Minimum uncertainty states for Dirac's number-phase pair

Z. Hradil

Y. Yamamoto, Susumu Machida, Nobuyuki Imoto +2 more

A.A Kulaga, F. Y. Khalili, David Book

Hong-Yi Fan

Based on Feynman's explanation that a Cooper pair is "a bound pair act as a Bose particle", we propose a bosonic phase operator formalism and a bosonic Hamiltonian model for Josephson junction. The Cooper pair number — phase uncertainty relation is thus established. The corresponding minimum uncertainty state is derived which turns out to be a phase state.

Y. Yamamoto, S. Machida, N. Imoto +2 more

The difference between the two nonclassical photon states, i.e., the squeezed state and the number-phase minimum-uncertainty state, is discussed. Four different generation principles for number-phase minimum-uncertainty states (and number states) are described. They are the following: (1) unitary evolution, using self-phase modulation and interference; (2) nonunitary state reduction, using either quantum nondemolition photon-number measurement or parametrically amplified idler-wave photon counting; (3) negative-feedback oscillators, incorporating a correlated photon-pair generator; and (4) pump-amplitude noise-suppressed lasers. A number-phase minimum-uncertainty state with photon-number noise reduced to 1 dB (20%) below the standard quantum limit in a frequency range over 100 MHz was produced by the fourth-generation principle.

PEKKA J. LAHTI, Maciej Maczynski