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arXiv:quant-ph/0104040 · Physical Review A

Effects of twin-beam “squashed” light on a three-level atom

L. K. Thomsen, Howard M. Wiseman

Published Sep 13, 2001• 8 citations
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Abstract

An electro-optical feedback loop can make in-loop light (squashed light) which produces a photocurrent with noise below the standard quantum limit (such as squeezed light). We investigate the effect of squashed light interacting with a three-level atom in the cascade configuration and compare it to the effects produced by squeezed light and classical noise. It turns out that one master equation can be formulated for all three types of light and that this unified formalism can also be applied to the evolution of a two-level atom. We show that squashed light does not mimic all aspects of squeezed light, and in particular, it does not produce the characteristic linear intensity dependence of the population of the upper-most level of the cascade three-level atom. Nevertheless, it has nonclassical transient effects in the de-excitation.

DOI
10.1103/physreva.64.043805

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An electro-optical feedback loop can make in-loop light (squashed light) which produces a photocurrent with noise below the standard quantum limit (such as squeezed light). We investigate the effect of squashed light interacting with a three-level atom in the cascade configuration and compare it to the effects produced by squeezed light and classical noise. It turns out that one master equation can be formulated for all three types of light and that this unified formalism can also be applied to the evolution of a two-level atom. We show that squashed light does not mimic all aspects of squeezed light, and in particular, it does not produce the characteristic linear intensity dependence of the population of the upper-most level of the cascade three-level atom. Nevertheless, it has nonclassical transient effects in the de-excitation.
We examine the quantum-limited behavior of an electro-optical intensity feedback loop and present a simple theory and experimental data showing excellent agreement. We show that, although the light incident upon the in-loop detector may be sub-Poissonian, this light has unique properties different from those of a freely propagating beam of intensity squeezed light. We support this by presenting the results of homodyne measurements of the phase noise of light extracted from the loop. The utility of the in-loop field is discussed, and it is shown that in all cases in which linear optical components are used, no advantage in signal-to-noise ratio is gained by taking measurements by using this light rather than a coherent source. We also discuss effects seen in the extracted or out-of-loop light. We demonstrate the existence of, and derive an expression for, an optimum gain for suppressing low-level classical noise. Conversely, in the high-gain limit, we demonstrate that the extra noise seen in the out-of-loop photocurrent that is due to the feedback process is expressible purely in terms of the mean photocurrents involved. Lastly, we introduce the novel concept of using an intensity feedback loop in conjunction with a squeezed source and show that the feedback loop has the capability of electronically transferring squeezing from one light beam to another.
Electro-optical feedback can produce an in-loop photocurrent with arbitrarily low noise. This is not regarded as evidence of ``real'' squeezing because squeezed light cannot be extracted from the loop using a linear beam splitter. Here I show that illuminating an atom (which is a nonlinear optical element) with ``in-loop'' squeezed light causes line narrowing of one quadrature of the atom's fluorescence. This has long been regarded as an effect that can only be produced by squeezing. Experiments on atoms using in-loop squeezing should be much easier than those with conventional sources of squeezed light.
Using a feedback loop it is possible to reduce the fluctuations in one quadrature of an in-loop field without increasing the fluctuations in the other. This effect has been known for a long time, and has recently been called `squashing' (Buchler et al 1999 Opt. Lett. 24 259), as opposed to the `squeezing' of a free field in which the conjugate fluctuations are increased. In this paper I present a general theory of squashing, including simultaneous squashing of both quadratures and simultaneous squeezing and squashing. I show that a two-level atom coupled to the in-loop light feels the effect of the fluctuations as calculated by the theory. In the ideal limit of light squeezed in one quadrature and squashed in the other, the atomic decay can be completely suppressed.
We study the squeezing properties of the light generated by nondegenerate three-level laser in which the three-level atoms are in cascade configuration with degenerate parametric oscillator. We obtain the c-number Langevin equations associated with the normal ordering using the pertinent master equation. Making use of the solutions of the c-number Langevin equations, we calculate the quadrature variances. The results show that the two-mode light produced by the system under consideration is in squeezed state and the squeezing occurs in the minus quadrature. The degree of squeezing increase with the linear gain coefficient and almost perfect squeezing can be obtained for large values of the linear gain coefficient and the atoms initially prepared in lower level slightly greater than in the upper level. Moreover, the presence of nonlinear crystal increases the degree of squeezing for single mode and two-mode lights.
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.
Light and atoms couple together via the electromagnetic interaction. The simplest form of this interaction is the electric dipole interaction, and in its quantised form it provides a useful starting point for the investigation of quantum effects in optics. Two examples of quantum noise manipulation of the light field due to interaction with atoms will be presented, as well as an analysis of a simple model for laser cooling of trapped atoms. The first example of quantum noise manipulation is the investigation of a quantum non-demolition measurement scheme based on a three-level atomic system in the ladder configuration. An effective two-level model of the atomic system is used, which enables the inclusion of spontaneous emission noise from the upper atomic level. The system is found to perform well, when detuned far from resonance. The second example is the treatment of squeezing in the intensity difference between two modes coupled by a three-level atomic system in the ladder configuration. The noise correlations are similar to those occurring in the optical parametric oscillator, and give rise to good squeezing when the system is well detuned from the intermediate level. The simple model of laser cooling consists of a single two-level atom with quantised centre-of-mass motion constrained to move in a one-dimensional harmonic potential while interacting with a single-mode classical travelling light field. It is shown that there is an analogy between this model and the Jaynes-Cummings model. This gives rise to interesting coherent effects including quantum collapses and revivals in the atomic inversion. Sideband cooling occurs for this model when the light field is tuned to the atom's first lower vibrational sideband. The strong sideband and Lamb-Dicke perturbation regimes are defined. Analytic results have previously been obtained for the latter regime, but we carry out a numerical investigation of the steady state and time evolution behaviour in the former regime. Differences in the behaviour in the two regimes are discussed. Finally the possibility of observing quantum jumps between trap levels is discussed.