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“Trapping States” - Revisited

Young-Tak Chough, H. J. Carmichael

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We revisit the “trapping states” of the micromaser from a quantum trajectory point of view, treating many simultaneously interacting atoms and a random atomic beam. Previous studies of trapping states are severely restricted by simplifying assumptions. We show that sub-Poissonian maser fields are generated still after the principal restrictions are lifted.

DOI
10.1364/iqec.2011.i446

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We revisit the “trapping states” of the micromaser from a quantum trajectory point of view, treating many simultaneously interacting atoms and a random atomic beam. Previous studies of trapping states are severely restricted by simplifying assumptions. We show that sub-Poissonian maser fields are generated still after the principal restrictions are lifted.
Trapping states in the one-atom maser or micromaser are predicted by maser theory and are a direct consequence of the quantization of the electromagnetic field. They have been found in our experiment when the inversion of atoms leaving the cavity is observed while the interaction time is scanned. They correspond to quantum states of the atom-cavity system and under certain conditions represent Fock states. The trapping states occur when the atom-field dynamics complete a full evolution (or multiples thereof). Owing to feedback through the maser dynamics, a stabilization of the photon number in the steady state field of the maser cavity is achieved.
We present a theory which can explain the micromaser as well as its optical counterpart, the microlaser, for appropriate values of dissipative parameters. We show that, in both the the cases, the cavity radiation fields can have sub-Poissonian photon statistics. We further analyse if it is possible to attain a Fock state of the radiation field. The microlaser is precluded for such analysics due to the damping of its lasing levels making transitions at optical frequencies. Hence, we focus our attention on the micromaser and our exact simulation of the dynamics shows that it is not possible to generate a Fock state of the cavity radiation field.
By applying a quantum-trajectory approach to a master equation for the cavity mode density operator, we investigate the dynamics and the trapping states of a micromaser or microlaser including the effects of cavity temperature, two-atom events, atomic velocity spread, and partial excitation of the atomic beam. In the description of two-atom collective effects we allow for the nonsimultaneous arrival of atoms in the cavity, generalizing to a mean number of atoms ${N}_{\mathrm{at}}\ensuremath{\approx}1,$ a recent treatment [M. I. Kolobov and F. Haake, Phys. Rev. A 55, 3033 (1997)]. We show that, in trapping regions, our treatment of two-atom events can give strikingly different effects with respect to the approximation of simultaneous arrival of atom pairs; e.g., detrapping instead of trapping, different times of approach to the steady state, and different photonstatistics. Also, we simulate micromaser dynamics with parameter values corresponding to the recent experimental observation of the trapping effect by Walther and collaborators [H. Weidinger et al., Technical Digest of the European Quantum Electronics Conference '98 (IEEE, Piscataway, NJ, 1998)].
A micromaser in standard operation produces entangled two-level atoms. This entanglement can be investigated in the correlations of atoms leaving the micromaser cavity in the upper and lower maser levels. The correlations contribute to the stabilization of the photon number in the cavity and are thus vital for the generation of sub-Poissonian statistics in the maser field. We review how various statistical signatures for this entanglement are calculated in micromaser theory, and report recent measurements that demonstrate the case. Ways are described leading to an optimal entanglement for the atoms in the micromaser.
A general theory of the micromaser is described. The model is based on treating the input atomic beam as a two-component quantum field so that the two-level atoms in the beam are ``quanta'' of this field. This approach makes it possible to formulate a general quantum Langevin description of the dynamics with the input atomic field as a source of quantum noise. The passage to a master-equation description is then effected by use of an adjoint-operator method, and by introducing a general class of statistical states for the atomic beam known as generalized shot noise. The result is a (non-Markovian) master equation for the field inside the cavity which is valid for a broad range of statistical properties of the input atomic beam. The approximate steady-state solutions to this master equation for the photon statistics of the cavity field for sub-Poissonian (antibunched) atomic beams found by other researchers are regained. The theory is then extended to treat super-Poissonian (bunched) atomic beams. An exact result is found in the limit of a strongly bunched beam in which the cavity-field state is shown to converge to a mixture of a thermal-field state and the state produced by a random beam of twice the intensity. A physical explanation of this result is also presented.