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Physical Review A

Coherent transition between adjacent Zeeman sublevels in an alkali-metal atom without populating other sublevels

Huidong Kim, Hyok Sang Han, Jinsin Park, Young-Sik Kim, D. Cho

Published Dec 16, 2013• 1 citation
Publisher

Abstract

We report on a spectroscopic method to coherently drive a selective transition between two levels in a ladder system of equally spaced energy levels. A typical example of such a ladder system is a set of Zeeman sublevels in the same hyperfine level of a ground-state alkali-metal atom. The scheme is based on a stimulated Raman transition with a Zeeman sublevel belonging to the other hyperfine level as an intermediate state. We identify quantization conditions on a single-photon detuning and Rabi frequencies for either a $\ensuremath{\pi}/2$ or a $\ensuremath{\pi}$ transition between adjacent Zeeman sublevels without populating the intermediate state. We experimentally demonstrate the scheme using lithium atoms in an optical trap. Application of the scheme includes manipulating a pair of Zeeman sublevels as a quantum bit or probing Zeeman coherence established by coherent population trapping.

DOI
10.1103/physreva.88.061404

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We report on a spectroscopic method to coherently drive a selective transition between two levels in a ladder system of equally spaced energy levels. A typical example of such a ladder system is a set of Zeeman sublevels in the same hyperfine level of a ground-state alkali-metal atom. The scheme is based on a stimulated Raman transition with a Zeeman sublevel belonging to the other hyperfine level as an intermediate state. We identify quantization conditions on a single-photon detuning and Rabi frequencies for either a \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2 or a \ensuremathπ\ensuremath{\pi}\ensuremathπ transition between adjacent Zeeman sublevels without populating the intermediate state. We experimentally demonstrate the scheme using lithium atoms in an optical trap. Application of the scheme includes manipulating a pair of Zeeman sublevels as a quantum bit or probing Zeeman coherence established by coherent population trapping.
We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the nPnPnP manifold via an optical transition on one of the spectroscopic DDD lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.
We propose a scheme to achieve one-dimensional velocity-selective coherent population trapping in a five-level system under two-frequency laser excitation. It may be applied to either D line of alkali-metal atoms. The trapped state is a time-dependent superposition of three sublevels from two different hyperfine ground states. Stable trapping may be produced by correctly detuning the laser beams to compensate for different hyperfine and kinetic energies of these ground states. We present numerical results for a five-level model, as well as for the complete level systems appropriate for alkali-metal atoms.
Coherent-population-trapping resonance in vapor cell is a quantum interference effect that appears in the two-photon transitions between the ground-state hyperfine levels of alkali-metal atoms and is often utilized in miniature and centimeter-scale clock devices. To quantitatively understand and predict the performance of this phenomenon, it is necessary to consider the transitions and relaxations between all hyperfine Zeeman sublevels involved in the different excitation processes of the atom. In this paper, we constructed a computational multilevel atomic model of the Liouville density-matrix equation for 32 Zeeman sublevels involved in the D1{D}_{1}D1​ line of 133Cs^{133}\mathrm{Cs}133Cs irradiated by two frequencies with circularly polarized components and then simulated the amplitude and shape of the resonance spectrum of the transmitted light through centimeter-scale Cs-vapor cells. We show that the numerical solutions of the equation and analytical investigations adequately explain a variety of the characteristics observed in the experiment.
Quantum computers are typically composed of an array of two-level systems, or qubits, encoded in some information carrier, such as an electron, photon, or quantized circuit. The size of this array is restricted by finite access to resources like laser power, cooling capacity, and control lines for trapping and manipulation. Under these constraints, the system's processing power can be increased by using more energy levels per information carrier, but common techniques for qubit control provide only limited connectivity between these additional states. We experimentally demonstrate transitions between electronic angular momentum states with a difference in magnetic quantum numbers $Δ\mathrm{m_J} = $ 3, 4, and 5 via resonant four- and six-photon stimulated Raman transitions in a single trapped atom. Derivation of the corresponding Rabi frequencies, which are verified experimentally, follows the standard treatment of two-photon transitions including the adiabatic elimination of intermediate states. Finally, we discuss pathways to increase the observed multi-photon transition fidelities to >99.99%>99.99\%>99.99%, providing a tool for efficient, high-fidelity control of qudits and single-atom logical qubits.
We consider the stimulated Raman transition between two long-lived states via multiple intermediate states, such as between hyperfine ground states in the alkali-metal atoms. We present a concise treatment of the general, multilevel, off-resonant case, and we show how the lightshift emerges naturally in this approach. We illustrate our results by application to alkali-metal atoms and we make specific reference to cesium. We comment on some artifacts, due solely to the geometrical overlap of states, which are relevant to existing experiments.
An optical pumping scheme is presented that uses incoherent Raman transitions to prepare a trapped cesium atom in a specific Zeeman state within the 6S1/26{S}_{1/2}6S1/2​, F=3F=3F=3 hyperfine manifold. An important advantage of this scheme over existing optical pumping schemes is that the atom can be prepared in any of the F=3F=3F=3 Zeeman states. We describe an experimental implementation of the scheme and show that a fraction $0.57\ifmmode\pm\else\textpm\fi{}0.02$ of the total population can be prepared in the desired state, with the remaining population distributed fairly uniformly among the six other states. We demonstrate the scheme in the context of cavity quantum electrodynamics, but the technique is equally applicable to a wide variety of atomic systems with hyperfine ground-state structure.