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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

The quadrature-phase squeezed state field in steady-state laser operation

Mahoro FUJII

Published Jan 20, 2003• 0 citations
Publisher

Abstract

It has widely been accepted that the laser field is a coherent state with phase diffusion. For example, in quantum theory of the laser it is conventional that the initial field state is given as a coherent state. But strictly speaking, this initial condition is a hypothesis which should be examined through experiments in terms of the quantum fluctuations of the held. In this study a new steady-state solution for the laser field density matrix is suggested, whose initial photon state is a quadrature-phase squeezed state, and whose photon number statistics is just the same as the conventional ansatz.

DOI
10.1109/cleopr.1999.817867

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It has widely been accepted that the laser field is a coherent state with phase diffusion. For example, in quantum theory of the laser it is conventional that the initial field state is given as a coherent state. But strictly speaking, this initial condition is a hypothesis which should be examined through experiments in terms of the quantum fluctuations of the held. In this study a new steady-state solution for the laser field density matrix is suggested, whose initial photon state is a quadrature-phase squeezed state, and whose photon number statistics is just the same as the conventional ansatz.
The rate at which pure initial states satisfying the detailed balance condition on the photon number states deteriorate into mixtures in the decoherence process is computed for a laser field above threshold in the Scully-Lamb laser model. In steady-state laser operation, the field state suggested by Scully and Lamb is shown to be the least increase of the error area in the complex amplitude plane, thus becoming the most stable field state among the squeezed states characterized by the phase order parameter Δ.
A squeezed state of light is usually taken to mean a state in which the fluctuations of one of the quadratures are below the level associated with a coherent or vacuum state. These squeezed fluctuations are phase sensitive in the sense that they vary periodically as the field evolves, but the relationship between squeezing and phase fluctuations is not trivial. While squeezed states can exhibit an arbitrarily low level of phase fluctuations, the phase states, which are eigenstates of the Hermitian optical phase operator are not themselves quadrature squeezed. A phasesqueezed state is one with a lower level of phase fluctuations than a coherent state with the same mean photon number. Phase squeezing is fundamentally different from quadrature squeezing in much the same way that sub-Poissonian photon statistics is different. For this reason optimally squeezed states and states with minimum phase noise will be distinct. We derive the form of the states which minimum phase noise for a given intensity. These have an Airy function behavior for the photon number probability distribution. These phase squeezed states have a far better phase resolution than coherent states of similar intensity, but do not seem to offer a significant reduction of phase fluctuations compared with conventional squeezed states.
We study the steady-state operation and noise properties of a laser (or maser) exhibiting phase locking when an ordinary vacuum is replaced by a squeezed vacuum. Such a phase-sensitive laser can be realized by preparing the active medium initially in a coherent superposition of levels involved in the laser transition. We develop a general formalism to treat number-phase fluctuations and quadrature fluctuations. When applied to a one-photon laser with injected atomic coherence, we find that not only is a complete quenching of the (spontaneous-emission) quantum noise possible, but the field can actually be in a squeezed state. The variance in either amplitude or phase quadrature can be below the vacuum noise level by a factor of 2 (50%) at the expense of enhanced fluctuations in the other quadrature.
A number-phase interaction is suggested that is analogous to the usual quadrature squeezing Hamiltonian for a mode of the electromagnetic field. Applied to an initial coherent state, it produces number-phase squeezed states. For moderate squeezing in either direction the result is close to a minimum uncertainty state. Two different ${\mathrm{\ensuremath{\chi}}}^{(3)}$ approximations to the ideal interaction are found, appropriate for the different directions of squeezing. Even with the approximate interaction, the fluctuations in photon number can be reduced to less than half a photon for an arbitrarily intense field.
Quantum statistical properties of laser light have been extensively studied for the last thirty years by using an operator Langevin equation, a density operator master equation, and a quantum mechanical Fokker-Planck equation. It has been generally accepted among physicists and quantum electronics engineers that an ideal laser operating at far above the threshold generates a coherent state of light. Various experimental facts such as the Poissonian photoelectron statistics, the shot noise limited photocurrent fluctuations, and the Gaussian distributions of optical homodyne detector output seem to support this. However, recent careful studies on a semiconductor laser have revealed that a semiconductor laser does not necessarily produce a coherent state of light, but generates a number-phase squeezed state, in which the photon-number noise is smaller than the standard quantum limit (shot noise limit or Poisson limit). This paper reviews the theoretical and experimental aspects of number-phase squeezed state generation by a semiconductor laser.