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arXiv:1307.5472 · Physical Review A

Visualization of superposition states and Raman processes with two-dimensional atomic deflection

Gor A. Abovyan, Gagik P. Djotyan, Gagik Yu. Kryuchkyan

Published Jan 30, 2012• 4 citations
arXivHTMLPDF

Abstract

The deflection of atoms in a $\ensuremath{\Lambda}$-type configuration passing through two crossed standing light waves is proposed for the probing and visualization of atomic superposition states. For this goal, we use both the large-dispersive and Raman-resonant regimes of atom-field interaction, giving rise to position-dependent phase shifts of fields, and perform double simultaneous spatial measurements on an atom. In this way, it is demonstrated that the deflection spatial patterns of atoms in a $\ensuremath{\Lambda}$-configuration passing through modes of standing waves are essentially modified if the atoms are initially prepared in coherent superpositions of their low-level states as well as when the superposition states are created during the process of deflection. There are similar results for the joint momentum distributions of atoms. Furthermore, considering both one-photon- and two-photon-excitation regimes of $\ensuremath{\Lambda}$ atoms, we also illustrate that the two-dimensional patterns of defected atoms qualitatively reflect the efficiency of the Raman processes.

DOI
10.1103/physreva.85.013846

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The deflection of atoms in a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type configuration passing through two crossed standing light waves is proposed for the probing and visualization of atomic superposition states. For this goal, we use both the large-dispersive and Raman-resonant regimes of atom-field interaction, giving rise to position-dependent phase shifts of fields, and perform double simultaneous spatial measurements on an atom. In this way, it is demonstrated that the deflection spatial patterns of atoms in a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-configuration passing through modes of standing waves are essentially modified if the atoms are initially prepared in coherent superpositions of their low-level states as well as when the superposition states are created during the process of deflection. There are similar results for the joint momentum distributions of atoms. Furthermore, considering both one-photon- and two-photon-excitation regimes of \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ atoms, we also illustrate that the two-dimensional patterns of defected atoms qualitatively reflect the efficiency of the Raman processes.
Deflection of an atomic beam passing through two crossed standing light waves is proposed for studies of transition through the Raman resonance in Λ -atomic systems. Considering different regimes of excitation of Λ -atoms by offresonant standing waves, we demonstrate that the deflection patterns, in the plane perpendicular to the direction of the center of atomic mass motion, are essentially different for the cases of one-photon and two-photon excitations. Visualization of the quantum superposition states of low atomic levels on the two-dimensional spatial patterns of atomic deflection is performed.
We investigate deflections, spatial entanglement, and localization of an atomic beam due to its interaction with two modes of a standing electromagnetic field in an optical cavity. It is demonstrated that the deflection properties of an atom passing through two crossed standing light waves are crucially modified when photon-number correlated states of light are used instead of independent waves. Depending on the atom-light interaction scheme, various periodic two-dimensional patterns in a subwavelength regime are reported.
We discuss formation of two-dimensional spatial structures of atoms due to atomic diffraction on two crossed standing electromagnetic fields. This analysis proposed for V-type atomic configuration under dispersive atom-field interactions in quantum regime. Localization of the position of atoms passing through standing light wave is initiated by making a quadrature phase measurement on the light fields. We develop the procedure for strong two-dimensional spatial localization of atomic beam within the optical wavelength. Considering atomic spatial localization in the presence of entanglement of two light beams various two-dimensional patterns for V-type atoms are reported.
We investigate deflection of atomic beams on two co-propagating standing waves excited in a bimodal cavity. The novelty is that the standing waves are in an entangled, photon-number correlated state and interactions with three-level atoms of V-type and Λ-type configurations are considered. The splitting of atomic states, quantum interference effects and spatial atomic localization due to phase measurements is investigated on the framework of both the conditional position distributions of atomic wave packets as well as the Wigner functions for atomic translation variables. It is demonstrated that these quantities for V-type atoms passing the cavity are essentially modified when entangled states of standing waves are used instead of statistically independent waves. The deflection patterns and the Wigner functions are also modified if atoms are initially prepared in a superposition of low-level states. It is best demonstrated for the Λ-type configuration, where transition through the Raman resonance is realized, and proposed for testing superposition states in a new non-spectroscopic manner.
A four-level N-type atom–field system exhibiting the Raman gain process is revisited for precision in position information of a single atom in a two-dimensional (2D) xy -plane. The atom interacts with two standing-wave fields where each standing-wave field is obtained via superposition of two orthogonal standing-wave fields, i.e., along the x and y directions, whereas a probe field is applied to observe the Raman gain process. The role of probe field detuning and phase shifts associated with the standing-wave fields in precision position information of a single atom in a 2D plane is investigated. The suggested scheme leads to enhancement in the spatial resolution in measuring the position of the atom, and a single atom localization peak in the xy -plane having a spatial resolution of the order of λ /10 is noticed.
We study the deflection of an atomic system with a resonant multilevel energy structure in classical and quantized wave light fields. We obtain that the shape of the momentum distribution is very sensitive to the energy level structure, whereas its moments are not. Comparison with a two-level case is made. PACS: 32.80, 33.80, 42.50 During the last two decades a remarkable development in mechanically manipulating atomary particles with resonant laser light has taken place (for a review, see for example [1, 2] and references therein). In addition to trapping and cooling of particles, the deflection of particles by a laser beam offers interesting possibilities, for example, to construct atomic interferometers or beam splitters [2-4]. This problem has been studied extensively both theoretically [2, 5, 8] and experimentally [9-12]. The fact that the momentum distribution caused by the scattering is connected to the quantum statistical properties of the scattered light has been known for some time [13]. Recently, one has also realized that the quantum statistics of the light causing the scattering can be important [14]. At low photon numbers, for example, the initial field state strongly influences the resulting momentum distribution. A related effect is that a standing wave and two counterpropagating traveling plane waves of equal emplitudes cause a different diffraction pattern when fields are treated quantum mechanically [15]. Most previous work on the deflection of particles by light fields used two-level atoms. In this paper we study how resonant multilevel systems scatter when they traverse a plane wave. In practical applications, molecules or highly excited atoms have similar energy structures as the models we use in this work. In most cases, we assume that the Raman-Nath regime is valid, i.e., the kinetic energy of the particle can be neglected. However, the field coupling is assumed to be sufficiently strong to make multiple scattering events possible. Our results show that the final momentum distribution of a multi-level system can strongly deviate from that of a two-level atom. It is of interest that the momentum distributions for resonant ladder systems are in general superpositions of few or several distributions similar to that of a two-level system. We also study the expectation values related to the momentum distribution and show that the spread in momentum is remarkably independent of the system considered. The absorption and reabsorption of photons during the scattering process causes the photon distribution to be smoothed out, and for long times a steady state is reached. The cases we studied did not show a creation of sub-Poissonian light. Our model and assumptions are described and discussed in Sect. 1. Some of the general properties of the momentum distribution are discussed in Sect. 2. In Sect. 3 we derive the generating function of the moments of momentum change in Raman-Nath regime. The main part of the paper is contained in Sects. 4 and 5, in which the momentum distribution itself is discussed for several model systems. In Sect. 4 a semiclassical field is assumed and in Sect. 5 a quantum field is used. The effects of the scattering on the field photon statistics are studied in Sect. 6. The final discussion of the results is given in Sect. 7.