The uncertainty principle in a QND measurement of photon number

Y. Yamamoto, N. Imoto, S. Machida

Fanglin Peng, Jing Zhang, Ruifang Dong +1 more

Hans Martens, Willem M. de Muynck

It is shown how a disturbance-type uncertainty principle can be derived from an uncertainty principle for joint measurements. To achieve this, we first clarify the meaning of 'inaccuracy' and 'disturbance' in quantum mechanical measurements. The case of photon number and phase is treated as an example, and it is applied to a quantum non-demolition measurement using the optical Kerr effect.

N. Imoto, H. A. Haus, Y. Yamamoto

This paper proposes a quantum nondemolition measurement scheme for the photon number. The signal and probe optical waves interact via the optical Kerr effect. The optical phase of the probe wave is selected as the readout observable for the measurement of the photon number of the signal wave. The measurement accuracy \ensuremath{\Delta}n and the imposed phase noise \ensuremath{\Delta}\ensuremath{\varphi} of the signal wave satisfy Heisenberg's uncertainty principle with an equality sign, 〈(\ensuremath{\Delta}n${)}^{2}$〉〈(\ensuremath{\Delta}\ensuremath{\varphi}${)}^{2}$〉=(1/4). .AE

S. Brattke, Benjamin T. H. Varcoe, HERBERT WALTHER

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.