Atom lasers, coherent states, and coherence II. Maximally robust ensembles of pure states

Abstract

As discussed in the preceding paper [Wiseman and Vaccaro,, the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of ρss as a stationary ensemble of pure states, is more natural. In the preceding paper we concentrated upon the question of whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy χ of the bosons in the laser mode, and the excess phase noise ν. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit (ν = χ = 0), the most robust states are coherent states. As the phase noise or phase dispersion is increased through ν or the self-interaction of the bosons χ, respectively, the most robust states become more and more amplitude-squeezed. We find scaling laws for these states, and give analytical derivations for them. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR ensemble being an ensemble of states with a well-defined coherent amplitude. This lends support to our approach of regarding robust PR ensembles as the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large. 03.65.Yz, 03.75.Fi, 42.50.Lc, 03.65.Ta

Atom-laser coherence and its control via feedback

“…It is interesting that this corresponds to the "conditionally coherent" regime µ 3/2 < χ < µ 2 as discussed in Ref. [34]. Since the nonlinearity C is effectively cancelled by this feedback scheme, the output power spectrum, Eq.…”

“…For the preliminary atom laser experiments of Refs. [8,9], the interaction strength C is always found to satisfy C ≫ κ/µ and hence χ ≫ 1 [34]. Atom lasers, therefore, have a linewidth far above the standard limit.…”

Physics with coherent matter waves

“…Corresponding experiments will be discussed in the following section. There have been many theoretical investigations on the physics of the output mechanism and the resulting matter wave field outside the trap [141,142,143,132,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162]. The internal degrees of freedom and their coherent manipulation with external fields opens more possibilities for this process than the optical analogue of tunneling through a potential barrier.…”

Classicalization of quantum state of detector by amplification process

“…This also can be verified, using a quantitative measure of macroscopicity. Lee (14) where W (α) is the Wigner function of the state and M is the number of modes. The measure S(ρ) was plotted for amplified coherent states with the first term, with first two terms and with first three terms in FIG.…”

“…Despite the promising classical features of coherent states, because of the linearity of Schrödinger equation, a system prepared in a coherent state can be driven into a superposition state by coupling it to a microscopic system [8][9][10][11][12][13][14][15][16]. In fact, the non-classical features of coherent states are even recognized to be useful in quantum information science [17,18].…”