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Physical Review A

Polarization-sensitive coherent control of atomic collisions with nonclassical light

Dmitriy V. Kupriyanov, Igor M. Sokolov, A. V. Slavgorodskii

Published Jun 18, 2002• 1 citation
Publisher

Abstract

In this paper we consider the mechanism of coherent control of atomic collisions by two-photon excitation of colliding atoms with nonclassical light characterized by polarization entanglement. Such modification of the well-known optical-collision method is proposed as a possible spectroscopic application of nonclassical light for study of collisional dynamics. We show that quantum correlations allow one to have a deeper control of the internal dynamics of atomic collision than do the principles of classical statistics. Our qualitative discussion is supported by numerical calculations made for ${}^{1}{S}^{1}{P}^{1}S$ optical transition of Mg perturbed by collisions with rare-gas atom.

DOI
10.1103/physreva.65.063412

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•Jan 1, 2004•0 citations
In this paper we consider the mechanism of coherent control of atomic collisions by two-photon excitation of colliding atoms with nonclassical light characterized by polarization entanglement. Such modification of the well-known optical-collision method is proposed as a possible spectroscopic application of nonclassical light for study of collisional dynamics. We show that quantum correlations allow one to have a deeper control of the internal dynamics of atomic collision than do the principles of classical statistics. Our qualitative discussion is supported by numerical calculations made for 1S1P1S{}^{1}{S}^{1}{P}^{1}S1S1P1S optical transition of Mg perturbed by collisions with rare-gas atom.
We describe a new method of coherent optical control of internal dynamics of atomic collisions by means of two correlated light beams having entangled polarizations. We show that, if excitation of a colliding pair of atoms is by two photons having entangled polarizations, it is possible to redirect the output fragments of the collision into certain channels with a selected type of internal transition symmetry. The transition symmetry is defined in the body-fixed coordinate frame which has random and originally unknown orientation in space.
We have analyzed by perturbation theory technique two-photon polarization-dependent fractional optical collisions. In its general form the cross section of the collision is expressed as the overlap integral of its spectral profile with the spectrum of the second order correlation function of the electromagnetic field. Based on the semiclassical expansion of radial wave functions and of a retarded Green function we have expressed the spectral profile of the cross section in terms of well understood semiclassical characteristics of the process such as the rotational transformations of the transition dipole moments and the transition amplitudes describing the adiabatic or nonadiabatic dynamics of the electronic subsystem along classical trajectories. As a practical example, we have calculated the Mg-He ${(3s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}3p{}^{1}{P}_{1}\ensuremath{\rightarrow}5s{}^{1}{S}_{0},4d{}^{1}{D}_{2})$ fractional optical collision cross section. The partial wave analysis for excitation up to the 5s1S05s{}^{1}{S}_{0}5s1S0​ state has shown the nonvalidity of quasistatic approximation based on successive single-photon transitions for some frequency detunings. For example, for the positive detuning from two-photon atomic resonance we have obtained the dominant contribution coming from the direct two-photon Franck-Condon transitions. Such a contribution gives the magnitude of the polarization ratio, characterizing the dependence of the cross section on mutual laser polarizations at the first and at the second steps of the photoexcitation, different than for successive single-photon Franck-Condon transitions. In the more complicated case of excitation up to the 4d1D24d{}^{1}{D}_{2}4d1D2​ state of magnesium the role of the interference between different photoexcitation channels becomes important. The polarization ratio has a stable value close to 17\frac{1}{7}71​ in a broad spectral range in the blue wing of the second frequency detuning. There is a strong dependence of the polarization ratio in the red wing of the second detuning. Such spectral behavior can be explained by the partial selection in the red wing of the atomic resonance line, perturbed by the collisions of those Zeeman transitions in which contributions in the polarization ratio have different orders and different signs.
The subtle and fundamental issue of indistinguishability and interference between independent pathways to the same target state is examined in the context of coherent control of atomic and molecular processes, with emphasis placed on possible "which-way" information due to quantum entanglement established in the quantum dynamics. Because quantum interference between independent pathways to the same target state occurs only when the independent pathways are indistinguishable, it is first shown that creating useful coherence between nondegenerate states of a molecule for subsequent quantum interference manipulation cannot be achieved by collisions between atoms or molecules that are prepared in momentum and energy eigenstates. Coherence can, however, be transferred from light fields to atoms or molecules. Using a particular coherent control scenario, it is shown that this coherence transfer and the subsequent coherent phase control can be readily realized by the most classical states of light, i.e., coherent states of light. It is further demonstrated that quantum states of light may suppress the extent of phase-sensitive coherent control by leaking out some which-way information while "incoherent interference control" scenarios proposed in the literature have automatically ensured the indistinguishability of multiple excitation pathways. The possibility of quantum coherence in photodissociation product states is also understood in terms of the disentanglement between photodissociation fragments. Results offer deeper insights into quantum coherence generation in atomic and molecular processes.
We have developed a full three-dimensional quantum scattering approach to optical suppression of ultracold-collision rates. These calculations are carried out assuming colliding atoms without fine or hyperfine structure, which have a $^{1}\ensuremath{\rightarrow}^{1}$P transition. The three-dimensional model predicts that the optical suppression of ultracold-collision rates saturates with light intensity much more slowly than predicted by two-level curve-crossing models. Circularly polarized light is significantly more effective for optical suppression, and causes less increase in atomic kinetic energy due to excited-state production than linearly polarized light. The suppressor optical field can also cause orders of magnitude increases in ground-state elastic-scattering rates.
We propose an extension of coherent control using laser-synthesized free-electron matter waves. In contrast to coherent control schemes exploiting optical coherences to steer the dynamics of matter waves, we analyze the opposite and investigate the control of quantum light emission driven by laser-sculpted coherent free-electron matter waves. We apply this concept to the control of entangled photon-pair emission in electron-atom collisions, in which the incident electron wave packet, colliding with a target atom BBB, is engineered by interferometric resonantly enhanced multiphoton ionization of a parent atom AAA. Each ionization pathway leads to electron wave packets that coherently interfere during temporal evolution in the continuum. Their mutual coherence can be controlled by adjusting the relative phases or time delays of the frequency components of the ionizing field contributing to the interfering pathways. We report coherent control of entangled photon-pair generation in radiative photocascade emission upon decay of the target atom after inelastic excitation triggered by the collision with the synthesized electron wave packet.
This thesis considers two types of applications of quantum feedback control; feedback creation of nonclassical states of light, and controlling nonclassical properties of an ensemble of atoms. An electro-optical feedback loop will create an in-loop field with nonclassical photon statistics similar to squeezed light, resulting in fluorescence line-narrowing of a two-level atom coupled to such light. We extend this theory to study a three-level atom coupled to broadband squashed light, and confirm the two-level atom line-narrowing using a more realistic non-Markovian description of the feedback loop. The second type of application utilizes continuous QND measurement of atomic ensembles. If we measure the collective spin, then the system experiences conditional spin squeezing dependent on the measurement results. We show that feedback based on these results can continuously drive the system into the same conditioned state, resulting in deterministically reproducible spin squeezing. If we measure the atom number fluctuations of a BEC, then, due to the nonlinearity of atomic self interactions, this is also information about phase fluctuations. We show that feedback based on this information can greatly reduce the collisional broadening of the linewidth of an atom laser out-coupled from the condensate.