Conditional Disappearance of Gravitational Dephasing in Multilevel Atomic Systems
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Journal of Applied Spectroscopy, Vol. 87, No. 4, September, 2020 (Russian Original Vol. 87, No. 4, July–August, 2020)
CONDITIONAL DISAPPEARANCE OF GRAVITATIONAL DEPHASING IN MULTILEVEL ATOMIC SYSTEMS V. P. Stefanov
UDC 530.145;535.14
The state of an ensemble of three-level atoms after absorption of a single photon and subsequent spontaneous decays in the presence of a weak gravitational field is shown to lose the phase matching of the emitted photons with the wave vector of the absorbed photon, similar to the case of an ensemble of two-level atoms. However, the spatial distribution of a second photon coincides with the result for a space without a gravitational field when averaging over the state of one of the emitted photons. Keywords: spontaneous emission, timed Dicke states, gravitational dephasing, atomic ensembles, multilevel atomic system. Introduction. The technical capabilities for studying optical quantum systems have now been developed to such a high level that even subtle changes due to gravitational interactions can be experimentally measured [1, 2]. Many properties of quantum-optics systems, including quantum interference, can now be refined. A gravitational field was found to have a destructive effect on quantum interference. Quantum gravitational fluctuations with standard linear quantization of a gravitational field lead unavoidably to decoherence [3–5]. Decoherence also appears in interactions of quantum particles with a classical gravitational field (so-called decoherence due to time dilation [6–10]). Studies of the effect of a gravitational field on entangled states exhibiting decoherence properties are noteworthy [11, 12]. Aspects of the quantum world can be refined and the nature of the gravitational interaction can be directly studied by considering the gravitational effect on quantum-optics systems [13, 14]. Therefore, many efforts were dedicated to the interaction of gravitational and electromagnetic fields in various quantum systems [15, 16]. The present work investigated the effect of a classical gravitational field on the timed Dicke state in an ensemble of three-level atoms with a cascade level configuration. If a single photon with wave vector k0 acts on a prepared state of unexcited and randomly positioned atoms, then the resulting superposition state contains a phase multiple depending on the position of an atom if the photon is absorbed. This state is called a timed Dicke state [17]. The wave vector of an emitted photon k with spontaneous decay for two-level atoms should match the wave vector of the absorbed photon k = k0. The sum of wave vectors of emitted and absorbed photons for three-level atoms with a cascade energy-level configuration is k + k′ = k0. This situation arises after averaging over all possible emitter positions because the phase is linearly dependent on the atomic positions. The dependence on atomic positions changes if the effect of a gravitational field is considered. The superposition state is dephased, even in a weak field, as shown before [18]. This allows a
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