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arXiv:0712.3752 · Physical Review A

Generalized minimum-uncertainty squeezed states

Evgeny V Shchukin, Th. Kiesel, W. Vogel

Published Apr 29, 2009• 9 citations
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Abstract

Generalized squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing the properties of such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples we deal with nonlinear generalizations of quadrature squeezed states and deformed nonlinear squeezed states, which may be useful for optimized measurements at a reduced level of quantum noise. The realization of such states is studied for the quantized center-of-mass motion of a trapped ion.

DOI
10.1103/physreva.79.043831

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Generalized squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing the properties of such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples we deal with nonlinear generalizations of quadrature squeezed states and deformed nonlinear squeezed states, which may be useful for optimized measurements at a reduced level of quantum noise. The realization of such states is studied for the quantized center-of-mass motion of a trapped ion.
The generalized purely squeezed states for primary shape-invariant potentials systems, quantum deformed by different models, are constructed by the ladder-operator method within an algebraic approach based on supersymmetric quantum mechanics. The characteristic properties of these states as well as their quantum statistical properties and squeezing effects for generalized quadrature observables are studied and analyzed in terms of the quantum deformation parameter q. An application is given for a quantum deformed Pöschl–Teller potential system, and numerical results are presented and discussed in detail.
The origin of quantum noise is addressed and it can be eliminated when the quantum state is optimally prepared for the single measured observable. Minimum uncertainty states are reviewed using Q (α) -representation, which include squeezed states and number-phase minimum uncertainty states. Squeezing is a concept of trading quantum uncertainties between two conjugate observables to optimize the state for the measurement. Need for optical nonlinearity to achieve squeezing is induced. Principles and experimental results for squeezing quadrature amplitude and photon number are delineated. Applications to optical communications and optical precision measurement are briefly stated.
We study several classical-like properties of qqq-deformed nonlinear coherent states as well as nonclassical behaviors of qqq-deformed version of the Schr\"odinger cat states in noncommutative space. Coherent states in qqq-deformed space are found to be minimum uncertainty states together with the squeezed photon distributions unlike the ordinary systems, where the photon distributions are always Poissonian. Several advantages of utilizing cat states in noncommutative space over the standard quantum mechanical spaces have been reported here. For instance, the qqq-deformed parameter has been utilized to improve the squeezing of the quadrature beyond the ordinary case. Most importantly, the parameter provides an extra degree of freedom by which we achieve both quadrature squeezed and number squeezed cat states at the same time in a single system, which is impossible to achieve from ordinary cat states.
Monitoring photon quadratures and free masses are useful tools to detect small disturbances such as gravitational waves.Here we report a large class of states for photon quadratures and free masses potentially useful for this purpose: (1)'generic coherent states' (GCS) of photons, whose width is independent of time and uncertainty product $σ(x) σ(p) $ is arbitrarily large (a generalization of the minimum uncertainty Schrödinger coherent states and (2) `squeezed generic contractive states' (SGCS) for photons and free masses (a generalization of the Yuen states \cite{Yuen}) whose width decreases with time ,uncertainty product is arbitrarily large, and the covariance squared $ ^2 $ has an arbitrary value within the allowed range (0,4σ2(x)σ2(p)−1 )(0,4 σ^2 (x) σ^2 (p) -1\>)(0,4σ2(x)σ2(p)−1). Dedicated to the 125th birth anniversary of S. N. Bose.
Squeezed states of light are minimum uncertainty states for which the mean square fluctuations in phase and in quadrature with respect to a reference signal are unequal. Among other interesting properties, they provide improved sensitivity of optical interferometric phase measurements. To understand this potential, one must note that quantum theory imposes measurement uncertainty only on a pair of noncommuting variables; the measurement of any one quantum observable could be done with no uncertainty.>