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Title: Atomic interferometer measurements of Berry and Aharonov-Anandan phases for isolated spins S>(1/2) nonlinearly coupled to external fields

Abstract

In a recent paper we have studied the peculiar features of the Berry and Aharonov-Anandan geometric phases for isolated spins S{>=}1. We have assumed that they are submitted to a dipole and quadrupole coupling to external E and B fields with the mild restriction E{center_dot}B=0. This implies discrete symmetries leading to remarkable simplifications of the geometry and algebra involved. The aim of the present work is to describe realistic proposals, within the realm of atomic physics, for the verification of some of our most significant theoretical predictions. There are several challenges to be overcome. For alkali-metal atoms, most commonly used in atomic interferometers, the only practical way to generate quadrupole coupling, with a strength comparable to the dipole one, is the ac Stark effect induced by a nearly resonant light beam. One then has to face the instability of the 'dressed' atom hyperfine (hf) level, a candidate for our isolated spin. One deleterious effect is the apparition of an imaginary part in the quadrupole to dipole coupling strength ratio, {lambda}. Fortunately we have found a simple way to get rid of I({lambda}) by an appropriate detuning. We are left with an unstable isolated spin. This implies an upper bound tomore » the quantum cycle duration T{sub c}. In the case of the Berry's phase, T{sub c} has a lower bound due to the necessity of keeping the nonadiabatic corrections below a predefined level. We have found a compromise in the case of the F=2,m=0 {sup 87}Rb ground-state hf level. This is our candidate for the measurement of the somewhat ''exotic'' Berry's phase acquired by the S=2,m=0 state at the end of a quantum cycle involving a rotation of {pi} of the E field--in practice, the linear polarization of the dressing beam --about the B field direction. We have found a way to implement, in a Ramsey-type interferometric measurement, the procedures aimed at controlling the nonadiabatic corrections, as described in detail in our previous theoretical paper. A numerical simulation of our experimental proposal shows that a 0.1% accurate determination of Berry's phase, free of nonadiabatic corrections, can be achieved. Measurements could also be considered for cold {sup 52}Cr chromium atoms with S=3, where values of {lambda}{approx_equal}1 can be obtained with an instability smaller than in the {sup 87}Rb case, due to a more favorable spectroscopic structure. The F=1,m=1 hf level of the {sup 87}Rb ground state offers the opportunity to extend the measurement of Aharonov-Anandan's phases beyond the case S=(1/2). We construct, using 'light shift', the Hamiltonian H{sub ||}(t) generating a closed circuit in the density-matrix space which satisfies at any time the 'parallel transport' condition, thus making the quantum cycle free from the adiabaticity condition. We also consider the case of half-integer spins (e.g., {sup 201}Hg, {sup 135}Ba, and {sup 137}Ba), with their own specific features. We show how the difference of Berry's phases for states S=(3/2) and S=(1/2), with m=(1/2), can be exploited to achieve a holonomic maximum entanglement of three qubits.« less

Authors:
;  [1]
  1. Laboratoire Kastler-Brossel, CNRS, UPMC, Ecole Normale Superieure, 24 rue Lhomond, FR-75005 Paris (France)
Publication Date:
OSTI Identifier:
21546715
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 83; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.83.052126; (c) 2011 American Institute of Physics; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ALKALI METALS; BARIUM 135; BARIUM 137; CHROMIUM 52; COMPUTERIZED SIMULATION; DENSITY MATRIX; DIPOLES; HAMILTONIANS; INTERFEROMETERS; MERCURY 201; PHASE STUDIES; PHOTON BEAMS; POLARIZED BEAMS; QUANTUM ENTANGLEMENT; QUANTUM STATES; QUBITS; RUBIDIUM 87; STARK EFFECT; ALKALINE EARTH ISOTOPES; BARIUM ISOTOPES; BEAMS; BETA DECAY RADIOISOTOPES; BETA-MINUS DECAY RADIOISOTOPES; CHROMIUM ISOTOPES; DAYS LIVING RADIOISOTOPES; ELEMENTS; EVEN-EVEN NUCLEI; EVEN-ODD NUCLEI; HEAVY NUCLEI; INFORMATION; INTERMEDIATE MASS NUCLEI; INTERNAL CONVERSION RADIOISOTOPES; ISOMERIC TRANSITION ISOTOPES; ISOTOPES; MATHEMATICAL OPERATORS; MATRICES; MEASURING INSTRUMENTS; MERCURY ISOTOPES; METALS; MICROSECONDS LIVING RADIOISOTOPES; MINUTES LIVING RADIOISOTOPES; MULTIPOLES; NUCLEI; ODD-EVEN NUCLEI; QUANTUM INFORMATION; QUANTUM OPERATORS; RADIOISOTOPES; RUBIDIUM ISOTOPES; SIMULATION; STABLE ISOTOPES; YEARS LIVING RADIOISOTOPES

Citation Formats

Bouchiat, Marie-Anne, Bouchiat, Claude, and Laboratoire de Physique Theorique de l'Ecole Normale Superieure, CNRS, UPMC, 24 rue Lhomond, FR-75005 Paris. Atomic interferometer measurements of Berry and Aharonov-Anandan phases for isolated spins S>(1/2) nonlinearly coupled to external fields. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.83.052126.
Bouchiat, Marie-Anne, Bouchiat, Claude, & Laboratoire de Physique Theorique de l'Ecole Normale Superieure, CNRS, UPMC, 24 rue Lhomond, FR-75005 Paris. Atomic interferometer measurements of Berry and Aharonov-Anandan phases for isolated spins S>(1/2) nonlinearly coupled to external fields. United States. https://doi.org/10.1103/PHYSREVA.83.052126
Bouchiat, Marie-Anne, Bouchiat, Claude, and Laboratoire de Physique Theorique de l'Ecole Normale Superieure, CNRS, UPMC, 24 rue Lhomond, FR-75005 Paris. 2011. "Atomic interferometer measurements of Berry and Aharonov-Anandan phases for isolated spins S>(1/2) nonlinearly coupled to external fields". United States. https://doi.org/10.1103/PHYSREVA.83.052126.
@article{osti_21546715,
title = {Atomic interferometer measurements of Berry and Aharonov-Anandan phases for isolated spins S>(1/2) nonlinearly coupled to external fields},
author = {Bouchiat, Marie-Anne and Bouchiat, Claude and Laboratoire de Physique Theorique de l'Ecole Normale Superieure, CNRS, UPMC, 24 rue Lhomond, FR-75005 Paris},
abstractNote = {In a recent paper we have studied the peculiar features of the Berry and Aharonov-Anandan geometric phases for isolated spins S{>=}1. We have assumed that they are submitted to a dipole and quadrupole coupling to external E and B fields with the mild restriction E{center_dot}B=0. This implies discrete symmetries leading to remarkable simplifications of the geometry and algebra involved. The aim of the present work is to describe realistic proposals, within the realm of atomic physics, for the verification of some of our most significant theoretical predictions. There are several challenges to be overcome. For alkali-metal atoms, most commonly used in atomic interferometers, the only practical way to generate quadrupole coupling, with a strength comparable to the dipole one, is the ac Stark effect induced by a nearly resonant light beam. One then has to face the instability of the 'dressed' atom hyperfine (hf) level, a candidate for our isolated spin. One deleterious effect is the apparition of an imaginary part in the quadrupole to dipole coupling strength ratio, {lambda}. Fortunately we have found a simple way to get rid of I({lambda}) by an appropriate detuning. We are left with an unstable isolated spin. This implies an upper bound to the quantum cycle duration T{sub c}. In the case of the Berry's phase, T{sub c} has a lower bound due to the necessity of keeping the nonadiabatic corrections below a predefined level. We have found a compromise in the case of the F=2,m=0 {sup 87}Rb ground-state hf level. This is our candidate for the measurement of the somewhat ''exotic'' Berry's phase acquired by the S=2,m=0 state at the end of a quantum cycle involving a rotation of {pi} of the E field--in practice, the linear polarization of the dressing beam --about the B field direction. We have found a way to implement, in a Ramsey-type interferometric measurement, the procedures aimed at controlling the nonadiabatic corrections, as described in detail in our previous theoretical paper. A numerical simulation of our experimental proposal shows that a 0.1% accurate determination of Berry's phase, free of nonadiabatic corrections, can be achieved. Measurements could also be considered for cold {sup 52}Cr chromium atoms with S=3, where values of {lambda}{approx_equal}1 can be obtained with an instability smaller than in the {sup 87}Rb case, due to a more favorable spectroscopic structure. The F=1,m=1 hf level of the {sup 87}Rb ground state offers the opportunity to extend the measurement of Aharonov-Anandan's phases beyond the case S=(1/2). We construct, using 'light shift', the Hamiltonian H{sub ||}(t) generating a closed circuit in the density-matrix space which satisfies at any time the 'parallel transport' condition, thus making the quantum cycle free from the adiabaticity condition. We also consider the case of half-integer spins (e.g., {sup 201}Hg, {sup 135}Ba, and {sup 137}Ba), with their own specific features. We show how the difference of Berry's phases for states S=(3/2) and S=(1/2), with m=(1/2), can be exploited to achieve a holonomic maximum entanglement of three qubits.},
doi = {10.1103/PHYSREVA.83.052126},
url = {https://www.osti.gov/biblio/21546715}, journal = {Physical Review. A},
issn = {1050-2947},
number = 5,
volume = 83,
place = {United States},
year = {2011},
month = {5}
}