Observation of quantum phase noise in a laser oscillator

Anthony E.. Siegman, Raymond Arrathoon

Samuel Böhringer, Fabian Kienle, Richard Lopp

We derive the equations of motion of arbitrary momentum-dependent observables for a fully first-quantized, driven two-level atom in a linear potential under the presence of a stochastic laser phase. In particular, we show that such momentum-dependent observables evolve under stochastic differential equations (SDEs) in the form of geometrical Brownian motion and find that these SDEs reduce to ordinary differential equations (ODEs) for the expectation values under white laser phase noise. As an example, we solve these ODEs numerically and determine the effect of laser phase noise on Rabi oscillations including quantized center-of-mass degrees of freedom of the atom. Moreover, the SDE formalism we derive holds for any phase noise source and can also be applied to extended noise models such as color noise.

Raymond Arrathoon, Anthony E.. Siegman

Valery M. Baev, Gerhard Gaida, H. Schröder +1 more

Anthony E.. Siegman, Raymond Arrathoon

Received 12 February 1968DOI:https://doi.org/10.1103/PhysRevLett.20.901©1968 American Physical Society

Rana Pratap, Harishankar Ramachandran

Quantum analysis has been done for the traveling-wave (TW) electro-optic phase modulator in the presence of the phase noise of a radio frequency (RF) oscillator and a laser source, in which the Hamiltonian for an active section of the phase modulator system is derived. The effect of RF phase noise from the oscillator and a phase velocity mismatch (PVM) between optical photons and the RF field are included in the Hamiltonian. The time evolution of the field operator of the laser in the TW electro-optic phase modulator is derived by the Heisenberg equation of motion. The action of a TW electro-optic phase modulator in the presence of the two distinct weak noises—classical phase noise because of RF and quantum phase noise caused by a laser—has been evaluated and explained in terms of the second-order temporal correlation function and power spectrum. The power spectrum has been written as a function of the semiconductor laser linewidth, an enhancement factor in the laser linewidth, and the RF oscillator linewidth. The results are applied to analyze the basic model of a frequency-coded quantum key distribution (FC-QKD) system. The quantum bit error rate (QBER), the first-order optical intensity correlation function, and the spectrum of intensity fluctuation have been calculated for the partially coherent regime to evaluate the performance of the FC-QKD system.