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Physical Review A

Theory of coherent optical transients with quantized atomic motion

P. R. Berman, Huy Minh Nguyen, A. Kuzmich

Published Jan 22, 2019• 1 citation
Publisher

Abstract

A theory of coherent transients is developed in which a sequence of optical pulses is incident on a sample of trapped atoms and gives rise to phase-matched emission from the sample. The trapping potential for the atoms can be state dependent, necessitating a quantum treatment of the center-of-mass motion. A source-field approach is followed, modified to account for the quantized motion of the atoms. The theory is illustrated with two examples, one involving the creation of ground-Rydberg level coherence in an optical lattice and the second Raman coherence between two ground-state sublevels of atoms in a dipole trap. For state-independent potentials, a comparison is made with a theory in which the center-of-mass motion is treated classically.

DOI
10.1103/physreva.99.013427

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A theory of coherent transients is developed in which a sequence of optical pulses is incident on a sample of trapped atoms and gives rise to phase-matched emission from the sample. The trapping potential for the atoms can be state dependent, necessitating a quantum treatment of the center-of-mass motion. A source-field approach is followed, modified to account for the quantized motion of the atoms. The theory is illustrated with two examples, one involving the creation of ground-Rydberg level coherence in an optical lattice and the second Raman coherence between two ground-state sublevels of atoms in a dipole trap. For state-independent potentials, a comparison is made with a theory in which the center-of-mass motion is treated classically.
We present a many-body theory of a driven and damped trapped gas of interacting bosons, and demonstrate that one of the trap levels can become coherently populated, thereby leading to a coherent atomic-beam generator, or ``laser for atoms.'' The specific system we consider consists of a sample of bosonic atoms interacting via the near-resonant dipole-dipole interaction. The transverse center-of-mass motion of the atoms is confined by a two-dimensional potential well created by an array of cooling laser beams, while their longitudinal motion is quantized by a Fabry-P\'erot for atoms. Under appropriate conditions, the dipole-dipole selection rules lead to the simplification that only two quantized levels of atomic motion need to be considered explicitly, the other levels being treated as reservoirs. One of the two levels is the ``pump level,'' while the other is the one where atomic coherence builds up (the ``lasing'' level). The master equation describing the dynamics of these levels can be solved numerically, and its solution exhibits a ``threshold behavior'' with a transition from super-Poissonian to Poissonian atom statistics in the ``lasing mode.'' \textcopyright{} 1996 The American Physical Society.
We present a new method of spectroscopy for atoms cooled and trapped in an optical lattice. This method which makes use of coherent transients permit to improve the signal to noise ratio by more than one order of magnitude by comparison with the previous optical detection methods such as probe transmission or atomic fluorescence [1]. We apply this method to the spectroscopy of cesium atoms first in a four-beam lattice [2] and second in a quasi-periodic structure obtained by adding supplementary incident beams. These structures are strongly connected with the field of quasi-crystals [3] which is very active in solid-state physics. Because of the topological invariance of the optical potential, the same spectra are obtained whatever the phases of the incident beams. Additional information about distribution of atoms among the potential wells can be deduced from the analysis of the coherent transients.
Optical response of an active medium can substantially be modified when coherent superpositions of states are excited, that is, when systems display quantum coherence and interference. This has led to fascinating applications in atomic and molecular systems. Examples include coherent population trapping, lasing without inversion, electromagnetically induced transparency, cooperative spontaneous emission, and quantum entanglement. \n \nWe study quantum coherence effects in several quantum optical systems and find interesting applications. We show that quantum coherence can lead to transient Raman lasing and lasing without inversion in short wavelength spectral regions--extreme ultraviolet and x-ray--without the requirement of incoherent pumping. For example, we demonstrate transient Raman lasing at 58.4 nm in Helium atom and transient lasing without inversion at 6.1 nm in Helium-like Boron (triply-ionized Boron). We also investigate dynamical properties of a collective superradiant state prepared by absorption of a single photon when the size of the sample is larger than the radiation wavelength. We show that for large number of atoms such a state, to a good approximation, decays exponentially with a rate proportional to the number of atoms. We also find that the collective frequency shift resulting from repeated emission and reabsorption of short-lived virtual photons is proportional to the number of species in the sample. Furthermore, we examine how a position-dependent excitation phase affects the evolution of entanglement between two dipole-coupled qubits. It turns out that the coherence induced by position-dependent excitation phase slows down the otherwise fast decay of the two-qubit entanglement. We also show that it is possible to entangle two spatially separated and uncoupled qubits via interaction with correlated photons in a cavity quantum electrodynamics setup. Finally, we analyze how quantum coherence can be used to generate continuous-variable entanglement in quantum-beat lasers in steady state and propose possible implementation in quantum lithography.
Master equations are derived for the time evolution of density-matrix elements characterizing atoms interacting with classical radiation fields that drive transitions between electronic-state manifolds of levels. The atomic center-of-mass motion is quantized and recoil accompanying absorption, stimulated emission, and spontaneous emission is included. An adiabatic elimination of the optical coherences is used to obtain quantum rate equations for ground- and excited-state density-matrix elements. Subsequent adiabatic elimination of excited-state density-matrix elements results in rate equations for the slow evolution of ground-state density-matrix elements. It is shown that recoil during spontaneous emission mixes spatial and internal atomic degrees of freedom. \textcopyright{} 1996 The American Physical Society.
A semiclassical theory of chaotic atomic transport in a one-dimensional nondissipative optical lattice, when the standing-wave field and center-of-mass motion are treated classically, is developed. Using the basic equations of motion for the Bloch and translational atomic variables, we derive a stochastic map for the synchronized component of the atomic dipole moment that determines the center-of-mass motion. We find the analytical relations between the atomic and lattice parameters under which atoms typically alternate between flying through the lattice and being trapped in the wells of the optical potential. We use the stochastic map to derive formulas for the probability density functions (PDFs) for the flight and trapping events. Statistical properties of chaotic atomic transport strongly depend on the relations between the atomic and lattice parameters. We show that there is a good quantitative agreement between the analytical PDFs and those computed with the stochastic map and the basic equations of motion for different ranges of the parameters. Typical flight and trapping PDFs are shown to be broad distributions with power law segments with the slope $\ensuremath{-}1.5$ and exponential ``tails.'' The lengths of the power law and exponential segments of the PDFs depend on the values of the parameters. We find analytical conditions under which deterministic atomic transport has fractal properties and explain a hierarchical structure of the dynamical fractals.