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Communications in Theoretical Physics

Quantum sensitivity of a photon-added molecular wave packet

Jayashree Das, Suranjana Ghosh, Utpal Roy

Published Dec 2, 2024• 3 citations
Publisher

Abstract

Abstract We study the temporal dynamics of a photon-added SU(2) coherent state, involving vibrational bound states of an iodine molecule. The nonclassicality of Schrödinger cat-like and compass-like photon-added states of this anharmonic potential is explored through the Mandel Q parameter and the negative region in their phase spaces. The Wigner phase space distribution is thoroughly studied for the photon-added molecular state and displayed for cat- and compass-like states. Generation and control of the sub-Planck interference structures become intriguing with photon addition. We ensure that the photon addition helps to improve the quantum sensitivity for a diatomic molecular system by comparing it between photon-added and photon-subtracted states. The detailed study of quantum sensitivity reveals that one can use a photon-added molecular wave packet as a probe to attain sensitivity to displacement that greatly exceeds the standard quantum limit. We also report that the nature of variation of the quantum sensitivity becomes qualitatively commensurate with that of the Wigner-negativity.

DOI
10.1088/1572-9494/ad98fd

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Abstract We study the temporal dynamics of a photon-added SU(2) coherent state, involving vibrational bound states of an iodine molecule. The nonclassicality of Schrödinger cat-like and compass-like photon-added states of this anharmonic potential is explored through the Mandel Q parameter and the negative region in their phase spaces. The Wigner phase space distribution is thoroughly studied for the photon-added molecular state and displayed for cat- and compass-like states. Generation and control of the sub-Planck interference structures become intriguing with photon addition. We ensure that the photon addition helps to improve the quantum sensitivity for a diatomic molecular system by comparing it between photon-added and photon-subtracted states. The detailed study of quantum sensitivity reveals that one can use a photon-added molecular wave packet as a probe to attain sensitivity to displacement that greatly exceeds the standard quantum limit. We also report that the nature of variation of the quantum sensitivity becomes qualitatively commensurate with that of the Wigner-negativity.
Quantum sensitivity is an important issue in the field of quantum metrology where sub-Planck scale structures play a crucial role in the Heisenberg limited measurement. We investigate the mesoscopic superposition structures, particularly for well-known catlike and compasslike states, in the rotating Morse system where sub-Planck scale structures originate in the dynamics of a suitably constructed SU(2) coherent state. A detail study of the sensitivity analysis reveals that rotational coupling in the vibrational wave packet can be used as a probe to enhance the sensitivity limit in a diatomic molecule. The maximum sensitivity limit is identified with the rotational amendment, and a quantitative measure of the angle of rotation for different rotational levels is also given. The correspondence of the numerical result with the angle of rotation is also delineated in phase-space Wigner representation.
The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale $\ensuremath{\hbar}$, which are crucial in determining the sensitivity of these states to phase-space displacements. In the present work we introduce compasslike states that may have connection to the contemporary experiments, which are obtained by either adding photons to or subtracting photons from the superposition of two squeezed-vacuum states. We show that when a significant quantity of photons is added (or subtracted), the Wigner functions of these states are shown to have phase-space structures of an area that is substantially smaller than the Planck scale. In addition, these states exhibit sensitivity to displacements that is much higher than the standard quantum limit. Finally, we show that both the size of the sub-Planck structures and the sensitivity of our states are strongly influenced by the average photon number, with the photon-addition case having a higher average photon number leading to the smaller sub-Planck structures and, consequently, being more sensitive to displacement than the photon-subtraction case. Our states offer unprecedented resolution to the external perturbations, making them suitable for quantum sensing applications.
We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopic-quantum-superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges are specified for observing these features.
In this Letter, we introduce four distinct classes of f-deformed photon-added nonlinear cat state. This would be achieved by recalling a nonlinear coherent states approach, as well as a particular class of Gilmore-Perelomov-type of SU(1,1) coherent state and a class of SU(2) coherent state. We then examine the role of photon addition and nonlinearity functions in the phase space structure and sub-Poissonianity of even, odd, and Yurke-Stoler nonlinear cat states. The effect of photon addition, which results in a π phase shift at the origin of the Wigner function toward negativity, interestingly enhances the nonclassicality by means of the Wigner function and Mandel parameter. Furthermore, owing to photon addition, we can observe a deformation in the Gaussian shape of the Wigner function, which may be found to be potentially useful in quantum noise reduction. Moreover, the deformation function shows a remarkable role in revealing the nonclassical behavior and can increase the depth and the domain of nonclassicality.
The phase space structure and statistics of the photon added cat state are studied in the state’s general form. Photon addition leads to a π phase shift at the origin in the observed phase space interference of the Wigner function, which may serve as an error syndrome detector. The maxima and minima of the sub-Planck tiles in the phase space of the kitten state are interchanged after photon addition, leading to their orthogonality. Interestingly, photon addition to the Yurke–Stoler state characterized by Poissonian statistics leads to a sub-Poissonian distribution, which may find potential use in quantum noise reduction.
We investigate the nonclassical properties of the photon-added-then-subtracted coherent squeezed state (PASCSS) via the sub-Poissonian statistics, the photon-number distribution, and the negativity of the Wigner function. It is found that the PASCSS is a superposition state of D (β) S (ζ)|0〉, D (β) S (ζ)|1〉, and D (β) S (ζ)|2〉. We find that the Mandel Q parameter, the photon-number distribution, and the negative volume of the Wigner function of the PASCSS are all periodic functions of the compound φ − θ/2 with a period π involved with squeezing and displacement parameters.