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Physical Review A

Quantum control of multilevel atoms with rotational degeneracy using short laser pulses

G. Demeter

Published Oct 5, 2010• 2 citations
Publisher

Abstract

We study the quantum control of multilevel atoms with rotationally degenerate levels using short laser pulses. Various control schemes are considered, ones using $\ensuremath{\pi}$ pulses, frequency-chirped pulses, two consecutive pulses, or two pulses that overlap each other partially. We study the possibilities of controlling the quantum state of an ensemble of atoms distributed randomly over one or more rotationally degenerate levels initially. For the sake of concreteness we use the hyperfine level scheme of the $^{85}\mathrm{Rb}$ $D$ line, but the results can easily be generalized for any of the alkali-metal atoms used in cooling and trapping experiments. We find that even though a number of difficulties arise, such as unequal coupling constants between rotational sublevels or dephasing between different hyperfine levels during the interaction, control schemes using simple or multiphoton adiabatic passage can be used to control the internal states of the atoms effectively as well as the center-of-mass motion. Furthermore, it is shown that in some cases it is possible to exploit the inequality of the coupling constants to entangle the rotational substates with specific distinct translational quantum states and hence separate these substates in momentum space.

DOI
10.1103/physreva.82.043404

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We study the quantum control of multilevel atoms with rotationally degenerate levels using short laser pulses. Various control schemes are considered, ones using \ensuremathπ\ensuremath{\pi}\ensuremathπ pulses, frequency-chirped pulses, two consecutive pulses, or two pulses that overlap each other partially. We study the possibilities of controlling the quantum state of an ensemble of atoms distributed randomly over one or more rotationally degenerate levels initially. For the sake of concreteness we use the hyperfine level scheme of the 85Rb^{85}\mathrm{Rb}85Rb DDD line, but the results can easily be generalized for any of the alkali-metal atoms used in cooling and trapping experiments. We find that even though a number of difficulties arise, such as unequal coupling constants between rotational sublevels or dephasing between different hyperfine levels during the interaction, control schemes using simple or multiphoton adiabatic passage can be used to control the internal states of the atoms effectively as well as the center-of-mass motion. Furthermore, it is shown that in some cases it is possible to exploit the inequality of the coupling constants to entangle the rotational substates with specific distinct translational quantum states and hence separate these substates in momentum space.
We study the force exerted on two-level atoms by short, counterpropagating laser pulses. When the counterpropagating pulses overlap each other partially, multiphoton adiabatic processes are possible in several configurations, which amplify the force exerted on the atoms. We investigate the practical usefulness of such multiphoton adiabatic transitions for the manipulation of the atoms' mechanical state. In particular, we compare the efficiency of a pair of constant frequency, oppositely detuned laser pulses and that of a pair of frequency-chirped pulses. We also consider the case of prolonged exposure to a sequence of laser pulses for a duration that is comparable to or much larger than the spontaneous lifetime of the atoms. We use numerical methods to calculate the reduction of the force and the heating of the atomic ensemble when spontaneous emission cannot be neglected during the interaction. In addition, we derive simple approximate formulas for the force and the heating, and compare them to the numerical results.
Quantum entanglement is a crucial resource in many quantum information and quantum communication tasks. In this work, we present a quantum control methodology to create entangled states of two basic classes, the W and the GHZ. A chain of 87 Rb atoms in an optical lattice is considered interacting with laser pulses to induce two-photon excitations to Rydberg states having a specific magnetic quantum number. Generation of the W and GHZ three-atomic states is demonstrated via the mechanism of the two-photon adiabatic passage in collective states implying the overlapping chirped pulses and the interplay of the Rabi frequency with the one-photon detuning and the strength of the Rydberg-Rydberg interactions. Copyright © VBRI Press.
Entangled states are crucial for modern quantum enabled technology which makes their creation key for future developments. In this paper, a robust quantum control methodology is presented to create entangled states of two typical classes, the W and the Greenberger-Horne-Zeilinger (GHZ). It was developed from the analysis of a chain of alkali atoms $^{87}Rb $ interaction with laser pulses, which lead to the two-photon transitions from the ground to the Rydberg states with a predetermined magnetic quantum number. The methodology is based on the mechanism of two-photon adiabatic passage using overlapping chirped pulses and interplaying the Rabi frequency, the one-photon detuning, and the strength of the Rydberg-Rydberg interactions.
We investigate the behavior of 85Rb{}^{85}\mathrm{Rb}85Rb atoms in the field of a sequence of frequency-chirped short laser pulses. The analysis is based on a numerical solution of equations for the probability amplitudes of the hyperfine levels of the ${5S}_{1/2}{\ensuremath{-}5P}_{3/2}$ transition in the 85Rb{}^{85}\mathrm{Rb}85Rb atom and the dressed-states analysis. We analyze different regimes of interaction, including relatively short laser pulses (when the width of the pulse envelope spectrum is of the order of or exceeds the frequency interval between the hyperfine levels resulting in effective mixing of them) and relatively long ones (when the ground hyperfine levels are resolved but the excited ones are not resolved). In the latter case dependence of the population transfer efficiency on the initial coherence of the ground states is analyzed. The case of long laser pulses when all working hyperfine levels are resolved is also discussed using numerical simulations and a dressed-states analysis. We show that in all regimes considered, the interaction of a frequency-chirped laser pulse with the multilevel 85Rb{}^{85}\mathrm{Rb}85Rb system is similar to the interaction with an effective two-level atom at sufficiently large peak intensities of the pulses. It allows us to perform efficient excitation of the multilevel atom by transferring populations of two hyperfine ground states to the excited ones and back to the ground states using a pair of frequency-chirped laser pulses. We propose to utilize this scheme of population transfer for the coherent manipulation of a beam of 85Rb{}^{85}\mathrm{Rb}85Rb atoms using sequences of counterpropagating frequency-chirped short laser pulses.
We propose and analyze a scheme for creation of coherent superposition of meta-stable states in a multilevel atom. The scheme is based on interaction of a frequency modulated (chirped) laser pulse and a pulse of a constant carrier frequency with the atom having two meta-stable (ground) states and multiple excited states. The negligible excitation of the atoms is a priority in the proposed scheme to eliminate the de-coherence processes caused by the decay of the excited states. The scheme is applied to create coherent superposition of magnetic sublevels of ground states of the 87Rb atom taking into account all allowed electric-dipole transitions between magnetic sublevels of the 5 2S1/2 - 52P3/2 transition (D2 line). In addition to the theoretical analysis we consider possible experimental realizations of the proposed coherence creation scheme and discuss their feasibilities and constraints. We concentrate on a detection of the superposition state in the Faraday-rotation experiment. Such detection reduces technical laser noise background and offers high sensitivity of the coherence detection. Moreover, it allows extra control of the atomic sample and the interaction dynamics by external magnetic field.
Entangled states are crucial for modern quantum enabled technology which makes their creation key for future developments. In this paper, a robust quantum control methodology is presented to create entangled states of two typical classes, the W and the Greenberger-Horne-Zeilinger (GHZ). It was developed from the analysis of a chain of alkali atoms [Formula: see text] interaction with laser pulses, which leads to the two-photon transitions from the ground to the Rydberg states with a predetermined magnetic quantum number. The methodology is based on the mechanism of the two-photon excitation, adiabatic for the GHZ and non-adiabatic for the W state, induced by the overlapping chirped pulses and governed by the Rabi frequency, the one-photon detuning, and the strength of the Rydberg-Rydberg interactions.