It is shown that the correlation between momenta of two atoms cooperatively deflected from an off-resonant quantized standing-wave light field arises due to the fluctuations of the field in the photon number. The normalized cross-correlation functions are calculated. The Cauchy-Schwartz-type inequalities for the joint distribution of the atomic transverse momenta are derived. The simultaneous deflection of the atoms allows one to determine the mean photon number and the width of the photon distribution and to produce predetermined correlations between atomic de Broglie waves.
It is shown that the correlation between momenta of two atoms cooperatively deflected from an off-resonant quantized standing-wave light field arises due to the fluctuations of the field in the photon number. The normalized cross-correlation functions are calculated. The Cauchy-Schwartz-type inequalities for the joint distribution of the atomic transverse momenta are derived. The simultaneous deflection of the atoms allows one to determine the mean photon number and the width of the photon distribution and to produce predetermined correlations between atomic de Broglie waves.
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 investigate to which extent the quantum nature of light modifies laser-induced atomic beam deflection in a plane standing wave. Our model considers a single two-level atom interacting with a single quantized standing wave mode of the electromagnetic field. We neglect spontaneous emission into other field modes, an approximation valid for short enough times. We find that there is an essential qualitative difference between the cases of a coherent field and a thermal field. For a coherent field, the atomic momentum distribution after interaction has two symmetric peaks on the wings and resembles the semiclassical result of Arimondo et al. [Phys. Rev. A 24, 898 (1981)]. For a thermal field, this distribution has its maximum at p = 0. It is characterized by a constant contribution at p = 0, some sharp interference features, and near-Gaussian wings. The only feature common to both cases is that in the Raman-Nath regime of scattering, the range on transverse momenta grows linearly with time at a rate proportional to 〈 n 〉 , where 〈 n 〉 is the mean number of photons in the field.
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.
We consider the deflection of a resonant two-level atom by a quantized electromagnetic field using the Jaynes-Cummings Hamiltonian. We show that a joint measurement of the atomic momentum and an appropriate field variable allows us to reconstruct the original photon statistics even for this demolition Hamiltonian. We demonstrate that the momentum distribution of atoms scattered at the nodes of the standing wave also follows the original photon statistics of the field. In this sense a recent experiment on the optical Stern-Gerlach effect [T. Sleator et al., Phys. Rev. Lett. 68, 1996 (1992)] measures the intensity fluctuations of the standing wave.
We report on criteria to detect entanglement between the light modes of two crossed optical cavities by analyzing the transverse deflection patterns of an atomic beam. The photon exchange between the modes and atoms occurs around the overlapping nodes of associated standing waves, which generates the two-dimensional (2D) version of the Optical Stern–Gerlach (OSG) effect. In this optical cross-cavity setup, we show that the discrete signatures of the field states, left in the momentum distribution of the deflected atoms, may reveal entanglement for a certain class of two-mode states. For a single photon, we present the possibility of quantifying entanglement by the rotation of the momentum distribution. For a larger number of photons, we demonstrate that quantum interference precludes the population of specific momentum states revealing maximum entanglement between the light modes.
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.