Atom lasers, coherent states, and coherence

Guo Qin Ge

Howard M. Wiseman, John A. Vaccaro

A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons (photons or atoms, respectively). Far above threshold, the stationary state ${\ensuremath{\rho}}_{\mathrm{ss}}$ of the laser mode is a mixture of coherent-field states with random phase, or, equivalently, a Poissonian mixture of number states. This paper answers the question: can descriptions such as these, of ${\ensuremath{\rho}}_{\mathrm{ss}}$ as a stationary ensemble of pure states, be physically realized? Here physical realization is as defined previously by us [H. M. Wiseman and J. A. Vaccaro, Phys. Lett. A 250, 241 (1998)]: an ensemble of pure states for a particular system can be physically realized if, without changing the dynamics of the system, an experimenter can (in principle) know at any time that the system is in one of the pure-state members of the ensemble. Such knowledge can be obtained by monitoring the baths to which the system is coupled, provided that coupling is describable by a Markovian master equation. Using a family of master equations for the (atom) laser, we solve for the physically realizable (PR) ensembles. We find that for any finite self-energy $\ensuremath{\chi}$ of the bosons in the laser mode, the coherent-state ensemble is not PR; the closest one can come to it is an ensemble of squeezed states. This is particularly relevant for atom lasers, where the self-energy arising from elastic collisions is expected to be large. By contrast, the number-state ensemble is always PR. As the self-energy $\ensuremath{\chi}$ increases, the states in the PR ensemble closest to the coherent-state ensemble become increasingly squeezed. Nevertheless, there are values of $\ensuremath{\chi}$ for which states with well-defined coherent amplitudes are PR, even though the atom laser is not coherent (in the sense of having a Bose-degenerate output). We discuss the physical significance of this anomaly in terms of conditional coherence (and hence conditional Bose degeneracy).

R. J. Ballagh, Craig M. Savage

K.M. Priyashanka, K.A.I.L. Wijewardena Gamalath

A mathematical model was developed to obtain the population inversion of the atoms in laser field in a laser cavity by considering the electric field in the optical cavity and the atomic states of the medium to be quantized. The master equation of the density operator of the laser field was studied analytically and numerically. Using coherent states, the Fokker-Plank equation for the phase space density for the laser field was solved analytically for the time dependent and steady state situations. The laser field above the threshold can be represented by a randomly phased mixture of coherent states. As the pump parameter increases in the laser process, the phase density becomes narrower, tending toward a delta function, creating a coherence laser field.

F. T. Arecchi, E. Courtens, Robert Gilmore +1 more

Sri Lanka

A mathematical model was developed to obtain the population inversion of the atoms in laser field in a laser cavity by considering the electric field in the optical cavity and the atomic states of the medium to be quantized. The master equation of the density operator of the laser field was studied analytically and numerically. Using coherent states, the Fokker-Plank equation for the phase space density for the laser field was solved analytically for the time dependent and steady state situations. The laser field above the threshold can be represented by a randomly phased mixture of coherent states. As the pump parameter increases in the laser process, the phase density becomes narrower, tending toward a delta function, creating a coherence laser field.