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arXiv:1012.4453 · Physical Review A

Tailoring quantum superpositions with linearly polarized amplitude-modulated light

Szymon Pustelny, Maria Koczwara, Łukasz Cincio, Wojciech Gawlik

Published Apr 26, 2011• 20 citations
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Abstract

Amplitude-modulated nonlinear magneto-optical rotation is a powerful technique that offers a possibility of controllable generation of given quantum states. In this paper, we demonstrate creation and detection of specific ground-state magnetic-sublevel superpositions in $^{87}\mathrm{Rb}$. By appropriate tuning of the modulation frequency and magnetic-field induction the efficiency of a given coherence generation is controlled. The processes are analyzed versus different experimental parameters.

DOI
10.1103/physreva.83.043832

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Amplitude-modulated nonlinear magneto-optical rotation is a powerful technique that offers a possibility of controllable generation of given quantum states. In this paper, we demonstrate creation and detection of specific ground-state magnetic-sublevel superpositions in 87Rb^{87}\mathrm{Rb}87Rb. By appropriate tuning of the modulation frequency and magnetic-field induction the efficiency of a given coherence generation is controlled. The processes are analyzed versus different experimental parameters.
Specific types of atomic coherences between Zeeman sublevels can be generated and detected using a method based on nonlinear magneto-optical rotation with frequency-modulated light. Linearly polarized, frequency-modulated light is employed to selectively generate ground-state coherences between Zeeman sublevels for which $\mathrm{\ensuremath{\Delta}}m=2$ and $\mathrm{\ensuremath{\Delta}}m=4$ in 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb atoms, and additionally $\mathrm{\ensuremath{\Delta}}m=6$ in 85Rb^{85}\mathrm{Rb}85Rb. The atomic coherences are detected with a separate, unmodulated probe light beam. Separation of the pump and probe beams enables independent investigation of the processes of creation and detection of the atomic coherences. With the present technique the transfer of the Zeeman coherences, including high-order coherences, from excited to ground state by spontaneous emission has been observed.
We study the possibility of creating quantum superposition states in alkali atoms. Our methodology is based on the phenomenon of nonlinear magneto-optical rotation (NMOR). The effect of magneto-optical rotation occurs whenever the resonant light propagates through the medium immersed in a longitudinal magnetic field and manifests itself as a rotation of the polarization plane of light. The effect is strongly enhanced by the nonlinearity of light-atom interaction and allows state-of-the art atomic magnetometry. On the other hand, the nonlinear magneto-rotation provides means to controllably affect and detect atom's quantum state. We present the work on this topic and report on some characteristics of superposition quantum states such as lifetimes or efficiency of it's creation in various conditions.
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.
The authors report on their investigations on nonlinear Faraday effect (NFE), i.e. light-intensity dependent rotation of the polarization plane of linearly polarized light upon its propagation through a medium placed in a magnetic field. The phenomenon is associated with quantum superpositions of atomic or molecular levels of particles constituting the medium. In this context it is based on the same grounds as electromagnetically induced transparency, coherent population trapping, storage and retrieval of light pulse from a medium. The paper also discusses the mechanisms of generation and detection of the superpositions with light and means of controllable tailoring of a quantum state in long-living (lifetimes >10 ms) atomic state.
Larmor precession of laser-polarized atoms contained in antirelaxation-coated cells, detected via nonlinear magneto-optical rotation (NMOR), is a promising technique for a new generation of ultrasensitive atomic magnetometers. For magnetic fields directed along the light propagation direction, resonances in NMOR appear when linearly polarized light is frequency or amplitude modulated at twice the Larmor frequency. Because the frequency of these resonances depends on the magnitude but not the direction of the field, they are useful for scalar magnetometry. Additional NMOR resonances at the Larmor frequency appear when the magnetic field is tilted away from the light propagation direction in the plane defined by the light propagation and polarization vectors. These resonances, studied both experimentally and with a density matrix calculation in the present work, offer a convenient method of achieving additional information about a direction of the magnetic field.
We report on experimental and theoretical study of the nonlinear Faraday effect under conditions of electromagnetically induced transparency at the $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{5/2}$ two-photon transition in rubidium vapor. These transitions realize the inverted YYY model which combines the $\ensuremath{\Lambda}$ and ladder systems. Strong nonlinearity allowing for large rotation angles of a probe beam tuned to the $S\ensuremath{\rightarrow}P$ transition was obtained by creation of quantum superpositions of magnetic sublevels (Zeeman coherences) in the rubidium ground state ($\ensuremath{\Lambda}$ scheme). Additionally, electromagnetically induced transparency was accomplished in a ladder scheme by acting with a second strong coupling laser on the $P\ensuremath{\rightarrow}D$ transition. Under conditions of a two-photon resonance the rotation was significantly reduced, which is interpreted as a competition between the coherent processes. The effect was observed in sub-Gauss magnetic fields and could be used for efficient coherent control of generation of the ground-state coherences, e.g., for controlling the polarization state of the probe light.