Rotational properties of quantum states

A Galindo, R. Tarrach

Gang Ren, Jian-ming Du, Hai-jun Yu

In this paper, we construct and investigate the nonclassical properties of the squeezing and rotating coherent state (SRCS) via a generalized squeezed operator by introducing a novel parameter r. In a particular case r = 0, SRCS reduces to the normal squeezed coherent state (SCS). The influence of r is studied in terms of squeezing and quantum statistical properties. Our results show that in the SCS not only is squeezing enhanced but also is rotated by the parameter r. Our discussion about the fidelity between SRCS and SCS shows that the fidelity values decrease with increasing parameter r. The experimental scheme for producing SRCS is also given via a self-Kerr medium and non-degenerate parametric amplifier.

Stephen Mark Barnett, David Thomas Pegg

The formulation of the quantum description of the rotation angle of the plane rotator has been beset by many of the long-standing problems associated with harmonic-oscillator phases. We apply methods recently developed for oscillator phases to the problem of describing a rotation angle by a Hermitian operator. These methods involve use of a finite, but arbitrarily large, state space of dimension 2l+1 that is used to calculate physically measurable quantum properties, such as expectation values, as a function l. Physical results are then recovered in the limit as l tends to infinity. This approach removes the indeterminacies caused by working directly with an infinite-dimensional state space. Our results show that the classical rotation angle observable does have a corresponding Hermitian operator with well-determined and reasonable properties. The existence of this operator provides deeper insight into the quantum-mechanical nature of rotating systems.

Otto C. W. Kong

Takaharu Otsuka

Christopher J. Stopera, Jorge A. Morales

Following our preceding work on spherical and linear rotors [C. Stopera and J. A. Morales, J. Chem. Phys. 152, 134112 (2020)], we reformulate an earlier rotational coherent state (CS) set to obtain a temporally stable (TS) CS set for symmetric rotors. Being TS, the new CSs remain within its own set during dynamics by evolving exclusively through their parameters. The TS CS set is now appropriate to reconstruct quantum rotational properties from classical-mechanics simulations of chemical reactions. Following literature precedents, we enforce temporal stability by incorporating action-angle-related phase factors into two parameters of the original CS set. Proofs and final expressions of the symmetric-rotor CS turn out more intricate than those of its spherical-rotor counterpart. We demonstrate and examine the key properties of the new CS set: continuity, resolution of unity, temporal stability, action identity, minimum uncertainty relationships, and quasi-classical behavior. Regarding the last property, we demonstrate that the body-fixed z-component of the CS angular momentum average evolves exactly as its classical counterpart, and that the x- and y-components display an astonishing analogy with their classical counterparts in terms of functional form, precession angular velocities, amplitudes, and phases. We elucidate some of these properties via computer simulations of a rotating benzene molecule represented with the CS set. We discuss the utilization of this CS set to reconstruct quantum rotational properties of symmetric-rotor molecules from classical-mechanics simulations. The new CS set is appropriate to establish quantum-classical connections for rotational properties in chemical dynamics, statistical mechanics, spectroscopy, nuclear physics, and quantum computing.