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arXiv:0812.1312 · Physical Review A

Quantum trajectory analysis of the two-mode three-level atom microlaser

Tarek A. Elsayed, Abdulaziz Aljalal

Published Jun 24, 2011• 1 citation
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Abstract

We consider a single-atom laser (microlaser) operating on three-level atoms interacting with a two-mode cavity. The quantum statistical properties of the cavity field at steady state are investigated by the quantum trajectory method which is a Monte Carlo simulation applied to open quantum systems. It is found that a steady-state solution exists even when the detailed balance condition may not be guaranteed. The differences between a single-mode microlaser and a two-mode microlaser are highlighted. The second-order correlation function ${g}^{(2)}(\ensuremath{\tau})$ of a single mode is studied and special attention is paid to the one-photon trapping state, for which a simple formula is derived for its correlation function. We show the effects of the velocity spread of the atoms used to pump the microlaser cavity on the second-order correlation function, trapping states, and phase transitions of the cavity field.

DOI
10.1103/physreva.83.063833

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We consider a single-atom laser (microlaser) operating on three-level atoms interacting with a two-mode cavity. The quantum statistical properties of the cavity field at steady state are investigated by the quantum trajectory method which is a Monte Carlo simulation applied to open quantum systems. It is found that a steady-state solution exists even when the detailed balance condition may not be guaranteed. The differences between a single-mode microlaser and a two-mode microlaser are highlighted. The second-order correlation function g(2)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ) of a single mode is studied and special attention is paid to the one-photon trapping state, for which a simple formula is derived for its correlation function. We show the effects of the velocity spread of the atoms used to pump the microlaser cavity on the second-order correlation function, trapping states, and phase transitions of the cavity 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)].
We investigate the transient and the steady-state behaviour of the photon statistics of a single-atom laser, consisting of a three-level Λ system, driven by an incoherent external pump field and strongly coupled to a single mode of an optical cavity. For several limiting cases we are able to obtain analytical results. A comparison with standard multi-atom laser theory reveals a surprisingly good agreement down to very small intracavity photon numbers. Under appropriate operating conditions a calculation of the second-order intensity correlation function yields sub-Poissonian statistics as well as strong antibunching induced by the nonlinear dynamics of the atom.
This thesis describes a study of a cavity QED microlaser in which many atoms are present simultaneously and atom-cavity interaction is well-defined. The microlaser is found to display multiple thresholds analogous to first-order phase transitions of the cavity field. Hysteresis is observed as a function of atom-cavity detuning and number of atoms. Data is compared with a rate equation model and fully quantized treatment based on micromaser theory. Good agreement between theory and experiment is found when the cavity is resonant with atoms of the most probable velocity, but long lifetimes of metastable states preclude the observation of true steady-state transition points. For nonzero atom-cavity detuning the microlaser displays broadenings and shifts which are not yet well-understood. Quantum trajectory simulations are performed to investigate many-atom and finite transit time effects in the microlaser. We show that over a wide range of parameters the many-atom microlaser scales with the single-atom theory, with a perturbation in the photon statistics due to cavity decay during the atom transit time.
We use the quantum theory of cascaded open systems to calculate the transmitted photon flux for a weak beam of photons from a cavity QED laser strongly focused onto a single, resonant two-state atom in the narrow-bandwidth limit. We study the dependence of the transmitted flux on the quantum statistics of the incident light. Both bunched and antibunched light generated by the microlaser are considered as input. Working within and outside the semiclassical perturbative regime, we explicitly demonstrate that the normalized transmitted photon flux may coincide with the second-order correlation function of the incident bunched light, but not for incident antibunched light both of which are generated by a cavity QED laser. Interestingly, the thresholdless cavity QED laser is ideal for investigating statistical saturation effects by virtue of its small system size and the large quantum fluctuations accompanying it. It has the advantage of characterizing to a certain extent the quantum noise responsible for the statistical saturation. One can also easily vary the degree of antibunching of the incident light by manipulating the pumping rate of the laser.
The properties of the two-mode mazer operating on V-type three-level atoms are studied. The effect of the one-atom pumping on the two modes of the cavity field in number-state is asymmetric, that is, the atom emits a photon into one mode with some probability and absorbs a photon from the other mode with some other probability. This effect makes the steady-state photon distribution and the steady-state photon statistics asymmetric for the two modes. The diagram of the probability currents for the photon distribution, given by the analysis of the master equation, reveals that there is no detailed balance solution for the master equation. The computations show that the photon statistics of one mode or both modes can be sub-Poissonian, that the two modes can have anticorrelation or correlation, that the photon statistics increases with the increase of thermal photons and that the resonant position and strength of the photon statistics are influenced by the ratio of the two coupling strengths of the two modes. These properties are also discussed physically.