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arXiv:2410.20910 · Physical Review A

Expression for the decoherence rate due to air-molecule scattering in spatial qubits

Martine Schut, Patrick Andriolo, Marko Toroš, Sougato Bose, Anupam Mazumdar

Published Apr 17, 2025• 12 citations
arXivHTMLPDF

Abstract

We provide an expression for the decoherence rate in spatial superpositions due to scattering or collision with air molecules which is independent of the wavelength of the air molecules. This result reproduces the short- and long-wavelength limits known in the literature. We compare the decoherence rate with several existing interpolations in the literature and evaluate the decoherence rate and experimental parameters when creating macroscopic quantum spatial superpositions (i.e., in micron-size spheres). The interpolation regime is relevant in, e.g., matter-wave interferometry, where one might switch between the wavelength limits during the experimental protocol. Finally, we consider the decoherence rate's time dependence while creating and closing the spatial superposition in an interferometer setup.

DOI
10.1103/physreva.111.042211

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We provide an expression for the decoherence rate in spatial superpositions due to scattering or collision with air molecules which is independent of the wavelength of the air molecules. This result reproduces the short- and long-wavelength limits known in the literature. We compare the decoherence rate with several existing interpolations in the literature and evaluate the decoherence rate and experimental parameters when creating macroscopic quantum spatial superpositions (i.e., in micron-size spheres). The interpolation regime is relevant in, e.g., matter-wave interferometry, where one might switch between the wavelength limits during the experimental protocol. Finally, we consider the decoherence rate's time dependence while creating and closing the spatial superposition in an interferometer setup.
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Molecular qubits held in conservative optical traps may lose coherence when they scatter photons from the trapping lasers. The rate for this process has two parts, one equal to the mean Raman scattering rate of the two qubit states, and the other proportional to the square of the difference in their Rayleigh scattering amplitudes. This paper calculates the decoherence rate, expressing results in terms of the vector and tensor parts of the molecular polarizability, α1α_1α1​ and α2α_2α2​. While the decoherence rate is generally much larger for molecules than for atoms, it is suppressed at wavelengths where α1α_1α1​ and α2α_2α2​ are both small. The wavelengths where this occurs are identified for CaF molecules.
We consider environment induced decoherence of quantum superpositions to mixtures in the limit in which that process is much faster than any competing one generated by the Hamiltonian Hsys{H}_{\mathrm{sys}}Hsys​ of the isolated system. This interaction-dominated decoherence limit is of importance for the emergence of classical behavior in the macroscopic domain, since it will always be the relevant regime for large enough separations between the superposed wave packets. The usual golden-rule treatment then does not apply, but we can employ a short-time expansion for the free motion while keeping the interaction Hint{H}_{\mathrm{int}}Hint​ in full. We thus reveal decoherence as a universal short-time phenomenon largely independent of the character of the system as well as the bath and of the basis the superimposed states are taken from. Simple analytical expressions for the decoherence time scales are obtained in the limit in which decoherence is even faster than any time scale emerging from the reservoir Hamiltonian Hres.{H}_{\mathrm{res}}.Hres​.
It is known that a macroscopic quantum superposition (MQS), when it is exposed to an environment, decoheres at a rate scaling with the separation of its component states in phase space. This is more or less consistent with the well-known proposition that a more macroscopic quantum state is reduced more quickly to a classical state in general. Effects of initial mixedness, however, on the subsequent decoherence of MQSs have been less known. We study the evolution of a highly mixed MQS interacting with an environment and compare it with that of a pure MQS having the same size as the central distance between its component states. Although the decoherence develops more rapidly for the mixed MQS in short times, its rate can be significantly suppressed after a certain time and becomes smaller than the decoherence rate of its corresponding pure MQS. In an optics experiment to generate a MQS, our result has the practical implication that nonclassicality of a MQS can still be observable in moderate times, even though a large amount of noise is added to the initial state.
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We analyze collisional decoherence of atoms or molecules prepared in a coherent superposition of nondegenerate internal states at ultralow temperatures and placed in an ultracold buffer gas. Our analysis is applicable for an arbitrary bath-particle to tracer-particle mass ratio. Both elastic and inelastic collisions contribute to decoherence. We obtain an expression relating the observable decoherence rate to pairwise scattering properties, specifically the scattering lengths and low-temperature scattering amplitudes. We consider the dependence on the bath-particle to tracer-particle mass ratio for the case of light bath and heavy tracer particles. The expressions obtained may be useful in low-temperature applications where accurate estimates of decoherence rates are needed. The results suggest a method for determining the scattering lengths of atoms and molecules in different internal states by measuring decoherence-induced damping of coherent oscillations.