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New Journal of Physics

Squeezing in su(2) intelligent states

Dylan H. Mahler, Patrick Joanis, R. Vilim, Hubert de Guise

Published Mar 23, 2010• 10 citations
Publisher

Abstract

Angular momentum intelligent states are defined to satisfy . They also share with angular momentum coherent states a number of features. In this paper we describe and illustrate the squeezing properties of angular momentum intelligent states. We analyze three classes of state: never squeezed, always squeezed and sometimes squeezed. Our conclusions are applicable for a broad range of definitions of the standard quantum limit for angular momentum systems.

DOI
10.1088/1367-2630/12/3/033037

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Angular momentum intelligent states are defined to satisfy . They also share with angular momentum coherent states a number of features. In this paper we describe and illustrate the squeezing properties of angular momentum intelligent states. We analyze three classes of state: never squeezed, always squeezed and sometimes squeezed. Our conclusions are applicable for a broad range of definitions of the standard quantum limit for angular momentum systems.
The second-,fourth-and sixth-order fluctuations have been discussed by making use of- SU-(2)Lie algebra.On the basis of higher-order uncertainty relation,the definition of higher-order squeezing for the fluctuations of angular momentum has been put forward.In particular,the second-,fourth-and sixth-order squeezing in atomic coherent states are investigated.These methods and definition can be used for studying much higher-order squeezing.The higher-order squeezing can be generalized to the fluctuations of atomic variances thereby.
The second ,fourth and sixth order fluctuations have been discussed by making use of SU (2)Lie algebra.On the basis of higher order uncertainty relation,the definition of higher order squeezing for the fluctuations of angular momentum has been put forward.In particular,the second ,fourth and sixth order squeezing in atomic coherent states are investigated.These methods and definition can be used for studying much higher order squeezing.The higher order squeezing can be generalized to the fluctuations of atomic variances thereby.
The atomic coherent states will evolve to the atomic Schrdinger cat states at some special times in a low-Q acvity. The fluctuations and higher-order fluctuations of angular momentum in these atomic Schrdinger cat states are discussed. According to the uncertainty principle, the squeezing and higher-order squeezing for atomic angular momentum are investigated. It shows that the atomic Schrdinger cat states can be squeezed to second-and sixth-order, but cannot be squeezed to fourth-order. The properties of squeezing of atomic Schrdinger cat states formed by superposing infinite terms of atomic coherent states are identical with those of atomic coherent states.
The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the inequality are state dependent and therefore the intelligent states, which satisfy the equality, do not necessarily give a minimum for the uncertainty product. In this paper, we highlight the difference between intelligent states and minimum uncertainty states by investigating a class of intelligent states which obey the equality in the angular uncertainty relation while having an arbitrarily large uncertainty product. To develop an understanding for the uncertainties of angle and angular momentum for the large-uncertainty intelligent states we compare exact solutions with analytical approximations in two limiting cases.
Abstract SU(1, 1) coherent and squeezed states have been widely studied in optical, hybrid atom–light, and spinor Bose–Einstein condensate experiments. Traditionally, the definition of SU(1, 1) squeezing refers to the uncertainty relationship, which implies that the SU(1, 1) coherent state is already squeezed if it is placed in an appropriate system of coordinates. In this report we investigate the basic concept of SU(1, 1) squeezing and discuss the principle for the generation of squeezed states. We establish a new definition of the squeezing criterion for the SU(1, 1) states. We study the dynamical properties in an atom–molecule system and show that the SU(1, 1) squeezed state can be generated with a nonlinear atomic interaction, which is similar to the one-axis twisting mechanism in spin squeezing. We also discuss the effect of the atomic number on squeezing, and show that the optimal squeezing and optimal squeezing angle exhibit a sudden transition at a fixed atomic number value.