional(2 D)ferromagnetic metal and can be tuned via strain engineering.There is no naturally van der Waals(vdW)layered MnTe_(2)bulk,leaving mechanical exfoliation impossible to prepare monolayer MnTe_(2).Herein,by means of molecular beam epitaxy(MBE),we successfully prepared monolayer hexagonal MnTe_(2)on Si(111)under Te rich condition.Sharp reflection high-energy electron diffraction(RHEED)and low-energy electron diffraction(LEED)patterns suggest the monolayer is atomically flat without surface reconstruction.The valence state of Mn^(4+)and the atom ratio of([Te]:[Mn])further confirm the MnTe_(2)compound.Scanning tunneling spectroscopy(STS)shows the hexagonal MnTe_(2)monolayer is a semiconductor with a large bandgap of~2.78 eV.The valence-band maximum(VBM)locates at theΓpoint,as illustrated by angle-resolved photoemission spectroscopy(ARPES),below which three hole-type bands with parabolic dispersion can be identified.The successful synthesis of monolayer MnTe_(2)film provides a new platform to investigate the 2D magnetism.
