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Physical Review A

Quantum dynamics of a single-atom cascade laser

Péter Horák, Klaus M. Gheri, Helmut Ritsch

Published Apr 1, 1995• 23 citations
Publisher

Abstract

We investigate a single-atom nondegenerate cascade laser model, based on a coherently pumped three-level atom coupled to two independently damped cavity modes. We show that while many features predicted within a recently proposed N-atom superradiant laser model [F. Haake et al., Phys. Rev. Lett. 71, 995 (1993)] can readily be obtained in the single-atom case, some of the quantum noise properties are significantly different. The influence of spontaneous decay and nonadiabatic effects due to the finite spectral width of the lower cavity mode are discussed. Finally, we show that the present model has a large potential for the stationary preparation of various nonclassical states of the atom-field system.

DOI
10.1103/physreva.51.3257

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We investigate a single-atom nondegenerate cascade laser model, based on a coherently pumped three-level atom coupled to two independently damped cavity modes. We show that while many features predicted within a recently proposed N-atom superradiant laser model [F. Haake et al., Phys. Rev. Lett. 71, 995 (1993)] can readily be obtained in the single-atom case, some of the quantum noise properties are significantly different. The influence of spontaneous decay and nonadiabatic effects due to the finite spectral width of the lower cavity mode are discussed. Finally, we show that the present model has a large potential for the stationary preparation of various nonclassical states of the atom-field system.
The cooperative dynamics of a microlaser consisting of two threelevel atoms interacting with a pump field and two quantized cavity modes forming a radiative cascade are studied. Adiabatic elimination of one mode leads to a strong dynamical entanglement between the internal states of the atoms which allows us to study the effects of a cavity-mediated dipole-dipole interaction. We show that the coherent dynamics of the two-atom system will preferentially couple symmetrical linear combinations of internal states. If this coupling dominates the dynamics, the two-atom system will behave like a single atom with correspondingly larger dipole moment, that is a superradiant two-atom system. Even very small spontaneous decay causes transitions from symmetrical to antisymmetrical states and conversely. The hopping between two subsets of the state space can give rise to intriguing phenomena such as bistability of the laser mode intensity. By a randomization of the two coupling phases we recover the standard independent-atom laser theory.
The spontaneous emission spectrum for a three-level cascade configuration atom in a single mode high-Q cavity coupled to a zero temperature reservoir of continuum external modes is determined from the atom–cavity mode master equation using the quantum regression theorem. Initially the atom is in its upper state and the cavity mode empty of photons. Following Glauber, the spectrum is defined via the response of a detector atom. Spectra are calculated for the detector located inside the cavity (case A), outside the cavity end mirror (case B—end emission), or placed for emission out the side of the cavity (case C). The spectra for case A and case B are found to be essentially the same. In all the cases the predicted lineshapes are free of instrumental effects and only due to cavity decay. Spectra are presented for intermediate and strong coupling regime situations (where both atomic transitions are resonant with the cavity frequency), for cases of non-zero cavity detuning, and for cases where the two atomic transition frequencies differ. The spectral features for cases B(A) and C are qualitatively similar, with six spectral peaks for resonance cases and eight for detuned cases. These general features of the spectra can be understood via the dressed atom model. However, case B and C spectra differ in detail, with the latter exhibiting a deep spectral hole at the cavity frequency due to quantum interference effects.
We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as \ensuremath{\beta}, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for \ensuremath{\beta} are $0.01<\ensuremath{\beta}<1.0.$ We find that for large enough \ensuremath{\beta}, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as \ensuremath{\beta} is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with \ensuremath{\beta} values in the range considered here. As \ensuremath{\beta} is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results.
We consider a nondegenerate three-level laser in which the three-level atoms are in a cascade configuration, the laser cavity contains a degenerate parametric oscillator, and one of the cavity modes is driven by coherent light.We have analyzed the effects of the degenerate parametric oscillator and the driving coherent light on the laser using the expectation values of the cavity mode variables at a steady state.The results show that the two-mode light produced by the system under consideration exhibits quadrature squeezing.The presence of nonlinear crystal in the laser cavity generates a single-mode squeezed light and also enhances the degree of squeezing of the two-mode light.Although the driving coherent light has no effect on quadrature squeezing, it increases the intensity of the cavity modes.
We discuss a laser with N three-level atoms resonantly and cooperatively interacting with two cavity modes. Its intensity is proportional to N2{\mathit{N}}^{2}N2, the linewidth scales as 1/N2{\mathit{N}}^{2}N2, and the output intensity fluctuations display up to 100% squeezing at low frequencies. We show that quantum fluctuations of the pump do not deteriorate the squeezing significantly. We also find that the fluctuation properties of the ``passive'' cavity mode which serves to collectively relax the atoms to the ground state are similar to those of the active mode. Finally we take into account spontaneous emission. Within a certain range of frequencies good squeezing can still be found. \textcopyright{} 1996 The American Physical Society.
Superradiant lasers based on atomic ensembles exhibiting ultranarrow optical transitions can emit light of unprecedented spectral purity and may serve as active atomic clocks. We consider two frequency-detuned active atomic clocks, which are coupled in a cascaded setup, i.e., as master and slave lasers, and study the synchronization of the slave to the master clock. In a setup where both atomic ensembles are coupled to a common cavity mode, such synchronization phenomena have been predicted by Xu et al. [M. Xu, D. A. Tieri, E. C. Fine, J. K. Thompson, and M. J. Holland, Phys. Rev. Lett. 113, 154101 (2014).] and experimentally observed by Weiner et al. (J. M. Weiner et al., arXiv:1503.06464). Here we demonstrate that synchronization still occurs in cascaded setups but exhibits distinctly different phase diagrams. We study the characteristics of synchronization in comparison to the case of coupling through a common cavity. We also consider synchronization through a classical channel where light of the master laser is measured phase sensitively and the slave laser is injection locked by feedback and compare to the results achievable by coupling through quantum channels.