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arXiv:quant-ph/0609225 · Physical Review Letters

Generating Quadrature Squeezing in an Atom Laser through Self-Interaction

Mattias Johnsson, Simon A. Haine

Published Jul 2, 2007• 48 citations
arXivHTMLPDF

Abstract

We describe a scheme for creating quadrature- and intensity-squeezed atom lasers that do not require squeezed light as an input. The beam becomes squeezed due to nonlinear interactions between the atoms in the beam in an analogue to optical Kerr squeezing. We develop an analytic model of the process which we compare to a detailed stochastic simulation of the system using phase space methods. Finally we show that significant squeezing can be obtained in an experimentally realistic system and suggest ways of increasing the tunability of the squeezing.

DOI
10.1103/physrevlett.99.010401

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Light emitted from laser-driven atoms often has squeezed quadrature fluctuations reflecting the phase dependence of the atomic source excited into a coherent superposition by the driving field. In this paper, we study the maximum squeezing in the emitted light fields from three-level atoms, paying particular attention to the role of atomic coherences in governing the optimum squeezing which is possible. Some phase dependent nonlinear optical processes have the potential for substantial quantum noise reduction at useful intensities: for example, four-wave mixing involving atomic systems has already been used to generate quadrature-squeezed light. The threoretical description of such a source is generally complicated with damping processes, coherent and incoherent pumping, and so on, all needing to be taken into account. Fully quantum treatments are available, but the basic physics of the process is often difficult to grasp in the necessarily complicated analysis. Although less important from the point of view of efficient practical sources of squeezed light, studying the generation of squeezed light in simpler systems such as two- or three-level atoms interacting with one or two modes (as in Jaynes-Cummings models) or in spontaneous emission or resonance fluorescence gives greater insight into the fundamentals of the squeezing process. In particular, the relationship between the atomic coherences and the degree of squeezing in the generated fields can be explored. We study the maximum (optimized) squeezing that can be obtained in the emitted fields from the irreversible decay from three-level atoms for any choice of initial conditions, excitations and decay process, for all quadrature components and for all possible configurations (V, \ensuremath{\Lambda}, and ``ladder'' systems).We show that for V and \ensuremath{\Lambda} systems, optimum squeezing is actually associated with a two-level state (in a suitable basis) involving a single one-photon coherence, but for ladder systems the state for maximum noise reduction is not equivalent to a two-level system and involves a single two-photon coherence and no intermediate state population. We pay particular attention to whether the total field is in a minimum uncertainty state, and the nature of the atomic state associated with maximum squeezing, especially whether it is a mixed or pure state. In the case where the initial free field has a zero amplitude at the detector and the source atoms are confined to a region small compared to the wavelength (Dicke source) we show that the squeezing in the total field is given in terms of the squeezing in the source field, and hence related to atomic populations and atomic one-photon and two-photon coherences for the case of three level atom. Previously unconsidered source-free field interferences terms are shown to be zero. The choice of quadrature phase and frequency is optimized to minimize the source field normally ordered variance. We then minimize further with respect to the choice of atomic density matrix elements subject to the constraints that the density matrix is Hermitean, positive, and has a trace equal to unity. In all cases we find that the optimum squeezing is produced when the source field is in a minimum uncertainty state.

Physical Review A•Sep 1, 1994•24 citations
We describe a scheme for creating quadrature- and intensity-squeezed atom lasers that do not require squeezed light as an input. The beam becomes squeezed due to nonlinear interactions between the atoms in the beam in an analogue to optical Kerr squeezing. We develop an analytic model of the process which we compare to a detailed stochastic simulation of the system using phase space methods. Finally we show that significant squeezing can be obtained in an experimentally realistic system and suggest ways of increasing the tunability of the squeezing.
We propose a method for generating quantum squeezing in atom-optical systems. We show that it is possible to generate squeezed atom lasers, and Bose-Einstein condensates with squeezed occupation numbers by utilising the nonlinear atomic interactions caused by s-wave scatting. We develop an analytic model of the process which we compare to a detailed stochastic simulation of the system using phase space methods. Finally we show that significant squeezing can be obtained in an experimentally realistic system and suggest ways of increasing the tunability of the squeezing.
In quantum optics, squeezing corresponds to the process in which fluctuations of a quadrature operator are reduced below the shot noise limit. In turn, nonlinear squeezing can be defined as reduction of fluctuations related to nonlinear combination of quadrature operators. Quantum states with nonlinear squeezing are a necessary resource for deterministic implementation of high-order quadrature phase gates that are, in turn, sufficient for advanced quantum information processing. We demonstrate that this class of states can be deterministically prepared by employing a single self-Kerr gate accompanied by suitable Gaussian processing. The required Kerr coupling depends on the energy of the initial system and can be made arbitrarily small. We also employ numerical simulations to analyze the effects of imperfections and to show to which extent can they be neglected.
Squeezed optical fields are a powerful resource for a variety of investigations in basic research and technology. However, the generation of intense squeezed light is challenging. Here, we show that intense squeezed light can be produced using strongly laser driven atoms and the so far unrelated process of high harmonic generation. We demonstrate that when the intensity of the driving field significantly depletes the ground state of the atoms, leading to dipole moment correlations, the quantum state of the driving field and the generated high harmonics are entangled and squeezed. Furthermore, we analyze how the resulting quadrature squeezing of the fundamental laser mode after the interaction can be controlled. The findings open the way for the generation of high intensity squeezed light states for a wide range of applications.
Kerr microresonators are integrated nonlinear devices widely used to generate classical optical frequency combs and nonclassical states of light. In particular, they provide a promising platform for squeezed light sources, which are important elements of emerging quantum sensing, communication, and computing technologies. Designing such sources requires numerical tools that efficiently incorporate realistic device physics and noise processes. Here, we show that established semi-classical frameworks based on the Lugiato-Lefever equation and the Ikeda map, instrumental in the development of classical light sources, can also predict the quadrature-noise properties of squeezed light when vacuum fluctuations are properly included. We consider three canonical configurations producing two-mode quadrature squeezing, single-mode quadrature squeezing, and intensity difference squeezing. In each case, the semi-classical simulations produce quadrature variances and noise spectra in close agreement with the quantum theoretical predictions. These frameworks therefore provide practical tools for designing squeezed light sources, with the capability to incorporate additional noise mechanisms, nonlinear effects, and complex resonator arrangements. More fundamentally, our results show that key experimental signatures of squeezing can be modeled as phase-sensitive amplification of properly normalized vacuum fluctuations within stochastic semi-classical field equations. This observation helps distinguish squeezing properties accessible through semi-classical field evolution from those intrinsically requiring a full quantum description.
Light emitted from laser-driven atoms often has squeezed quadrature fluctuations reflecting the phase dependence of the atomic source excited into a coherent superposition by the driving field. In this paper, we study the maximum squeezing in the emitted light fields from three-level atoms, paying particular attention to the role of atomic coherences in governing the optimum squeezing which is possible. Some phase dependent nonlinear optical processes have the potential for substantial quantum noise reduction at useful intensities: for example, four-wave mixing involving atomic systems has already been used to generate quadrature-squeezed light. The threoretical description of such a source is generally complicated with damping processes, coherent and incoherent pumping, and so on, all needing to be taken into account. Fully quantum treatments are available, but the basic physics of the process is often difficult to grasp in the necessarily complicated analysis. Although less important from the point of view of efficient practical sources of squeezed light, studying the generation of squeezed light in simpler systems such as two- or three-level atoms interacting with one or two modes (as in Jaynes-Cummings models) or in spontaneous emission or resonance fluorescence gives greater insight into the fundamentals of the squeezing process. In particular, the relationship between the atomic coherences and the degree of squeezing in the generated fields can be explored. We study the maximum (optimized) squeezing that can be obtained in the emitted fields from the irreversible decay from three-level atoms for any choice of initial conditions, excitations and decay process, for all quadrature components and for all possible configurations (V, \ensuremath{\Lambda}, and ``ladder'' systems).We show that for V and \ensuremath{\Lambda} systems, optimum squeezing is actually associated with a two-level state (in a suitable basis) involving a single one-photon coherence, but for ladder systems the state for maximum noise reduction is not equivalent to a two-level system and involves a single two-photon coherence and no intermediate state population. We pay particular attention to whether the total field is in a minimum uncertainty state, and the nature of the atomic state associated with maximum squeezing, especially whether it is a mixed or pure state. In the case where the initial free field has a zero amplitude at the detector and the source atoms are confined to a region small compared to the wavelength (Dicke source) we show that the squeezing in the total field is given in terms of the squeezing in the source field, and hence related to atomic populations and atomic one-photon and two-photon coherences for the case of three level atom. Previously unconsidered source-free field interferences terms are shown to be zero. The choice of quadrature phase and frequency is optimized to minimize the source field normally ordered variance. We then minimize further with respect to the choice of atomic density matrix elements subject to the constraints that the density matrix is Hermitean, positive, and has a trace equal to unity. In all cases we find that the optimum squeezing is produced when the source field is in a minimum uncertainty state.