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Journal of Experimental and Theoretical Physics Letters

Quantum deviation of an atom at coherent scattering

Andrew I. Trubilko

Published May 1, 2017• 5 citations
Publisher

Abstract

Effects of quantum deviation of a two-level atom at coherent scattering on an inhomogeneous optical potential created by crossed electromagnetic fields are considered. The region of interaction is formed by a lowfrequency quantized standing wave from a micromaser and a coherent traveling optical wave generated by an optical fiber located inside a cavity. The atom interacts with both fields under the conditions of two-photon two-wave resonance. It is shown that two effects of quantum deviation of translational motion of the atom can be observed. Interaction with the standing wave is caused under these conditions by a harmonic potential the character of scattering of the atom on which depends significantly on the initial conditions of preparation of the atom and quantized mode. The other effect—deviation of the atom by the classical traveling wave—is also completely quantum mechanical under these conditions and is produced by the noncommutative contribution of the kinetic energy operator of the atom and the interaction energy.

DOI
10.1134/s0021364017090144

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Effects of quantum deviation of a two-level atom at coherent scattering on an inhomogeneous optical potential created by crossed electromagnetic fields are considered. The region of interaction is formed by a lowfrequency quantized standing wave from a micromaser and a coherent traveling optical wave generated by an optical fiber located inside a cavity. The atom interacts with both fields under the conditions of two-photon two-wave resonance. It is shown that two effects of quantum deviation of translational motion of the atom can be observed. Interaction with the standing wave is caused under these conditions by a harmonic potential the character of scattering of the atom on which depends significantly on the initial conditions of preparation of the atom and quantized mode. The other effect—deviation of the atom by the classical traveling wave—is also completely quantum mechanical under these conditions and is produced by the noncommutative contribution of the kinetic energy operator of the atom and the interaction energy.
Coherent scattering of a two-level atom in the field of a quantized standing wave of a micromaser is considered under conditions of initial quantum correlation between the atom and the field. Such a correlation can be produced by a broadband parametric source. The interaction leading to scattering of the atom from the nonuniform field occurs in the dispersion limit or in the wing of the absorption line of the atom. Apart from the quantized field, the atom simultaneously interacts with two classical counterpropagating waves with different frequencies, which are acting in the plane perpendicular to the atom’s propagation velocity and to the wavevector of the standing wave. Joint action of the quantized field and two classical waves induces effective two-photon and Raman resonance interaction on the working transition. The effective Hamiltonian of the interaction is derived using the unitary transformation method developed for a moving atom. A strong effect is detected, which makes it possible to distinguish the correlated initial state of the atom and the field in the scattering of atom from the state of independent systems. For all three waves, scattering is not observed when systems with quantum correlation are prepared using a high-intensity parametric source. Conversely, when the atom interacts only with the nonuniform field of the standing wave, scattering is not observed in the case of the initial factorized state.
We consider the interference of atoms caused by the wave nature of their motion. Coherently interfering beams of particles may be obtained by using the diffraction of atoms from separated standing waves resonant with the transition between the ground and excited states of the atoms. Interference arises with and without spatial separation of the diffracted atomic beams. A problem concerning two-quantum perturbation of the wave function of an atom in the ground state by a standing-wave field has been solved. Both amplitude and phase perturbation are taken into account. We show that in spite of the absence of coherence in the incident beam and a rapid decay of the coherence induced by the standing wave for scattered spatially overlapping beams, the interference can be observed for the conditions of an echo. We first consider the phenomenon of an echo under the quantum-mechanical action of light on the translational degrees of freedom. We show that owing to this phenomenon phase memory can be transferred through the ground state over unlimitedly large distances. Owing to the interference of the density harmonics, a periodic structure in the spatial distribution of the atomic density with a period of less than one wavelength of the light is localized at distances of the order of the distance between the fields. The harmonic amplitude is calculated for instantaneous excitation in the case in which the duration of the excitation is comparable with the backward Doppler linewidth in the beam and for scattering under Bragg conditions. In the latter case we show that the effective temperature of the atoms participating in the interference is less than one recoil energy.
We study the diffraction of quantum-degenerate fermionic atoms off of quantized light fields in an optical cavity. We compare the case of a linear cavity with standing-wave modes to that of a ring cavity with two counterpropagating traveling wave modes. It is found that the dynamics of the atoms strongly depends on the quantization procedure for the cavity field. For standing waves, no correlations develop between the cavity field and the atoms. Consequently, standing-wave Fock states yield the same results as a classical standing wave field while coherent states give rise to a collapse and revivals in the scattering of the atoms. In contrast, for traveling waves the scattering results in quantum entanglement of the radiation field and the atoms. This leads to a collapse and revival of the scattering probability even for Fock states. The Pauli exclusion principle manifests itself as an additional dephasing of the scattering probability.
The quasiclassical theory of the Landau-Zener resonance arising because of the atomic motion in the field of a strong standing light wave is developed. A resonance atom in a spatially inhomogeneous field as two effective potentials and two trajectories of motion. The Landau-Zener (LZ) transitions from one trajectory to the other take place in the regions of quasi-intersection of the terms (standing-wave nodes). This effect leads to the appearance of strong quantum fluctuations which break the potential character of the atomic motion and result in the interference of the translational motion states. Therefore a number of the features of the atomic dispersion in the standing-wave field arise (anomalous widths of the forbidden gaps and allowed bands in the under-barrier energetic region and oscillations of the density of states in the over-barrier energetic region). The manifestation of LZ resonance in non-linear spectroscopy and for bipotential scattering of atoms by light is considered.