Present State of the Statistical Theory of Atoms

János A. Bergou, Peter G. Kalman

We present a theory of the micromaser including the effect of the arrival-time statistics of the active atoms in the theoretical treatments. Our starting point is an approach that explicitly incorporates the effect of pump statistics into the dynamical description of lasers and masers. We show that the application of standard laser theory to the micromaser is tantamount to the tacit assumption of Poissonian arrival-time statistics. Hence standard laser theory and the theory of the micromaser are, in general, not equivalent, but the latter contains the former, as a limiting case, for completely random arrival times. We show, as an application, that the steady-state value of the average photon number (first moment) is essentially unaffected by the pump statistics since it depends only on the flux of active atoms (average number of atoms entering the cavity per unit time) provided the flux is constant. The intensity fluctuations (second moment), however, exhibit a stronger dependence on the pump statistics. In particular, for sub-Poissonian pump statistics the sub-Poissonian character of the field is enhanced.

Massimo V. Fischetti, William G. Vandenberghe

Alexander Semenovich Holevo

Jérôme Roccia

We investigate finite particle systems of cold atoms bound in a local potential V(r). We derive the ground state energy and the particle density using a recently developed semiclassical theory (2008 Phys. Rev. Lett. 100 200408), and assuming the particles are described by the Haldane-Wu fractional exclusion statistics (FES) at unitarity. This approach is applied to atoms trapped into a three dimensional harmonic oscillator. We show that the parameter-free FES semiclassical theory yields results that are consistent with numerical simulations by Chang and Bertsch [2007 Phys. Rev A 76 021603(R)] and Bulgac (2007 Phys. Rev. A 76 040502).

George P. Miroshnichenko

We develop a theory of the discrete photodetection model where individual unexcited atoms from the atomic beam passing through a cavity are used as pointers. Atomic energy state selective detectors (ionization chambers) measure the escape statistics of ground-or excited-state atoms. Mandelstam’s method of successive indirect quantum measurements underlies the theory being developed. In contrast to the available works, the suggested approach takes into account the atomic beam statistics, the operation nonideality (quantum efficiencies) of ionization chambers, the detector recovery time, the back action of the probe on the quantized mode, and the relaxation process in the time interval when the cavity is empty (without atoms). We derive formulas that relate the a posteriori probabilities of photodetector clicks to the elements of the main diagonal of the initial density matrix for the cavity mode. Our numerical simulations confirm that the inverse problem of reconstructing the initial photon number distribution in a cavity can be solved using the statistics of detector clicks measured during the transient process.

Marco Baldovin, Giacomo Gradenigo, Angelo Vulpiani +1 more